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The emotional block in mathematics : a multivariate study Gaskill, James Leslie 1979

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THE EMOTIONAL BLOCK IN MATHEMATICS: A MULTIVARIATE STUDY by JAMES LESLIE GASKILL B.Sc, University of B r i t i s h Columbia, 1964 M.A., University of B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF ED- D. i n THE FACULTY OF GRADUATE STUDIES ' x%aeuit:y-i-S£ E d u c a t i o n We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1979 © ffames Leslie G a s k i l l } \<VH In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers ity of B r i t i s h Columbia, I agree that the Library shal l make i t f ree ly avai lable for reference and study. I further agree that permission for extensive copying of th i s thesis for scholar ly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publ icat ion of th i s thesis for f inanc ia l gain shal l not be allowed without my written permission. Department of Mathematics Education The Univers ity of B r i t i s h Columbia 2075 Wesbrook Place . Vancouver, Canada V6T 1W5 nat.P A p r i l 27, 1979 ABSTBACT Tie purpose of t h i s study was to study the r e l a t i o n s h i p s between a group of a f f e c t i v e v a r i a b l e s , a s s o c i a t e d with the notion of an "emotional b l o c k " i n mathematics, and achievement i n mathematics. F i v e independent v a r i a b l e s - were c o n s i d e r e d : achievement r e s p o n s i b i l i t y ( l o c u s of c o n t r o l ) , measured by the I n t e l l e c t u a l Achievement B e s p o n s i b i l i t y Scale; anxiety i n mathematics, value of mathematics t o s o c i e t y , s e l f - c o n c e p t of a b i l i t y to l e a r n mathematics and enjoyment of mathematics, measured by s c a l e s from the Sandman bat t e r y ; and value of mathematics f o r o n e s e l f , measured by an author c o n s t r u c t e d s c a l e . The t h r e e dependent achievement•variables were computation, measured by the S t a n f o r d Achievement Test and concepts and problem s o l v i n g measured by the Canadian Test of Basic S k i l l s . Nonlinear and i n t e r a c t i v e hypotheses were suggested by the theory o f Achievement M o t i v a t i o n . The s c a l e s were admi n i s t e r e d t o 1033 students at t h e grade s i x l e v e l . The s c o r e s were s t a n d a r d i z e d within each c l a s s t o remove c l a s s e f f e c t s . The sample was randomly s p l i t i n t o two samples, one to be r e t a i n e d f o r c r o s s v a l i d a t i o n . No s i g n i f i c a n t d i f f e r e n c e was found between the v a r i a n c e - c o v a r i a n c e matrix of males and t h a t of the females. The data were subsequently pooled. Stepwise r e g r e s s i o n a n a l y s i s i n d i c a t e d t h a t i i i s e l f - c o n c e p t alone explained approximately 20% of the achievement variance;. In the case of computation* mathematics anxiety was a l s o i n c l u d e d accounting f o r an a d d i t i o n a l 2%,. P r i n c i p a l component a n a l y s i s and orthogonal r o t a t i o n o f the s e t o f a f f e c t i v e s c a l e s r e v e a l e d t h r e e f a c t o r s . These were i n t e r p r e t e d as a m o t i v a t i o n a l f a c t o r (loadings from s e l f - c o n c e p t , a n x i e t y and enjoyment), a value f a c t o r ( l o a d i n g s from the two value s c a l e s ) , and an achievement r e s p o n s i b i l i t y f a c t o r s F a c t o r scores f o r each student were c a l c u l a t e d . Using these s c o r e s , stepwise r e g r e s s i o n showed th a t , with the e x c e p t i o n of the value f a c t o r e n t e r i n g i n t o the equation f o r computation, the m o t i v a t i o n f a c t o r was the only one r e t a i n e d . None o f the n o n - l i n e a r or i n t e r a c t i v e hypotheses were s i g n i f i c a n t . The above analyses were repeated u s i n g the c r o s s v a l i d a t i o n samplei A l l the f i n d i n g s were confirmed. I t was concluded that the group of three v a r i a b l e s , s e l f - c o n c e p t of a b i l i t y , enjoyment and anxiety i n mathematics should be i n c l u d e d i n s t u d i e s d e a l i n g with mo t i v a t i o n i n mathematics. I t was suggested t h a t s e l f - c o n c e p t c o u l d be i n t e r p r e t e d as the c o g n i t i v e component of a n x i e t y and t h a t enjoyment as the emotional component. I t was also suggested t h a t attempts to a l t e r a n x i e t y i n mathematics c o u l d be made by a l t e r i n g s e l f - c o n c e p t and enjoyment. Chairman: Dr. G a i l S p i t l e r i v TABLE OF CONTENTS Page L i s t o f Tables .. i x Acknowledgements x i i Chapter ' 1. THE FBOBLEM . . ,. . ; . i ,. 1 BACK GBOUND .... ........... 1 I n t r o d u c t i o n ............................, . ...L... 1 Emotional Block , 2 V a r i a b l e s A s s o c i a t e d With An " E m o t i o n a l 1 B l o c k " .... 6 Problem i ....... . 7 CASE FOB A NON—LINEAB MULTIVARIATE APPBOACH ' 8 Independent V a r i a b l e s 8 Dependent V a r i a b l e s 11 Importance Of The Problem 13 .RESEARCH HYPOTHESES ................... 1 . . . . . . . 15 Summary Of The Problem 15 G e n e r a l i z a t i o n Across Sex ......................... 16 A f f e c t i v e I n t e r - S c a l e C o r r e l a t i o n s ................. 16 Aff e c t i v e - A c h i e v e m e n t Scale B e l a t i o n s h i p s . . . . . . . . . 17 STATISTICAL HYPOTHESES ... i . . . . . . . . . i . . . i . . il 8 S i g n i f i c a n c e Versus S t r e n g t h Of B e l a t i o n s .» ...18 G e n e r a l i z a t i o n Across Sex 18 A f f e c t i v e I n t e r - S c a l e B e l a t i o n s h i p s 19 Affec t i v e - A c h i e v e m e n t Scale B e l a t i o n s h i p s , . i . . ; . . . 1 9 V 2. BELATED EESEABCH .,. .. 21 INTRODUCTION ....................... i ..... i '. . i -. . 21 ATTITUDE VARIABLES 22 Number Of S t u d i e s ................... . ..... . ... '.... * 22 T y p i c a l S t u d i e s 23 ANXIETY IN MATHEMATICS . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . 25 G e n e r a l A n x i e t y ................................... 25 S p e c i f i c A n x i e t y 29 VALUE .... . . i . . . , 3 1 SELF—CONCEPT OF ABILITY TO LEARN MATHEMATICS ......... 32 G l o b a l S e l f - C c n c e p t 32 S p e c i f i c S e l f - C o n c e p t ......... i . i . . . . . . . 33 LOCUS OF CONTROL ... A 36 SUMMARY OF INDIVIDUAL AFFECTIVE VARIABLES .......... 39 THE MODEL OF ACHIEVEMENT MOTIVATION . , , i . . . . . . . . . . . . . . - 40 Achievement M o t i v a t i o n 40 V a r i a b l e s Of T h i s Study R e l a t e d To The'Model ...... 46 SUMMARY 50 3,. INSTRUMENTATION, DESIGN AND PROCEDURE i ........ ... . 51 ' INTRODUCTION ..... .. I. ......... .. . . . . . i . . i . . . . - .i. . 51 INSTRUMENTATION .... . .. .... 52 The Sandman Study . , 1 . . . . . . . . . . . . . . . i, ... ^ .. i ...... . 52 B a s i s Of S c a l e S e l e c t i o n 55 ANXIETY IN MATHEMATICS .............. 58 ENJOYMENT . i ... . 60 VALUE 61 v i Value Of Mathematics To Society ... 61 Value Of Mathematics For Oneself ............ i . . . . . . . 61 SELF-CONCEPT OF ABILITY IN MATHEMATICS ... 63 LOCUS OF CONTROL w . i. .. i ....... . 64 ACHIEVEMENT TESTS ..... i . . . . . . . . . . . . . ,i . . . . . , i i . . . . . . 65 TEACHEE RESPONSE SCALES ...... . 67 AGE AND GRADE LEVEL CHOSEN . . . . . . . . . . . . . . 71 SUBJECTS 73 PILOT 75 MATERIALS ...................... ................... 76 Affec t i v e Scales . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . 76 Achievement Tests 78 PBOCEDUBE . . . . . . . . . . . . . . . . . . . . * L i . .......... 80 DATA DESCRIPTION ........... '. ........... i . 82 Teacher Besponses 82 Affective Scales .. '............... ............. 83 Data R e l i a b i l i t y i .... . i . . 84 Achievement Tests . i i i.. .4 . . . . . . . . . 85 PRELIMINARY ANALYSES . . . . . . . . . . . . . . . i . . i a . . i . i . . . . . . . . 85 Unit Of Analysis 86 Inclusion Or Exclusion Of TASC .. i ......... . 90 STATISTICAL PROCEDUBES ......... . , ...94 S t a t i s t i c a l Significance ..............±.......... . 94 Sex Differences 95 Affec t i v e Inter-*Scale Relationships ............... 96 Affective-Achievement Relationships ,. i * . ; , , ; t l . . . . . . . 98 v i i C ross V a l i d a t i o n ....101 Cr o s s V a l i d a t i o n Hypotheses i .... 102 4. BESULTS . . . . . . . . . . . . . ..i 103 INTRODUCTION . . . . . i i ................. . i . i . . . ; i. . ,i . .. 1 03 SEX DIFFERENCES i ... i ., .i ...... i . 1 05 AFFECTIVE INTER-SCALE HYPOTHESES ., i .. 106 C o r r e l a t i o n s ..................... .'.Vi. . . i . - . 1 06 F a c t o r A n a l y s i s .....109 AFFECTIVE-ACHIEVEMENT RELATIONSHIPS . . . . . . 1 1 1 C o r r e l a t i o n s ...... ............ .................... i ...111 Re g r e s s i o n A n a l y s i s ........112 F a c t o r A n a l y s i s . . . . . . . . . . . . . . . . . . i . . i ....... . i . i i . . . 115 CROSS VALIDATION ............. . . . . . . . . . . . i . . . 119 Equivalence, Of C o r r e l a t i o n s . ^ . . . . . . . . . . . . . . i . . i . . . . 119 F a c t o r A n a l y s i s - i ...... L : . . . . . . 120 Regression A n a l y s i s 122 SUMMARY ^ ..... . .... . . . i . i . . . ; i . . . . i i . . . . 1 2 3 5. DISCUSSION AND CONCLUSIONS . . . . . . . . . . . . . . . - , i I... i i . i ..... 1 26 INTRODUCTION . .... ..... 126 SEX DIFFEBENCES ...................... i .... i I .... fl 29 INTEB—BELATIONS OF THE "BLOCK" VABIABLES 130 THE BELATION OF THE "BLOCK" VABIABLES TO ACHIEVEMENT. .136 C o r r e l a t i o n s 136 M u l t i p l e B e g r e s s i o n Of Standardized . Scores And Factor Scores .................................. 139 LIMITATIONS OF THE S1U DY ......... ^ .... i , . ,i. ..... i ..... i .. 1 41 v i i i CONCLUSIONS .. ........ i . . . . 143 FUTURE RESEARCH ............................ i . . ... . 146 C o r r e l a t i o n a l S t u d i e s . . . . . . . . . . . . . . . . . . . . i 1 4 7 Experimental S t u d i e s ........................149 REFERENCE LIST ., i . '. i . i ..... 152 APPENDICES . . .... . . . . 1 . .... 4 166 A. INSTRUCTIONS FOR BEHAVIORAL CHECKLIST . ......166 B. INSTRUCTIONS FOR RANKING OF STUDENTS . ,i .... ,i 168 C. ADMINISTRATION BOOKLET .. ,i ,,; .170 D. QUESTIONNAIRE BOOKLET ......... 183 E. LAYOUT OF THE STUDENT RESPONSE FORMS . ; ....... '. . ^  .. 1 95 F. CLASS MEANS AND STANDARD DEVIATIONS OF THE ACHIEVEMENT AND AFFECTIVE VARIABLES 196 G. DIFFERENCES BETWEEN MEANS FOR MALES AND FEMALES ...192 H. INTER—CORRELATIONS OF STUDENT—BEHAVIORS i . . . ..194 LIST OF TABLES Table Page 1. Percentages o f D i s s e r t a t i o n s and J o u r n a l - P u b l i s h e d fieports D e a l i n g with A f f e c t i v e V a r i a b l e s L i s t e d i n Suydam Reports (1974-78).. ...... '., 22 2. C o r r e l a t i o n s Between General and S p e c i f i c Anxiety S c a l e s and S e v e r a l Measures of Achievement .. .> .., 28 3. C o r r e l a t i o n s Between General Self-Concept of A b i l i t y , Mathematics S e l f - C o n c e p t , S o c i a l S t u d i e s S e l f - C o n c e p t , and Mathematics Achievement... 35 4. C o r r e l a t i o n s Between an Achievement M o t i v a t i o n Measure and Various Behaviors f o r I n t e r n a l and E x t e r n a l Locus of C o n t r o l S u b j e c t s . . . . 39 5. C o r r e l a t i o n s Between the Sub-Scales of the Sandman 1 Inventory. 56 6. C l a s s Type, Sex and Number of S u b j e c t s . . . . . 74 7. S c a l e s , A b b r e v i a t i o n s , Number of Items f o r the A f f e c t i v e S c a l e s . 78 8. S c a l e s , A b b r e v i a t i o n s , Number of Items* R e l i a b i l i t i e s , and Normed Means of the Achievement T e s t s . i ...... 79 9. P r e f e r e d Sequence and Spacing of S c a l e A d m i n i s t r a t i o n . . 80 10. Means, Standard D e v i a t i o n s , Maximum Score, and Hoyt R e l i a b i l i t y f o r the Achievement and A f f e c t i v e S c a l e s . . . 86 11. U n i v a r i a t e A n a l y s i s of Variance using Each of the Achievement and A f f e c t i v e V a r i a b l e s as Independent X V a r i a b l e s and C l a s s as Dependent V a r i a b l e . . . , i .. 88 12. R e s u l t s of the B a r t l e t - B o x T e s t s of Homogenieity of Variance on Each o f the A f f e c t i v e and Achievement Measures 89 13. C o r r e l a t i o n s Between Achievement and A f f e c t i v e V a r i a b l e s V a r i a b l e s u sing Scores S t a n d a r d i z e d Within C l a s s , and Raw Scores. ......... ......................... .. ... 91 14. Squared C o r r e l a t i o n s Between MANX, TASC and the Achievement V a r i a b l e s . . 9 2 •1.5. P a r t i a l C o r r e l a t i o n s , and M u l t i p l e Squared C o r r e l a t i o n s of TASC when p r e d i c t i n g Achie vement Scores, i 93 16;. I n t e r - C o r r e l a t i o n s Among BANK, C h a r a c t e r i s t i c s from a B e h a v i o r a l C h e c k l i s t , the Achievement V a r i a b l e s , TASC, and MANX-. . . i . . . . . 95 (17,i C o r r e l a t i o n s o f the A f f e c t i v e and Achievement Sc a l e s f o r Males and Females..... „ .106 18. I n t e r - C o r r e l a t i o n s of the A f f e c t i v e Variables;..>......i.107 19. C o r r e l a t i o n s Between the A f f e c t i v e V a r i a b l e s ^ BANK, and the Student-Behavior C h e c k l i s t . . . . . . . . . . . . . . . . 108 20. F a c t o r Loadings of the A f f e c t i v e V a r i a b l e s on the Orth o g o n a l l y Botated, P r i n c i p a l Component F a c t o r s . 1 1 0 21. C o r r e l a t i o n s of the F i r s t and Second Degree Terms of Orth o g o a l Polynomials of the A f f e c t i v e V a r i a b l e s with the Three Achievement V a r i a b l e s . . . . . . . . . . . . . . . ....113 22. Summary of the Stepwise Analyses Using Standardized A f f e c t i v e Scores as Independent V a r i a b l e s . . . . . ; . . . . . . . . 1 1 4 x i 23. F a c t o r Score C o e f f i c i e n t Matrix ...................116 24. C o r r e l a t i o n s Between Standardized F a c t o r Scores and Standardized Achievement Scores 116 25. R e g r e s s i o n Equations of the Three Factor Scores P r e d i c t i n g the Stepwise Regression Equations Using F a e t o r Scores and F a c t o r Score I n t e r a c t i o n s as Independent V a r i a b l e s ... ............ 117 26. Summary of the Stepwise Analyses Usinq F a c t o r Scores and F a c t o r Score I n t e r a c t i o n s as Independent Var i a b l e s . 1 1 8 27. C o r r e l a t i o n s o f the A f f e c t i v e and Achievement S c a l e s o f Sample 2 120 28. F a c t o r Loadinqs From the Analyses of Sample 1 and Sample 2., - . .......... 121 29 i E r r o r Matrix From a Procrustean R o t a t i o n of the Sample 2 F a c t o r s to a Tarqet Matrix of Sample 1 Loadinqs. ........121 30. Summary o f the Stepwise A n a l i s e s Usinq Sample 2 Stand a r d i z e d Scores as Independent V a r i a b l e s . ........... 122 x i i ACKNOWLEDGEMENTS To my daughter Kimberly, from whom much time was taken* To my w i f e , Sheiagh, who accepted my time committment so g r a c i o u s l y . To G a i l S p i t l e r , my a d v i s o r , whose c o n f i d e n c e i n my de t e r m i n a t i o n to f i n i s h made i t p o s s i b l e , and whose i n f l u e n c e was i n s t r u c t i v e and supportive r a t h e r than d i r e c t i v e . To the other members of my committee who saw me through s e v e r a l r e v i s i o n s . l o the E d u c a t i o n a l Eesearch I n s t i t u t e of B r i t i s h Columbia which supported the study with a grant f o r m a t e r i a l s and t e s t s . 1 Chapter 1 THE PROBLEM BACKGROUND I n t r o d u c t i o n I f a p u p i l "performs badly and i s s u b j e c t e d to continued f r u s t r a t i o n , he may develop an emotional block t h a t makes f u t u r e l e a r n i n g i m p o s s i b l e . Such blocks are not unusual i n mathematics" [ I t a l i c s added.j (Marks, Purdy & Kinney, 1965, p. 47). I f t h i s i s t r u e , then the prevention of the estab l i s h m e n t of the "block" and the removal, or at l e a s t t he r e d u c t i o n o f the "emotional b l o c k " whenever i t occurs, should be major concerns of mathematics educators*. To do t h i s e f f e c t i v e l y , i t s b e h a v i o r a l c h a r a c t e r i s t i c s s hould be ascertained;. I t w i l l be argued t h a t the concept of an "emotional b l o c k " i n mathematics i s a common one, o f t e n a s s o c i a t e d with repeated f a i l u r e . C e r t a i n v a r i a b l e s such as a n x i e t y , value and enjoyment of mathematics are o f t e n used i n the mathematics t e a c h i n g l i t e r a t u r e t o c h a r a c t e r i z e such a "block". 2 For the purpose of t h i s study "emotional" was c o n s i d e r e d synonymous with " a f f e c t i v e " . A " b l o c k " was d e f i n e d i n terms of s c a l e s c o r e s of one, or a number o f , the a f f e c t i v e v a r i a b l e s a s s o c i a t e d with an "emotional b l o c k . " In order t o v a l i d a t e the p e d a g o g i c a l l i t e r a t u r e , the r e l a t i o n s h i p s among the " b l o c k " v a r i a b l e s and between those v a r i a b l e s and mathematics achievement were examined. Research on the presence and e f f e c t s of these v a r i a b l e s , as a group, i n the context o f mathematics e d u c a t i o n , has been r a t h e r l i m i t e d . I t w i l l be shown, i n t h i s and the next chapter, that t y p i c a l l y only one of the v a r i a b l e s was s e l e c t e d and i t s r e l a t i o n s h i p to a g l o b a l measure of mathematics achievement examined. There i s , however, some evidence t h a t the v a r i a b l e s might i n t e r a c t with each other and with other a f f e c t i v e v a r i a b l e s when s t u d i e d i n r e l a t i o n t o achievements Consequently, the p r e s e n t study was designed to examine the l i n e a r , n o n - l i n e a r , and i n t e r a c t i v e r e l a t i o n s h i p s between v a r i a b l e s a s s o c i a t e d with an "emotional b l o c k " i n mathematics, and t h r e e components of mathematics achievement; computation, concepts, and problem s o l v i n g . Emotional Block F a c t o r s a f f e c t i n g success^ Crowder and Wheeler (1972) c h a r a c t e r i z e d the s u c c e s s f u l c h i l d i n a mathematics program as one who 1. f e e l s t h a t he i s competent. 3 2. f e e l s t h a t he i s accepted by h i s t e a c h e r . 3. f e e l s t h a t h i s best e f f o r t w i l l be accepted by h i s t e a c h e r . 4. knows t h a t h i s teacher w i l l plan work that w i l l g i ve him success* 5. knows t h a t each day*s work w i l l be a c h a l l e n g e , (p. 4) C h a r a c t e r i s t i c s 1, 4, and 5 may be summarized i n the f o l l o w i n g way: h i s past work e s t a b l i s h e d a success p a t t e r n a l l o w i n g him to p r e d i c t success at a c u r r e n t task even i f i t was a c h a l l e n g e . To convince t e a c h e r s t h a t there was a commonality among l e a r n i n g t h e o r i e s and t h a t there were p r i n c i p l e s u s e f u l f o r g u i d i n g p r a c t i c e i n the mathematics classroom Fremont (1969) c i t e d H i l g a r d ' s l i s t of f o u r t e e n p r i n c i p l e s common t o most t h e o r i e s of l e a r n i n g . Of thes e , three d e a l t with success and i t s r e l a t i o n s h i p t o f a i l u r e : 4. Success and reward y i e l d more f a v o u r a b l e outcomes than f a i l u r e and punishment. 6. Tolerance f o r f a i l u r e i s b u i l t by success e x p e r i e n c e s . 12. Learning i s aided by knowledge of mistakes and successe s . (p. 43) Fremont (1969) r e i t e r a t e d t he above p o i n t s i n h i s d i s c u s s i o n o f the slow l e a r n e r i n mathematics; The teacher should " t r y t o i n v o l v e the students i n new expe r i e n c e s o f f e r i n g s u c c e s s " (p. 253). When such i s the case Fremont d e s c r i b e d t h e student's r e a c t i o n as f o l l o w s : " A f t e r years of f a i l u r e i n mathematics ± there (J i s a s e r i e s of quick successes - a s e r i e s of experiences t h a t cause the student t o ex c l a i m , 'Hey, I can do t h e s e ! * " (p. 524). He continued, "These i n i t i a l s u ccess 4 e x p e r i e n c e s cannot be o v e r e s t i m a t e d i n i m p o r t a n c e . They are t h e f i r s t s t e p s on t h e road hack f o r many of t h e s e low a c h i e v e r s " (p. 525). Cooney, Davis and Henderson (1975) were q u i t e s p e c i f i c : Slow l e a r n e r s need t o have s u c c e s s f u l e x p e r i e n c e s ; they need t o g e t c o r r e c t answers. T h i s i s p a r t i c u l a r l y t r u e f o r s t u d e n t s dominated by f e a r o f f a i l u r e o r h o s t i l i t y . . . . They need c o n f i d e n c e and encouragement more than t h e y need t o know t h e b a s i s f o r p a r t i c u l a r p r o c e d u r e s . (p. 334) The importance of s u c c e s s when b e g i n n i n g new m a t e r i a l was s t r e s s e d by Marks, Purdy and Kinney (1965, p. 47). They s u g g e s t e d t h a t , " i n t e r e s t i n a new a c t i v i t y d e v e l o p s most r e a d i l y i f the p u p i l has some c o n f i d e n c e i n h i s a b i l i t y t o succeed w i t h i t . " They f e l t t h a t t h e t e a c h e r s h o u l d space the d i f f i c u l t y of the new m a t e r i a l so t h a t "the p u p i l always f e e l s t h a t he has a chance t o s u c c e e d " (p. 4 7 ) . The problems a s s o c i a t e d w i t h c a r r y i n g out t h i s d i r e c t i v e were noted ay B i g g s and McLean (1969) who s t a t e d t h a t d e t e r m i n i n g t h e r e a d i n e s s o f a c h i l d r e q u i r e s a g r e a t d e a l o f s k i l l and e x p e r i e n c e . I t i s t h i s k i n d o f s k i l l combined w i t h t h e a r t o f d e v i s i n g o r c o n t r i v i n g s i t u a t i o n s where e v e r y c h i l d e x p e r i e n c e s some s u c c e s s e s each day t h a t d i s t i n g u i s h e s the t r u l y p r o f e s s i o n a l t e a c h e r from t h e t e c h n i c i a n . [ I t a l i c s a d d ed J (p. 8.) Running t h r o u g h a l l t h e s e s t a t e m e n t s about the e f f e c t s of s u c c e s s i s t h e theme t h a t a s u c c e s s e x p e r i e n c e changes t h e c h i l d * s assessment of t h e p r o b a b i l i t y o f b e i n g s u c c e s s f u l i n a new s i t u a t i o n . I m p l i c i t i s the a s s u m p t i o n t h a t t h e s u c c e s s e x p e r i e n c e i s m o t i v a t i n g : t h a t the c h i l d would expend nrexre 5 e f f o r t i n the accomplishment of the new t a s k . On t h e o t h e r hand, one might expect t h a t the e x p e r i e n c e s o f f a i l u r e would be d i s a b l i n g and i n h i b i t i n g r a t h e r than m o t i v a t i n g and e n a b l i n g as a r e t h e e x p e r i e n c e s of s u c c e s s . Indeed such e f f e c t s a re r e f e r r e d t o i n the l i t e r a t u r e . F a c t o r s a f f e c t i n g f a i l u r e . I n the p r e f a c e t o The Slow L e a r n e r i n Mathematics (Lowry, 1972) t h e e d i t o r i a l p a n e l s t a t e d t h a t "because of a h i s t o r y of f a i l u r e and near f a i l u r e , a lmost a l l o f them have a low o p i n i o n o f t h e i r worth a t l e a s t as mathematics s t u d e n t s . " W e l l s and S h u l t e (1970) i n t h e same volume s t a t e d t h a t "One of the most s t r i k i n g c h a r a c t e r i s t i c s o f low a c h i e v e r s i s t h e i r f e a r o f f a i l u r e . . . . t h e i r r e p e a t e d f a i l u r e s have made them s k e p t i c a l o f t h e v a l u e of s c h o o l " (p. 344). Cooney, D a v i s and Henderson (1975) s t a t e d t h a t : " S t u d e n t s who have had d i f f i c u l t y i n l e a r n i n g mathematics are l i k e l y t o have n e g a t i v e a t t i t u d e s t o w a r d i t and be c o n v i n c e d t h a t they cannot understand or do a n y t h i n g of a m a t h e m a t i c a l n a t u r e " (p. 325). Dreger and Aiken (1 957) noted t h a t "Many p e r s o n s r e p o r t i n c l i n i c a l s e s s i o n s and i n academic c l a s s e s t h a t they are e m o t i o n a l l y d i s t u r b e d i n the presence o f mathematics" (p. 344) . In t h e same v e i n P i k a a r t and W i l s o n (1972) d i s t i n g u i s h e d between c o n s t r u c t i v e l y and d e f e n s i v e l y m o t i v a t e d l e a r n e r s . They s t a t e d , " c o n s t r u c t i v e l y " m o t i v a t e d s t u d e n t s a r e t h o s e who have a h i g h l e v e l of achievement m o t i v a t i o n and a low a n x i e t y , whereas " d e f e n s i v e l y " m o t i v a t e d s t u d e n t s a r e tho s e who have the o p p o s i t e p a t t e r n . (P. 33) 6 An i n d i v i d u a l who experienced repeated f a i l u r e at a given task would begin t o expect f a i l u r e and when co n f r o n t e d with such a task would tend t o avoid or reduce the e f f o r t a p p l i e d to the task,. T h i s e f f e c t was l a b e l l e d " l e a r n e d h e l p l e s s n e s s " by Weiner (1972) who d e s c r i b e d i t as the "low achievement syndrome, s i n c e persons low i n achievement m o t i v a t i o n do not p e r c e i v e t h a t e f f o r t i n f l u e n c e s outcome" (p. 210). In t h i s study t h i s e f f e c t was a s s o c i a t e d with r e s p o n s i b i l i t y f o r ac c e p t i n g the r e s u l t s of a c t i o n s taken i n achievement o r i e n t e d s i t u a t i o n s . V a r i a b l e s A s s o c i a t e d with an "Emotional_Blpck'| In summary, Dreger and Aiken (1957) c i t e d Schonel who observed, " t h a t backwardness i n a r i t h m e t i c i s due as much t o emotional as to i n t e l l e c t u a l f a c t o r s " (p. 344). The f a c t o r s i d e n t i f i e d above i n the previous s e c t i o n e n t i t l e d "Emotional Block" were: a n x i e t y and f e a r of f a i l u r e ; l a c k o f i n t e r e s t ; low e s t i m a t i o n o f mathematics and i t s value; low o p i n i o n of worth as a l e a r n e r and l a c k of co n f i d e n c e i n l e a r n i n g ; and t h e i n a b i l i t y t o accept c h a l l e n g e s , low m o t i v a t i o n and a b e l i e f t h a t e f f o r t would not produce any r e t u r n * For the present study, t h i s l i s t was condensed to the f o l l o w i n g f i v e v a r i a b l e s : a) high anxiety i n mathematical s i t u a t i o n s (M—ANXIETY) , b) low enjoyment of mathematics (M—ENJOYMENT) c) low value of mathematics (M—VALUE) , d) low s e l f ^ -concept of t h e a b i l i t y to l e a r n mathematics (M—SELFCONCEPT), and e) 7 u n w i l l i n g n e s s to accept r e s p o n s i b i l i t y i n achievement s i t u a t i o n s (ACHIEVEMENT RESPONSIBILITY). I t should be noted t h a t ACHIEVEMENT RESPONSIBILITY and I n t e r n a l - E x t e r n a l Locus of C o n t r o l have been used i n t e r c h a n g e a b l y (Weiner, 1972). C r a n d a l l , Katkovsky and C r a n d a l l (1965) developed the I n t e l l e c t u a l Achievement R e s p o n s i b i l t y Scale based upon R o t t e r ' s (1966) theory of i n t e r n a l - e x t e r n a l l o c u s of c o n t r o l . Since the above v a r i a b l e s were a s s o c i a t e d with the a f f e c t i v e domain the f o l l o w i n g phrases or terms w i l l be used i n t e r c h a n g e a b l y ; " b l o c k " v a r i a b l e s , v a r i a b l e s a s s o c i a t e d with an "emotional b l o c k , " a.nd a f f e c t i v e v a r i a b l e s . Problem The purpose of t h i s study was t o c l a r i f y t h e i n t e r r e l a t i o n s h i p s o f t i e " b l o c k " v a r i a b l e s e x h i b i t e d by some st u d e n t s when performing mathematics. Cronbach and Meehl (1955) o p e r a t i o n a l i z e t i e c l a r i f i c a t i o n procedure as f o l l o w s : "to 'make c l e a r what something i s ' means to s e t f o r t h the laws i n which i t occurs" (p. 290). They a l s o s t a t e d t h a t "a c o n s t r u c t i s some pos t u l a t e d a t t r i b u t e of people, assumed t o be r e f l e c t e d i n t e s t performance" (p. 283).. In short, the meth o d o l o g i c a l l i t e r a t u r e expressed the b e l i e f t h a t some stud e n t s experience an "emotional b l o c k " when c o n f r o n t e d with mathematical problems. I t was a l s o h e l d t h a t these students, who experi e n c e constant or near constant f a i l u r e i n 8 mathematics, evidenced c e r t a i n b e h a v i o r s and b e l i e f s t e n d i n g to reduce the i n d i v i d u a l ' s a b i l i t y to f u n c t i o n i n mathematical s i t u a t i o n s . The major h y p o t h e s i s of t h i s study, then, was t h a t mathematics achievement (M—ACHIEVEMENT) would be a f u n c t i o n of the above v a r i a b l e s , M—ACHIEVEMENT = f(M—ANXIETY, M-ENJOYMENT, M—VALUE, M—SELFCONCEPT, ACHIEVEMENT RESPONSIBILITY). T h i s does not imply t h a t the c o n s t r u c t of an "emotional b l o c k " was t o be v a l i d a t e d . However, i t does mean t h a t the s e t of v a r i a b l e s which have o f t e n been d e s c r i p t i v e l y l i n k e d to an "emotional block" were to be v a l i d a t e d i n terms of t h e i r r e l a t i o n s h i p s with achievement. CASE FOR A NON—LINEAR MULTIVARIATE APPROACH Independent V a r i a b l e s M u l t i p l e d e f i n i t i o n s : ; of attitude,; Separate s c a l e s measuring v a l u e , enjoyment, and a n x i e t y i n mathematics were not t y p i c a l a t the time of t h i s study* Measures of a t t i t u d e had been used e x t e n s i v e l y i n mathematics and were being s u b j e c t e d to i n c r e a s i n g l y i n t e n s i v e and c r i t i c a l a n a l y s i s . In one review of s e v e r a l a t t i t u d e s t u d i e s Aiken (H972) i d e n t i f i e d some commonalities i n the d e f i n i t i o n s of a t t i t u d e . A t t i t u d e as used i n the s t u d i e s r e f e r r e d to here means approximately the same t h i n g as enjoyment, i n t e r e s t , and to some ex t e n t , l e v e l of a n x i e t y , (p. 229) Neal (1969) while g i v i n g a l i s t of a t t i t u d e v a r i a b l e s claimed t h a t the the d e f i n i t i o n o f a t t i t u d e " i s not p r e c i s e , but 9 i n v e n t o r i e s t h a t measure i t i n c l u d e such i n g r e d i e n t s as l i k i n g or d i s l i k i n g of mathematics, a tendency to engage i n or a v o i d mathematical a c t i v i t y , a b e l i e f t h a t mathematics i s u s e f u l or u s e l e s s " (p. 632). Khan (1969) c o r r e l a t e d s e v e r a l v a r i a b l e s such as study h a b i t s , achievement a n x i e t y * need achievement, academic i n t e r e s t , and a t t i t u d e toward teacher* with a s t a n d a r d i z e d achievement t e s t score. He noted t h a t h i s r e s u l t s "suggest the u s e f u l n e s s of subscore as compared to an o v e r a l l score and c a s t doubt on the assumption t h a t a t t i t u d e s , m o t i v a t i o n , and study h a b i t s can be represented u n i d i m e n s i o n a l l y " (p. 219) . Complex I n t e r r e l a t i o n s . The suggestion of a m u l t i v a r i a t e approach to the study of the e f f e c t of n o n c o g n i t i v e v a r i a b l e s upon achievement was based on the assumption t h a t the i n d i v i d u a l s c a l e s , i n s o f a r as they d i d not measure the same c o n s t r u c t , would give more i n f o r m a t i o n than a composite s c o r e . A simple i n t e r p r e t a t i o n of t h i s was t h a t the s c o r e s on s e v e r a l s c a l e s would have a h i g h e r m u l t i p l e c o r r e l a t i o n with mathematics achievement than any s i n g l e scale> A l p e r t and flaber (1960) measured the c o n s t r u c t of anxiety with two s c a l e s , p o s i t i v e ( f a c i l i t a t i n g ) and n e g a t i v e ( d e b i l i t a t i n g ) a n x i e t y s c a l e s . . The i n c r e a s e i n e x p l a i n e d v a r i a n c e of achievement when us i n g the two s c a l e s i n d i c a t e d t h a t a m u l t i p l e s c a l e approach was p r o d u c t i v e ; T h e r e f o r e , the hypothesis t h a t each sc a l e would add more i n f o r m a t i o n l e d to the p o s t u l a t i o n o f a m u l t i v a r i a t e l i n e a r f u n c t i o n such, as, 10 M-ACHIEVEMENT = M—ANXIETY + M—ENJOYMENT + M—VALUE + M—SELFCONCEPT + ACHIEVEMENT RESPONSIBILITY However, more complex r e l a t i o n s might a l s o occur* In p a r t i c u l a r i t co u l d be the case t h a t one v a r i a b l e may moderate the e f f e c t o f another v a r i a b l e . That i s to say, there may be an i n t e r a c t i o n e f f e c t . Wolk and DuCette (il 973) , showed t h a t l o c u s of c o n t r o l had a moderating e f f e c t on a measure o f achievement mot i v a t i o n which was c o r r e l a t e d with achievement. In f a c t , R o t t e r (1966) conceived the c o n s t r u c t of l o c u s of c o n t r o l as a moderator v a r i a b l e . The e f f e c t of reinforcement f o l l o w i n g some behavior . . . depends upon whether or not the person p e r c e i v e s a c a u s a l r e l a t i o n s h i p between h i s own behavior and the reward. (p* 1) He continues Perhaps one of the major conceptions which bears some r e l a t i o n s h i p to the b e l i e f i n i n t e r n a l versus e x t e r n a l c o n t r o l o f " r e i n f o r c e m e n t i s t h a t of need f o r achievement; . . . people who are high i n the need f o r achievement, i n a l l p r o b a b i l i t y have some b e l i e f i n t h e i r own a b i l i t y or s k i l l to determine the outccme of t h e i r e f f o r t s . The r e l a t i o n s h i p i s probably not l i n e a r * (p. 3) S i l v e r b l a n k (1973) noted another i n t e r a c t i o n e f f e c t . She found t h a t when the means of v a r i a b l e s cores were c o n s i d e r e d , groups could appear s i m i l a r . However, mathematics majors tended towards extremes of a n x i e t y ; they were e i t h e r u n u s u a l l y secure or s e v e r e l y anxious* The d i s t r i b u t i o n of the sc o r e s was as important as the mean.. To f a c i l i t a t e the statement of hypotheses which would r e l a t e the v a r i a b l e s of t h i s study, a t h e o r e t i c a l framework 11 was c o n s i d e r e d important. I n s t r u m e n t a l i t y t h e o r i e s were found t o address the i n t e r r e l a t i o n s of value of s u c c e s s , e x p e c t a t i o n of success, m o t i v a t i o n t o succeed and m o t i v a t i o n to avoid f a i l u r e . The theory o f Achievement M o t i v a t i o n , a s p e c i f i c i n s t a n c e of i n s t r u m e n t a l i t y t h e o r i e s ( M i t c h e l S B i g l a n , 1971, p. 432) , w i l l be presented i n some d e t a i l i n Chapter 2* I t i s s u f f i c i e n t t o note here t h a t the Achievement M o t i v a t i o n model was composed of three f a c t o r s , m o t i v a t i o n to succeed, p r o b a b i l i t y o f s u c c e s s , and value of success, i n t e r a c t i n g with each ot h e r i n the p r e d i c t i o n of achievement o r i e n t e d a c t i v i t y . The model a l s o p r e d i c t e d some n o n - l i n e a r c o r r e l a t i o n s between i t s f a c t o r s and achievement o r i e n t e d a c t i v i t y . The r e l a t i o n s h i p o f the v a r i a b l e s of the present study and the thr e e f a c t o r s w i l l be d i s c u s s e d i n Chapter 2. Dependent, V a r i a b l e s _ , _ E , , ,, A t t i t u d e measures have been l i m i t e d not onl y by confused c o n s t r u c t s but a l s o by po o r l y d e l i n e a t e d r e f e r e n t s . That i s , the s c a l e s have c o n t a i n e d items from s e v e r a l d i f f e r e n t c o n s t r u c t s and those s c a l e s have been' used t o measure a f f e c t towards s e v e r a l d i f f e r e n t a s p e c t s of mathematics. Some unexpected f i n d i n g s tended t o confirm t h i s . Higgins (1970) i n h i s study of a t t i t u d e changes i n the s e t t i n g o f a mathematics l a b o r a t o r y found t h a t students were e n t h u s i a s t i c about the o p p o r t u n i t y t o p a r t i c i p a t e but "something l e s s than e n t h u s i a s t i c about the content m a t e r i a l " 12 (p. 55). A t t i t u d e s about the v e h i c l e and the content should be c o n s i d e r e d s e p a r a t e l y . Aiken (1969) pointed out that A t t i t u d e toward m a t e r i a l t o be le a r n e d by r o t e , such as the m u l t i p l i c a t i o n t a b l e , i s not the same v a r i a b l e as a t t i t u d e toward problems and a l g e b r a i c symbols. (p. 8) The measurement of mathematics achievement i s o f t e n broken i n t o t h r e e components; computation, concepts, and problem s o l v i n g . Because of the p o s s i b i l i t y of each of the a f f e c t i v e v a r i a b l e s having d i f f e r e n t r e l a t i o n s h i p s with each of the achievement v a r i a b l e s , i t was f e l t t h a t i n the present study each of the three achievement components should be analyzed s e p a r a t e l y . T h i s r e s u l t e d i n f i v e major independent v a r i a b l e s and three dependent v a r i a b l e s * Aiken (Aiken & Dreger, 1961) s t a t e d t h a t unpublished data c o l l e c t e d by him demonstrated " t h a t a t t i t u d e s c a l e s c o r e s are more h i g h l y c o r r e l a t e d with both a b i l i t y and achievement measures i n the case of females than i n males" (p. 14). In a study of sex d i f f e r e n c e s i n problem s o l v i n g Carey (1978) found t h a t the c o r r e l a t i o n s between a t t i t u d e and problem s o l v i n g were c o n s i d e r a b l y higher f o r males than f o r females. In summary, Aiken (1970) c a l l e d f o r a r e s e a r c h program . . . to i n v e s t i g a t e the i n t e r a c t i o n s among the e n t i r e domain of a f f e c t i v e and c o g n i t i v e v a r i a b l e s i n t h e i r e f f e c t s on mathematics l e a r n i n g . . Such a program should be m u l t i v a r i a t e i n terms of both i n p u t and output v a r i a b l e s , and would e n t a i l a composite of c o r r e l a t i o n a l and experimental rese a r c h methods, (p. 253) 13 The present study was c o n s i d e r e d to be p a r t of such a program. Importance of the Problem The - v a l i d a t i o n o f a c o n s t r u c t . Because of the m u l t i v a r i a t e , non-Iineat o r i e n t a t i o n of t h i s study the number of p o t e n t i a l hypotheses was quite l a r g e * A number of the p o s s i b l e r e s u l t s could have been s t a t i s t i c a l l y s p u r i o u s and t h e o r e t i c a l l y u n i n t e r p r e t a b l e . Therefore, hypotheses were formed which were based upon r e l a t i o n s h i p s suggested by e x i s t i n g r e s e a r c h and accepted t h e o r e t i c a l models.. T h i s was an important a s p e c t of t h i s study,. I f the v a r i a b l e s a s s o c i a t e d with an "emotional b l o c k " were to be c o n s i d e r e d a u s e f u l set then not only s h o u l d the r e l a t i o n s h i p of each to mathematics achievement be s t u d i e d but the r e l a t i o n s h i p s among themselves should be e l u c i d a t e d . As Nunnally (1970) s t a t e d , a c o n s t r u c t i s something t h a t the s c i e n t i s t puts t o g e t h e r from h i s own i m a g i n a t i o n , something t h a t does not e x i s t as an i s o l a t e d , o b s ervable dimension of behavior. A c o n s t r u c t r e p r e s e n t s a h y p o t h e s i s ( u s u a l l y h a l f formed) that a v a r i e t y of behaviors w i l l c o r r e l a t e with one another i n s t u d i e s of i n d i v i u a l d i f f e r e n c e s and/or w i l l be s i m i l a r l y a f f e c t e d by experimental treatments. (p. 139) He continued, "determining to what extent a l l , or some, of those v a r i a b l e s c o r r e l a t e with one another or are a f f e c t e d a l i k e by experimental treatments i s a necessary step i n the v a l i d a t i o n process" (p. 141) . I t may be u s e f u l here to note the concept of a nomological net as d e f i n e d by Cronbach and Meehl (1955). 14 1) to "make c l e a r what something i s " means to s e t f o r t h the laws i n which i t occurs,. 2) The laws . . may r e l a t e (a) observable p r o p e r t i e s or q u a n t i t i e s to each other; or (b) t h e o r e t i c a l c o n s t r u c t s to o b s e r v a b l e s ; or (c) d i f f e r e n t t h e o r e t i c a l c o n s t r u c t s to one another . 3) a c o n s t r u c t £mustj . . . occur i n a nomoloqical net, a t l e a s t some of whose laws i n v o l v e observables. ^ 4) "Learning more.about" a t h e o r e t i c a l c o n s t r u c t i s a matter o f e l a b o r a t i n g the nomological network i n which i t o c c u r s , 5) An enrichment of the net such as adding a c o n s t r u c t or a r e l a t i o n to theory i s j u s t i f i e d i f i t generates nomologicals t h a t are confirmed by o b s e r v a t i o n or i f i t reduces the number of nomologicals r e q u i r e d to p r e d i c t the same o b s e r v a t i o n s . 6) " o p e r a t i o n s " which are q u a l i t a t i v e l y very d i f f e r e n t " o v e r l a p " or "measure the same t h i n q " i f t h e i r p o s i t i o n s i n the nomological net t i e them to the same c o n s t r u c t v a r i a b l e * (pp« 290—291) I f the m u l t i v a r i a t e nature of the s e t of a f f e c t i v e v a r i a b l e s was confirmed by t h i s study, then the v a r i a b l e s used would suggest s p e c i f i c c o u n t e r a c t i n g experiences which should then be examined i n f u t u r e r e s e a r c h f o r those s u b j e c t s i d e n t i f i e d as having the " b l o c k " . I f the hypothesis of a complex i n t e r a c t i v e r e l a t i o n s h i p between the n o n c o g n i t i v e v a r i a b l e s and mathematics achievement was confirmed then i t would suggest t h a t any e x p e r i m ental manipulation of one v a r i a b l e must be done expe c t i n g d i f f e r e n t e f f e c t s a t s e v e r a l l e v e l s of a second* This study was c o n s i d e r e d important then because i t would d e l i n e a t e the i n t e r r e l a t i o n s of a number of v a r i a b l e s 15 c u r r e n t l y of i n t e r e s t i n d i v i d u a l l y and c o l l e c t i v e l y * I t was a l s o c o n s i d e r e d an.important f i r s t step i n the g e n e r a t i o n of e xperimental hypotheses. I t would provide i n s i g h t i n t o t h e the degree of complexity of the a t t i t u d i n a l domain. Moreover, the e stablishment of a t h e o r e t i c a l framework a p p r o p r i a t e to a complex c o n c e p t u a l i z a t i o n of a t t i t u d e v a r i a b l e s i n mathematics educ a t i o n i s the t h e o r e t i c a l c o n t r i b u t i o n of t h i s study and w i l l be e l u c i d a t e d i n Chapter 2. RESEARCH HYPOTHESES Summary of the Problem The reviewed l i t e r a t u r e a s s o c i a t e d with methods of t e a c h i n g i n mathematics e d u c a t i o n s t a t e s t h a t an "emotional b l o c k " i s r e l a t e d t o mathematics achievement. The l i t e r a t u r e a l s o suggests t h a t the " b l o c k " i s composed of s e v e r a l more s p e c i f i c c o n s t r u c t s which are t y p i c a l of a t t i t u d e s c a l e s : a n x i e t y , enjoyment, value, and s e l f - c o n c e p t . Achievement r e s p o n s i b i l i t y , or l o c u s of c o n t r o l , i s a l s o suggested i n r e l a t i o n to " l e a r n e d h e l p l e s s n e s s " . The l i t e r a t u r e on a t t i t u d e toward mathematics i n d i c a t e d t h a t a t t i t u d e v a r i a b l e s are probably r e l a t e d d i f f e r e n t l y to s e v e r a l d i f f e r e n t r e f e r e n t s of mathematics. T h e r e f o r e , the " block" or a f f e c t i v e v a r i a b l e s were r e l a t e d to t h r e e achievment measures; computation, concepts, and problem s o l v i n g * I t was a l s o argued t h a t complex i n t e r a c t i o n s might e x i s t between the v a r i a b l e s , and that the achievement 16 m o t i v a t i o n model d e s c r i b e d t h r e e a f f e c t i v e c o n s t r u c t s which i n t e r a c t e d i n achievement r e l a t e d a c t i v i t y . G e n e r a l i z a t i o n a c r o s s Sex Nunnally (1S67) d e c l a r e d t h a t : i f both sexes are i n c l u d e d i n an a n a l y s i s , i t i s wise t o s t a n d a r d i z e scores s e p a r a t e l y f o r the two befo r e c o r r e l a t e s are computed. I f t h a t i s not done, sex should be i n c l u d e d as another v a r i a b l e i n the a n a l y s i s . (p. 370) Bather than s t a n d a r d i z i n g s c o r e s s e p a r a t e l y f o r the two sexes which would l e a d to r e s u l t s with e f f e c t s of sex removed, t h i s study i n c l u d e d an a n a l y s i s f o r sex e f f e c t s * I t was hypothesized that there would be no s i g n i f i c a n t l y d i f f e r e n t c o r r e l a t i o n s among the a f f e c t i v e and achievement v a r i a b l e s f o r males and females* I f t h i s hypothesis was not accepted then a l l the f o l l o w i n g hypotheses would be t e s t e d s e p a r a t e l y f o r males and females* A f f e c t i v e _ I n t e r - S c a l e C o r r e l a t i o n s , I t was hypothesized t h a t t h e r e would be s i g n i f i c a n t * c o r r e l a t i o n s among the v a r i a b l e s a s s o c i a t e d with the "b l o c k . " I t was hypothesized t h a t a p r i n c i p a l component a n a l y s i s o f the a f f e c t i v e v a r i a b l e s would r e s u l t i n a three f a c t o r s o l u t i o n which, a f t e r orthogonal r o t a t i o n , would be i n t e r p r e t a b l e as the f o l l o w i n g three f a c t o r s and t h e i r 4 I h e word s i g n i f i c a n t when unmodified w i l l mean s t a t i s t i c a l l y s i g n i f i c a n t * 17 components-F a c t o r 1: M—ANXIETY, M-rENJOYMENT, ACHIEVEMENT EESPONSIBILITY F a c t o r 2: M—SELFCONCEPT F a c t o r 3: M—VALUE Aff e c t i v e - A c h i e v e m e n t Scale flelationships I t was hypothesized t h a t each of the a f f e c t i v e s c a l e s would be c o r r e l a t e d with each of the t h r e e aspects of mathematics achievment. Because the achievement m o t i v a t i o n model suggested t h a t the p r o b a b i l i t y of success may have a n o n - l i n e a r r e l a t i o n t o achievement i t was hypothesized t h a t s e l f - c o n c e p t would have a r e l a t i o n of the second degree with the measures of achievement. The e q u i v a l e n c e o f s e l f - c o n c e p t and p r o b a b i l i t y of success, to be d i s c u s s e d i n Chapter 2, was based on l o g i c a l arguments r a t h e r than on e m p i r i c a l f i n d i n g s . T h e r e f o r e , i t was hypothesized t h a t some of the other a f f e c t i v e v a r i a b l e s would a l s o be n o n - l i n e a r l y r e l a t e d t o achievement. I t was f u r t h e r hypothesized t h a t when grouped t o g e t h e r by m u l t i p l e r e g r e s s i o n a sub-set of the independent v a r i a b l e s would be c o r r e l a t e d more with each of the t h r e e achievement measures than any i n d i v i d u a l independent variable'. I t was hypothesized t h a t one or more a d d i t i o n a l v a r i a b l e s would add s i g n i f i c a n t l y t o the variance e x p l a i n e d by the v a r i a b l e having the maximum c o r r e l a t i o n with the achievement v a r i a b l e s . I t was a l s o hypothesized t h a t l i n e a r composites d e r i v e d from the f a c t o r score c o e f f i c i e n t matrix of t h e 18 r o t a t e d s o l u t i o n would c o r r e l a t e s i g n i f i c a n t l y with the achievement s c o r e s . As the Achievement M o t i v a t i o n model suggested i n t e r a c t i o n s among the t h r e e f a c t o r s of the model, i t was hypothesized t h a t the i n t e r a c t i o n terms of the l i n e a r composites r e p r e s e n t i n g those f a c t o r s would add f u r t h e r e x p l a i n e d v a r i a n c e to t h a t o f the achievement s c o r e s . STATISTICAL HYPOTHESES S i g n i f i c a n c e versus Strength of R e l a t i o n s wherever an a p p r o p r i a t e t e s t c o u l d be made, the f o l l o w i n g n u l l hypotheses were t e s t e d a t the .01 l e v e l of s i g n i f i c a n c e . T h i s l e v e l was chosen to reduce the o v e r a l l e r r o r r a t e of the a n a l y s e s . I t should be noted t h a t as the sample s i z e was l a r g e and as t e s t s of s i g n i f i c a n c e are r e l a t e d t o sample s i z e t h a t the degree or s i z e of the r e l a t i o n was most important. Thorndike (1971) s t a t e d : The emphasis cn c o n s t r u c t v a l i d a t i o n should be on the s t r e n g t h of each r e l a t i o n r a t h e r than merely on i t s s t a t i s t i c a l s i g n i f i c a n c e . C o n s t r u c t v a l i d a t i o n aims more a t comprehension than numerical r e s u l t s , (p. 465) I n a d d i t i o n the l a r g e sample s i z e gave adequate power so t h a t the .01 alpha l e v e l would not make the p r o b a b i l i t y of a Type I I e r r o r i n o r d i n a t e l y l a r g e . G e n e r a l i z a t i o n a c r o s s Sex I t was hypothesized t h a t : (1) There would be no s i g n i f i c a n t d i f f e r e n c e between the 19 v a r i a n c e - c o v a r i a n c e matrix of the males and that of the females. I t s h o u l d be understood t h a t i f the n u l l h y p o t h e s i s was r e j e c t e d a separate t e s t f o r males and females would be made f o r the f o l l o w i n g hypotheses. A f f e c t i v e I n t e r - S c a l e R e l a t i o n s h i p s I t was hypothesized t h a t : (2) There would be no s i g n i f i c a n t c o r r e l a t i o n s among the "block" v a r i a b l e s , M—ANXIETY, M—ENJOY MENT, M—V ALOE, M-SELFCONCEPT, and ACHIEVEMENT RESPONSIBILITY. (3) No simple f a c t o r s t r u c t u r e would emerge from a p r i n c i p a l component a n a l y s i s of M—ANXIETY, M-ENJOYMENT, M—VALUE, M—SELFCONCEPT, and ACHIEVEMENT RESPONSIBILITY. (4) I f a simple s t r u c t u r e emerged from a p r i n c i p a l component a n a l y s i s the orthogonal r o t a t i o n would not r e v e a l the f o l l o w i n g l o a d i n g p a t t e r n : V a r i a b l e F a c t o r Loading F1 F2 F3 M—ANXIETY high low low M—ENJOYMENT high low low ACHIEVEMENT RESPONSIBILITY high low low M—SELFCONCEPT low high low M—VALUE low low high A f f e c t i v e - A c h i e v e m e n t , S c a l e , R e l a t i o n s h i p s I t was hypothesized t h a t : (5) Each o f M—ANXIETY, M-ENJOYMENT, M—VALUE, M—SELF C ONCE PT 20 and ACHIEVEMENT RESPONSIBILITY would not be s i g n i f i c a n t l y c o r r e l a t e d with each of the achievement measures; computation, concepts, and problem s o l v i n g ; (6) The q u a d r a t i c component of each o f M—ANXIETY, M-ENJOYMENT, M—VALUE, M-SELFCONCEPT, and ACHIEVEMENT EES EONS IBILITY. would not be s i q n i f i c a n t l y c o r r e l a t e d with measures of computation, concepts or problem s o l v i n q . (7) L i n e a r m u l t i p l e r e q r e s s i o n u s i n g the " b l o c k " v a r i a b l e s M—ANXIETY, M-ENJOYMENT, M-VALUE, M-SELFCONCEPT, and ACHIEVEMENT BESPONSIBILITY would not s i g n i f i c a n t l y i n c r e a s e the ex p l a i n e d v a r i a n c e of the l a r g e s t o f the c o r r e l a t i o n s i n (5) . (8) Stepwise r e g r e s s i o n would not i n c l u d e a d d i t i o n a l v a r i a b l e s beyond the v a r i a b l e maximally c o r r e l a t e d with each of the achievement s c o r e s . (9) I f a simple s t r u c t u r e d i d emerge then near o r t h o g o n a l measures from the f a c t o r s c o r e s would not c o r r e l a t e with the t h r e e measures of achievement. (10) I n t e r a c t i o n s from the f a c t o r s c o r e s i n (9) would not s i g n i f i c a n t l y i n c r e a s e t h e - e x p l a i n e d v a r i a n c e of each of the achievement measures. 21 Chapter 2 BELATED RESEARCH • " INTRODUCTION I t was shown i n Chapter 1 t h a t an "emotional b l o c k " may be c h a r a c t e r i z e d by a number of c o n s t r u c t s ; a n x i e t y * enjoyment, value , and s e l f - c o n c e p t i n mathematics. I t was a l s o suggested t h a t i f Atkinson's (1956, 1958) theory of Achievement M o t i v a t i o n was used, these v a r i a b l e s might i n t e r a c t , among themselves and with a measure, of achievement r e s p o n s i b l i l i t y when r e l a t e d to achievement i n mathematics. In t h i s chapter r e s e a r c h s p e c i f i c a l l y r e l a t e d t o mathematics a t t i t u d e i n c l u d i n g a n x i e t y , enjoyment* value, and s e l f - c o n c e p t o f mathematics, and l o c u s of c o n t r o l , i s reviewed. I n each of the separate s e c t i o n s sex r e l a t e d e f f e c t s w i l l be noted* The t h r u s t of the argument i n the s e c t i o n s devoted to the i n d i v i d u a l c o n s t r u c t s w i l l be t h a t the more c l o s e l y the s c a l e s measuring the c o n s t r u c t s are r e l a t e d t o the s u b j e c t matter i n quest i o n the s t r o n g e r the r e l a t i o n between measures of the c o n s t r u c t and achievement i n the s u b j e c t area. The theory of achievement mot i v a t i o n w i l l be presented i n some d e t a i l and a model w i l l be i d e n t i f i e d based on the th e o r y . 22 Each of the a f f e c t i v e v a r i a b l e s w i l l be i d e n t i f i e d with one of the t h r e e c o n s t r u c t s o f the achievement motivation model. ATTITUDE VARIABLES Number of St u d i e s — 1 T - " — As an i n d i c a t i o n of the importance of these v a r i a b l e s i t s h ould be noted t h a t f o r the years 1974-1978 16.1% of the d i s s e r t a t i o n s and 9.4% of the j o u r n a l - p u b l i s h e d r e p o r t s as l i s t e d by Suydam and Weaver (1974, 1975, 1976, 1977, 1978) i n the J o u r n a l f o r Research i n Mathematics Education i n c l u d e d measures o f s e l f - c o n c e p t , a n x i e t y , achievement r e s p o n s i b i l i t y or a t t i t u d e * The numbers and percentages f o r each of the f i v e years may be found i n Table 1. Table 1 Percentages of D i s s e r t a t i o n s and J o u r n a l - P u b l i s h e d Reports Dealing with A f f e c t i v e V a r i a b l e s L i s t e d i n the Suydam Reports (1974-78) Reports D i s s e r t a t i o n s Year N T o t a l * % N T o t a l * % 1974 7 76 9,2 44 299 14.7 1975 5 112 4.5 44 264 16.7 1976 5 99 5.0 37 266 13.9 1977 11 112 9.8 52 273 19.0 1978 26 176 14.8 56 343 16.3 T o t a l 54 575 9-: 4 233 1145 16. 1 i T o t a l number o f r e p o r t s 2 T o t a l number o f d i s s e r t a t i o n s 23 T y p i c a l : S t u d i e s The importance of the present study stems from the b e l i e f , expressed i n the mathematics teaching l i t e r a t u r e , t h a t low a c h i e v e r s have some-form of "emotional b l o c k " r e v e a l e d by c e r t a i n a f f e c t i v e c h a r a c t e r i s t i c s . although s t u d i e s have c o r r e l a t e d i n d i v i d u a l v a r i a b l e s with achievement and have attempted t o change some of the v a r i a b l e s e x p e r i m e n t a l l y , a l l the v a r i a b l e s have not been c o n s i d e r e d s i m u l t a n e o u s l y . The m u l t i v a r i a t e approach was emphasized by Wylie (1974) and Aiken (1970, 1976) when complex phenomena such as s e l f — c o n c e p t or a t t i t u d e were to be studied* DuCette and Wolk (1972) noted t h a t d i f f i c u l t i e s are encountered when studying dependent v a r i a b l e s , such as achievement, using only one independent v a r i a b l e . I t i s a l s o h i g h l y c h a r a c t e r i s t i c of such r e s e a r c h [ I n t e r n a l — E x t e r n a l Locus of Control*] t h a t h i g h l y molar dependent v a r i a b l e s such as o v e r a l l academic performance or s o c i a l a c t i v i s m have been s t u d i e d . While such b e h a v i o r s are undoubtedly more i n t e r e s t i n g than v a r i a b l e s such as l e v e l of a s p i r a t i o n or r i s k - t a k i n g , the problem i n s t u d y i n g them i s t h a t they are so h i g h l y overdetermined that the p r e d i c t a b i l i t y from any one s p e c i f i c v a r i a b l e w i l l be s l i g h t * (p. 494) U n d e r l y i n g the concern f o r a t t i t u d e i s the n o t i o n t h a t p o s i t i v e a t t i t u d e s would i n c r e a s e the l i k e l i h o o d t h a t a student would attend t o mathematics and thereby i n c r e a s e the p r o b a b i l i t y t h at he would l e a r n . Krathwohl, Bloom and Masias (1964) supported the n o t i o n of two d i f f e r e n t approaches to the s£udy o f the r e l a t i o n s h i p between achievement and a t t i t u d e . 24 As viewed from the c o g n i t i v e p o l e , the student may be t r e a t e d as an a n a l y t i c a l machine, a "computer" t h a t s o l v e s problems. In c o n t r a s t ; viewed from the a f f e c t i v e p o l e , we take g r e a t e r cognizance of the m o t i v a t i o n , d r i v e s , and emotions t h a t are the f a c t o r s b r i n g i n g about achievement of c o g n i t i v e behavior. (p. 57) As an example they c o n t i n u e d , "Note f o r i n s t a n c e the prevalence o f g i r l s who d i s l i k e mathematics and so cannot l e a r n i t " (p,i 57) . There i s an i m p l i e d r e l a t i o n s h i p of c a u s a l i t y . Khan and Weiss (1973) suggested that the r e l a t i o n s h i p was f u n c t i o n a l r a t h e r than c a u s a l . They s t a t e d , "academic successes help promote s a t i s f a c t i o n with s c h o o l , which i n t u r n i n c r e a s e s the p o s s i b i l i t y of f u t u r e s u c c e s s e s " (p. 770) . i I t should be noted here t h a t a number of statements were found which i n d i c a t e d c a u s a l r e l a t i o n s and yet were based upon c o r r e l a t i o n a l data. For example Poffenberger and Norton (1959) s t u d i e d the d i f f e r e n c e s between a group t h a t l i k e d mathematics and one t h a t d i d not* They used a number of s c a l e s such as the a t t i t u d e toward mathematics of parents and s i b l i n g s , and the encouragement and grade e x p e c t a t i o n s of the parents* They concluded " t h a t s e l f - c o n c e p t s i n regard to mathematical a b i l i t y are w e l l e s t a b l i s h e d i n the e a r l y s c h o o l years and i t i s very d i f f i c u l t f o r even the best teacher to change them" (p. 174). The i m p l i c a t i o n was t h a t i f s e l f - c o n c e p t c o u l d be r a i s e d then achievement would r i s e as a r e s u l t * Another example was t h a t of Lindgren, S i l v a , Faraco, and De Rocha (1964) who c o r r e l a t e d a t t i t u d e toward problem 25 s o l v i n g , and success i n a r i t h m e t i c as measured by achievement t e s t s . In t h e i r d i s c u s s i o n of. r e s u l t s they asked "Why are p r oblem-solving a t t i t u d e s more of a f a c t o r i n a r i t h m e t i c achievement i n some c l a s s e s than o t h e r s ? " (p; 45). Again, although the study was c o r r e l a t i o n a l , there was an i m p l i c a t i o n t h a t poor a t t i t u d e s cause poor a r i t h m e t i c achievement; The c o r r e l a t i o n s of a t t i t u d e with achievement are u s u a l l y low but c o n s i s t e n t ; Aiken (1969) noted t h a t , "the c o r r e l a t i o n s between a t t i t u d e and achievement i n elementary s c h o o l , although s t a t i s t i c a l l y s i g n i f i c a n t , are t y p i c a l l y not very l a r g e " (p. 9),. A number of problems have l i m i t e d the c o n t r i b u t i o n of p r e d i c t i v e power by measures of the a f f e c t i v e domain; L i m i t a t i o n s of measuring instruments (Aiken, 1973, p. 416), degree of s e l f - i n s i g h t , c o n s c i e n t i o u s n e s s with which p u p i l s f i l l out the i n v e n t o r y (Aiken, 1969, p. 9), and t h e s t a b i l i t y of a t t i t u d e s ^ v a r y i n g w i t h the maturity of the p u p i l s (Aiken, 1372, p. 230). As one of the- problems noted above was t h a t the a f f e c t i v e v a r i a b l e s have been s t u d i e d i n i s o l a t i o n , some o f the l i t e r a t u r e a s s o c i a t e d witb each v a r i a b l e w i l l be presented; ANXIETY IN MATHEMATICS General Anxiety There are some c o n f l i c t i n g r e s u l t s on the e f f e c t s of a n x i e t y ; Denny (1966) provided evidence t h a t h i g h a n x i e t y , as measured by the Manifest Anxiety S c a l e , f a c i l i t a t e d the 2 6 achievement of s u b j e c t s with high i n t e l l i g e n c e but t h a t the r e v e r s e was t r u e f o r those with low i n t e l l i g e n c e . Mazzei and Goulet (1969) , using the Test Anxiety Q u e s t i o n n a i r e (TAQ) , found that- "high a n x i e t y (TAQ) d i d not u n e q u i v o c a l l y l e a d to i n f e r i o r performance ( r e l a t i v e t o low anxiety) when Ss are given e g o - s t r e s s i n s t r u c t i o n s " (p. 602). However, both s e t s of r e s u l t s i n d i c a t e d a d i s o r d i n a l i n t e r a c t i o n with high a n x i e t y being more f a c i l i t a t i n g than low a n x i e t y f o r s t u d e n t s with high i n t e l l i g e n c e , and more i n h i b i t i n g than low a n x i e t y f o r students with low i n t e l l i g e n c e . The d i f f e r e n c e s i n the r e s u l t s of the two s t u d i e s may be e x p l a i n e d by the f a c t t h a t whereas Mazzei and Goulet used the Test Anxiety S c a l e (TAQ) Denny used the Manifest Anxiety S c a l e (MAS). I t may be the case t h a t the two s c a l e s measured a n x i e t y toward two d i f f e r e n t s e t s of o b j e c t s , s i t u a t i o n s , or c o n d i t i o n s * The theory behind t h i s p o s s i b i l i t y was s t a t e d by Sarasoh (1975): Our behavior i s determined i n p a r t by the i n f o r m a t i o n a v a i l a b l e t o us* I n f o r m a t i o n a t our d i s p o s a l i s , i n t u r n , i n f l u e n c e d by whether we attend to i t * (p. 175) He continued In my view, a person's l e v e l of t e s t a n x i e t y i s , to a s i g n i f i c a n t degree a product of experiences t h a t i n f l u e n c e what he a t t e n d s to i n h i m s e l f and t h e world . . . . Two response components .have been emphasized by w r i t e r s who espouse t h i s view. One i s emotional and autonomic r e a c t i v i t y - sweating, a c c e l e r a t e d heart r a t e , e t c * The other concerns c o g n i t i v e events - e.g., saying to o n e s e l f while t a k i n g a t e s t , "I am s t u p i d , " "Maybe I won't pass." (p. 175) 27 In d i s c u s s i n g t e s t a n x i e t y he gave a s p e c i f i c example. In Test a n x i e t y Type A, a person gets upset before, d u r i n g , and a f t e r t e s t s because of r e l a t i v e l y i s o l a t e d u n fortunate experiences ( f o r example, a t r a u m a t i z i n g teacher i n the t h i r d g r a d e ) . Test Anxiety Type B i s c h a r a c t e r i z e d by (a) a n x i e t y and worry i n o t h e r areas and (b) c o n f l i c t and ambivalence over achievement and being evaluated, (p. 175) That the TAQ and the MAS, measures of a n x i e t y , are r e l a t e d to two d i f f e r e n t s e t s of c o n d i t i o n s i s supported by the r e s u l t s of a study done by O s i e r (1954),; He found t h a t s t r e s s r e l a t e d to task performance ( f a i l u r e on a s i m i l a r t e s t i n g s i t u a t i o n ) had d i f f e r e n t e f f e c t s than s t r e s s r e s u l t i n g from an u n r e l a t e d source such as a note from the school o f f i c e about a complaint a g a i n s t the student* The former group d i s p l a y e d depressed t e s t performance, the l a t t e r d i d not. S i m i l a r e f f e c t s of s t r e s s r e s u l t i n g from academic f a i l u r e were found by Gibby and Gibby (1967) who had teachers t e l l s t u d e n t s t h a t they were di s a p p o i n t e d with the s t u d e n t s ' E n g l i s h marks and passed out f a i l grades as well'; They found "a s i g n i f i c a n t decrement i n word f l u e n c y score f o l l o w i n g the stress" of the experimental c o n d i t i o n s " (p. 37). Tiiey a l s o found s i g n i f i c a n t changes on f i v e of the s i x c a t e g o r i e s of the I n t e l l i g e n c e E a t i n g Schedule which asked the student how parents, peers, and themselves would r a t e t h e i r i n t e l l i g e n c e . Along t h i s same l i n e Dreger and Aiken (1957) c i t e d a f a c t o r a n a l y s i s by O'Connor of the T a y l o r Manifest Anxiety 28 Scale which d i s p l a y e d f i v e d i s t i n c t f a c t o r s . . From t h i s they argued t h a t attempts to measure more s p e c i f i c a n x i e t y c o n s t r u c t s would he more pr o d u c t i v e . A l p e r t and Haber (1960) s t u d i e d the r e l a t i o n s h i p s o f three g e n e r a l a n x i e t y s c a l e s and three s p e c i f i c anxiety s c a l e s with the S c h o l a s t i c A p t i t u d e Test, c o l l e g e grade point average (GPA) , and grades given i n a psychology c o u r s e . They found t h a t c o r r e l a t i o n s among the s p e c i f i c s c a l e s were higher than those among general s c a l e s as w e l l as those between general and s p e c i f i c s c a l e s . F u r t h e r , c o r r e l a t i o n s between gen e r a l s c a l e s and the c o g n i t i v e t e s t s were t y p i c a l l y lower than those between the s p e c i f i c s c a l e s and the c o g n i t i v e t e s t s . (See Table 2 ) . Table 2 C o r r e l a t i o n s Between General and S p e c i f i c Anxiety S c a l e s and S e v e r a l Measures of Achievement B e l AI AS TS AAT- AAT+ GPA Psych SAT *- i — T n — — ^  — i MAS . 89 .39 .32 .32 .38 -.33 .01 -.08 . 10 AI .84 .34 .28 .37 -.25 -.04 -.05 . 13 AS .73 .38 .30 -.24 -. 06 .14 -.24 TAS . 82 .64 -. 40 -. 24 -.21 -. 18 AAT- .87 -.48 -;35 - i 2 6 -. 29 AAT+ .83 .37 .23 .21 T a y l o r Manifest Anxiety S c a l e (MAS) ; Welsh A n x i e t y Index (AI) ; Freeman Anxiety Scale (AS); Mandler-Sarason Test Anxiety S c a l e (TAS); Achievement Anxiety T e s t - D e b i l i t a t i n g (AAT-); Achievement Anxiety T e s t - F a c i l i t a t i n g (AAT+) ( A l p e r t & Haber, 1960, p. 209.) They concluded, S p e c i f i c a n xiety s c a l e s and gen e r a l a n x i e t y s c a l e s measure, t o a s i g n i f i c a n t extent* something 29 d i f f e r e n t * Furthermore, i t appears t h a t the v a r i a b l e which the s p e c i f i c s c a l e s measure, and which general s c a l e s do not, i s i n v o l v e d i n academic performance to such an e x t e n t t h a t the s p e c i f i c s c a l e s are b e t t e r p r e d i c t o r s of academic performance than are the g e n e r a l a n x i e t y s c a l e s . (p,. 209) A l p e r t and Haber a l s o considered t h e d i f f e r e n c e between f a c i l i t a t i n g and d e b i l i t a t i n g a n x i e t y * They s t a t e d t h a t an absence of response to a negative item may not be a measure of m o t i v a t i o n wien s t r e s s i s present and t h e r e f o r e items sampling responses to the p o s i t i v e e f f e c t s of a n x i e t y should be i n c l u d e d i n a s c a l e . They found t h a t i n three groups (N = 93, 92, 96) the c o r r e l a t i o n s between GPA and the f a c i l i t a t i n g a n x i e t y s c a l e were .36, .32, .50 and between GPA and d e b i l i t a t i n g anxiety -.45, -.08, and -.40. However, the combined m u l t i p l e c o r r e l a t i o n s with the two a n x i e t y s c a l e s p r e d i c t i n g GPA were ,*50* .32, and .54. S p e c i f i c c A n x i e t y S u i n , E d i e , N i c p l e t t i , and S p i n e l l i (1972) c i t i n g an e a r l i e r p u b l i c a t i o n (Suin, 1970) s t a t e d . Over one t h i r d of the students who a c t i v e l y sought he l p through a c o u n s e l l i n g c e n t e r behavior therapy program d e s c r i b e d t h e i r primary problem as connected with mathematics. (p* 373) On the b a s i s of t h i s they developed a Mathematics Anxiety Rating S c a l e (MARS). The s c a l e was composed of 98 items " d e s c r i b i n g p r a c t i c a l s i t u a t i o n s t h a t i n v o l v e mathematics e.g*, 'working on an income tax form,' 'checking over your monthly bank account*' or ' f i g u r i n g the s a l e s t a x . ' " (p. 30 373). They found t h a t the s c a l e had a t e s t — r e t e s t r e l i a b i l i t y of .78 and a c o r r e l a t i o n of -.35 with the D i f f e r e n t i a l A p t i t u de T e s t . The mean score f o r the students seeking therapy f o r mathematics a n x i e t y was 256.9 and t h a t o f the norming group was 187.3. These r e s u l t s on the s p e c i f i c i t y of a n x i e t y suggested t h a t a s c a l e measuring a n x i e t y i n a mathematcs s i t u a t i o n be examined and compared to a more g e n e r a l measure. Dreger and aiken (1957) began the "endeavor t o detect the presence of a syndrome of emotional r e a c t i o n s to a r i t h m e t i c and mathematics t e n t a t i v e l y c a l l e d 'Number a n x i e t y ' " (p. 344). They administered the T a y l o r Manifest Anxiety Scale !(TMAS) to 704 s u b j e c t s with three items of r e l a t i v e l y low r e l i a b i l i t y r e p l a c e d by three items r e l a t i n g to number a n x i e t y . They then s u b j e c t e d the f o u r t e e n most v a l i d items of t-he T a y l o r s c a l e and the three mathematics a n x i e t y items to a c l u s t e r a n a l y s i s * The t h r e e mathematics anxiety items c l u s t e r e d together. They found t h a t the three items had a c o r r e l a t i o n of -.44 with mathematics grade* On the other hand, S z e t e l a (1973) found t h a t Mathematics Anxiety had a s t r o n g r e l a t i o n t o the T e s t Anxiety Q u e s t i o n n a i r e (p < .0001) . Some sex d i f f e r e n c e s have been noted. Kahn (1969) c o r r e l a t e d achievement anxiety with a t t i t u d e s c o r e s on the SCAT. • The c o r r e l a t i o n s were .305 f o r males and .509 f o r females. S z e t e l a (1973) found t h a t t e s t anxiety and i n t e l l i g e n c e c o r r e l a t e d -.24 f o r males and -.11 f o r females. 31 In summary these s t u d i e s i n d i c a t e d t h a t measures of achievement anxiety are b e t t e r p r e d i c t o r s of achievement than more gen e r a l measures of a n x i e t y . However, t h e r e was no c l e a r evidence t h a t mathematics a n x i e t y s c a l e s were s u p e r i o r t o the t e s t s o f achievement a n x i e t y ; The s t u d i e s a l s o i n d i c a t e d p o s s i b l e sex d i f f e r e n c e s . VALUE The value component may be d i v i d e d i n t o a t l e a s t two s u b - c o n s t r u c t s ; one, the value of mathematics f o r s o c i e t y , another, the value of mathematics f o r o n e s e l f * . No l i t e r a t u r e was found t h a t i n d i c a t e d which of these value c o n s t r u c t s would be the most important f o r the p r e d i c t i o n of mathematics achievement* However, i n f o r m a t i o n from the theory of achievement m o t i v a t i o n suggested that the value of mathematics f o r o n e s e l f would be the more a p p r o p r i a t e . Baynor (1974) s t a t e d a g e n e r a l i z e d theory of expectancy value: the s t r e n g t h of tendency to a c t i n a c e r t a i n way depends upon the s t r e n g t h of expectancy that an a c t i v i t y w i l l r e s u l t i n a consequence and the value of t h a t consequence to the i n d i v i d u a l summated oyer a l l expected consequences of the a c t i v i t y . (p. 126) In h i s study he found t h a t C o l l e g e students c l a s s i f i e d high i n n-Achievement i.need f o r achievement (J and low i n Test Anxiety (Ms > Maf) r e c e i v e d higher grades i n an i n t r o d u c t o r y psychology course, and were r e l a t i v e l y more concerned about doing w e l l than anxious when the grade was seen as h i g h l y r e l a t e d to f u t u r e g o a l s than when i t was not* (p. 132) 32 W r i t i n g about t i e same st u d y i n a d i f f e r e n t a r t i c l e Raynor (1970) c o n c l u d e d , t h a t a s t u d e n t ' s c i a r a c t e r i s t i c a c i i e v e m e n t m o t i v a t i o n f o r t i i s p a r t i c u l a r c o u r s e i s r e v e a l e d o n l y when immediate performance i s i m p o r t a n t f o r f u t u r e c a r e e r s u c c e s s . (p. 32) I t appeared n e c e s s a r y t h a t some account s h o u l d be made of t he p e r c e p t i o n s t u d e n t s have o f the i n c e n t i v e s t h a t s u c c e s s i n mathematics might have f o r them. A l t h o u g h t h e p o s s i b l e s e t of i n c e n t i v e s was l a r g e , a number were i d e n i t f i e d which would p o s s i b l y be a p p r o p r i a t e f o r upper gr a d e , elementary s c h o o l s t u d e n t s . Career g o a l s , as Raynor s u g g e s t e d , might be i m p o r t a n t t o some el e m e n t a r y s c h o o l s t u d e n t s . They might a l s o p e r c e i v e s u c c e s s i n mathematics as h a v i n g an e f f e c t on t h e i r f u t u r e l i f e , a l t h o u g h not n e c e s s a r i l y c a r e e r o r i e n t e d . They might f e e l t h a t s u c c e s s i n mathematics was i m p o r t a n t f o r s u c c e s s i n o t h e r c o u r s e s b e i n g t a k e n c o n c u r r e n t l y * I f t h e s t u d e n t v a l u e d t h o s e f u t u r e outcomes and c o u r s e s then t h a t v a l u e might have an e f f e c t on t h e i r o r i e n t a t i o n t o mathematics. A i k e n (1974) developed a Value of Mathematics s c a l e f o r use a t the c o l l e g e l e v e l . The s c a l e c o r r e l a t e d .27 (Pearson r ) w i t h t h e SAT-M and .40 w i t h h i g h s c h o o l g r a d e s . SELF-CONCEPT OF ABILITY TO LEARN MATHEMATICS G l o b a l S e l f - C c n c e p t As w i t h the c o n s t r u c t of a n x i e t y i t w i l l be argued, 33 with somewhat more c o n s i s t e n t evidence* t h a t a measure of s e l f - c o n c e p t of achievement i n a s p e c i f i c s u b j e c t would p r e d i c t achievement more s t r o n g l y than a gen e r a l measure* S e l f - c o n c e p t has been used i n a g l o b a l sense of s e l f - w o r t h such as " i n t e g r i t y of the whole or any part of h i s s e l f - s t r u c t u r e " (Anderson, 1965, p. 9 ) , or as "a complex and dynamic system of b e l i e f s which an i n d i v i d u a l h o l d s t r u e .about h i m s e l f , each b e l i e f with a corresponding v a l u e " (Purkey, 1970, p. 7). On t h e other hand. Smith (1960) analyzed 70 b i p o l a r a d j e c t i v e s i n t o f i v e f a c t o r s : s e l f - e s t e e m , a n x i e t y — t e n s i o n , independence, estrangement, and body image. He noted t h a t h i s f i n d i n g s helped e x p l a i n the poor r e l a t i o n s h i p between t e s t s of s e l f - c o n c e p t and e x t e r n a l c r i t e r i o n of adjustment. " I t seems l i k e l y t h a t i n v e s t i g a t o r s d e a l t with measures which may have u n w i t t i n g l y confounded s e v e r a l s e l f - c o n c e p t v a r i a b l e s " (p. 191). The n o t i o n of a g l o b a l s e l f - c o n c e p t appears t o have the same problems a s s o c i a t e d with i t as d i d the n o t i o n of a g l o b a l a t t i t u d e . The argument w i l l be made t h a t a s e l f - c o n c e p t s c a l e r e l a t e d to mathematics achievement i s t h e most a p p r o p r i a t e f o r t h i s study. S p e c i f i c ..Self-Concept The r e s t r i c t i o n , or narrowing, of the c o n s t r u c t has a b a s i s i n the l i t e r a t u r e * Brodkover, E r i c k s o n and J o i n e r (13967) d e f i n e d s e l f - c o n c e p t of academic a b i l i t y as being 34 symbolic behavior such t h a t "when i n d i v i d u a l s p u b l i c l y d e f i n e t h e i r academic a b i l i t y , we may observe what we r e f e r t o as s e l f - c o n c e p t of academic a b i l i t y b e h a v i o r " (p* 9). To f i n d out i f t h i s was an adequate r e s t r i c t i o n P a t t e r s o n (1967) c o r r e l a t e d a qeneral s e l f - c o n c e p t of academic a b i l i t y (SCA) and s e v e r a l s p e c i f i c s u b j e c t o r i e n t e d s c a l e s with s u b j e c t achievement* He found that the s p e c i f i c SCA S c a l e s were, with one e x c e p t i o n , s i q n i f i c a n t l y b e t t e r p r e d i c t o r s of achievement i n the p a r a l l e l s u b j e c t than was the q e n e r a l SCA s c a l e , (p.. 163) However, sex d i f f e r e n c e s occurred. Patterson (1967), i n the same study, found t h a t "Amonq female 'uniform' a c h i e v e r s , the q e n e r a l SCA s c a l e i s a s i g n i f i c a n t l y b e t t e r p r e d i c t o r of s p e c i f i c grade achievement than are the s p e c i f i c SCA S c a l e s i n a l l s u b j e c t s except s o c i a l s t u d i e s " (p. 163). T h i s was not t r u e f o r males. In a study r e l a t e d to mathematics achievement Bachman (1970) found t h a t a g e n e r a l s e l f - c o n c e p t of a b i l i t y s c a l e p r e d i c t e d mathematics achievement b e t t e r than e i t h e r the mathematics self--concept or s o c i a l s t u d i e s s c a l e s . However, with i n t e l l i g e n c e c o n t r o l l e d the mathematics s e l f - c o n c e p t -predicted mathematics achievement b e t t e r , f o r males, than d i d the: g e n e r a l s e l f - c o n c e p t * For g i r l s , the mathematics s e l f - c o n c e p t s c a l e and the g e n e r a l s e l f - c o n c e p t s c a l e were e q u a l l y good p r e d i c t o r s . (See Table 3.) One problem a s s o c i a t e d with Bachman's study i s t h a t 35 Table 3 C o r r e l a t i c n s between General Self-Concept o f A b i l i t y , Mathematics S e l f - C o n c e p t , S o c i a l S t u d i e s S e l f - C o n c e p t , and Mathematics Achievement 1 Zero-Order IQ C o r r e l a t i o n s C o n t r o l l e d V a r i a b l e s C o r r e l a t e d Males Females Males Females with Math Achievement General Self-Concept .45 .60 .20 .37 Math S e l f - C o n c e p t .48 -55 ;29 .36 S o c i a l S t u d i e s Self-Concept .32 .46 .03 .20 lEachman, 1970, p. 176. when a g e n e r a l i n t e l l i g e n c e s c a l e was used t o p a r t i a l out r e s u l t s o f a " c o g n i t i v e " c h a r a c t e r i t p a r t i a l l e d out some of the d e s i r e d v a r i a n c e i n s o f a r as the i n t e l l i g e n c e s c a l e c o n t a i n s numerical items. Indeed, when mathematics achievement was c o n t r o l l e d the c o r r e l a t i o n between mathematics s e l f - c o n c e p t and i n t e l l i g e n c e was .05 f o r males and -.16 f o r females (Bachman, 1970, p, 177). I t should be noted t h a t using a more g e n e r a l s e l f — c o n c e p t s c a l e P i e r s and H a r r i s (1964) found no sex differences,. From the evidence c i t e d there i s no c l e a r - c u t s u p e r i o r i t y o f a mathematics s e l f - c o n c e p t of a b i l i t y s c a l e over a g e n e r a l s c a l e . However, the f i n d i n g s of other s t u d i e s i n d i c a t e d a c o n s i s t e n t t r e n d i n t h a t d i r e c t i o n . . For example. P i e r s and H a r r i s (1964), using t h e i r own wide range s e l f - c o n c e p t s c a l e , found t h a t i t s c o r r e l a t i o n with grade s i x achievement was .32. Koch (1972) c o r r e l a t e d the Tennessee Se l f — C o n c e p t S c a l e , another wide range s c a l e , with mathematics 3 6 achievement and found a r e l a t i o n of .25. These r e s u l t s were q u i t e low compared to the r e s u l t s of Bachman noted above* Moreover* the use o f a measure of general i n t e l l i g e n c e as a c o v a r i a t e may have masked a s t r o n g e r r e l a t i o n s h i p than has been demonstrated. F i n a l l y , i n terms of the f a c e v a l i d i t y of the c o n s t r u c t i t was c o n s i d e r e d more a p p r o p r i a t e to use the mathematics s e l f - c o n c e p t of a b i l i t y s c a l e than a g e n e r a l s c a l e . LOCOS OF CONTBOL Although l o c u s of c o n t r o l had been studied i n the context of achievement, the work appeared to have been done by i n d i v i d u a l s i n t e r e s t e d i n the c o n s t r u c t i t s e l f r a t h e r than by mathematics educators* Some of the l a c k of i n t e r e s t c o u l d be a t t r i b u t e d to the seemingly c o n f l i c t i n g f i n d i n g s of a number of s t u d i e s . H j e l l e (1970) found no r e l a t i o n s h i p between q u a l i t y p o i n t averaqe (QPA) cf grades given a t u n i v e r s i t y and B o t t e r ' s I n t e r n a l - E x t e r n a l Locus of C o n t r o l s c a l e ( I - E ) . He gave two p o s s i b l e . e x p l a n a t i o n s . F i r s t t h e r e may be an over abundance of c o l l e g e Ss who • have a r r i v e d a t an e x t e r n a l view of the world as a defense a g a i n s t f a i l u r e but who are i n i t i a l l y h i g h l y c o m p e t i t i v e . Thus, e x t e r n a l s would s t i l l maintain c o m p a r a t i v e l y strong achievement m o t i v a t i o n i n c l e a r l y s t r u c t u r e d c o m p e t i t i v e s i t u a t i o n s . . ... Second, the I-E dimension i s probably not g e n e r a l i z a b l e a c r o s s s i t u a t i o n s , and i n the h i g h l y s t r u c t u r e d academic achievement s i t u a t i o n there i s probably more s p e c i f i c i t y determining QPA than i n other k i n d s of competitive s i t u a t i o n s . (p. 326) 37 I f the f i r s t e x p l a n a t i o n i s true then the r e l a t i o n s h i p between grades and l o c u s of c o n t r o l s h o u l d he s t u d i e d a t a t younger age- However, Weston (1968) c o r r e l a t e d a r i t h m e t i c achievement with s t y l e s of l e a r n i n g , r e s p o n s i b i l i t y f o r i n t e l l e c t u a l academic achievement, and p a r e n t a l a t t i t u d e s * He found t h a t measures on the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y Q u e s t i o n n a i r e were not r e l a t e d to grade s i x mathematics achievement and only t o problem s o l v i n g and t o t a l a r i t h m e t i c a t grade four* I t should be noted t h a t the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y Q u e s t i o n n a i r e i s a s c a l e more s p e c i f i c to achievement than the R o t t e r s c a l e . Thus H j e l l e ' s second e x p l a n a t i o n f o r low c o r r e l a t i o n s with achievement appeared to be u n s a t i s f a c t o r y * C r a n d a l l , Katkovsky and C r a n d a l l (1965) using the same s c a l e found that i t c o r r e l a t e d p o s i t i v e l y and s i g n i f i c a n t l y with almost a l l the s c a l e s of the Iowa Tes t o f B a s i c S k i l l s f o r c h i l d r e n , i n grades 3, 4, and 5 but o n l y o c c a s i o n a l l y r e l a t e d to s c a l e s on the C a l i f o r n i a Achievement T e s t i n grades 6, 8, 10, and 13,. I t would appear then, t h a t the l o c u s of c o n t r d l v a r i a b l e s might be r e l a t e d to mathematics achievement at a younger age* However, as the r e l a t i o n s h i p i s not l a r g e enough nor c o n s i s t e n t enough t o be c o n s i d e r e d an "emotional b l o c k " , the s i t u a t i o n may be more complex than can be d e s c r i b e d by simple f i r s t order c o r r e l a t i o n s . Wolk and DuCette (1973) s t u d i e d the r e l a t i o n s h i p o f an achievement m o t i v a t i o n s c a l e with an estimate of success at 38 " p u r s u i t r o t o r t a s k s " , an estimate of the l e v e l of t a s k d i f f i c u l t y p r e f e r r e d by the s u b j e c t , an estimate of the percentage of f e l l o w s t u d e n t s who would be surpassed by the s u b j e c t on a psychology examination, performance on midterm and f i n a l exams i n psychology, and performance on the S c h o l a s t i c A p t i tude Test Verbal and Q u a n t i t a t i v e s c a l e s . The c o r r e l a t i o n s were c a l c u l a t e d f o r each of the two l e v e l s on I n t e r n a l - E x t e r n a l Locus of C o n t r o l . Table 4 shows t h a t with one e x c e p t i o n only the i n t e r n a l s u b j e c t s demonstrated s i g n i f i c a n t c o r r e l a t i o n s , . That exception i s with the q u a n t i t a t i v e s c a l e of the SAT. The " s i g n i f i c a n t l y d i f f e r e n t c o r r e l a t i o n s between v a r i a b l e s f o r the moderated groups" (Wolk & DuCette, 1973, p. 66) suggested t h a t l o c u s of c o n t r o l was a moderator v a r i a b l e * Tbat i s t o say, the c o r r e l a t i o n s between achievement and the studied measures d i f f e r e d among groups of s u b j e c t s who were at d i f f e r e n t l e v e l s on the I—E dimension. The data suggested t h a t l o c u s of c o n t r o l may be a c t i n g as a moderator v a r i a b l e f o r other n o n c o g n i t i v e v a r i a b l e s . T h i s may be a t h i r d e x p l a n a t i o n of the low and i n c o n s i s t e n t r e l a t i o n s between t h i s v a r i a b l e and achievement. Another example i s t h a t o f L i n t n e r and DuCette (1974) who s t u d i e d l o c u s of c o n t r o l , academic f a i l u r e and student response to p r a i s e * On a coding task they found a d i s o r d i n a l i n t e r a c t i o n f o r males on l o c u s of c o n t r o l and p r a i s e , whereas, females showed a s m a l l , n o n - s i g n i f i c a n t response t o p r a i s e . On a second t a s k , the Gates-McGintie Reading T e s t , they found sex Table 4 39 C o r r e l a t i o n s between an Achievement M o t i v a t i o n Measure and Various Behaviors f o r I n t e r n a l and E x t e r n a l Locus of C o n t r o l Subjects I n t e r n a l s E x t e r n a l s Z ( i n t - e x t ) 1 Ps est Task 2 -.28** + .01 1.24 Ps e s t T e s t 3 _,29** + .04 1.65** Pr e f e r e n c e •.44*** + . HO 1.81** Test P e r f Midterm + * 39*** -* V4 2;70*** Test Perf F i n a l +.37*** -*04 2*09** SAT V e r b a l +.41*** -.09 2.18** SAT Q u a n t i t a t i v e +.33** -. 27* 3*02*** *p < .10 **p < .05 ***p < .01 4Z s t a t i s t i c of the d i f f e r e n c e between the scores of the I n t e r n a l s and the E x t e r n a l s * 2 E s t i m a t e d p r o b a b i l i t y ox success at the p u r s u i t r o t o r task. [ ^Estimated p r o p o r t i o n of f e l l o w students surpassed by the s u b j e c t * d i f f e r e n c e s on the main f a c t o r s o f p r i o r f a i l u r e , and p r a i s e , but no i n t e r a q t i o n s w i t h i n the sex f a c t o r * Again i n t e r a c t i o n s appeared i n c o n s i s t e n t l y w i t h i n the same study. D a n i e l s and Stevens (1976) us i n g H o t t e r 1 s I-E s c a l e found a d i s o r d i n a l i n t e r a c t i o n with i n s t r u c t i o n a l methods. T h e r e f o r e , because of the p o t e n t i a l i n t e r a c t i o n s between l o c u s of c o n t r o l and the other a f f e c t i v e v a r i a b l e s i t was deemed important to i n c l u d e t h i s v a r i a b l e i n the present study. The only i n f o r m a t i o n found t h a t s p e c i f i c a l l y r e l a t e d l o c u s of c o n t r o l to sex was C r a n d a l l , C r a n d a l l and Katkovsky (1964) who found that there were no s i g n i f i c a n t d i f f e r e n c e s . SUMMARY OF INDIVIDUAL AFFECTIVE VARIABLES In summary, the l i t e r a t u r e d e a l i n g with a f f e c t i v e v a r i a b l e s showed t h a t the r e l a t i o n of the v a r i a b l e s with mathematics achievement was s i g n i f i c a n t but low. However, the 40 l i t e r a t u r e o u t s i d e the area of mathematics e d u c a t i o n , p a r t i c u l a r l y t h a t r e l a t e d to achievement m o t i v a t i o n , suggested an a l t e r n a t i v e approach t o the c o n c e p t u a l i z a t i o n of the v a r i a b l e s as an i n t e r - r e l a t e d s e t with some of the v a r i a b l e s a c t i n g as moderators of ot h e r s . That i s , the r e l a t i o n s h i p of one v a r i a b l e with a second may be d i f f e r e n t at s e v e r a l l e v e l s of a t h i r d * An example of t h i s was Marjoribanks* study (1976). She found t h a t with 12 year o l d E n g l i s h c h i l d r e n the r e l a t i o n between a t t i t u d e and achievement v a r i e d with l e v e l of a b i l i t y . T h i s l i n e of argument l e d to the hyp o t h e s i s t h a t a much more complex f u n c t i o n than had been t e s t e d might r e l a t e mathematics achievement t o the a f f e c t i v e v a r i a b l e s o f t h i s study; In Chapter 1 i t was suggested t h a t l o o k i n g f o r i n t e r a c t i o n s and hon-rlinear r e l a t i o n s h i p s with no t h e o r e t i c a l framework c o u l d not be . j u s t i f i e d . However, the Achievement M o t i v a t i o n Model d i d provide such a framework and w i l l t h e r e f o r e be presented i n some d e t a i l . THE MODEL OF ACHIEVEMENT MOTIVATION Achievement M o t i v a t i o n Assumptions of: the .model. I t should be understood i n = , —-r^- 1 r — the f o l l o w i n g d i s c u s s i o n t h a t . i n the l i t e r a t u r e of Achievement M o t i v a t i o n the words "motive" and " m o t i v a t i o n " are not used synonymously; Feather (1966 b) d e s c r i b e d motive as a l a t e n t d i s p o s i t i o n of p e r s o n a l i t y whereas s t r e n g t h of m o t i v a t i o n depended upon l e v e l of e x p e c t a t i o n and i n c e n t i v e v a l u e . 41 Atkinson and Eeitman (1956) were q u i t e s p e c i f i c : we conceive a motive as a l a t e n t d i s p o s i t i o n to s t r i v e f o r a p a r t i c u l a r g o a l - s t a t e or aim, e.g.; achievement, a f f i l l i a t i o n , power* . . . The term m o t i v a t i o n can then be used to designate the aroused s t a t e of the person t h a t e x i s t s when a motive has been engaged by the a p p r o p r i a t e expectancy, i . e . ; an expectancy t h a t performance of some a c t i s i n s t r u m e n t a l t c attainment of the g o a l of t h a t motive. (p 361) Achievement M o t i v a t i o n has a l a r g e l i t e r a t u r e e x e m p l i f i e d by the works of Atkinson (1958), Atkinson and Feather (1966), Atkinson and Eaynor (1974), Atkinson and Eeitman (1956), Weiner (1972), and Weiner and Kukla (1970). I t i s a s p e c i f i c i n s t a n c e of i n s t r u m e n t a l i t y t h e o r i e s which are " d i s t i n g u s h e d by the hypothesis t h a t the behavior of an i n d i v i d u a l i s i n p a r t determined by a) h i s e x p e c t a t i o n s t h a t the behavior w i l l l e a d t o v a r i o u s outcomes and b) h i s e v a l u a t i o n of those outcomes 1 1 ( M i t c h e l l & B i g l a n , 1971, p. 432). D i f f e r e n c e s between these t h e o r i e s concern the way i n which s u b j e c t i v e p r o b a b i l i t y i s i n c l u d e d i n the d i f f e r e n t a n a l y s e s . The disc r e p a n c y concerns whether or not concepts which are a k i n t o u t i l i t y i n v a r i o u s models are taken to be independent of s u b j e c t i v e p r o b a b i l i t y . (Feather, 1966, p. 32) Atkinson's model g i v e s motives and i n c e n t i v e values independent s t a t u s and he suggests t h a t "the valence or u t i l i t y of an i n c e n t i v e may be considered as a f u n c t i o n of s t r e n g t h of motive and i n c e n t i v e value ..(Feather, 1966 a, p. 35) The theory of Achievement M o t i v a t i o n proposes t h a t both the i n d i v i d u a l ' s e x p e c t a t i o n of success and f a i l u r e and h i s e v a l u a t i o n of t h a t success and f a i l u r e be assessed. 42 Atkinson's (1974) model of Achievement M o t i v a t i o n i s r e a l l y cne of r e s u l t a n t achievement o r i e n t e d tendency. He assumes, t h a t a l l i n d i v i d u a l s have ac q u i r e d a motive to achieve (Ms) and a motive to avoid f a i l u r e (Maf) . That i s to say a l l persons have some c a p a c i t y f o r i n t e r e s t i n achievement and some c a p a c i t y f o r a n x i e t y about f a i l u r e * . . . One of these motives produces a tendency to undertake a c t i v i t y . . . . I t i s assumed t h a t the two opposed t e n d e n c i e s combine a d d i t i v e l y and y i e l d a r e s u l t a n t achievement o r i e n t e d tendency (p* 18) A l g e b r a i c a l l y , T r = Ts + T-f where Tr stands f o r r e s u l t a n t tendency, Ts f o r success o r i e n t e d tendency and T-f the f a i l u r e avoidance tendency. However, the s u c c e s s component i s modified by the e x p e c t a t i o n of success a t the t a s k and by the i n c e n t i v e s which may accrue upon s u c c e s s f u l completion o f the t a s k . Although mo t i v a t i o n to succeed i s enhanced by the ease of the task i t may a l s o be somewhat decreased by the reduced i n c e n t i v e to expend energy on an easy task. The f a i l u r e component i s modified i n a p a r a l l e l way but i n the opposite d i r e c t i o n . Again, a l g e b r a i c a l l y ; Ts = Ms x Ps x I s and, T-f = Maf x Pf x I f where Ms, Ps, and I s a r e , r e s p e c t i v e l y , motivation toward success, p r o b a b i l i t y of s u c c e s s and i n c e n t i v e value of success. Maf> Pf and I f a r e , r e s p e c t i v e l y , m o t i v a t i o n t o avoid f a i l u r e , p r o b a b i l i t y of f a i l u r e , and the i n c e n t i v e v a l u e of f a i l u r e . The s i x independent v a r i a b l e s are reduced i n 43 number by p o s t u l a t i n g t h a t the sum of t h e . p r o b a b i l i t y of success and the p r o b a b i l i t y of f a i l u r e i s one (1.0). Two other p o s t u l a t e s reducing the number of v a r i a b l e s are t h a t the sum of the i n c e n t i v e value of success and t h e . p r o b a b i l i t y o f success i s one (1.0) and that the i n c e n t i v e value of f a i l u r e i s the n e g a t i v e o f the p r o b a b i l i t y of success. S y m b o l i c a l l y these assumptions are: Is = (1 - Ps) , Pf = (1 - Ps) and. I f = — P s The model and e m p i r i c a l support* L i t win (1 966) t e s t e d the h y p o t h e s i s t h a t estimated value of success was a n e g a t i v e l i n e a r f u n c t i o n (1 - Ps) of the estimated p r o b a b i l i t y of s u c c e s s . He had s u b j e c t s designate a monetary value to be a s s o c i a t e d with v a r i o u s r i n g s on a r i n g t o s s game. He found t h a t the estimates were l i n e a r , and the average slope of a l l the value e s t i m a t e s was approximately equal to the 1 - Ps l i n e * However, the s l o p e of the achievement-oriented Ss value estimates was somewhat l a r q e r than the 1 - Ps l i n e . (p. 114) Combining the above e x p r e s s i o n s : Tr = Ms x Ps x (1 - Ps) + Maf x (1 - Ps) x (-Ps) = (Ms - Maf) x Ps x (1 - Ps) This l a s t e x p r e s s i o n l e d to a q u a d r a t i c i n t e r a c t i o n of Ms - Maf with P s 2 . There was some e m p i r i c a l support f o r t h i s i n t e r a c t i o n . P r o b a b i l i t y of success i s assessed by askinq s u b j e c t s t h e i r p e r c e p t i o n o f t h e i r p o t e n t i a l l e v e l of achievement (Atkinson & F e a t h e r , 1966; Moulton, 1974). This was 44 con s i d e r e d s i m i l a r to the measurement of self-r-concept of a b i l i t y to l e a r n . Brookover and E r i c k s o n (1969) h e l d t h a t p o s i t i v e s e l f - c o n c e p t was a necessary but not s u f f i c i e n t c o n d i t i o n f o r achievement. Although a s i g n i f i c a n t p r o p o r t i o n of students with high s e l f - c o n c e p t s achieved at a r e l a t i v e l y lower l e v e l (approximately 50 per cent) p r a c t i c a l l y none of the stu d e n t s with low s e l f - c o n c e p t s of a b i l i t y achieved at a hig h l e v e l . (p. 106) When graphed with achievement as the a b c i s s a and s e l f - c o n c e p t as the o r d i n a t e t h i s would appear much l i k e an i n v e r t e d c a p i t a l "L" ( r) which would suggest a g u a d r a t i c r e l a t i o n * Karabenick and Youseff (1968) grouped p a i r s of words i n t o t h r e e s e t s . The s e t s of words were to be used i n a p a i r e d a s s o c i a t e l e a r n i n g t a s k . The three groups of words were equated on mean d i f f i c u l t y and on the v a r i a n c e , o f d i f f i c u l t y . The three groups were randomly designated easy, i n t e r m e d i a t e , or hard. D i f f e r e n t c o l o r s were a s s o c i a t e d with each group. The words were presented t o the s u b j e c t s i n t h e i r r e s p e c t i v e c o l o r s . The'subjects were t o l d the s i g n i f i c a n c e of the c o l o r s . The r e s u l t s of the study showed t h a t : persons f o r whom Ms > Mf £Mf i s e q u i v a l e n t to MafJ performed b e t t e r than those f o r whom Mf > Ms a t task s designated as being of i n t e r m e d i a t e d i f f i c u l t y , but the performance of these groups d i d not d i f f e r when ta s k s were easy or d i f f i c u l t . In a d d i t i o n , whereas persons f o r whom Ms > Mf tended t o perform b e t t e r at i n t e r m e d i a t e d i f f i c u l t y t a s k s , than at easy or d i f f i c u l t t a s k s , persons f o r whon Mf > Ms performed b e t t e r on easy or d i f f i c u l t t a s k s than a t those designated as being of in t e r m e d i a t e d i f f i c u l t y . (p. 418) Thi s was supported by Feather (1961) who found t h a t 45 s u b j e c t s w i t h Ms > Mf tended to p e r s e v e r e l o n g e r at t a s k s p e r c e i v e d as b e i n g o f i n t e r m e d i a t e d i f f i c u l t y t h a n t h o s e which were p e r c e i v e d as b e i n g easy or h a r d . On t h e o t h e r hand, s u b j e c t s w i t h Mf > Ms tended t o p e r s e v e r e a t easy or d i f f i c u l t t a s k s . I t might be expected t h a t i f s u b j e c t s tended t o behave as F e a t h e r found t h e n achievement would be h i g h e r on those t a s k s a t which the s u b j e c t s tended t o p e r s e v e r e . In summary, the achievement m o t i v a t i o n model s u g g e s t e d t h a t t h e l e v e l s o f M o t i v a t i o n t o Succeed, P r o b a b i l i t y o f S u c c e s s , and Value of Success i n f l u e n c e d t h e degree o f a t t e n t i o n and p e r s e v e r a n c e . The p r e s e n t a u t h o r h e l d t h a t i n the s c h o o l s i t u a t i o n v a r i a t i o n s i n p e r s e v e r a n c e would l e a d t o v a r i a t i o n s i n academic achievement. These r e l a t i o n s , which may be r e p r e s e n t e d as f o l l o w s , w i l l s e r v e as t h e Achievement M o t i v a t i o n model used i n t h e p r e s e n t s t u d y ; 1. M o t i v a t i o n t o Succeed A t t e n t i o n 2. P r o b a b i l i t y o f Success > - — > Achievement Pe r s e v e r a n c e 3. V a l u e o f Success The arrows above s e r v e o n l y t o i n d i c a t e a r e l a t i o n s h i p . I t i s not i n t e n d e d t h a t t h e y imply a c a u s a l r e l a t i o n s h i p , nor t h a t the d i r e c t i o n i s o n l y as i n d i c a t e d * There were f i v e v a r i a b l e s i d e n t i f i e d i n t h e s e c t i o n o f the " e m o t i o n a l b l o c k " i n mathematics; a n x i e t y , enjoyment, v a l u e , s e l f - c o n c e p t and achievement r e s p o n s i b i l i t y * Yet the Achievement M o t i v a t i o n model i s t r i p a r t i t e ; The f o l l o w i n g 46 d i s c u s s i o n w i l l r e l a t e each of the f i v e v a r i a b l e s to one of the t h r e e l e v e l s of the Achievement M o t i v a t i o n model which are i n d i c a t e d i n the above diagram. That the model i s q u i t e f l e x i b l e i n t h i s r e s p e c t i s supported by Moulton (1974) who s t a t e d i t i s r e c o g n i z e d t h a t t h e t o t a l s t r e n g t h of tendency to perform a task r e q u i r i n g s k i l l i n c l u d e s t e n d e n c i e s a s s o c i a t e d with other i n c e n t i v e s c o n t i n g e n t upon s u c c e s s f u l performance. An important f a c t about many of these " e x t r i n s i c " i n c e n t i v e s such as s o c i a l a p p r o v a l , p r e s t i g e , money, e t c . , i s t h a t the more d i f f i c u l t the task i s p e r c e i v e d to be by o t h e r s , the g r e a t e r the magnitude and/or q u a l i t y of these i n c e n t i v e s r e c e i v e d as a r e s u l t of success. (p. 81) The "block" v a r i a b l e s were a s s o c i a t e d with each of the achievement mot i v a t i o n c a t e g o r i e s , as p r e s e n t l y worded, i n t h e f o l l o w i n g way. V a r i a b l e s of t h i s Study Belated t o - t h e Model L e v e l one,: ,motivation to succeedi. Anxiety about mathematics was, i n t h i s study, r e l a t e d to the M o t i v a t i o n dimension (Ms - Maf). M o t i v a t i o n to succeed has u s u a l l y been assessed by using the Thematic Aperception T e s t . However, the t e s t i s somewhat u n r e l i a b l e i n t h a t "the c o n d i t i o n s under which the t e s t i n g i s done may be s u f f i c i e n t l y m o t i v a t i n g to produce marked changes i n the l e v e l of achievement or a f f i l i a t i o n imagery f o r the groups as a whole" (Atkinson, 1958, p. 35). The Test Anxiety Questionnaire has been t y p i c a l l y used to measure the m o t i v a t i o n to a v o i d f a i l u r e . In some s t u d i e s r a t h e r than using the d i f f e r e n c e between measures 47 of Ms and Maf a measure of.Maf has been used by i t s e l f . In the present study the achievement motivation model was used to suggest possible interactions between variables and not to validate the model i t s e l f . Therefore i t was proposed that Mathematics Anxiety c l o s e l y corresponded to the Test Anxiety Questionnaire and was therefore related to the motivation dimension of the model. Enjoyment of mathematics was considered somewhat the opposite of anxiety.' Sandman (1973) found a co r r e l a t i o n of -.76 between anxiety and enjoyment of mathematics, tending to confirm t h i s supposition; Therefore, enjoyment was also associated with Motivation to Succeed,. Achievement E e s p o n s i b i l i t y , or locus of control, i s c l o s e l y related to the theory of Achievement Motivation. Weiner (1972) held that persons with low achievement motivation f e l t that e f f o r t did not influence the outcome of an a c t i v i t y and that the opposite was true f o r persons with high achievement motivation. . As this dimension was represented by achievement r e s p o n s i b i l i t y i t was proposed that achievement r e s p o n s i b i l i t y would also correspond to motivation to succeed. Woulk and DuCette ( 1973) commented on the degree of correspondence of the two theories. Both theories, for example, make predictions about the type of risk that c e r t a i n subjects prefer, . . . . persistence, s h i f t s i n l e v e l of aspiration, and success estimation . . . . Even more than t h i s , both theories make very s i m i l a r predictions about the performance of c e r t a i n subjects on these dependent variables; . . Indeed, there i s so much 48 o v e r l a p i n these t h e o r i e s i n both t h e o r e t i c a l s t r u c t u r e and p r e d i c t i o n s t h a t a q u e s t i o n can be r a i s e d as to t h e i r d i s c r i m i n a n t v a l i d i t y . (p. 61) L e v e l two: p r o b a b i l i t y , of-:: success; S e l f - c o n c e p t of mathematics achievement was c o n s i d e r e d t o be r e l a t e d to P r o b a b i l i t y of Success* The technique f o r a s s e s s i n g t h e p r o b a b i l i t y of success (Ps) was "simply t o ask Ss to s t a t e t h e i r own p r o b a b i l i t y of success with r e s p e c t to t a s k s " (Moulton, 1974, p* 79) or an estimate was o f t e n i n f e r r e d from the value give to a c h i e v i n g a t a c e r t a i n l e v e l at a t a s k or from an estimate of the p r o p o r t i o n of the p o p u l a t i o n the s u b j e c t would surpass a t the t a s k . These procedures appeared to be reasonably c l o s e t o a s k i n g students t o e v a l u a t e the s t r e n g t h of agreement with items such as, " T h i s task i s easy" or " T h i s task i s hard;" As t h i s was c l o s e to what the student was asked t o do i n a s s e s s i n g the s e l f - c o n c e p t of h i s a b i l i t y i n mathematics, s e l f - c o n c e p t was a s s o c i a t e d with p r o b a b i l i t y of success. Level, t h r e e : value of, success. Value of Mathematics — , . — . . - - .-... • — — • ' ^-— — was c o n s i d e r e d c l o s e to Value of Success i n the Achievement M o t i v a t i o n model and t h e r e f o r e was a s s o c i a t e d with t h a t dimension; The hypothesized r e l a t i o n s h i p s between the three l e v e l s of v a r i a b l e s of the theory of Achievement M o t i v a t i o n and the f i v e v a r i a b l e s of i n t e r e s t i n t h i s study may be summarized as f o l l o w s : M o t i v a t i o n to Succeed = Anxiety i n Mathematics 49 + Achievement R e s p o n s i b i l i t y + Enjoyment of Mathematics P r o b a l i l i t y of Success = Self-Concept of A b i l i t y i n Mathematics Value of Success = Value of Mathematics I t was not expected t h a t there would be a c l e a r d i s t i n c t i o n among these t h r e e l e v e l s of the Achievement M o t i v a t i o n model because of the a l r e a d y i d e n t i f i e d r e l a t i o n s between some of the c o n s t r u c t s of t h i s study. For example Kempler (1962) admi n i s t e r e d the Lu c h i n ' s water j a r t e s t which he termed a mechanization on problem s o l v i n g s c a l e t o 107 c o l l e g e s t u d e n t s . He i d e n t i f i e d 30 students as r i g i d problem s o l v e r s and 30 as n o n r i g i d . He found t h a t on a q u e s t i o n n a i r e of s e l f - c o n f i d e n c e i n mathematical a b i l i t y r i q i d students were s i g n i f i c a n t l y l e s s c o n f i d e n t than n o n r i q i d and t h a t the rank order c o r r e l a t i o n between r e s u l t s on the Luchin's water j a r t e s t and the s e l f - c o n f i d e n c e q u e s t i o n n a i r e was .32 (p < .01).. He s t a t e d "the r a t i o n a l e f o r t h i s study was t h a t • low s e l f - c o n f i d e n c e should arouse a n x i e t y which i n t u r n w i l l l e a d to r i g i d i t y " (p. 51). Moreover, DeAnda (1977) found t h a t the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y Scale accounted f o r 12% of the v a r i a n c e of the Coopersmith Self-Esteem S c a l e . T h i s corresponded to a c o r r e l a t i o n of .35. However, S i u (1973) c l a s s e d the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y S c a l e , the Test Anxiety Scale f o r C h i l d r e n and the Gumpgookies' M o t i v a t i o n to Achieve Scale as m o t i v a t i o n s c a l e s . Because of these c o n f l i c t i n g r e s u l t s and i n t e r p r e t a t i o n s the 50 above r e l a t i o n s h i p s are deemed a reasonable h y p o t h e s i s . SUMMABY In t h i s chapter t h e l i t e r a t u r e r e l a t e d to the f i v e "emotional b l o c k " v a r i a b l e s was examined and evidence presented t h a t s c a l e s measuring those c o n s t r u c t s should be c l o s e l y r e l a t e d t o the s u b j e c t area being considered,. One of the c o n s t r u c t s , a n x i e t y , had somewhat ambiguous evidence i n t h i s r e s p e c t . Therefore both s p e c i f i c and g e n e r a l s c a l e s were i n c l u d e d . I t was a l s o argued t h a t the f i v e v a r i a b l e s c o u l d reasonably be a s s o c i a t e d with one of the three independent c o n s t r u c t s of the Achievement M o t i v a t i o n model,. This model was a l s o used to j u s t i f y t e s t i n g n o n - l i n e a r and i n t e r a c t i v e hypotheses. In g e n e r a l the evidence pointed to p o t e n t i a l sex r e l a t e d e f f e c t s which would have to be taken i n t o c o n s i d e r a t i o n * 51 Chapter 3 INSTfiUMENTATION, DESIGN AND PEOCEDOEE INTBODUCTION i n Chapter 1 i t was shown t h a t t h e r e i s a l i t e r a t u r e i n d i c a t i n g - t h a t a s i g n i f i c a n t p r o p o r t i o n of mathematics students - appears t o have an "emotional b l o c k " i n h i b i t i n g t h e i r achievement i n mathematics. Anxiety, enjoyment, value, and s e l f — c o n c e p t of mathematics were i d e n t i f i e d as the components of the " b l o c k " . The Achievement M o t i v a t i o n model was used t o suggest p o s s i b l e i n t e r a c t i o n s among the components when r e l a t e d to achievement m o t i v a t i o n . A f u r t h e r v a r i a b l e , l o c u s of c o n t r o l or achievement r e s p o n s i b i l i t y , was suggested by t h e model* In Chapter 2 i t was argued t h a t the more c l o s e l y an a t t i t u d e s c a l e was r e l a t e d t o a s u b j e c t area the more s t r o n g l y c o r r e l a t e d i t would be with achievement i n t h a t area. I t was f u r t h e r suggested t h a t although there was some evidence t h a t a n x i e t y i n mathematics i s more h i g h l y c o r r e l a t e d with mathematics achievement than a more g e n e r a l measure, t h a t a general measure should be in c l u d e d * Evidence o f sex r e l a t e d e f f e c t s occurs i n the l i t e r a t u r e and t h e r e f o r e the s t a t i s t i c a l design was c o n s t r u c t e d a c c o r d i n g l y . 52 I n t h i s c h a p t e r , the i n s t r u m e n t a t i o n , design and procedure w i l l he described* The r e s u l t s of a p r e l i m i n a r y a n a l y s i s concerning the d e c i s i o n to i n c l u d e o r exclude TASC i n the t e s t i n g o f the major hypotheses w i l l be presented. The procedure used f o r e l i m i n a t i n g i n t e r - c l a s s d i f f e r e n c e s w i l l a l s o be d e s c r i b e d . .INSTBUMENTATIQN As four o f the seven a f f e c t i v e s c a l e s used i n t h i s study were taken from the Sandman (1973) b a t t e r y , a g e n e r a l d e s c r i p t i o n o f h i s study w i l l be presented. The d e t a i l s a s s o c i a t e d with each o f the f o u r s c a l e s w i l l be d e s c r i b e d i n the s e c t i o n s r e l a t e d to the i n d i v i d u a l a f f e c t i v e c o n s t r u c t s . F o l l o w i n g t h a t the t h r e e achievement s c a l e s and the teacher response s c a l e s w i l l be d i s c u s s e d . The.Sandman Study Sandman11 s review. In h i s study Sandman (1973) reviewed the c o n s t r u c t i o n and v a l i d a t i o n procedures used f o r some of the mere prominent mathematics a t t i t u d e s c a l e s such as Dutton's (1954) Thurstone S c a l e , Aiken and Dreger«s (1961) Mathematics A t t i t u d e S c a l e , (which has a number of items s i m i l a r t c those used on a n x i e t y s c a l e s ) , Hoyt and McEachern's (1958) s c a l e , and Hoyt's (1960) f i f t e e n s u b - s c a l e Minnesota P u p i l O p i nions S c a l e . He a l s o reviewed E r i c k s e n ' s (1962) study i n which the Hoyt-McEachern s c a l e was d i v i d e d i n t o s i x 53 s u b - s c a l e s , and Antonnen's (1967) use of the Hoyt s c a l e i n the l o n g i t u d i n a l study of mathematics a t t i t u d e . In the Antonnen study f a c t o r l o a d i n g s of the s c a l e s on the p r i n c i p a l component were used to generate a s i n g l e score f o r a t t i t u d e . In g e n e r a l . Sandman's c r i t i c i s m s were t h a t the s u b - s c a l e s were formed on a b a s i s of f a c e v a l i d i t y , no attempt at item f a c t o r a n a l y s i s was made, and t h a t only c o r r e l a t i o n s with other mathematics a t t i t u d e s c a l e s , achievement and IQ were presented* These data e s t a b l i s h e d only convergent v a l i d i t y . For example, he c i t e d Mastantiiono and Antonnen (1971) who administered Dutton's Thurstone S c a l e , a L i k e r t - t y p e v e r s i o n of Dutton's s c a l e , Hoyt's Minnesota P u p i l Opinions S c a l e , a semantic d i f f e r e n t i a l s c a l e developed by Antonnen, an i n t e l l i g e n c e t e s t , and the Iowa Test of B a s i c S k i l l s . The c o r r e l a t i o n s among the a t t i t u d e s c a l e s were between .66 and .79; the c o r r e l a t i o n s of a t t i t u d e with achievement and i n t e l l i g e n c e ranged, r e s p e c t i v e l y , between .07 and .25, and .03 and .14. The a t t i t u d e s c a l e s tended to measure something i n common, and they had a r e l a t i o n s h i p with mathematics achievement s l i g h t l y s t r o n g e r than with i n t e l l i g e n c e . Sandman c i t e d s e v e r a l m u l t i - d i m e n s i o n a l s c a l e s of a t t i t u d e * Hussen (1967) used one i n the I n t e r n a t i o n a l Study of Achievement i n Mathematics. The s u b - s c a l e s were a t t i t u d e toward mathematics as a p r o c e s s , a t t i t u d e toward the p l a c e of mathematics i n s o c i e t y , and views about mathematics t e a c h i n g . However, Sandman noted t h a t the r e l i a b i l i t i e s were so low t h a t 54 Johnson (1970) was advised not to use the s c a l e s when he asked permission to use them. A second m u l t i — d i m e n s i o n a l s c a l e noted by Sandman was t h a t used i n the N a t i o n a l L o n g i t u d i n a l Study of Mathematics Achievement (Eomberg & Wilson, 1969). Each of the seven s u b - s c a l e s i s a L i k e r t s c a l e . They were Math vs* Non-Math, Math Fun vs. D u l l , Math Easy vs* Hard, Actual Math Sel f — C o n c e p t , I d e a l Math S e l f — C o n c e p t , F a c i l i t a t i n g A n x i e t y , and D e b i l i t a t i n g Anxiety. There was no attempt to v a l i d a t e the s c a l e s i n terms cf the s t a t e d c o n s t r u c t s but some evidence from r e l a t i o n s h i p s between r e s u l t s on the p r e l i m i n a r y forms and other v a r i a b l e s was noted. I t was q u i t e c l e a r from Sandman's review t h a t a t t i t u d e s c a l e , c o n s t r u c t i o n i n mathematics educ a t i o n had proceeded r a t h e r haphazardly and a t a somewhat u n s o p h i s t i c a t e d l e v e l . The Sandman Scale C o n s t r u c t i o n . A t t i t u d e measures have been l e s s than adequate because of confounded c o n s t r u c t s as well as confused r e f e r e n t s . As noted i n Chapter 1, Sandman (1973) was q u i t e c r i t i c a l of the c o n s t r u c t i o n of a t t i t u d e s c a l e s . His a l t e r n a t i v e was to take items from seven of the already c i t e d a t t i t u d e instruments, r e w r i t i n g many and a s s i g n i n g them to one o f e i g h t c o n s t r u c t s : P e r c e p t i o n of the Mathematics Teacher by the Student* Anxiety Toward Mathematics, Value of Mathematics i n S o c i e t y , Self-Concept i n Mathematics, P e r c e p t i o n of Mathematics C l a s s , P e r c e p t i o n of Mathematics M a t e r i a l s , Enjoyment of Mathematics, and 55 M o t i v a t i o n i n Mathematics. Although the s c a l e s were s i m i l a r to the s c a l e s used i n the N a t i o n a l L o n g i t u d i n a l Study of Mathematics Achievement, Sandman noted t h a t many of the items i n those s c a l e s d i d not appear t o be measuring the c o n s t r u c t s of i n t e r e s t and t h a t some of the vocabulary used seemed i n a p p r o p r i a t e f o r younger secondary s t u d e n t s . Ten items f o r each c o n s t r u c t were s e l e c t e d f o r a p r e l i m i n a r y s c a l e (equal p o s i t i v e and ne g a t i v e items) and the s c a l e s were d i s t r i b u t e d to persons s k i l l e d i n t e s t c o n s t r u c t i o n and mathematics edu c a t i o n . The M a t e r i a l s Scale was e l i m i n a t e d , as were two items from each of the other s c a l e s , because of a lack of c o n s i s t e n c y of the items. T h i s l e f t seven s c a l e s o f e i g h t items eachw. The s c a l e s were p i l o t e d , and on the b a s i s of c o r r e l a t i o n s between the items and the s c a l e s f o u r questionable items were i d e n t i f i e d and reworded. The s c a l e s were then administered t o 2547 stu d e n t s i n grades e i g h t and eleven i n C a l i f o r n i a and I n d i a n a . The item c o r r e l a t i o n matrix was subjected to p r i n c i p a l component a n a l y s i s f o l l o w e d by varimax r o t a t i o n . Seven f a c t o r s emerged, s i x of which c o u l d be i d e n t i f i e d with the s i x a t t i t u d e c o n s t r u c t s t h a t the instrument was designed t o measure. As the items of the P e r c e p t i o n of the Mathematics C l a s s s c a l e d i d not l o a d on the seventh f a c t o r , the s c a l e was e l i m i n a t e d . The c o r r e l a t i o n s between the s i x remaining s c a l e s are shown i n Table 5. 56 Table 5 C o r r e l a t i o n s Between the Sub-scales of the Sandman Inventory 1 2 3 5 1 Teacher 1.00 2 Anxiety -.46 3 Value .36 4 Self - C o n c e p t .34 5 Enjoyment .41 6 M o t i v a t i o n .36 1.00 -.40 -.72 -.76 -.64 1.00 ;33 . 45 .45 1. 00 . 66 .59 1.00 .76 B a s i s o f , S c a l e S e l e c t i o n I t i s on the b a s i s of the more r i g o r o u s c o n s t r u c t i o n o f the Sandman s c a l e s and t h e i r i d e n t i f i a b l e f a c t o r s t r u c t u r e t h a t f o u r o f the s c a l e s were s e l e c t e d f o r use i n t h i s study. The Teacher s c a l e was not used because p e r c e p t i o n o f the teacher by the student d i d not appear from the l i t e r a t u r e to be r e l a t e d t o an "emotional b l o c k " i n mathematics. The M o t i v a t i o n s c a l e was not used because only three o f e i g h t items loa d e d on the moti v a t i o n f a c t o r ; Thus, s c a l e s measuring anxiety i n mathematics, enjoyment of mathematics, value of mathematics, and s e l f - c o n c e p t of mathematics a b i l i t y were a l l taken from the Sandman b a t t e r y . Apart from the reasons t h a t w i l l be given f o r - each of the s c a l e s s p e c i f i c a l l y , some general c o n s i d e r a t i o n s that governed the s e l e c t i o n of the Sandman s c a l e s f o r t h i s study were: (1) The development of the s c a l e s was based upon a s e t of c o n s t r u c t s s i m i l a r to t h a t used i n the N a t i o n a l L o n g i t u d i n a l Study of Mathematics Achievement. These c o n s t r u c t s had appeared i n other v a r i o u s , o f t e n used 57 mathematics a t t i t u d e • s c a l e s . I t was apparent then t h a t these c o n s t r u c t s were o f recog n i z e d importance. As the items were s e l e c t e d from the pool of items c o n t a i n e d i n a number of popular a t t i t u d e s c a l e s , c o n s t r u c t s i m i l a r i t y was f u r t h e r ensured. Sandman f o l l o w e d a c r e d i b l e procedure i n c o n s t r u c t i o n of h i s s c a l e s : c o n s t r u c t i d e n t i f i c a t i o n , item s e l e c t i o n , f a c e v a l i d a t i o n by e x p e r t s , p r e t e s t a n a l y s i s , r e - w r i t i n g , and then e m p i r i c a l v a l i d a t i o n of s c a l e s by f a c t o r a n a l y s i s of the items* Factor a n a l y s i s o f the Sandman s c a l e s c o u l d be an a i d to the i n t e r p r e t a t i o n o f the r e s u l t s of the present study* To the extent t h a t the s c a l e s shared common v a r i a n c e and items c o u l d be shown to load on f a c t o r s a s s o c i a t e d with other v a r i a b l e s , an e x p l a n a t i o n of v a r i o u s f i n d i n g would be enhanced. The l e n g t h of the Sandman s c a l e s was an important c o n s i d e r a t i o n . Together with the a d d i t i o n o f the va l u e of mathematics f o r s o c i e t y s c a l e , the Test Anxiety Scale f o r C h i l d r e n , and three achievement t e s t s some two hours of t e s t i n g time was represented. Although longer s c a l e s o f t e n have g r e a t e r r e l i a b i l i t y , the i n c r e a s e d a d m i n i s t r a t i o n time of a number of l o n g e r t e s t s would l i k e l y have caused reduced r e l i a b i l i t y because of f a t i g u e . In a d d i t i o n i t was f e l t t h a t the c o e f f i c i e n t s of homogeity of the s c a l e s (.77 to .86) were q u i t e 58 a c c e p t a b l e . For f u r t h e r j u s t i f i c a t i o n of the i n c l u s i o n of each of the s c a l e s r e f e r t o the corresponding s e c t i o n i n the f o l l o w i n g more d e t a i l e d a n a l y s i s . ANXIETY IN MATHEMATICS From the evidence presented i n Chapter 2 i t was concluded t h a t s p e c i f i c achievement a n x i e t y s c a l e s tended to r e l a t e more s t r o n g l y to achievement than d i d g e n e r a l a n x i e t y s c a l e s . However, i t was not c l e a r t h a t mathematics a n x i e t y s c a l e s were more s t r o n g l y r e l a t e d to achievement i n mathematics than a more g e n e r a l a n x i e t y s c a l e . T h e r e f o r e two anxiety s c a l e s were i n c l u d e d i n t h i s study; 1 Sandman's (1973) Anxiety Toward Mathematics Scale and Sarason's (1958) Test Anxiety S c a l e f o r C h i l d r e n . Sandman f a c t o r analysed the items of t h i s s c a l e along with other a t t i t u d i n a l items. The a n a l y i s produced l o a d i n g s of the items from the a n x i e t y s c a l e on the i d e n t i f i e d a n x i e t y f a c t o r as f o l l o w s ; .20,-.31, .54, -.34, .58, .62, .58, -.24. The second and e i g h t h items loaded -.59 and .61 on the enjoyment f a c t o r . This accounts to some ex t e n t f o r the c o r r e l a t i o n s of the a n x i e t y and enjoyment s c a l e s (-.76). The s c a l e i s reproduced below. The numbering i s not the o r i g i n a l ; . 1. I f e e l at ease i n a mathematics c l a s s . 2. When I hear the word mathematics, I have a f e e l i n g of d i s l i k e . 59 3. I f e e l tense when someone t a l k s t o me about mathematics. 4. I t doesn't d i s t u r b me to work mathematics problems* 5. Working with numbers upsets me. 6. I t makes me nervous t o even think about doing mathematics. 7. I t s c a r e s me to have to take mathematics. 8. I have a good f e e l i n g toward mathematics* S e v e r a l reasons l e d to the s e l e c t i o n of t h i s s c a l e . F i r s t , t h e r e were p o s i t i v e as well as negative items i n the s c a l e , which was shown to be important by A l p e r t and Haber (1960)* Second, the s c a l e was s h o r t yet had a moderately high i n t e r n a l c o n s i s t e n c y (-86) compared with the r e l i a b i l i t y of .82 pf the TAQ (Alpert & Haber, 1960). T h i r d , although the s c a l e c o r r e l a t e d with another, the e x i s t i n g f a c t o r a n a l y s i s i d e n t i f i e d the i n d i v i d u a l items a c c o u n t i n g f o r the degree of o v e r l a p , thus a i d i n g i n t e r p r e t a t i o n . The Test Anxiety Scale f o r C h i l d r e n (TASC) (Sarason, Davidson, L i g h t h a l l S Waite, 1958) was s e l e c t e d as the more general achievement anxiety s c a l e because i t was the s c h o o l age analog of the Test Anxiety Q u e s t i o n a i r e which was developed f o r c o l l e g e age s t u d e n t s . (See the f i r s t s e t of 30 items i n Appendix D.) as can be seen from Table 2 i n Chapter 2 the r e s u l t s of the A l p e r t and Haber (1960) study i n d i c a t e d t h a t the t e s t a n x i e t y measures were more s t r o n g l y a s s o c i a t e d with achievement measures than were the more g e n e r a l measures 60 of a n x i e t y . The TASC was a r e l a t i v e l y short* 30 item, t e s t with a fo u r month t e s t - r e s t e s t r e l i a b i l i t y of .666 (Sarason, Davidson, L i g h t h a l l , Waite & fiubush, 1960) ENJOYMENT Scale s measuring enjoyment of mathematics and value of mathematics were developed by Aiken (1974),. The enjoyment s c a l e had an Alpha C o e f f i c i e n t .95 and c o r r e l a t e d *38 with the mathematics s c a l e o f the S c h o l a s t i c Aptitude Test a n d . 2 3 with high s c h o o l grade. As the s c a l e was developed f o r c o l l e g e s t udents i t was f e l t t h a t one w r i t t e n f o r younger s t u d e n t s would be more a p p r o p r i a t e . Sandman's s c a l e f i l l e d t h i s need. I t was f e l t t h a t an i n t e r n a l c o n s i s t e n c y of .85 f o r an e i g h t item s c a l e was acceptable f o r t h i s study,: Again the items from t h i s s c a l e loaded on a s i n g l e f a c t o r when analysed t o g e t h e r with other a t t i t u d e items. According t o the Sandman a n a l y s i s the l o a d i n g s were .73, .62, -.55, -.47, -.49, .47, .32 and .32. Item 4 loaded on the a n x i e t y f a c t o r and item 8 on the s e l f - c o n c e p t f a c t o r . The s c a l e i s reproduced below. The numbering i s not the o r i g i n a l . 1. Mathematics i s something which I enjoy very much. 2. Working mathematics problems i s fun. . 3. I would l i k e to spend l e s s . t i m e i n s c h o o l doing mathematics. 4. I don't l i k e anything about mathematics. 5. I would l i k e a job which doesn't use any 61 mathematics. 6* I enjdy t a l k i n g to other people about mathematics. 7. I l i k e t o play games t h a t use numbers. 8. Mathematics i s more of a game than i t i s hard work. VALUE Value of Mathematics to S o c i e t y Although Aiken (1974) had developed a value of mathematics s c a l e i t was f e l t t h a t the s h o r t e r Sandman s c a l e w r i t t e n f o r the lower secondary grades was more a p p r o p r i a t e . I t has been argued t h a t Sandman's s e t of s c a l e s was a c a r e f u l l y c o n s t r u c t e d , w e l l documented instrument. The e s t a b l i s h e d i n t e r - r e l a t i o n s h i p s of the s c a l e s (See Table 5.), i t was argued, would a i d i n t e r p r e t a t i o n i n the present study. However, Sandman's f a c t o r a n a l y s i s i n d i c a t e d a degree of independence and v a l i d i t y of the value s c a l e . The item l o a d i n g s on the value of mathematics f o r s o c i e t y were .55, -,.45, .41, .58, .64, .61, and -.45 with item 8 l o a d i n g ;31 on the a n x i e t y f a c t o r ; The items are reproduced i n the next s e c t i o n together with the items from the Value of Mathematics f o r Oneself Scale; I t should be noted t h a t the Sandman s c a l e , 8 items l o n g , had an i n t e r n a l c o n s i s t e n c y of .77. Value of Mathematics f o r Oneself I t has been argued that the measures of the value of 62 mathematics used i n t h i s study should i n c l u d e items p e r t a i n i n g to i n c e n t i v e s r e l a t e d d i r e c t l y to the student. N e i t h e r Sandman's (1974) Value of Mathematics t o S o c i e t y nor h i s M o t i v a t i o n i n Mathematics s c a l e s f i t t h i s c r i t e r i o n * I t was f e l t t h a t , i n a d d i t i o n t o the Value of Mathematics t o S o c i e t y S c a l e , a s c a l e more s t u d e n t — o r i e n t e d should be i n c l u d e d . To accomplish t h i s end, a s c a l e p u r p o r t i n g t o measure Value of Mathematics f o r Oneself was developed by the present author. I t was developed from a number of items s e l e c t e d from v a r i o u s a t t i t u d e s c a l e s and reworded to s u i t the rea d i n g and comprehension l e v e l s of grade 6 students. Wherever p o s s i b l e the items were c o n s t r u c t e d p a r a l l e l t o those of the Sandman value s c a l e . Because of the e s t a b l i s h e d v a l i d i t y of the Sandman value s c a l e , items were chosen t h a t c l o s e l y p a r a l l e d the items of t h a t s c a l e * The two s c a l e s are compared below. Value o f Math to S o c i e t y Value of Math f o r O n s e l f 1. Mathematics i s u s e f u l f o r 1. Mathematics i s u s e f u l f o r the problems of everyday my problems i n everyday l i f e * l i f e . 2. There i s l i t t l e need f o r - 2. There i s l i t t l e need f o r mathematics i n most jobs. mathematics i n the jobs I would want. 3. Most people should study 3. Doing w e l l i n mathematics some mathematics. h e l p s me i n other s u b j e c t s . 4. Mathematics i s . h e l p f u l i n 4. Mathematics h e l p s me under-understanding today's world. stand today's world. 5. Mathematics i s of gr e a t im- 5. I f I got b e t t e r marks i n portance to a country's mathematics I would enjoy development. mathematics more. 6. I t i s important t o know 6. I t i s important f o r me t o 63 mathematics i n order to get a good job* 7. You can get along p e r f e c t l y well i n everyday l i f e with-out mathematics: 8. Most o f the i d e a s i n mathe-matics aren't very u s e f u l * know mathematics i n order to get a good job. 7. I can get along p e r f e c t l y w e l l i n everyday l i f e with-out mathematics. 8. Most of the: i d e a s i n math-ematics a r e n ' t very u s e f u l to me,. SELF-CONCEPT OF ABILITY IN MATHEMATICS Although P a t t e r s o n (1967) and Bachman (1970) used s c a l e s of s e l f ^ -concept of a b i l i t y to achieve i n mathematics, the s c a l e i n the Sandman (1973) b a t t e r y was used* The major reason was t h a t the Sandman s c a l e appeared as a f a c t o r when the items, along with other a t t i t u d i n a l items, were subjected to f a c t o r a n a l y s i s . The l o a d i n g s of the items on the a n x i e t y f a c t o r were -.62, .68, .56, -.49, -.31, . 69, - 38, and -.17. Item 2 loaded .31 on the enjoyment f a c t o r while items 4, 5, and 8 loaded .46, .32, and .39 r e s p e c t i v e l y on the a n x i e t y f a c t o r . The i n t e r n a l c o n s i s t e n c y was .83. The s c a l e i s repreduced below. The numbering i s not the o r i g i n a l . 1. I don't do very w e l l i n mathematics. 2. Mathematics - i s easy f o r me. 3. I u s u a l l y understand what we are t a l k i n g about i n mathematics c l a s s . 4. No matter how hard I t r y , I cannot understand mathem a t i c s . 5. I o f t e n t h i n k , "I can't do i t , " when a mathematics problem seems hard. 64 6. I am good at working mathematics problems. 7. I remember most of the t h i n g s I l e a r n i n mathematics. 8. I f I don't see how t o work a mathematics problem r i g h t away, I never get i t . LOCUS OF CONTBOL The s c a l e s e l e c t e d t o measure l o c u s o f c o n t r o l was the I n t e l l e c t u a l Achievement B e s p o n s i b i l i t y Scale ( C r a n d a l l , Katkovsky & C r a n d a l l , 1965). They s t a t e d t h a t "there has been no demonstration so f a r t h a t such b e l i e f s [ i n l o c u s of c o n t r o l 0 are c o n s i s t e n t a c r o s s a l l areas of e x p e r i e n c e " (p. 93). As t h e i r major concern was with s c h o o l achievement they developed the IAB s c a l e which d i f f e r e d from B o t t e r ' s (1966) I-E s c a l e , B a t t l e 6 B o t t e r ' s (1963) C h i l d r e n ' s P i c t u r e Test o f I n t e r n a l E x t e r n a l Locus of C o n t r o l , and B a i l e r ' s (1961) Locus of C o n t r o l Scale i n s e v e r a l r e s p e c t s . F i r s t , the other s c a l e s " c o n t a i n items d e s c r i b i n g r e i n f o r c e m e n t i n a number of m o t i v a t i o n a l and b e h a v i o r a l areas such as a f f i l i a t i o n , dominance, achievement and dependency" (p. 93). Second, the other s c a l e s i n c l u d e a v a r i e t y of sources and agents such as l u c k , f a t e , impersonal s o c i a l f o r c e s , more-personal " s i g n i f i c a n t e t h e r s , " e t c . , the IAB l i m i t s t h e source of e x t e r n a l c o n t r o l to those persons who most o f t e n come i n f a c e - t o - f a c e c o n t a c t with a c h i l d , h i s p a r e n t s , t e a c h e r s and peers. (p. 93) In t h e i r i n i t i a l a d m i n i s t r a t i o n of the s c a l e they found a two month t e s t - r e t e s t r e l i a b i l i t y of ,.69 f o r the whole s c a l e , no s i g n i f i c a n t sex d i f f e r e n c e s , moderate c o r r e l a t i o n s 65 w i t h IQ (.26 a t grades 3, 4, 5: .16 a t grades 6, 8, 10, 12) and s o c i o - e c o n o m i c s t a t u s (.08 a t grades 3,4, 5: .11 at grades 6, 8, 10, 12). They noted t h a t t h e Locus o f C o n t r o l S c a l e and t h e C h i l d r e n ' s P i c t u r e Test had a much s t r o n g e r r e l a t i o n s h i p t o s o c i o - e c o n o m i c s t a t u s t h a n t h e l A f i s c a l e . I n a second s t u d y ( C r a n d a l l , C r a n d a l l & K a t k o v s k y , 1965) th e y found t h a t t h e s c o r e s on the n e g a t i v e i t e m s , the p o s i t v e i t e m s , and t h e t o t a l s c a l e f o r both younger and o l d e r c h i l d r e n , r e s u l t e d i n o n l y two s i g n i f i c a n t c o r r e l a t i o n s w i t h t h e C h i l d r e n ' s D e s i r e a b i l i t y Q u e s t i o n a i r e (a measure of t h e degree t o which c h i l d r e n g i v e s o c i a l l y d e s i r e d r e s p o n s e s ) : -.26 f o r younger c h i l d r e n on t h e t o t a l I-E s c a l e and -.15 f o r o l d e r c h i l d r e n on th e p o s i t i v e i t e m s * I t s h o u l d be noted t h a t i n t h i s l a t t e r s t u d y t h e y a n a l y s e d t h e s u c c e s s i t e m s and t h e f a i l u r e i t e m s s e p a r a t e l y . T h i s procedure was a l s o used by L i n t n e r and DuCette (1974). They f e l t t h a t a s the p o s i t i v e and n e g a t i v e s c a l e s c o r r e l a t e d * 45 t b e y would combine them* Because o f the low c o r r e l a t i o n the two s c a l e s were c o n s i d e r e d s e p a r a t e l y i n t h i s s t u d y . They were r e f e r r e d t o as t h e I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y S c a l e - Success (IARS) and t h e I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y S c a l e - F a i l u r e (IAJBF). ACHIEVEMENT TESTS The s e t of achievement s c a l e s was made up o f t h e Mathematics Concepts and Mathematics Problem S o l v i n g s c a l e s 66 ( l e v e l 12) from the Canadian Test of B a s i c S k i l l s : Form 4 and the a r i t h m e t i c Computation t e s t from S t a n f o r d achievement Test (1964). The Canadian Test o f B a s i c S k i l l s (CTBS) was s e l e c t e d because i t was s t a n d a r d i z e d and v a l i d a t e d on 30 000 Canadian s u b j e c t s . F u r t h e r , i t s p r e c u r s o r , the Iowa Test of B a s i c S k i l l s , o f t e n had been used i n a t t i t u d e - achievement s t u d i e s (e.g., antonnen, 1974; Mastantuono, 1971; and Weston, 1 968),. In a review of the CTBS B i r c h (1972), McDonald P r o f e s s o r o f Education, M c G i l l U n i v e r s i t y s t a t e d , Unless a user i s able to s e l e c t an a p p r o p r i a t e sample of s u b j e c t s , c a r r y out h i s own item a n a l y s i s and r e l i a b i l i t y and v a l i d i t y s t u d i e s , he must . accept, on the r e p u t a t i o n of the t e s t d e s i g n e r , many of the bases upon which h i s c o n c l u s i o n s are made. I t i s thus r e a s s u r i n g to be a b l e to use a t e s t l i k e the Canadian l e s t of B a s i c S k i l l s . I t i s i n f a c t * simply a Canadian v e r s i o n of the w e l l known Iowa Test of B a s i c S k i l l s . (p. 16) Form 4, although not m e t r i c a t e d , r e f l e c t e d some r e c e n t c u r r i c u l a r changes made i n B r i t i s h Columbia. Even though te a c h e r s had been using the metric system e x c l u s i v e l y i n mathematics c l a s s e s i n the t h r e e years preceding the t e s t i n g , the B r i t i s h system of measurement was s t i l l i n common use i n the community and the students had been taught t h a t system i n e a r l i e r grades. Moreover, o n l y two items r e q u i r e d knowledge of the . r e l a t i o n between u n i t s (e.g., Which of the f o l l o w i n g measurements i s the g r e a t e s t ? 1) 5 quarts 2) 6 p i n t s 3) 1 g a l l o n 4) 3 quarts 1 p i n t ; ) . Thus i t was f e l t t h a t the s c a l e was v a l i d and t h a t i f students c o u l d not answer the q u e s t i o n s the e f f e c t would be c o n s i s t e n t a c r o s s the sample. 67 There was no computational s c a l e i n c l u d e d with the Canadian T e s t of B a s i c S k i l l s . The a r i t h m e t i c Computation s c a l e of the SAT: Form W (1964) was s e l e c t e d to f i l l t h i s v o i d . B i e d e s e l ' s . (1965) only c r i t i c i s m of the S t a n f o r d Achievement t e s t was the emphasis on computation i n l i g h t of changes i n mathematics content emphasis. However, as. the s c a l e was being s e l e c t e d f o r use as a computational instrument, the c r i t i c i s m was considered an advantage. F u r t h e r , as t h e r e had been no change i n the format of the p r e s e n t a t i o n of computational guestiohs the e a r l y date was not deemed s i g n i f i c a n t * In more r e c e n t v e r s i o n s the number of q u e s t i o n s had been reduced. However, an advantage to t h i s v e r s i o n was t h a t i t was w e l l reviewed, widely accepted and s t i l l used by the s c h o o l d i s t r i c t p a r t i c i p a t i n g i n t h i s present study. TEACHEB EESPONSE SCALES In order to g i v e some s t r e n g t h t o the c o n s t r u c t v a l i d a t i o n of the chosen a f f e c t i v e s c a l e s i n r e l a t i o n t o the c h a r a c t e r i s t i c s a s s o c i a t e d with the "emotional b l o c k " i n mathematics, t e a c h e r s ' o p i n i o n s were sought about p u p i l s who may have such b l o c k s . Two methods were used* The f i r s t was a response to a check l i s t of nine c h a r a c t e r i s t i c s using each student as a r e f e r e n t * The c h a r a c t e r i s t i c s were behaviors t h a t students with an "emotional b l o c k " might e x h i b i t . T h i s 68 was s i m i l a r t o the procedure used by Sarason, Davidson, L i g h t h a l l and Waite (1958) i n t h e i r i n i t i a l v a l i d a t i o n o f the Test Anxiety S c a l e f o r C h i l d r e n (TASC),; They asked t e a c h e r s to respond to a 17 item s c a l e of a n x i e t y behavior which i n c l u d e d items such as Does the c h i l d e x h i b i t unwarranted f i d g e t i n g (e.g., squirming, r e s t l e s s behavior) when c a l l e d upon t o r e c i t e i n c l a s s ? Does the c h i l d become upset or anxious when a t e s t i s announced i n c l a s s or he i s c a l l e d upon t o r e c i t e ? (p. 106) In the c u r r e n t study i t was hypothesized t h a t an "emotional block" e x i s t e d which would l e a d t o negative forms of behavior i n response to mathematics thus r e d u c i n g achievement. The Krathwohl, Bloom and Masias (1964) taxonomy of a f f e c t i v e o b j e c t i v e s was used to c o n s t r u c t the check l i s t i tems. I t was f e l t t h a t the l e v e l of a f f e c t d i s p l a y e d by students with an "emotional b l o c k " would be high i n the taxonomy. L e v e l 2.3, S a t i s f a c t i o n i n Besponse, was the lowest l e v e l a t which responses could f a l l and s t i l l be co n s i d e r e d a " b l o c k . " i Krathwohl et a l s t a t e d t h a t The t e s t i n g f o r o v e r t m a n i f e s t a t i o n s of s a t i s f a c t i o n i n v o l v e s two matters: (1) d e c i d i n g which behaviors 1 They noted t h a t "the c a t e g o r i e s o f the a f f e c t i v e domain s t r u c t u r e are developed t o handle p r i m a r i l y p o s i t i v e v a l u e s r a t h e r than a v e r s i o n s * f e a r s , and d i s l i k e s . " However, they c o n t i n u e d , " I t i s b e l i e v e d t h a t , with very l i t t l e i n t e r p r e t a t i o n . . . , the framework can be used f o r those • n e g a t i v e 1 types o f o b j e c t i v e s one i s l i k e l y to f i n d i n the s c h o o l c u r r i c u l u m " (p. v i i ) . 69 are i n d i c a t i v e of s a t i s f a c t i o n ; (2) developing a method o f s y s t e m a t i c a l l y r e c o r d i n g the m a n i f e s t a t i o n s of s a t i s f a c t i o n . (p* 133) The above q u o t a t i o n was a p o s i t i v e statement of a f f e c t whereas the c o n s t r u c t of an "emotional b l o c k " was n e q a t i v e l y o r i e n t e d . A n e g a t i v e statement a t the same l e v e l would have " s a t i s f a c t i o n " r e p l a c e d with d i s s a t i s f a c t i o n * a v e r s i o n or d i s l i k e * Examples i n the taxonomy i n c l u d e d b e h a v i o r s such as v o l u n t a r y statements, l a u g h i n g , and v a r i o u s body movements. The next l e v e l i n the taxonomy was 3, V a l u i n g , The Krathwohl et a l d e s c r i p t i o n was, At the lowest l e v e l of V a l u i n g , he i s at l e a s t w i l l i n g t c permit h i m s e l f t o be so p e r c i e v e d and at the higher l e v e l s he may behave so as t o f u r t h e r t h i s i m p r e s s i o n a c t i v e l y . (p. 139) For example a student who remarked d i r e c t l y t o the teacher t h a t he hated mathematics would be c o n s i d e r e d at l e v e l 3.2, Preference f o r a Value. Avoidance behavior and i n v o l u n t a r y p h y s i c a l r e a c t i o n s would be i n t e r p r e t e d as being at l e v e l 3;3, Commitment, because Krathwohl e t a l s t a t e d , "there must a l s o be a c o n s i d e r a b l e investment of energy i n the o b j e c t or phenomenon". There was no attempt to have teachers gather evidence of a f f e c t i v e responses above l e v e l 3. For example, l e v e l 4. 1, C o n c e p t u a l i z a t i o n of a Value, r e q u i r e d evidence t h a t the student has developed e v a l u a t i v e judgements with regard t o the o b j e c t he values; (2) evidence of a b s t r a c t or symbolic t h i n k i n g about the value o b j e c t ; (3) evidence o f g e n e r a l i z a t i o n about a s e t or c l a s s of values of which the o b j e c t i s a member. (p. 157) 70 Apart from a l l t e a c h e r s not having o p p o r t u n i t i e s to observe such b e h a v i o r , the l i s t of b e h a v i o r s would have become unacceptably long. The l i s t of c h a r a c t e r i s t i c s were i d e n t i f i e d from the l i t e r a t u r e c i t e d i n Chapter 1. An attempt was made to sample both v e r b a l and p h y s i c a l behaviors and to f o l l o w the examples of Sarason e t a l (1S58) . The l i s t of behaviors had t o be kept s h o r t o t h e r w i s e , f o r a c l a s s of 30 students, the r e q u i r e d number of responses would i n c r e a s e r a p i d l y and thus tend to reduce the amount of c o n s i d e r a t i o n q i v e n to each response. The f o l l o w i n g nine c h a r a c t e r i s t i c s were decided upon. A s h o r t l a b e l appears i n parentheses f o l l o w i n g each one; These l a b e l s w i l l be used i n the subsequent t a b l e s and d i s c u s s i o n . While the student i s doings-mathematics have you observed t h a t he/she 1. tends to give random answers to q u e s t i o n s during mathematics c l a s s ? (Eandom Answers) 2. appears tense d u r i n g mathematics less o n s ? (Appears Tense) 3. expresses a n x i e t y or nervousness about mathmetics? (Expresses Anxiety) 4. tends to i n c r e a s e d i s r u p t i v e behavior d u r i n g mathematics c l a s s ? ( D i s r u p t i v e Behavior) 5. says t h a t no matter what he/she does he/she can't do mathematics? (Expresses I n a b i l i t y ) 6. has hands t h a t shake when doing mathematics? (Hands Shake) 7. says t h a t mathematics i s u s e l e s s ? (Says Mathematics Useless) 8. sometimes r e f u s e s to answer q u e s t i o n s d u r i n g 71 mathematics period? (Refuses t o Answer) 9. f i d g e t s more during mathematics l e s s o n s ? (Fidgets More) Appendix A has the complete s e t of i n s t r u c t i o n s given to the t e a c h e r s f o r the use of t h i s s c a l e . As t h i s was a teacher-response, student-behavior c h e c k l i s t , and the b e h a v i o rs entered the a n a l y s i s i n d i v i d u a l l y t h i s was r e f e r r e d t o as the s e t of student behaviors or simply Student-Behaviors i The second form of teacher response was to have them rank the students as to the degree to which they f e l t the students f i t a d e s c r i p t i o n based upon the above c h a r a c t e r i s t i c s . The d e s c r i p t i o n f o l l o w s ; A student with the block may g i v e random answers to questions or may r e f u s e to answer them at a l l * He/she may appear tense, have hands t h a t shake as he/she w r i t e s , f i d g e t or i n c r e a s e d i s r u p t i v e behavior i n the mathematics c l a s s . The student may t e l l you t h a t he/she f e e l s anxious or nervous about mathematics or t h a t mathematics i s u s e l e s s . He/she may s t a t e t h a t no matter how hard he/she works i t seems t o make no d i f f e r e n c e . The procedure f o r ranking.was a simple o r d e r i n g of a l l the names of the grade s i x students i n the c l a s s i n terms of the above c h a r a c t e r i s t i c s . The s e t of i n s t r u c t i o n s given to the t e a c h e r s f o r the above s c a l e may be found i n Appendix B. Thi s measure was r e f e r r e d to as RANK. AGE AND GRADE LEVEL CHOSEN 72 Antonnen (1963) st u d i e d the d i f f e r e n c e s i n a t t i t u d e s between 1017 s t u d e n t s i n grades 5 and 6 and the same group of students i n grades 11 and 12. He found t h a t a t t i t u d e s c o r e s d e c l i n e d s h a r p l y . Evidence c i t e d e a r l i e r i n the d i s c u s s i o n of l o c u s o f c o n t r o l suggested t h a t t h i s study be done with students who were as young as p o s s i b l e i n order to reduce the l i k e l i h o o d o f students " a r r i v i n g at an e x t e r n a l view of the world as a defense a g a i n s t f a i l u r e " ( H j e l l e , 1970, p. 326). However, the a b i l i t y of the students t o answer s e l f - r e p o r t items i n a d i s c r i m i n a t i n g manner suggested t h a t the sample be chosen from an o l d e r group i f p o s s i b l e . The Sandman i n v e n t o r y was w r i t t e n f o r grade 8 s t u d e n t s and had been ad m i n i s t e r e d s u c c e s s f u l l y t o t h a t group* The I n t e l l e c t u a l Achievement . R e s p o n s i b i l i t y Scale was developed f o r s c h o o l c h i l d r e n i n both elementary and secondary l e v e l s . I t would appear that the optimum grade l e v e l was grade e i g h t . But because, i n the l o c a l e of t h i s s tudy, there was an elementary-secondary s c h o o l s p l i t between grades seven and e i g h t t i e present study was done with grade s i x s u b j e c t s . Grade seven students were not s e l e c t e d because i t was f e l t t h a t at the time of the t e s t i n g , s p r i n g , they would be q u i t e concerned about t h e i r forthcominq move to the secondary s c h o o l . I t was a l s o noted by Aiken (1976) t h a t "The l a t e elementary and e a r l y j u n i o r - h i g h qrades are viewed as b e i n g p a r t i c u l a r l y important to the development of a t t i t u d e toward 73 mathematics." (p* 269) Because the Sandman s c a l e s had not been a d m i n i s t e r e d t o grade 6 s t u d e n t s , there was some concern about t h e ap p r o p r i a t e n e s s o f the language and phrasing i n the items. In order to compensate f o r lower comprehension l e v e l s , the items of a l l s c a l e s were recorded on tape by the present author. The tape was then d u p l i c a t e d and played back t o the s t u d e n t s as the s c a l e s were being presented i n w r i t t e n form. SUBJECTS The s u b j e c t s were s e l e c t e d from a l a r g e s c h o o l d i s t r i c t i n B r i t i s h Columbia. There were 64 elementary schools and annexes e n r o l l i n g approximately 14 000 students. The d i s t r i c t bridged both r u r a l and urban areas with l i t t l e i n d u s t r y or b u s i n e s s . The l a r g e s t p r o p o r t i o n of the working p o p u l a t i o n commuted to a nearby urban center. For a d m i n i s t r a t i v e convenience the d i s t r i c t was d i v i d e d i n t o f i v e areas: two r e s i d e n t i a l - c o m m e r c i a l areas, two r e s i d e n t i a l areas i n t e r s p e r s e d with s m a l l farms, and one farmland area. As there were m a t e r i a l s f o r approximately 450 s t u d e n t s , i t was p o s s i b l e t o adm i n i s t e r the t e s t s and q u e s t i o n n a i r e s t o 14 t o 16 c l a s s e s at a time. Schools w i t h i n each area were contacted i n order of s i z e and were asked to take p a r t i n the study. T h i s was done u n t i l the s e t of m a t e r i a l s was committed, i n t h i s manner some 63 c l a s s e s from 74 29 s c h o o l s were contacted* Because of l a s t minute c o n s i d e r a t i o n s such as s p o r t s days and camping t r i p s the f i n a l number of c l a s s e s was 59. Three more c l a s s e s were e l i m i n a t e d from the study because t e a c h e r s f a i l e d to supply a l l the requested i n f o r m a t i o n * The f i n a l sample c o n s i s t e d of 56 c l a s s e s from 26 s c h o o l s with 1186 students p a r t i c i p a t i n q . As much of the a n a l y s i s was to be done with complete s e t s o f data, s u b j e c t s who missed t a k i n q a t e s t were e l i m i n a t e d , thus q i v i n g the f i n a l t o t a l of 1033 s u b j e c t s from grade s i x . Some of the c l a s s e s i n the study were composed of grades f i v e and s i x , or s i x and seven* Such c l a s s e s were c a l l e d " s p l i t s " . These s p l i t s a r e r e f e r r e d t o as " c l a s s t y p e s " i n the f o l l o w i n g t e x t . Only the grade s i x s u b j e c t s from these c l a s s e s Were i n c l u d e d i n the study although grade f i v e and seven students were i n c l u d e d i n the a d m i n i s t r a t i o n of the t e s t s at the t e a c h e r ' s request. Table 6 summarizes the c l a s s type, sex and number of s u b j e c t s * Table 6 Table of C l a s s Type, Sex and Number of Sub j e c t s C l a s s e s Boys G i r l s T o t a l 5- 6 s p l i t 11 53 63 116 6 o n l y 33 410 380 790 6- 7 s p l i t J 2 66 M 127 T o t a l 56 529 504 1033 75 PILOT A p i l o t study was conducted to assess the adequacy of the w r i t t e n i n s t r u c t i o n s f o r both students and tea c h e r s , the h a n d l i n g of the m a t e r i a l s , the a u d i b i l i t y of the tapes, and r e l i a b i l i t y of the experimenter made Value of Mathematics f o r Oneself Scale* The two teacher response s c a l e s were i n c l u d e d f o r purposes of e v a l u a t i n g the a d m i n i s t r a t i v e i n s t r u c t i o n s and the response procedures. No attempt was made to gather evidence f o r the r e l i a b i l i t y o f t e a c h e r responses, or of the v a l i d i t y of the two s c a l e s as i t was c o n s i d e r e d t h a t the number o f teachers i n the p i l o t sample was too s m a l l . A s c h o o l i n the same d i s t r i c t was s e l e c t e d * Two c l a s s e s , with a t o t a l of 50 s t u d e n t s , undertook the p i l o t a d m i n i s t r a t i o n . A meeting with the p a r t i c i p a t i n g t e a c h e r s was h e l d i n order to convey the purpose o f the p i l o t * The teachers were asked to be as c r i t i c a l of the format of t e s t b o o k l e t s , response sheets and the a d m i n i s t r a t i o n b o o k l e t as p o s s i b l e * They a l s o were asked to i n d i c a t e any sources of d i f f i c u l t y or c o n f u s i o n t h a t arose d u r i n g the a d m i n i s t r a t i o n . The f i n a l forms of the m a t e r i a l s may be found i n Appendices A, B, C, D, and E. A d e s c r i p t i o n o f the set of m a t e r i a l s given to each teacher w i l l be found i n the s e c t i o n e n t i t l e d " M a t e r i a l s " . The e i g h t items of the Value of Mathematics f o r Oneself Scale were admi n i s t e r e d together with e i g h t randomly s e l e c t e d items from the achievement r e s p o n s i b i l i t y s c a l e and 76 s i x items from the Test Anxiety Scale f o r C h i l d r e n . Items from the three s c a l e s were i n c l u d e d because of the d i f f e r e n t response formats and a d m i n i s t r a t i o n i n s t r u c t i o n s * As a r e s u l t of the p i l o t the a d m i n i s t r a t i o n b o o k l e t was r e o r g a n i z e d and some wordings changed. The Hoyt e s t i m a t e of the r e l i a b i l i t y of the Value of Mathematics f o r O n s e l f Scale was .63 which was c o n s i d e r e d adequate i n the l i g h t of the l a r g e sample of the main study. I t should be noted t h a t the l a r g e sample would not a f f e c t the r e l i a b i l i t y (unless the t e s t v a r i a n c e was increased) but would tend to balance the e f f e c t of i n c r e a s e d e r r o r v a r i a n c e i n the t e s t i n g of hypotheses. Item-scale c o r r e l a t i o n s were c a l c u l a t e d a f t e r t h e item s c o r e s were c o r r e c t e d f o r r e v e r s e p o l a r i t y . A l l the items had p o s i t i v e c o r r e l a t i o n s r anging from .17 t o .56. The mean was 17.56 and the standard d e v i a t i o n was 5*15 with a maximum p o s s i b l e of 40 and a minimum of 8, MATERIALS A f f e c t i v e S c a l e s - ..., •..-, — .. • ^ Each teacher was qiven an a d m i n i s t r a t i o n booklet which o u t l i n e d the order i n which the m a t e r i a l s were to be administered, the timinq of the t e s t a d m i n i s t r a t i o n , and t h e i n s t r u c t i o n s t h a t were to be read to the students b e f o r e the students were to begin r e s p o n d i n g . See Appendix C f o r the complete a d m i n i s t r a t i o n b o o k l e t . The a f f e c t i v e s c a l e s were s p l i t i n t o t h r e e p a r t s each 77 c h a r a c t e r i z e d by response s t y l e ; The Test Anxiety S c a l e f o r C h i l d r e n (TASC), the f i r s t p art, r e q u i r e d the students to respond yes or no,; The second p a r t , the I n t e l l e c t u a l Achievement B e s p o n s i b i l i t y S c a l e , r e q u i r e d the students to s e l e c t one cf two p o s s i b l e a l t e r n a t i v e statements which they thought best completed a sentence. Items from the two s c a l e s were p l a c e d i n the same order as i n the o r i g i n a l study of C r a n d a l l , Katkovsky, and C r a n d a l l (1965).. P a r t t h r e e was composed of items from the f o u r a f f e c t i v e s c a l e s s e l e c t e d from the Sandman b a t t e r y (Anxiety Toward Mathematics, Value of Mathematics i n S o c i e t y , S elf-Concept i n Mathematics, Enjoyment of Mathematics), and an author c o n s t r u c t e d s c a l e Value o f Mathematics f o r On e s e l f . The response mode f o r t h i s s e t of items was a f i v e p o i n t L i k e r t s c a l e ; s t r o n g l y agree, agree, don't know, d i s a g r e e , and s t r o n g l y d i s a g r e e . . Items from each of the s c a l e s used i n the t h i r d p a r t were randomly ordered. The r e p o r t e d r e l i a b i l i t i e s of each of the s c a l e s together with the number o f items and the a b b r e v i a t i o n s used i n the t e x t can be found i n Table 7. F o r a f u l l e r d e s c r i p t i o n of each o f t h e s c a l e s see Chapter 3. The t h r e e p a r t s together with d i r e c t i o n s and examples f o r the students were placed i n t o a b o o k l e t which i s reproduced completely i n Appendix D. An added b e n e f i t of the order noted i n Table 7 was t h a t the s c a l e s p e r t a i n i n g s p e c i f i c a l l y t o mathematics were placed l a s t ; Thus, a bia s toward mathematics would not be present when the s t u d e n t s 78 Table 7 Table of S c a l e s , A b b r e v i a t i o n s , Number of Items f o r the A f f e c t i v e S c a l e s Scale Abbr* Items T e s t Anxiety Scale f o r C h i l d r e n TASC 30 I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y : Success IARS 17 I n t e l l e c t u a l Achievement B e s p o n s i b i l i t y : F a i l u r e IARF 17 Anxiety Toward Mathematics MANX 8 Enjoyment i n Mathematics ENJOY 8 Value of Mathematics VALSOC 8 Sel f - C o n c e p t i n Mathematics SELFCON 8 Value of Mathematics f o r O n e s e l f VALSEL 8 answered the more g e n e r a l s c a l e s . TASC was placed f i r s t because the response mode was considered t o be the s i m p l e s t and t h e r e f o r e a good i n t r o d u c t i o n to responding t o an a f f e c t i v e s c a l e * I t was f e l t t h a t d i f f e r i n g reading a b i l i t i e s of students might a f f e c t the number of guestions answered on the a f f e c t i v e s c a l e s and the l e v e l of understanding with which the students responded t o the items. In order to reduce these e f f e c t s a c a s s e t t e tape was prepared with the experimenter r e a d i n g the items. Twenty c o p i e s were made of the tape t o ensure c o n s i s t e n c y o f the o r a l d e l i v e r y . The student responses were, f o r a l l the above s c a l e s , made on one response sheet, The sheet was developed e s p e c i a l l y f o r t h i s study i n order t o f a c i l i t a t e key-punching of the data d i r e c t l y from the sheets. See Appendix E f o r an example of the answer sheets. 79 Achievement Tests The t h r e e achievement t e s t s were to be a d m i n i s t e r e d i n the f o l l o w i n g o r d e r : A r i t h m e t i c Computation, Mathematics Concepts,- and Mathematics Problem S o l v i n g . This order was chosen because i t was thought t h a t the computation s c a l e would be the most f a m i l i a r and s h o u l d be f i r s t ; The concepts and problem s o l v i n g s c a l e s were c o n t a i n e d i n the standard CTBS bookl e t and were a d m i n i s t e r e d i n the order t h a t they appeared. T h i s tended to reduce complexity of the a d m i n i s t r a t i o n * I t was a l s o thought t h a t the word problems may have tended to i n c r e a s e anxiety more than the concepts q u e s t i o n s and, as anxiety was one of the c h a r a c t e r i s t i c s under examination i n t h i s study, the p l a c i n g of the problem s o l v i n g s c a l e l a s t would e l i m i n a t e i t s e f f e c t on the other s c a l e s . The t e s t s , names, a b b r e v i a t i o n s used i n t h i s study, the number of items, r e l i a b i l i t y , and the p u b l i s h e r ' s normed means f o r grade s i x appear i n Table 8. Each o f the t e s t s had a 1 m u l t i p l e c h o i c e response format; Again students responded on a s p e c i a l answer sheet to f a c i l i t a t e key-punching. As the f i r s t items f o r t h i s grade l e v e l i n the CTBS was item 52 f o r the concept s c a l e and 40 f o r the problem s o l v i n g s c a l e the response sheets were numbered a c c o r d i n g l y . See Appendix E f o r an example of the answer sheets. Table 9 summarizes the sequencing of the t e s t s and the T a b l e 8 80 S c a l e s , A b b r e v i a t i o n s , Number of Ite m s , E e l i a b i l i t i e s , and Normed Means o f t h e Achievement T e s t s Number o f Norm S c a l e Abbr. Items E e l * Mean S t a n f o r d Achievement T e s t : A r i t h m e t i c Computation Canadian l e s t of B a s i c S k i l l s : Mathematics Concepts Problem S o l v i n g COMP 39 .87 24,3 CONC 45 .86 20. 1 PBOB 31 .83 13.3 most d e s i r a b l e t i m i n g o f t h e t e s t a d m i n i s t r a t i o n * T a b l e 9 P r e f e r e d Sequence and Spacing of S c a l e A d m i n i s t r a t i o n * Mon. Tues. Wed. Thur. F r i . TASC MANX VALSEL break VALSOC no Morning SELFC t e s t s COMP PEOB IABS ENJOY IABF A f t e r n o o n CONC *In a l l cases t h e s e q i i e n c i n q and the two day s e p a r a t i o n between a f f e c t i v e and achievement t e s t s were t o be m a i n t a i n e d * Timinq c o u l d be a l t e r e d t o s u i t t h e s c h o o l o r q a n i z a t i o n . Timing here r e f e r s t o t i m e a t which t h e t e s t s s h o u l d be a d m i n i s t e r e d , not t h e t i m e a l l o w e d f o r the t e s t i n g s e s s i o n * PBOCEDUBE M a t e r i a l s f c r a p p r o x i m a t e l y 375 s t u d e n t s were assembled* T h i s s e t was s u f f i c i e n t l y l a r g e t o a d m i n i s t e r t o t h e s t u d e n t s of one ge o g r a p h i c r e g i o n . The a d m i n i s t r a t i o n o f the t e s t s was done i n 5 s e s s i o n s , each a week l o n g , one f o r each o f the f i v e g e o g r a p h i c r e g i o n s . A f t e r the i n i t i a l 81 c o n t a c t had been made with the p r i n c i p a l s of the p a r t i c i p a t i n g s c h o o l s , a l l t e a c h e r s of a r e g i o n with c l a s s e s i n v o l v e d i n the study' were i n v i t e d t o a meeting. a t the meeting the purpose and d e s c r i p t i o n of m a t e r i a l s were given* Questions about use of the r e s u l t s , c o n f i d e n t i a l i t y of the data, and time r e q u i r e d were answered. a s e t of m a t e r i a l s was provided to each p a r t i c i p a t i n g teacher* I t i n c l u d e d an a d m i n i s t r a t i v e b o o k l e t , a s e t of c a r d s f o r r a n k i n g the students on the d e s c r i p t i o n of a student who might have an "emotional b l o c k " i n mathematics, a s e t of IBM mark-sense c a r d s , one f o r each student, upon which they recorded the students i d e n t i f i c a t i o n number and observed Student-Behaviors, a c l a s s s e t of the a f f e c t i v e s c a l e b o o k l e t s , a copy of the c a s s e t t e tape, answer sheets f o r the three a f f e c t i v e s c a l e s , a c l a s s s e t of each of the S t a n f o r d a r i t h m e t i c Test and the Canadian Test of B a s i c S k i l l b o o k l e t s , and answer sheets f o r the achievement t e s t s . The a f f e c t i v e s c a l e s were administered b e f o r e the achievement s c a l e s i n order to reduce p o s s i b l e e f f e c t s of the l o n g e r achievement t e s t i n g s e s s i o n . I t was suggested t o the t e a c h e r s t h a t the a f f e c t i v e s c a l e s be administered i n two s e s s i o n s ; p r e f e r a b l y oh two c o n s e c u t i v e mornings* However, because of s c h o o l o r g a n i z a t i o n and p l a t o o n i n g the only a b s o l u t e requirements were the t e s t order and the r e s t p e r i o d between each cf the three qroupinqs of s c a l e s ; l a s c , i a E , and the a t t i t u d e s c a l e s . 82 The achievement t e s t s had s i m i l a r requirements with a two day l a p s e between the a d m i n i s t r a t i o n of the a f f e c t i v e and achievement scales,. See Table 9 above f o r the p r e f e r r e d a d m i n i s t r a t i o n schedule. DATA DESCRIPTION For each student the f o l l o w i n q p i e c e s of data were gathered: i d e n t i f i c a t i o n number, sex, t e a c h e r i d e n t i f i e d b e haviors from the Student Behavior c h e c k l i s t , rank on the d e s c r i p t i o n of b e h a v i o r s t h a t may be a s s o c i a t e d with an "emotional block" i n mathmatics, three achievement t e s t s c o r e s , and e i g h t a f f e c t i v e t e s t s c o r e s . Teacher Responses Sex was coded 1 f o r male, 0 f o r female* The t e a c h e r s were asked to mark the number on IBM cards which corresponded t o an observed behavior from the Student Behavior c h e c k l i s t . Blank cards were allowed* The rank was obtained by having the t e a c h e r s put the names and i d e n t i f i c a t i o n numbers of the students on the cards p r o v i d e d . They p l a c e d the c a r d s i n order from most to l e a s t l i k e the d e s c r i p t i o n provided* They then c o p i e d down the i d e n t i f i c a t i o n numbers of the students i n the order t h a t they appeared on the c a r d s . Appendix B has the i n s t r u c t i o n s g i v e n to the t e a c h e r s . The i d e n t i f i c a t i o n numbers were then numbered from 1 to the number of students i n the c l a s s by the experimenter. A rank score was obtained by 83 - ••;) ' .*'•'! g i v i n g a l l s t u d e n t s above the median rank a one (1), and those below a zero (0). A f f e c t i v e S c a l e s The TASC s c a l e , which c o n s i s t e d of yes and no answers, was coded 1 i f yes and 0 i f no. The items of the IARS and IARF s c a l e s were made up of two a l t e r n a t i v e endings t o a given statement. The a l t e r n a t i v e s were coded 1, 2. Items with n e g a t i v e p o l a r i t y were reversed. MANX, and VALSOC, SELFCON, ENJOY, and VAISEL were 5 l e v e l L i k e r t s c a l e s which were coded S t r o n g l y Agree = 1 to S t r o n g l y Disagree = 5. For each o f the f i v e s c a l e s those items with negative p o l a r i t y were r e v e r s e d . For each o f the e i g h t a f f e c t i v e s c a l e s the score on each was c a l c u l a t e d by adding up the value of the items,. Because some of the items were omitted, the s c o r e s were adju s t e d by u s i n g the f o l l o w i n g author developed formula which had the e f f e c t of r e p l a c i n g the missed items with a value e g u i v a l e n t to the mean of the answered items,* (N + M) N Y = £ X i N i=1 In the formula above N denotes the number of answered items, M denotes the number of omitted items, and X i the item s c o r e . Thus a student who t y p i c a l l y chose higher valued item responses would have the unanswered items weighted more h e a v i l y than would a student who chose the lower valued item responses. 84 Data B e l i a b i l i t y The clata were key-punched by the s t a f f a t the u n i v e r s i t y computer c e n t e r . Because of the volume of data, s e v e r a l computer programs were w r i t t e n by the author to check f o r key-punching e r r o r s . As each item had a l i m i t e d number of p o s s i b l e answers, a computer program was w r i t t e n t o check through a l l the d a t a and s e l e c t those student r e c o r d s t h a t had responses out of range. Another key-punching e r r o r was the dropping or the adding of an item or two thus f i n i s h i n g a s e t of data i n the wrong column. A computer program was w r i t t e n t o p r i n t out the number of the l a s t column of each of the s c a l e s * These were then checked with the o r i g i n a l answer sheets. A t h i r d program was w r i t t e n to c a l c u l a t e the s c o r e s f o r the t h r e e achievement t e s t s which were then scanned. Any s e t of s c o r e s which was widely d i v e r g e n t was checked. A random s e t of 50 answer sheets f o r both the a f f e c t i v e and achievement s c a l e s were checked item by item with the e d i t e d data. The r e s u l t i n g e r r o r r a t e was 0.5%. An item a n a l y s i s program, LEBTAP, (Nelson,1974) was run on the a f f e c t i v e s c a l e s and each item was checked f o r extreme l o a d i n g s which might i n d i c a t e i n c o r r e c t coding, r e v e r s i n g , or s c o r i n g . Only one item on one s c a l e , IABF was n e g a t i v e (-.0 1). The item was checked f o r proper s e l e c t i o n and p o l a r i t y and found c o r r e c t . R e l i a b i l i t i e s were c a l c u l a t e d b efore f u r t h e r a n a l y s e s because of the shortness of the Sandman s c a l e s and because t h e study used s u b j e c t s two years 85 younger t h a n the sample Sandman used f o r development. There was a s l i g h t a t t e n t u a t i o n o f r e l i a b i l i t y , the l a r g e s t o f which was VALSOC which showed a drop from .77 t o .69. Of g r e a t e r c o n c e r n were the drops of IABS, from .66 t o .52 and IABF, from .74 t o .59. However, the r e l i a b i l i t i e s were c o n s i d e r e d adequate, p a r t i c u l a r l y as t h e sample s i z e (1033) would g i v e adeguate power f o r the a n a l y s e s . Achievement T e s t s „—,. , A s i m i l a r procedure was c a r r i e d out on t h e achievement s c a l e s . Each i t e m was examined f o r e x t r e m e l y low o r n e g a t i v e c o r r e l a t i o n s w i t h the whole t e s t which may have i n d i c a t e d i n c o r r e c t c o d i n g , r e v e r s i n g , o r s c o r i n g . Only one i t e m on the t h r e e achievement t e s t s had a d i s t r a c t o r which had an e q u a l or h i g h e r c o r r e l a t i o n w i t h t h e whole s c a l e t h a n d i d t h e c o r r e c t response. T h i s i t e m was checked f o r k e y i n g and c o d i n g and found c o r r e c t . The Hoyt e s t i m a t e s of r e l i a b i l i t y f o r the t e s t s were c a l c u l a t e d and are r e p o r t e d i n T a b l e 10 t o g e t h e r w i t h the means, s t a n d a r d d e v i a t i o n s , maximums and minimums of the s c a l e s . PEE LI MI N A BY ANALYSES B e f o r e t h e h y p o t h e s i z e d models were t e s t e d two p r e l i m i n a r y i s s u e s had t o be a d d r e s s e d : the f i r s t was t h e u n i t o f a n a l y s i s and t h e second was whether or not TASC s h o u l d be i n c l u d e d i n the e n s u i n g a n a l y s e s . 86 Table 10 Means, Standard D e v i a t i o n s , Maximum Score, And Hoyt B e l i a b i l i t y f o r the Achievement and A f f e c t i v e Scales N = 1033 Scal e Mean S.D, Min Max Hoyt B e l . Bep. R e l i COMP 18.76 7 . 3 3 0 39 . 8 8 .87 CONC 23.94 8 . 5 4 0 45 * 88 . 86 PBOE 16. 33 6.23 0 32 .85 .83 TASC 12 . 5 5 5.78 0 30 i 84 . 6 7 2 IABS 29.52 2 . 3 9 17 34 ,*52 . 6 6 IARF 27. 54 2.83 17 34 .61 . 7 4 MANX 18.89 5 . 9 4 8 40 . 81 . 86 VALSOC 31. 91 4.91 8 40 .69 . 7 7 SELFCON 28 . 3 3 5 . 9 4 8 40 . 81 . 83 ENJOY 24 . 9 5 6.81 8 40 .82 .85 VALSEL 29.81 5.23 8 40 . 68 .69 l B e p o r t e d r e l i a b i l i t y , 2 F o u r month t e s t - r e t e s t r e l i a b i l i t y . U n i t of A n a l y s i s The l i t e r a t u r e upon which the hypotheses were based i n v a r i a b l y used the i n d i v i d u a l as the u n i t of d i s c u s s i o n or a n a l y s i s . However, the majori t y of the l i t e r a t u r e was based on s t u d i e s i n experimental psychology i n which i n d i v i d u a l s c o u l d be randomly assigned t o treatment groups. In t h i s study s u b j e c t s were part of i n t a c t groups and i t was h e l d d e s i r a b l e t o remove c l a s s e f f e c t s i n the case t h a t a student's s e l f — c o n c e p t , f o r example, was not formed independently of the environment or c l a s s i n which the student found h i m s e l f * For example, Fennema and Sherman (1978), i n t h e i r review o f the l i t e r a t u r e on sex r e l a t e d d i f f e r e n c e s i n mathematics achievement, s t a t e d t h a t The s p o t t y nature of the f i n d i n g of s u p e r i o r 87 mathematics £for malesJ which was always found i n c o n j u n c t i o n w i t h a h o s t of l e s s f a v o u r a b l e a t t i t u d e s by f e m a l e s , s u g g e s t s t h a t i m p o r t a n t n e g a t i v e i n f l u e n c e s may e x i s t w i t h i n t h e s c h o o l s t h e m s e l v e s , (p. 202) The u n i t of a n a l y s i s i s s u e was r e s o l v e d i n two s t e p s ; t h e f i r s t d e a l i n g w i t h d i f f e r e n c e s among c l a s s means, and the second w i t h d i f f e r e n c e s among c l a s s v a r i a n c e s * I n the f i r s t s t e p u n i v a r i a t e a n a l y s e s were done f o r each o f t h e e l e v e n v a r i a b l e s w i t h i n each c l a s s t ype (grade l e v e l s p l i t ) u s i n g computer programs from t h e S t a t i s t i c a l Package f o r t h e S o c i a l S c i e n c e s (SPSS) ( N i e , H u l l , J e n k i n s , S t e i n b r e n n e r & Bent, 1975). Of t h e 33 a n a l y s e s t h e n u l l h y p o t h e s i s was not r e j e c t e d a t t h e .05 l e v e l i n o n l y 9 c a s e s : TASC, IABS, AND IABF i n the grade 5-6 s p l i t , MANX and SELFCON i n t h e grade 6 c l a s s e s , and TASC, MANX, SELFCON, and ENJOY i n t h e grade 6-7 s p l i t ; See Table 11 f o r a summary o f t h e s e r e s u l t s , . A t a b l e of the 56 c l a s s means and s t a n d a r d d e v i a t i o n s may be found i n Appendix F* The grand means f o r t h e a f f e c t i v e s c a l e s were: TASC, 12.5; IABS, 29.5; IABF, 27.5; MANX, 18.9; VALSOC, 31.9; SELFCON, 28.3; ENJOY, 25.0; and VALSEL, 29.8. The grand means f o r t h e achievement t e s t s w i t h t h e normed means i n pa r e n t h e s e s were: COMP, 18.8 (24.3); CONC, 23.9 ( 2 0 . 1 ) ; and PBOB, 16.3 (13.3). Because the c l a s s means were s i g n i f i c a n t l y d i f f e r e n t i n most i f not a l l c a s e s i t was de c i d e d t o a d j u s t t h e raw s c o r e s by t a k i n g d e v i a t i o n s from t h e c l a s s means. Fo r the second s t e p a B a r t l e t t - B o x t e s t s o f 88 T a b l e i l l U n i v a r i a t e A n a l y s i s of V a r i a n c e U s i n g Each o f t h e Achievement and A f f e c t i v e V a r i a b l e s as Independent V a r i a b l e s and C l a s s as Dependent V a r i a b l e df df V a r i a b l e MSB Between MSW W i t h i n F r a t i o F prob Grade 5-6 s p l i t COMP 116. 1 10 42. 94 105 2.71 .005* CONC 117.5 10 59.04 105 1,99 .041* PEOB 66.7 10 31.06 105 2.15 .027* TASC 24. 7 10 25. 15 105 .98 .463 IARS 7.3 10 4.67 105 1.56 . 129 IABF 9.3 10 8. 10 105 1,15 .333 MANX 10 3. 2 10 29.11 105 3.55 .001* VAL SOC 54.5 10 21.18 105 2.57 .008* SE1FC0N 55.8 10 26.41 105 2.11 .030* ENJOY 135.6 10 43.23 105 3, 14 .002* VAL SEL 77.2 10 29.06 105 2:66 *006* Grade 6 o n l y C CM E 318.3 32 42.97 756 7.41 .000* CONC 422.7 32 60.24 756 7.0 2 .000* PEOE 172. 2 32 33.89 756 5.08 .000* TASC 93.0 32 32.89 756 2.83 .000* IAES 11.0 32 5.67 756 1.94 i 0 0 2 * IARF 18. 1 32 7.47 756 2,42 .000* MANX 41.6 32 35.98 1 756 1. 16 .254 VALSOC 60. 1 32 22.96 1 756 2.62 .000* SELFCON 47.5 32 36.23 756 1.31 ,118 ENJOY 87.0 32 44.49 756 1.96 ,001* VALSEL 74. 1 32 25.38 756 2*92 .000* Grade 6-7 s p l i t COMP 179.4 11 37.46 115 4. 79 .000* CONC 355. 5 11 39.80 115 8*93 .000* PROB 204.6 11 18.99 115 10,77 .000* TASC 39.2 11 29.01 115 1i45 . 160 IARS 11.8 11 5.07 115 2,33 .013* IARF 25.6 11 6.92 115 3,70 .000* MANX 28.7 11 , 30.03 115 196 :490 VALSOC 48. 0 11 19.46 115 2.47 .008 SELFCON 57.0 11 32.71 115 1.74 i 0 7 3 * ENJOY 54,. 8 11 43.23 115 1.27 .252* VALSEL 44. 8 11 20.52 115 2, 19 .020 *p < .05 89 homogeneity of variance f o r the c l a s s v a r i a n c e s were c a l c u l a t e d . T h i s was done with the c l a s s e s grouped again a c c o r d i n g to grade type, and a l s o on a l l c l a s s e s t o g e t h e r . T h i s a n a l y s i s was a l s o done by a computer program from SPSS. As can be seen from Table 12 when a l l c l a s s e s were grouped only two v a r i a b l e s CONC and IARS showed s i g n i f i c a n t d i f f e r e n c e s i n va r i a n c e between c l a s s e s . Table 12 Table of the R e s u l t s of the Bart l e t - B o x T e s t s of Homogenieity Of Va r i a n c e on Each o f the A f f e c t i v e And Achievement Measures Grade O r g a n i z a t i o n 5-6 S p l i t 6 Only 6-7 S p l i t Combined Scale STAT PEOB STAT PROB STAT PROB STAT PROB CALC 1.11 . 3 5 1 .45 . 0 5 * 1. 18 . 3 0 1*30 . 0 7 CONC 1.52 . 12 1 .55 . 0 2 * 1 .09 . 3 6 1 .54 , . 0 1 * PEOB . 3 7 . 9 6 1.02 . 4 4 . 6 1 , 8 3 1 .04 , 4 0 TASC . 9 5 . 4 9 1.34 . 10 1. 43 . 1 5 1*32 . 06 IARS a. 2 0 . 2 9 1 .11 . 3 1 2 . 4 5 . 0 0 5 * 1 .39 . 0 3 * IARF . 9 2 . 5 1 1, 17 . 2 3 1 .96 , 0 3 * 1 . 2 6 . 10 MANX 1.04 . 41 1 .25 . 16 1. 25 ,*25 1 .22 . 12 VALSOC . 7 7 . 6 6 1. 12 . 2 9 . 6 6 ,:78 , 9 5 . 5 8 SELFCON . 9 4 . 5 0 1 .45 . 0 5 * . 86 , i58 1 .26 . 09 ENJOY 1.04 . 4 0 . 7 5 . 84 . 9 5 . 4 9 . 8 2 , 83 VALSEL . 4 1 . 9 4 1 .56 . 0 2 * . 6 6 . 7 8 1 .17 L18 *p < . 0 5 Since moderate d e p a r t u r e s from the assumption of homogeneity of variance do not s e r i o u s l y a f f e c t the sampling d i s t r i b u t i o n of the F - s t a t i s t i c (Winer, 1 9 7 1 , p, 205) i t was decided not to r e j e c t the n u l l h y p o t h e s i s that there would be 90 no s i g n i f i c a n t d i f f e r e n c e s among the c l a s s v a r i a n c e s . The analyses proceded as i f a l l the c l a s s v a r i a n c e s were es t i m a t e s of the same pooled v a r i a n c e . Thus the d e v i a t i o n s c o r e s were s t a n d a r d i z e d w i t h i n each c l a s s t o a mean of 0 and a standard d e v i a t i o n of 1. From the t e s t s of a n a l y s i s of v a r i a n c e and homogeneity of v a r i a n c e on s e p a r a t e types of c l a s s o r g a n i z a t i o n s ( s p l i t s ) i t appeared t h a t none of the grade groupings was any more extreme than the other* T h e r e f o r e , grade type groupings were net c o n s i d e r e d i n f u r t h e r a n a l y s e s . The e f f e c t s of the s t a n d a r d i z a t i o n on the i n t e r - s c a l e c o r r e l a t i o n s may he seen i n Table 13. The d i f f e r e n c e s are s l i g h t . In a l l f u t u r e d i s c u s s i o n the word " s c o r e s " , when used i n c o n j u n c t i o n with achievement or a f f e c t i v e s c a l e s , w i l l mean sc o r e s s t a n d a r d i z e d w i t h i n c l a s s with mean zero and standard d e v i a t i o n one. I n c l u s i o n or E x c l u s i o n of TASC The second p r e l i m i n a r y question to be c o n s i d e r e d was whether or not the Test Anxiety Scale f o r C h i l d r e n (TASC) was t o be i n c l u d e d i n f u r t h e r a n a l y s e s . T h i s d e c i s i o n r e s t e d on whether or not TASC c o u l d be shown to measure something d i f f e r e n t from Anxiety i n Mathematics (MANX) and which s c a l e c o u l d be shewn t c have g r e a t e r p r e d i c t i v e and c o n c u r r e n t v a l i d i t y i n the measurement of a n x i e t y i n the mathematics classroom. A l l c o r r e l a t i o n a l and l i n e a r r e g r e s s i o n a n a l y s e s 91 Table 13 Table of C o r r e l a t i o n s Between Achievement and A f f e c t i v e V a r i a b l e s Using Scores Standardized Within C l a s s , and Baw Scores* COMP CONC PBOB TASC IABS IABF MANX VSOC SCON ENJOl COMP 1. 00 CONC S E ' . 6 4 . 7 0 1.00 PBOB S E . 6 6 . 6 9 . 6 6 .72 1.00 TASC S E - . 23 - . 2 4 - . 3 3 - . 3 3 - , .28 - . 3 1 1.00 IAES S E . 16 . 1 6 . 0 9 . 13 .10 .13 - . 14 - . 1 4 1.00 IABF S B . 01 . 0 3 - . 0 3 .01 - , 0 6 - . 0 3 .08 .09 .26 .28 1.00 MANX S B - . 42 - . 3 6 - . 3 9 - . 3 3 - i 3 5 - . 3 2 . 33 .32 - . 2 5 - . 2 4 . 0 2 .01 1.00 VALSOC S B . 18 . 16 . 2 5 .21 . 1 7 . 15 - . 0 9 -,.03 .16 .18 .09 . 12 - . 3 6 - . 3 6 1.00 SELFCON S B . 4 5 .41 . 4 9 .46 . 4 5 .43 - . 4 3 - . 4 4 . 2 6 , 2 7 - . 0 7 - . 0 4 - . 7 1 - , 72 .34 . 3 2 1.00 ENJOY S B . 32 . 2 5 . 27 .21 . 2 7 .22 - . 1 1 - . 0 9 .22 .21 . 0 7 . 10 - .72 - . 72 .41 , 42 . 5 5 . 55 1.00 VALSEL S B . 17 . 1 5 . 1 9 .16 .14 .12 - . 0 3 , 0 2 . 16 . 16 . 10 ,. 12 - . 3 7 - . 37 .67 . 7 0 .30 - 29 . 4 9 * 51 *S = Standardized score c o r r e l a t i o n s , E = Baw score c o r r e l a t i o n s were performed u s i n g the T r i a n g u l a r B e g r e s s i o n Package (TBP) w r i t t e n and supported by the U n i v e r s i t y of B r i t i s h Columbia computing s t a f f (Le S T e n i s c i , 1977). F i r s t , the c o r r e l a t i o n between MANX and TASC was . 3 2 . T h i s i n d i c a t e d t h a t the two s c a l e s were measuring d i f f e r e n t 92 c o n s t r u c t s . Moreover from T a b l e 14 i t can be seen t h a t MANX accounted f o r a g r e a t e r p r o p o r t i o n of v a r i a n c e i n t h e achievement v a r i a b l e s than d i d TASC. A l t h o u g h MANX and TASC T a b l e 14 Sguared C o r r e l a t i o n s Between MANX, TASC and t h e Achievement V a r i a b l e s COMP CONC PEOB MANX MANX .17 .15 .13 1.00 TASC .05 .11 .08 .10 MANX • TASC .18 .20 .16 combined t o c o n t r i b u t e a s i g n i f i c a n t p r o p o r t i o n o f e x p l a i n e d v a r i a n c e (p < , 0 0 1 ) , the a d d i t i o n a l p r o p o r t i o n o f e x p l a i n e d v a r i a n c e a t t r i b u t a b l e t o 1ASC was a t most 5% i n t h e case of CONC. However, when compared w i t h t h e p r o p o r t i o n of v a r i a n c e e x p l a i n e d by MANX alone (15%) , t h e 5% was c o n s i d e r e d s u b s t a n t i a l . On t h e o t h e r hand the d a t a i n T a b l e 15 showed t h a t when t h e o t h e r mathematics a f f e c t i v e s c a l e s were t a k e n i n t o a c c o u n t the i n c r e a s e i n e x p l a i n e d v a r i a n c e o f t h e achievement v a r i a b l e s when TASC was added was a t most 2%. I t appeared t h a t the i n f l u e n c e of TASC was s m a l l * I n terms o f c o n s t r u c t v a l i d i t y MANX appeared t o be t h e most a p p r o p r i a t e measure to use i n t h e f o l l o w i n g a n a l y s e s . However, the i s s u e o f whether c r not MANX c o u l d be shown t o have a degree o f c o n c u r r e n t v a l i d i t y as a measure of mathematics a n x i e t y was s t i l l t o be addressed* 93 T a b l e 15 P a r t i a l C o r r e l a t i o n s , and M u l t i p l e Squared C o r r e l a t i o n s of TASC when P r e d i c t i n g Achievement S c o r e s S q u a r e d 2 M u l t i p l e E P a r t i a l C o r r e l a t i o n Without With of TASC* F prob TASC TASC COMP -.0341 .446 .2192 .2193 CONC -.1218 .006 .2447 .2560 PEOB -. 1597 .0004 .2069 *2271 *A11 o t h e r a f f e c t i v e v a r i a b l e s h e l d c o n s t a n t . 2A11 o t h e r a f f e c t i v e v a r i a b l e s i n t h e r e g r e s s i o n e q u a t i o n * There were two v a l i d a t i n q measures used. The f i r s t o f th e s e was BANK (the r a n k i n g by t e a c h e r s o f s t u d e n t s on a d e s c r i p t i o n of b e h a v i o r s which may be a s s o c i a t e d w i t h an " e m o t i o n a l b l o c k " ) , The second was the s e t of o b s e r v e d b e h a v i o r a l c h a r a c t e r i s t i c s o f a n x i e t y n o t i c e d by t e a c h e r s i n th e mathematics c l a s s r o o m . The BANK s c o r e s were d i c h o t o m i z e d w i t h i n each c l a s s , t he lower h a l f h a v i n q a s c o r e o f z e r o (0) and t h e upper h a l f a s c o r e o f one ( 1 ) . To q i v e some e v i d e n c e o f c o n s i s t e n c y p o i n t b i s e r i a l c o r r e l a t i o n s were then c a l c u l a t e d between BANK and each o f t h e b e h a v i o r a l c h a r a c t e r i s t i c s . They ranged between .09 and .23. See T a b l e 16. A t a b l e c f i n t e r c o r r e l a t i o n s of t h e c h a r a c t e r i s t i c s may be found i n Appendix H. T r e a t i n g each o f t h e b e h a v i o r s as an i t e m of a t e s t , a Hoyt e s t i m a t e of r e l i a b i l i t y was c a l c u l a t e d . The r e s u l t was .70. T h i s was not a l e g i t i m a t e use of t h e Hoyt e s t i m a t e as t h e 1033 response s e t s were made by o n l y 56 t e a c h e r s . Although i t d i d suggest t h a t t h e t e a c h e r 94 r e p o r t v a r i a b l e s were c o n s i s t e n t with each o t h e r , i t may a l s o have been a r e s u l t of the "halo e f f e c t . " T y p i c a l l y a s t r o n g i n i t i a l p o s i t i v e or negative impression o f a person, group, or event tends to i n f l u e n c e r a t i n g s on a l l subsequent o b s e r v a t i o n . (Isaac S M i c h a e l , 1971, p. 58.) In t u r n , only one of the t e a c h e r r e p o r t v a r i a b l e s , #6, Hands Shake, c o r r e l a t e d more s t r o n q l y with with TASC than i t d i d with MANX. The d i f f e r e n c e was not s i g n i f i c a n t . In a d d i t i o n the c o r r e l a t i o n s o f the behaviors with the achievement v a r i a b l e s , although not h i g h , are a l l i n the expected d i r e c t i o n . The n e g a t i v e c o r r e l a t i o n s are an a r t i f a c t of the s c o r i n g of the b e h a v i o r a l c h a r a c t e r i s t i c s ; one f o r the presence o f the behavior and zero f o r i t s absence. A summary of these data may be found i n Table 16* This evidence of concurrent v a l i d i t y , i n a d d i t i o n to t h a t of the c o n s t r u c t v a l i d i t y noted above, suggested MANX was the most a p p r o p r i a t e v a r i a b l e to r e t a i n f o r the analyses of the hypotheses of the study,. STATISTICAL PBOCEDOBES S t a t i s t i c a l S i g n i f i c a n c e The l e v e l o f s i g n i f i c a n c e chosen f o r t h i s study was .01. This l e v e l was chosen i n order to reduce the o v e r a l l e r r o r r a t e f o r the e n t i r e s e t of analyses. I t was f e l t t h a t t h i s was necessary because of the l a r g e number of i m p l i e d t e s t s o f s i g n i f i c a n c e i n r e g r e s s i o n a n a l y s i s . Indeed, f o r any 95 Table 16 I n t e r - c o r r e l a t i o n s among BANK, C h a r a c t e r i s t i c s from a B e h a v i o r a l C h e c k l i s t , t h e Achievement V a r i a b l e s , TASC, and MANX C h a r a c t e r i s t i c 1 2 3 4 5 6 7 8 9 BANK BANK -.33 -. 40 -.34 -. 18 -.26 -. 16 -.18 -.17 -.26 1.00 TASC .13 . 14 .16 .04 .09 . 10 .07 .08 . 13 -.22 MANX . 23 .20 .23 .13 . 18 .09 ,16 .09 .18 -.36 COME -.34 -. 24 25 -. 17 -.19 -.10 -.14 -.14 -.29 .40 CONC -.32 -,.24 -.26 -.14 -.21 -. 12 -.in - . 1 5 r.25 .42 PBOB -.30 -.25 -.25 -.13 -.22 -. 10 -.15 -.11 -,25 .41 1. Bandom Answers 2. Appears Tense 3. Expresses Anxiety 4. D i s r u p t i v e Behavior 5. Expresses I n a b i l i t y 6. Hands Shake 7. Says Mathematics Useless 8. Befuses to Answer 9. F i d g e t s More s i n g l e s e l e c t i o n o f a v a r i a b l e as the st r o n g e s t p r e d i c t o r from amongst k independent v a r i a b l e s , Kupper, Stewart, and Wi l l i a m s (1976) suggest t h a t alpha d i v i d e d by k would be an a p p r o p r i a t e l e v e l with which t o c o n t r o l Type I e r r o r , They a l s o note that t h i s would i n c r e a s e the p r o b a b i l i t y of a Type I I e r r o r which may be j u s t as s e r i o u s and th a t a more l i b e r a l alpha c o u l d be chosen "when s p e c i f i c s i g n i f i c a n t r e l a t i o n s h i p s are a n t i c i p a t e d a p r i o r i " (p. 14). Th e r e f o r e , as the number of independent v a r i a b l e s f o r the t e s t s of t h i s study t y p i c a l l y were between t h r e e and seven, an alpha l e v e l of .01 was consi d e r e d reasonable. I n a d d i t i o n , because of the l a r g e s i z e of the sample, the power was co n s i d e r e d adequate to keep the Type I I e r r o r r a t e t o an accept a b l e l e v e l . Sex D i f f e r e n c e s The n u l l h ypothesis was t h a t t h e r e was no s i g n i f i c a n t d i f f e r e n c e between the v a r i a n c e - c o v a r i a n c e matrix o f the males 96 and t h a t o f t h e f e m a l e s . A l t h o u g h sex d i f f e r e n c e s a r e o f t e n n o t e d i n terms of d i f f e r e n c e s between means, t h e hypotheses of the p r e s e n t s t u d y were c o r r e l a t i o n a l i n n a t u r e o r , as i n t h e case o f t h e f a c t o r a n a l y s i s , dependent upon the v a r i a n c e - c o v a r i a n c e m a t r i x . D i f f e r e n c e s between means were o f l i t t l e i m p o r t a n c e * However, f o r i n t e r e s t , t h e raw s c o r e means and d i f f e r e n c e s were examined and i n c l u d e d i n Appendix G. I n t h e e vent t h a t t h e n u l l h y p o t h e s i s was r e j e c t e d s e p a r a t e a n a l y s e s by sex were t o be u ndertaken. To reduce t h e r i s k o f a Type I I e r r o r t h i s h y p o t h e s i s was t e s t e d w i t h p = .10. G l a s s and S t a n l e y (1970) note t h a t " I t might be a d v i s e a b l e i n some c i r c u m s t a n c e s t o run a r i s k of a Type I e r r o r as l a r g e as .10, . . . t o i n s u r e a r e a s o n a b l e power f o r a t e s t " (p. 287). The Bex procedure as d e s c r i b e d by Winer (1971, p. 595) was used and was c a l c u l a t e d by a one way m u l t i v a r i a t e a n a l y s i s o f v a r i a n c e program (OWMAB) developed by the F a c u l t y o f P s y c h o l o g y at t h e U n i v e r s i t y o f B r i t i s h C o lumbia; I t s h o u l d be understood t h a t i n t h e f o l l o w i n g d e s c r i p t i o n i t was assumed t h a t a s e p a r a t e a n a l y s i s f o r males and f e m a l e s was t o be done i f the n u l l h y p o t h e s i s o f e q u a l v a r i a n c e - c o v a r i a n c e m a t r i c e s was not a c c e p t e d . However, f o r b r e v i t y t h e d e s c r i p t i o n w i l l be o f one t e s t . A f f e c t i v e I n t e r - S c a l e B e l a t i o n s h i p s The n u l l h y p o t h e s i s of no s i q n i f i c a n t Pearson product-moment c o r r e l a t i o n s between a f f e c t i v e s c a l e s was 97 t e s t e d with, p = .01. The F r a t i o s and p r o b a b i l i t i e s were c a l c u l a t e d by the computer program, T r i a n g u l a r Regression Package (TRP) (Le & T e n i s c i , 1977) To study the independence of the a f f e c t i v e v a r i a b l e s a p r i n c i p a l component f a c t o r a n a l y s i s was performed f o l l o w e d by ortho g o n a l varimax rotation,. The r e s u l t s were compared with the f a c t o r s t r u c t u r e p r e d i c t e d by the achievement M o t i v a t i o n model. a l l f a c t o r a n a l y s e s , r o t a t i o n s and f a c t o r s c o r e c o e f f i c i e n t generations were performed with the a l b e r t a General F a c t o r a n a l y s i s Program (aGFaP) at the U n i v e r s i t y of B r i t i s h Columbia computer c e n t r e . The program was authored by Hakstian and Bay (1973). Reasons f o r using the r e s u l t s of the p r i n c i p a l component a n a l y s i s r a t h e r than the r e s u l t s of a common f a c t o r a n a l y s i s were (1) the c u r r e n t study was c o n s i d e r e d to be one of e x p l o r a t i o n , (2) orthogonal or near orthogonal measures were d e s i r e d , and (3) there was no indeterminacy present i n the f a c t o r score c o e f f i c i e n t computation (Hakstian & Bay, 1973, p. 42-3.) Two c r i t e r i a were used to determine the number of f a c t o r s to be r e t a i n e d i n the a n a l y s i s ; the Kaiser-Gutman eigen-value c r i t e r i o n and the C a t t e l l " s c r e e " t e s t . The Kaiser-Gutman c r i t e r i o n s t a t e d t h a t the number of f a c t o r s t o be r e t a i n e d s h o u l d equal the number of eigen-values g r e a t e r than 1.00 as " t h i s marks the l a s t f a c t o r with s i g n i f i c a n t 98 a l p h a c o e f f i c i e n t c f homogeniety" ( C a t t e l l , 1966, p. 207). The " s c r e e " t e s t s u g g e s t e d t h a t the number of f a c t o r s t o be r e t a i n e d s h o u l d be determined by t h e " s c r e e " r e m a i n i n g a t the bottom of t h e c u r v e when the e i g e n - v a l u e s were p l o t t e d from h i g h e s t t o l o w e s t . T y p i c a l l y t h e c u r v e f a l l s i n a c u r v i l i n e a r f a s h i o n and t h e n becomes a b s o l u t e l y s t r a i g h t ( e x c e p t , sometimes, f o r minor, i r r e g u l a r d e p a r t u r e s ) . . . . I n l a r g e samples t h e r e a r e u s u a l l y c l e a r r e p r e s e n t a t i o n s of two not one, s u c c e s s i v e s t r a i g h t s c r e e s l o p e s . In t h i s case one t a k e s the l i n e o f t h e upper s l o p e . ( C a t t e l l , 1966, p. 206) To st u d y the f a c t o r s t r u c t u r e t h e components were o r t h o g o n a l l y r o t a t e d u s i n g t h e varimax p r o c e d u r e . C a t t e l l (1966) noted t h a t a l l a n a l y t i c methods (methods maximizing a s i n g l e m a t h e m a t i c a l f u n c t i o n ) of f i n d i n g s i m p l e s t r u c t u r e by r o t a t i o n o f f a c t o r s were s u b j e c t t o l i m i t a t i o n s . However, N u n n a l l y (1967) s t a t e d The varimax method has proved v e r y s u c c e s s f u l as an a n a l y t i c a l approach t o o b t a i n i n g an o r t h o g o n a l r o t a t i o n o f f a c t o r s . Even i n t h o s e c a s e s where t h e r e s u l t s do n o t meet t h e i n v e s t i g a t o r ' s c o n c e p t of a s i m p l e s t r u c t u r e , the s o l u t i o n u s u a l l y i s c l o s e enough t o g r e a t l y reduce t h e l a b o r of f i n d i n g a s a t i s f a c t o r y s o l u t i o n . (p. 333) A f f e c t i v e - a c h i e v e m e n t R e l a t i o n s h i p s T h i s a n a l y s i s was done i n two s t a g e s . The f i r s t s e t o f a n a l y s e s used t h e s c o r e s s t a n d a r d i z e d w i t h i n each c l a s s . The second s e t used f a c t o r s c o r e s which were a l s o s t a n d a r d i z e d w i t h i n each c l a s s . S t a n d a r d s c o r e a n a l y s i s . The h y p o t h e s i s of no 99 s i g n i f i c a n t P e a r s o n p r o d u c t moment c o r r e l a t i o n s between each a f f e c t i v e v a r i a b l e and each achievement v a r i a b l e was t e s t e d w i t h p = .01 u s i n g the computer program TEP. The q u a d r a t i c r e l a t i o n s h i p o f a f f e c t i v e t o achievement v a r i a b l e s was t e s t e d by c o r r e l a t i n g t h e squared s c o r e s o f t h e a f f e c t i v e v a r i a b l e s w i t h t h e s c o r e s of the achievement v a r i a b l e s . The h y p o t h e s i s o f no s i q n i f i c a n t m u l t i p l e c o r r e l a t i o n s was t e s t e d u s i n q t h e Le and T e n i s c i (1977) T r i a n g u l a r R e g r e s s i o n Packaqe (TEP) computer proqram. A m u l t i p l e r e g r e s s i o n e q u a t i o n h a v i n q a minimum number o f a f f e c t i v e v a r i a b l e s was developed by s t e p w i s e r e q r e s s i o n . S t e p w i s e r e g r e s s i o n a n a l y s i s i s the p r o c e s s of s e l e c t i n g an in d e p e n d e n t v a r i a b l e w i t h t h e l a r g e s t s i g n i f i c a n t p a r t i a l c o r r e l a t i o n . The p a r t i a l c o r r e l a t i o n i s the c o r r e l a t i o n o f th e g i v e n v a r i a b l e w i t h t h e dependent v a r i a b l e h a v i n g the e f f e c t s of t h e a l r e a d y s e l e c t e d v a r i a b l e s h e l d c o n s t a n t . The s e l e c t e d v a r i a b l e s a r e t h e n scanned i n case any o f t h e s e l e c t e d v a r i a b l e s have had t h e i r p a r t i a l c o r r e l a t i o n reduced below s i g n i f i c a n c e by the a d d i t i o n of the new member. Those w i t h n o n - s i g n i f i c a n t p a r t i a l s a r e d e l e t e d and the p r o c e s s b e g i n s a g a i n u n t i l no new v a r i a b l e s have a s i g n i f i c a n t p a r t i a l * The h y p o t h e s i s t h a t t h e r e was no s i g n i f i c a n t d i f f e r e n c e between t h e E 2 of the r e s u l t i n g m i n i m a l e q u a t i o n and t h a t produced w i t h a l l t h e a f f e c t i v e v a r i a b l e s was t e s t e d u s i n q f o r m u l a from K e r l i n g e r and Pedhazur (1973, p. 71) 100 where k^ _ equals the number of independent v a r i a b l e s of the s m a l l e s t B 2 and k^ equals the number of independent v a r i a b l e s of the l a r q e s t E 2 . f a c t o r score analysis,. The f a c t o r s were used t o generate a f a c t o r s c o r e s c o e f f i c i e n t matrix. The f a c t o r s c o r e c o e f f i c i e n t s were the m u l t i p l e r e g r e s s i o n c o e f f i c i e n t s which r e l a t e d each of the a f f e c t i v e v a r i a b l e s to each f a c t o r . F a c t o r s c o r e s were c a l c u l a t e d by m u l t i p l y i n g the score of each student on each a f f e c t i v e s c a l e by the corresponding c o e f f i c i e n t f o r a gi v e n f a c t o r and summing acr o s s the seven a f f e c t i v e v a r i a b l e s f o r each o f the t h r e e f a c t o r s . Because the a f f e c t i v e v a r i a b l e s were i n t e r r e l a t e d and because the Achievement M o t i v a t i o n model suggested i n t e r a c t i o n s among i t s t h r e e components, s e v e r a l m u l t i p l e r e g r e s s i o n a n a l y s e s were performed using the f a c t o r s c o r e s and t h e i r i n t e r a c t i o n s . The i n t e r a c t i o n terms were c a l c u l a t e d by t a k i n g the product of the s c o r e s of the f a c t o r s and using the r e s u l t i n g s c o r e s as independent v a r i a b l e s i n the r e g r e s s i o n equations. The hypothesis t h a t f a c t o r s c o r e i n t e r a c t i o n s would not s i g n i f i c a n t l y i n c r e a s e the e x p l a i n e d v a r i a n c e of each o f the a f f e c t i v e v a r i a b l e s was t e s t e d , with p = .01, using stepwise r e g r e s s i o n . 101 Cross V a l i d a t i o n C ross v a l i d a t i o n i s the process of c o n f i r m i n g the r e s u l t s o f an a n a l y s i s performed on one sample through the comparison of the same an a l y s e s performed on a s i m i l a r sample. In e d u c a t i o n a l r e s e a r c h i t i s o f t e n d i f f i c u l t t o get a second s i m i l a r sample. The l a r g e i n i t i a l sample of t h i s study was i d e a l because s p l i t t i n g the sample i n two equal p a r t s would not s u b s t a n t i a l l y reduce the power to t e s t the hypotheses. Because i t was the i n t e n t i o n t o examine a number of p o s s i b l e models and to s e l e c t the best one, the sample was randomly d i v i d e d i n t o two p a r t s . The f i r s t sample, the normative sample, would be used as the set from which the best model was chosen. I f a l a r q e number of models was qenerated t h i s procedure would tend to maximize on chance. Thus the second sample would be r e s e r v e d s o l e l y f o r c r o s s - v a l i d a t i o n . The procedure used to s e l e c t the samples was to a s s i q n each s u b j e c t a random number and then f o r each c l a s s the median random number was found. A l l the s u b j e c t s with a number below the median were put i n t o one qroup and a l l above were put i n t o the o t h e r . A second random number was assigned to the s u b j e c t with the median random number, I f the second number was above .5 the s u b j e c t was assigned to one group and i f below, to the o t h e r . The r e s u l t i n g N's were 511 (M = 275, F = 236) f o r the normative sample (Sample 1) and 522 (M = 254, F = 268) f o r the c r o s s - v a l i d a t i o n sample (Sample 2 ) . The f o l l o w n g comparisons were made between Sample 1 and Sample 2. 102 Cross V a l i d a t i o n Hypotheses I t was hypothesised t h a t there was no s i g n i f i c a n t d i f f e r e n c e between the v a r i a n c e - c o v a r i a n c e matrix of the males and t h a t of the females. I t was hypothesized t h a t the c o r r e l a t i o n s among the a f f e c t i v e and achievement v a r i a b l e s would be s i m i l a r t o those i n Sample 1. . T h i s was t e s t e d using the Box t e s t f o r equal v a r i a n c e - c o v a r i a n c e matrices* The f a c t o r a n a l y s i s was repeated using the same number of f a c t o r s found i n the i n i t i a l a n a l y s i s . &n or t h o g o n a l Procrustean t r a n s f o r m a t i o n was made r o t a t i n g the f a c t o r s of the second s o l u t i o n to the f a c t o r space of the f i r s t * The stepwise r e g r e s s i o n a n a l y s i s was repeated f o r Sample 2. 103 Chapter 4 BESULTS INTEODUCTION I n C h a p t e r s 1 and 2, a l i t e r a t u r e was c i t e d which i n d i c a t e d t h a t an " e m o t i o n a l b l o c k " i n h i b i t e d t h e mathematics achievement of a s i g n i f i c a n t p r o p o r t i o n o f mathematics s t u d e n t s . A n x i e t y , enjoyment, v a l u e , and s e l f - c o n c e p t of a b i l i t y i n mathematics were i d e n t i f i e d as t h e components o f the "block",* The Achievement M o t i v a t i o n model s u g g e s t e d p o s s i b l e i n t e r a c t i o n s among t h e components when r e l a t e d t o achievement m o t i v a t i o n . A f u r t h e r v a r i a b l e , l o c u s o f c o n t r o l o r achievement r e s p o n s i b i l i t y , was suggested by t h e model. In Chapter 3 i t was argued t h a t f o u r o f the Sandman (1973) s c a l e s would be the most a p p r o p r i a t e measures o f t h e f o l l o w i n g v a r i a b l e s : a n x i e t y o f mathematics (MANX) 1, enjoyment o f mathematics (ENJOY), v a l u e o f mathematics f o r s o c i e t y (VALSOC), and s e l f - c o n c e p t o f mathematics achievement (SELFCON). A l s o i n c l u d e d were the Test A n x i e t y S c a l e f o r C h i l d r e n (TASC), a more g e n e r a l measure o f a n x i e t y , the Value i l h e c a p i t a l i z e d terms i n the p a r e n t h e s e s w i l l be used t h r o u g h o u t t h e d i s c u s s i o n and i n the t a b l e s . 104 of Mathematics f o r Oneself Scale (VALSEL) (developed by the experimenter) and the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y s c a l e , a measure of Locus of C o n t r o l * T h i s s c a l e was s p l i t i n t o two components; r e s p o n s i b i l i t y f o r success (IARS) and r e s p o n s i b i l i t y f o r f a i l u r e (IABF). Teachers ranked s t u d e n t s on a d e s c r i p t i o n of behaviors t y p i c a l of an "emotional b l o c k " (BANK), and checked a l i s t of s p e c i f i c behaviors a s s o c i a t e d with the " b l o c k . " Three achievement measures were s e l e c t e d ; the A r i t h m e t i c Computation s c a l e from the S t a n f o r d Achievement Test; Form W (COMP) and the Mathematics Concepts (CONC) and Mathematics Problem S o l v i n g s c a l e s (Level 12) from the Canadian Test o f B a s i c S k i l l s ; Form 4 (PBOB). The d e s i g n , procedure and a d m i n i s t r a t i o n of the m a t e r i a l s used with a sample of 1033 s u b j e c t s were a l s o d e s c r i b e d i n Chapter 3. In a d d i t i o n , a p r e l i m i n a r y a n a l y s i s showed t h a t some c l a s s means were s i g n i f i c a n t l y d i f f e r e n t and t h a t homogeneity of c l a s s v a r i a n c e could be accepted. T h e r e f o r e , the s c o r e s were s t a n d a r d i z e d with a c l a s s mean of z e r o and a standard d e v i a t i o n of one. A second p r e l i m i n a r y a n a l y s i s of the concurrent and c o n s t r u c t v a l i d i t y of the TASC i n comparison with the Sandman Mathematics Anxiety Scale was performed using the t h r e e achievement measures and the two forms of teacher response. I t was decided t o r e t a i n the Mathematics Anxiety Scale and to e l i m i n a t e TASC from f u r t h e r a n a l y s e s . A summary of hypotheses and s t a t i s t i c a l procedures used may be found i n the l a s t 105 s e c t i o n of C h a p t e r 3. In t h i s c h a p t e r the r e s u l t s o f the a n a l y s e s and c r o s s v a l i d a t i o n p e r t a i n i n g t o the h y p o t h e s e s a r e p r e s e n t e d . SEX DIFFERENCES The f o c u s o f t h i s s t u d y was t h e r e l a t i o n s h i p o f the a f f e c t i v e v a r i a b l e s t o the achievement v a r i a b l e s . T h e r e f o r e , d i f f e r e n c e s , due t o s e x , between c o r r e s p o n d i n g c o r r e l a t i o n s were o f more i n t e r e s t t h a n d i f f e r e n c e s between means* However, the raw s c o r e s c a l e means, s t a n d a r d d e v i a t i o n s and d i f f e r e n c e s between means f o r males and f e m a l e s may be found i n Appendix G. The c o r r e l a t i o n s among the v a r i a b l e s f o r b o t h sexes may be found i n Table 17. Because o f the redundancy of i n f o r m a t i o n i n t h e m a t r i x the h y p o t h e s i s t h a t t h e r e was no s i g n i f i c a n t d i f f e r e n c e s between the v a r i a n c e - c o v a r i a n c e m a t r i x o f t h e males and t h a t o f t h e f e m a l e s was t e s t e d u s i n g t h e Box procedure as o u t l i n e d i n Winer (1971, p, 595). I n o r d e r t o reduce t h e p r o b a b i l i t y o f f a l s e l y a c c e p t i n g the n u l l h y p o t h e s i s the s i g n i f i c a n c e was s e t a t .10. The F r a t i o was 1.245 w i t h degrees of freedom 55 and 798 277. F o r p < .10 and c o r r e s p o n d i n g degrees of freedom F = 1.25. The n u l l h y p o t h e s i s was n o t r e j e c t e d , and t h e data from t h e male and female data s e t s were pool e d and the f o l l o w i n g h y p o t h e s e s were t e s t e d u s i n g o n l y the pooled d a t a . 106 T a b l e 17 C o r r e l a t i o n s of the a f f e c t i v e and Achievement S c a l e s f o r Males and Females Males COMP CONC PBOB IABS IABF MANX VSOC SCON ENJOY CONC .64 1.00 PBOB .66 -64 1 .00 IABS . 15 . 13 . 13 1.00 IABF -.03 -.07 -.12 .20 1.00 MANX -.40 -.39 -.33 -.29 -.04 1.00 VALSOC .19 ,.19 .11 .15 .11 -.35 1. 00 SELFCON .51 .54 .48 .33 -.05 -.68 .34 1.00 ENJOY .34 .26 .26 .25 .02 -.73 :37 .56 1.00 VALSEL .12 . 12 .06 ,19 .07 -.37 . 59 .34 .51 Female CONC .70 1.00 PBOB .67 .69 1.00 IABS .24 . 10 .12 1.00 IABF .08 -.02 .02 .37 1.00 MANX •.43 -.39 -.33 -.19 -.06 1.00 VAL SOC .23 .25 .15 .15 .11 -.33 1, 00 SELFCON .44 ,49 -45 .15 -.03 -.74 .241.00 ENJOY .30 .21 .22 .18 .23 -.73 .35 .57 VALSEL .24 ,19 .14 .14 . 10 -.38 .71 .26 AFFECTIVE INTEB-SCALE HYPOTHESES C o r r e l a t i o n s I n the f o l l o w i n g a n a l y s e s r e f e r e n c e w i l l be made to c o r r e l a t i o n s , m u l t i p l e c o r r e l a t i o n s , s q u a r e d m u l t i p l e c o r r e l a t i o n s , and p r o p o r t i o n o f e x p l a i n e d v a r i a n c e . The term c o r r e l a t i o n w i l l be used to. denote a Pearson p r o d u c t moment c o r r e l a t i o n . Note t h a t when e i t h e r t h e c o r r e l a t i o n or m u l t i p l e c o r r e l a t i o n i s sq u a r e d t h e r e s u l t i s t h e p r o p o r t i o n of v a r i a n c e of t h e dependent v a r i a b l e e x p l a i n e d or p r e d i c t e d by t h e independent v a r i a b l e o r v a r i a b l e s . C o r r e l a t i o n s between each p a i r of the a f f e c t i v e 1 0 7 v a r i a b l e s were c a l c u l a t e d * The hyp o t h e s i s t h a t the c o r r e l a t i o n s were not s i g n i f i c a n t l y d i f f e r e n t from zero was t e s t e d a t the , 0 1 l e v e l * The r e s u l t s are shown i n Table 1 8 . Table 1 8 I n t e r - c o r r e l a t i o n s o f the A f f e c t i v e V a r i a b l e s IARS IAEF MANX VALSOC SELFCON ENJOY I A R F . 2 7 6 * * 1 , 0 0 0 MANX - . 2 5 1 * * - . 0 0 4 1 . 0 0 0 VALSOC . 1 4 3 * * . 1 0 4 * - . 3 4 1 * * 1 . 0 0 0 SELFCON . 2 4 4 * * - . 0 4 3 - . 7 0 2 * * . 2 9 6 * * 1 . 0 0 0 ENJOY . 2 2 0 * * . 1 1 6 * * - . 7 2 8 * * . 3 6 0 * * . 5 6 4 * * 1 . 0 0 0 VALSEL . 1 6 2 * * . 0 7 7 * - . 3 7 2 * * . 6 5 2 * * . 3 0 7 * * . 5 1 1 * * *p < . 0 5 ; * * F < . 0 1 Only two of the IARF c o r r e l a t i o n s with the other v a r i a b l e s were s i g n i f i c a n t (p < . 0 1 ) . Excepting the c o r r e l a t i o n with IARS of . 2 7 6 , the maximum was . 1 1 6 with ENJOY. Except f o r four o f t h e IARF c o r r e l a t i o n s , a l l oth e r s were d i f f e r e n t frcm zero a t the * 0 1 l e v e l or b e t t e r . T herefore i n 1 7 out of 2 1 c o r r e l a t i o n s the n u l l hypothesis was not accepted. Table 1 8 suggests t h a t there were a t l e a s t two groups of v a r i a b l e s ; the IABS and IARF p a i r and the r e s t of the v a r i a b l e s . T h i s was born out i n subsequent f a c t o r a n a l y s es. Althouqh net part of the formal hypotheses of the study, the a f f e c t i v e v a r i a b l e s were c o r r e l a t e d with teacher rankings of students and the Student-Behavior c h e c k l i s t . Note t h a t as the absence of a behavior was coded 0 and the presence 108 1, p o s i t i v e c o r r e l a t i o n s were expected with a n x i e t y and the a b i l i t y t o accept r e s p o n s i b i l i t y f o r f a i l u r e and n e g a t i v e c o r r e l a t i o n s were expected with the other v a r i a b l e s . The summary appears i n Table 19. Although the c o r r e l a t i o n s were weak (the maximum was .23 between MANX and Eandom Answers) o n l y seven out of 70 c o r r e l a t i o n s were i n the unexpected d i r e c t i o n . Of those seven, only one was s i g n i f i c a n t l y d i f f e r e n t from z e r o (p < ;01). The r e s u l t s gave some evidence o f the c o n s t r u c t v a l i d i t y of the a f f e c t i v e v a r i a b l e s . T able 19 C o r r e l a t i o n s between the A f f e c t i v e V a r i a b l e s , BANK, and the Student-Behavior C h e c k l i s t Behavior IAES IARF MANX VALSOC SELFCON ENJOY VALSEL Random -. 10** .04 .23** -. 13** -.20** -.13** -,06 Answers Appears -. 13**-.04 .15** -, 09* -.21** -.11** -.07 Tense Expresses -.05 .06* .20** -. 10** -.23** -, 16** -,i06 Anxiety D i s r u p t i v e -.10** .02 .09* -. 02 -.08* -.07* -.06 Behavior Expresses -.06 -.01 .19** -. 09* -.22** -.14** -.05 I n a b i l i t y Hands -.04 .02 ,05 05 -.06 .02 -06 Shake S t a t e s -,09* .03 .20** - .11** -.17** -.17** -.11** Mathematics Useless Refuses t o -.05 .03 .04 03 -.09* -.03 .00 Answer F i d g e t s -.11** .03 .16** -. 05 -.22** -.16** -.07 More RANK .07 -.03 -.29** , 18** .35** .16** .09* *p < ,05; **p < .01 109 F a c t o r A n a l y s i s A p r i n c i p a l component a n a l y s i s of the a f f e c t i v e v a r i a b l e s was performed which generated the f o l l o w i n g s e t of e i g e n - v a l u e s : 3.068, 1.206, 1,077, 0.683, 0.446, 0.310, and 0.210. See the graph below f o r the p l o t of the e i g e n - v a l u e s . "Scree" of the Eigen-Values from the P r i n c i p a l Component A n a l y s i s of the A f f e c t i v e V a r i a b l e s 3 Eigen- 2 Values 1 1 2 3 4 5 6 7 F a c t o r s I t was c l e a r from the graph t h a t t h r e e f a c t o r s should be r e t a i n e d a c c o r d i n g t o the " s c r e e " t e s t . T h i s agreed with the Kaiser-Guttman c r i t e r i o n , s i n c e t h e r e were three eigen-values g r e a t e r than 1.0. I t should be noted t h a t t h i s was the number of f a c t o r s p r e d i c t e d by the Achievement M o t i v a t i o n theory* 110 The t h r e e f a c t o r s accounted f o r 76% of the varian c e of the a f f e c t i v e v a r i a b l e s . T h i s was considered a c c e p t a b l e f o r f u r t h e r a n a l y s i s . In o r d e r to a i d the i n t e r p r e t a t i o n of the f a c t o r s , the thr e e f a c t o r s were o r t h o g o n a l l y r o t a t e d u s i n g the varimax procedure. The f a c t o r l o a d i n g s are shown i n Table 20. The Table 20 Fa c t o r l o a d i n g s o f the a f f e c t i v e V a r i a b l e s on the Or t h o g o n a l l y B c t a t e d , P r i n c i p a l Component Factors F a c t o r 1 F a c t o r 2 F a c t o r 3 IABS .3206 .7372 -.0252 IABF -.1441 ,8427 .1358 MANX -.8927 -.0554 -.1992 VALSOC .1695 .0662 .8794 SELFCON .8672 .0130 ,1096 ENJOY .7603 .1290 .3621 VALSEL .2589 .0544 .8657 three f a c t o r s were r e a d i l y i n t e r p r e t a b l e - F a c t o r 1, having the h i g h e s t l o a d i n g s from MANX, SELFCON and ENJOY, was c a l l e d the M o t i v a t i o n a l F a c t o r (MF) . Note t h a t the negative l o a d i n g s of MANX were a r t i f a c t s of the s c o r i n g . F a c t o r 2 having high l o a d i n g s from the two I n t e l l e c t u a l Achievement E e s p o n s i b i l i t y s c a l e s , was c a l l e d the Achievement E e s p o n s i b i l i t y F a c t o r (ABF). F a c t o r 3 was i d e n t i f i e d as the Value F a c t o r (VF) because of the high l o a d i n g s from the VALSOC and VALSEL S c a l e s . With r e s p e c t to the hypothesized simple s t r u c t u r e , IABS loaded .321 on Factor 1 and ENJOY loaded .362 on F a c t o r 1 1 1 2. However, i n t h e l i g h t of t h e much s t r o n g e r l o a d i n g s of the main components, the s t r u c t u r e was w e l l d e f i n e d . The c o m p l e x i t i e s t h a t o c c u r r e d may have been a r e s u l t o f t h e r e q u i r e m e n t o f o r t h o g o n a l i t y m a i n t a i n e d i n t h i s p r e s e n t s t u d y . C a t t e l l (1966) says " o r t h o g o n a l i t y and s i m p l e s t r u c t u r e a r e c o n t r a d i c t i o n s . Only i n v e r y r a r e c a s e s do f a c t o r s happen t o be o r t h o g o n a l " (p. 186). T h i s a n a l y s i s d i d not s u p p o r t the f a c t o r s t r u c t u r e h y p o t h e s i z e d i n Chapter 1 which was d e r i v e d from t h e t h e o r y of Achievement M o t i v a t i o n . C o n t r a r y t o what was e x p e c t e d IARS and IAEF d i d not l o a d on the m o t i v a t i o n a l f a c t o r but l o a d e d on a f a c t o r of t h e i r own. I n a d d i t i o n SELFCON, r a t h e r t h a n f o r m i n g a f a c t o r of i t s own l o a d e d w i t h MANX and ENJOY, The c o r r e l a t i o n s among the a f f e c t i v e v a r i a b l e s showed a degree of dependence. From the Sandman . (1973) f a c t o r a n a l y s i s of the i t e m s of f o u r of t h e a f f e c t i v e s c a l e s i t was known t h a t t h e s c a l e s are not p e r f e c t r e p r e s e n t a t i o n s o f t h e i r c o n s t r u c t s . The o r t h o g o n a l r o t a t i o n , t h e n , a l l o w e d an i n t e r p r e t a t i o n o f the v a r i o u s components o f v a r i a n c e because by d e f i n i t i o n o r t h o g o n a l f a c t o r s a re independent and have c o r r e l a t i o n z e r o . AFFECTIVE-ACHIEVEMENT RELATIONSHIPS C o r r e l a t i o n s To t e s t t h e hypotheses t h a t t h e r e were l i n e a r and n o n - l i n e a r r e l a t i o n s between each o f t h e a f f e c t i v e v a r i a b l e s 112 and t h e achievement v a r i a b l e s , o r t h o g o n a l p o l y n o m i a l s o f degree t h r e e were c a l c u l a t e d . None o f t h e t h i r d degree terms were s i g n i f i c a n t l y c o r r e l a t e d w i t h t h e achievement s c o r e s and t h e r e f o r e o n l y the f i r s t and second degree terms were c o n s i d e r e d . Of t h e second degree terms two c o r r e l a t i o n s were m a r g i n a l , MANX wi t h PBOB and VALSOC with COMP, and none were s i g n i f i c a n t a t the ,*01 l e v e l . F u r t h e r , w i t h c o r r e l a t i o n s o f a t most .097 t h e p r o p o r t i o n o f e x p l a i n e d v a r i a n c e was a t most 0.94%. The second degree terms were n ot r e t a i n e d f o r f u r t h e r a n a l y s i s . In 17 o f t h e 21 f i r s t degree r e l a t i o n s the n u l l h y p o t h e s i s was n o t a c c e p t e d a t the .01 l e v e l . See T a b l e 21 f o r a summary o f t h e c o r r e l a t i o n s of l i n e a r and o r t h o g o n a l second degree terms o f t h e a f f e c t i v e v a r i a b l e s w i t h the achievement v a r i a b l e s * Three o f t h e IABS l i n e a r c o r r e l a t i o n s were s i g n i f i c a n t a t t h e ,.01 l e v e l o r b e t t e r . None of the IABF l i n e a r c o r r e l a t i o n s were s i g n i f i c a n t a t the .01 l e v e l . However, the IABF was r e t a i n e d i n t h e a n a l y s i s . The t h e o r e t i c a l i m p o r t a n c e o f t h e achievement r e s p o n s i b i l i t y v a r i a b l e was as a moderator v a r i a b l e . Thus i t was r e t a i n e d t o t e s t p o s s i b l e i n t e r a c t i o n s w i t h t h e o t h e r a f f e c t i v e v a r i a b l e s i n p r e d i c t i n g achievement. R e g r e s s i o n A n a l y s i s A s e r i e s o f r e g r e s s i o n a n a l y s e s were performed. The f i r s t model t o be t e s t e d was t h a t of s i m p l e l i n e a r m u l t i p l e 113 Table 21 C o r r e l a t i o n s of the F i r s t and Second Degree Terms of Orthogonal Polynomials of the A f f e c t i v e V a r i a b l e s with the Three Achievement V a r i a b l e s COMP CONC PBOB V a r i a b l e De gree and r F B a t i o F Prob r F B a t i o F Prob F r B a t i o F Prob I ABS 1 . 1 9 0 2 - . 0 0 6 1 9 . 1 . 0 2 1 . 0 0 0 . 8 5 6 . 1 2 1 . 2 0 3 7 . 5 7 . 2 6 9 . 0 0 6 , 6 1 1 . 128 *025 8 . 5 1 . 3 2 9 . 0 0 4 . 5 7 4 IABF 1 . 0 3 0 2 - . 0 0 3 . 4 5 1 . 0 0 5 . 5 6 0 . 9 0 1 - . 0 4 9 . 0 0 2 1 .24 . 0 0 2 . 2 6 5 -, 9 1 9 . 0 5 4 . 0 3 9 1. 48 . 7 9 1 . 2 2 2 . 3 7 8 MANX 1 - . 4 1 0 2 . 0 4 9 1 0 3 . 1 .23 , 0 0 0 . 2 6 7 - . 3 8 7 . 0 6 9 8 9 . 7 2 . 4 0 , 0 0 0 -. 1 1 7 . 3 3 1 . 0 8 8 6 2 . 6 3 . 94 . 0 0 0 . 0 4 5 VALSOC 1 . 194 2 . 0 9 7 1 9 . 9 4 . 7 9 ;000 .. 028 . 2 2 2 . 0 7 9 2 6 . 3 . 3 1 7 . 0 0 0 . 0 7 2 *124 . 0 6 0 7 . 9 6 1 .85 . 0 0 5 . 171 SELFCON 1 . 4 5 7 2 . 0 7 5 1 3 5 , 2 . 8 7 . 0 0 0 . 0 8 7 . 5 1 8 . 0 0 6 1 8 7 . . 0 1 6 - 0 0 0 . 8 6 8 . 4 6 2 . 0 2 8 138 . , 4 0 3 . 0 0 0 . 5 3 3 ENJOY 1 . 3 2 0 2 . 0 8 3 5 8 . 1 3 . 5 1 . 0 0 0 i 0 5 9 . 2 3 6 . 0 3 9 3 0 . 4 . 7 7 7 , 0 0 0 . 3 8 2 , 241 . 0 6 0 3 1 . 5 1.87 . 0 0 0 . 1 6 9 VALSEL 1 . 157 2 . 0 3 4 1 2 . 9 5 . 9 7 . 0 0 1 , 4 4 6 . 151 . 0 1 7 1 1 . 8 . 153 . 001 , 6 9 7 . 0 9 4 . 0 3 3 4 . 5 7 - 5 4 2 . 031 . 4 6 9 r e g r e s s i o n . F or each of the achievement v a r i a b l e s a l l the a f f e c t i v e s c a l e s ; were used as independent v a r i a b l e s . The m u l t i p l e c o r r e l a t i o n s . with the squared i m u l t i p l e c o r r e l a t i o n s i n parentheses. of the a f f e c t i v e v a r i a b l e s with COMP, CONC, and PBOB were: . 4 8 3 ( . 2 3 3 ) , . 5 3 7 ( . 2 8 8 ) , and . 4 6 8 ( . 219) r e s p e c t i v e l y . The n u l l h y p o t hesis t h a t the a f f e c t i v e v a r i a b l e s would not account f o r a s i g n i f i c a n t p r o p o r t i o n of the achievement v a r i a b l e s was not accepted at the , . 01 l e v e l . I t should be noted that t h i s i s not a l a r g e i n c r e a s e over the c o r r e l a t i o n s between SELFCON and the achievement v a r i a b l e s 114 (.457, .518, .462). A s e r i e s of st e p w i s e a n a l y s e s was performed t o s e l e c t a m i n i m a l s u b - s e t of a f f e c t i v e v a r i a b l e s which would p r e d i c t t h e achievement s c o r e s . The c r i t e r i o n was s e t so t h a t no v a r i a b l e s were added t o the r e g r e s s i o n e q u a t i o n u n l e s s t h e i n c r e a s e i n v a r i a n c e accounted f o r was s i g n i f i c a n t a t the .01 l e v e l . The a f f e c t i v e v a r i a b l e s SELFCON and MANX a p p e a r e d - i n one e g u a t i o n and o n l y SELFCON i n the o t h e r s . The summary o f th e a n a l y s e s appears i n T a b l e 22. T a b l e 22 Summary of the Stepwise A n a l y s e s U s i n g S t a n d a r d i z e d A f f e c t i v e Scores a s Independent V a r i a b l e s Dependent Independent P a r t i a l F F Squared M u l t i p l e V a r i a b l e s V a r i a b l e s C o r r e l a t i o n s 1 R a t i o 2 Prob C o r r e l a t i o n s COMP SELFCON .457 37.2 .000 .225 MANX -.140 10.2 .002 CONC SELFCON .518 187. A000 .268 PROB SELFCON .462 138. *000 .213 * T h i s i s t h e p a r t i a l p r i o r t o e n t r y i n the e q u a t i o n . V a r i a b l e s a r e i n the or d e r of e n t r y f o r each e q u a t i o n 2 F R a t i o s and F Probs a r e t h o s e a s s o c i a t e d w i t h t h e Beta c o e f f i c i e n t s of the f i n a l e g u a t i o n . I n comparison w i t h the maximal e q u a t i o n s t h e l o s s o f e x p l a i n e d v a r i a n c e was q u i t e s m a l l ; a maximum of 2.08%. Usinq t h e K e r l i n g e r and Pedhazur e g u a t i o n (1973, p. 71) t h i s d i f f e r e n c e was s i g n i f i c a n t a t the .05 l e v e l b ut not a t .0 1. T h e r e f o r e t h e n u l l h y p o t h e s i s was not r e j e c t e d . 115 I t would appear that MANX and SELFCON c o n t r i b u t e most to the p r e d i c t i o n of the achievement s c o r e s . However, st u d e n t s may have been responding to the items on those s c a l e s i n f l u e n c e d by how they responded to other s t i m u l i r e l a t e d t o mathematics. In other words, the s c a l e s may not be u n i -dimensional. Thus the equations o u t l i n e d above co u l d w e l l have r e s u l t e d from MANX and SELFCON accounting f o r v a r i a n c e common to other v a r i a b l e s . F a c t o r A n a l y s i s By c o r r e l a t i n g the ort h o g o n a l f a c t o r s with the achievement v a r i a b l e s through m u l t i p l e r e g r e s s i o n the i d e n t i f i c a t i o n o f the c o n s t r u c t or f a c t o r making the maximal c o n t r i b u t i o n was achi e v e d . T h i s was a s t a t i s t i c a l way of devel o p i n g independent measures t o a i d i n t e r p r e t a t i o n . As the th r e e f a c t o r s i d e n t i f i e d i n the p r i n c i p a l component a n a l y s i s c o u l d be i n t e r p r e t e d i n terms of the three f a c t o r s o f the Achievement M o t i v a t i o n model, the hypothesized i n t e r - r a c t i o n e f f e c t s c o u l d be t e s t e d . The r o t a t e d p r i n c i p a l component f a c t o r s were used t o generate a f a c t o r score matrix. F a c t o r scores were c a l c u l a t e d f o r each student from the st a n d a r d i z e d a f f e c t i v e scores u s i n g the weights i n Ta b l e 23. The s c o r e s were again s t a n d a r d i z e d w i t h i n c l a s s e s as was done i n i t i a l l y f o r the a f f e c t i v e and achievement raw sc o r e s . I t should be noted t h a t t he s t a n d a r d i z a t i o n was done u s i n g only the s u b j e c t s from Sample 116 Table 23 F a c t o r Score C o e f f i c i e n t M a t r i x F a c t o r 1 F a c t o r 2 F a c t o r 3 IARS IARF MANX VALSOC SELFCON ENJOY VALSEL .1267 -.1736 -.4224 -.1490 .4357 .3024 -.0965 .5801 .6852 .0354 -.0339 -.0604 -.0199 -.0487 -. 1679 *0652 .0980 .5923 -. 1531 .0503 . 5594 1. The c o r r e l a t i o n m a t r i x of f a c t o r s c o r e s and achievement s c o r e s i s shown i n Table 24. I t can be seen t h a t t h e c o r r e l a t i o n s between t h e f a c t o r s c o r e s a r e v i r t u a l l y z e r o . T a b l e 24 C o r r e l a t i o n s between S t a n d a r d i z e d F a c t o r Scores and S t a n d a r d i z e d Achievement S c o r e s 1 COMP CONC PROB MF ARF VF COMP 1.00 CONC .66** 1.00 PSOB .67** .66** 1.00 MF .43** . 44** .40** 1.00 ARF .07 -.04 -.02 .00 1.00 VF .09* .08 ,01 .01 .0 1 *p <".05 **p < .01 *As the t h r e e f a c t o r s c o r e s a r e v i r t u a l l y o r t h o g o n a l the squared c o r r e l a t i o n s of the f a c t o r s c o r e s w i t h t h e achievement s c o r e s are qood e s t i m a t e s o f the p r o p o r t i o n of v a r i a n c e accounted by any one f a c t o r s c o r e i n d e p e n d e n t l y o f t h e o t h e r s . In o r d e r t o e s t a b l i s h t h e p r o p o r t i o n of v a r i a n c e o f the achievement v a r i a b l e s a c c o u n t e d f o r by the t h r e e f a c t o r s , r e g r e s s i o n e q u a t i o n s were q e n e r a t e d w i t h the t h r e e f a c t o r s as inde p e n d e n t v a r i a b l e s . The p r o p o r t i o n s o f e x p l a i n e d v a r i a n c e were as f o l l o w s w i t h v a r i a n c e accounted f o r by t h e seven 117 a f f e c t i v e v a r i a b l e s shown i n parentheses f o r comparison: COMP, . 1 9 6 ( . 2 3 3 ) ; CONC, . 2 0 2 ( . 2 8 8 ) ; and PROB, . 1 6 2 ( . 2 1 9 ) . The eguations are shown i n Table 2 5 . The r e d u c t i o n i n the p r o p o r t i o n of e x p l a i n e d v a r i a n c e was not of g r e a t importance as a r e d u c t i o n of approximately 24% was expected because the three f a c t o r s accounted f o r only 76% of the varian c e of the seven a f f e c t i v e measures. I t should be noted t h a t the 24% c o u l d have been e r r o r v a r i a n c e due to s c a l e r e l i a b i l i t i e s l e s s than 1 . 0 0 . Table 25 Regression Eguations of the Three F a c t o r Scores P r e d i c t i n g the Three achievement Scores Dependent Independent Regression F F Squared M u l t i p V a r i a b l e V a r i a b l e We i g h t s Ratio Prob C o r r e l a t i o n s COMP MF . 4 3 5 9 1 1 5 . . 0 0 0 . 1 9 6 ARF . 0 7 2 2 3 . 17 . 0 7 2 v r . 0 8 8 9 4 . 8 0 . 0 2 7 CONC MF . 4 4 2 7 1 2 3 . . 0 0 0 , 2 0 2 ARF - . 0 3 5 0 . 7 5 6 . 3 8 9 VF . 0 7 4 5 3 . 4 3 , 0 6 1 PROB MF . 4 1 5 3 9 7 . 3 . 0 0 0 ,*162 ARF - . 0 2 2 5 . 2 8 6 . 6 0 0 VF . 0 0 7 1 . 0 2 9 . 8 4 2 The next hypothesis to be t e s t e d was t h a t t h e r e would be no s i g n i f i c a n t i n t e r a c t i o n s of the a f f e c t i v e f a c t o r s i n p r e d i c t i n g the achievement v a r i a b l e s . To t h i s end the f a c t o r s c o r e s were combined m u l t i p l i c a t i v e l y . Four a d d i t i o n a l s c o r e s were c a l c u l a t e d ; MF x A£F, MF x VF, ARF x VF, and MF x ARF x 118 VF* These a d d i t i o n a l s c o r e s were used t o g e t h e r w i t h t h e f a c t o r s c o r e s i n a s t e p w i s e r e g r e s s i o n p r o c e d u r e . A g a i n the c r i t e r i o n f o r a d d i t i o n t o the e q u a t i o n was a s i g n f i c a n t i n c r e a s e i n e x p l a i n e d v a r i a n c e a t the .01 l e v e l , ; The n u l l h y p o t h e s i s not r e j e c t e d ; That i s no i n t e r a c t i o n terms were i n c l u d e d . 1 See Table 26 f o r the summary o f t h e a n a l y s e s . T a b l e 26 Summary o f Stepwise A n a l y s e s Using F a c t o r S c o r e s and F a c t o r S c ore i n t e r a c t i o n s as Independent V a r i a b l e s Dependent Independent P a r t i a l F F Squared M u l t i p l e V a r i a b l e V a r i a b l e C o r r e l a t i o n s 1 B a t i o 2 Prob C o r r e l a t i o n s COMP MF .429 114. .000 . 191 CONC MF .442 97.5 .000 .195 PBOB MF .401 97.7 .000 .161 i l h i s i s the p a r t i a l p r i o r t o e n t r y i n the e q u a t i o n . V a r i a b l e s a r e i n t h e o r d e r o f e n t r y f o r each e q u a t i o n . 2 F B a t i o s and P r o b a b i l i t i e s a r e t h o s e a s s o c i a t e d w i t h t h e b e t a c o e f f i c i e n t s of the f i n a l e q u a t i o n . C l e a r l y t he c o n s t r u c t u n d e r l y i n g the M o t i v a t i o n F a c t o r (MF) was t h e most i m p o r t a n t p r e d i c t o r o f achievement. MF, however, d i d not acco u n t f o r a g r e a t e r p r o p o r t i o n of t h e v a r i a n c e o f achievement than d i d SELFCON a l o n e . Indeed i t c o u l d be argued t h a t u s i n g the p r i n c i p a l o f parsimony SELFCON was the o n l y 1 For i n t e r e s t g u a d r a t i c f u n c t i o n s o f the f a c t o r s c o r e s were c a l c u l a t e d and a l s o used i n t e r a c t i v e l y i n p r e d i c t i n q achievement. T h i s was o f i n t e r e s t because t h e Achievement M o t i v a t i o n model p r e d i c t e d a q u a d r a t i c i n t e r a c t i o n o f p r o b a b i l i t y o f s u c c e s s w i t h m o t i v a t i o n t o succeed. However, none o f the q u a d r a t i c or i n t e r a c t i v e terms were s i q n i f i c a n t l y r e l a t e d t o achievement. 119 e x p l a n a t o r y v a r i a b l e necessary. More d i s c u s s i o n on t h i s p o i n t w i l l appear i n Chapter 5. CROSS VALIDATION The c r o s s v a l i d a t i o n analyses were performed on the second of two samples randomly s e l e c t e d from the i n i t i a l sample as d e s c r i b e d at the end of Chapter 3. The sample was composed of 522 students, 254 male and 268 female. The c r o s s v a l i d a t i o n proceded i n s e v e r a l s t e p s . The f i r s t s t e p c o n s i s t e d of t e s t i n g the equivalence of the male and female v a r i a n c e - c o v a r i a n c e m a t r i c e s . The second s t e p was the c a l c u l a t i o n o f the i n t e r c o r r e l a t i o n s of the a f f e c t i v e and achievement s c a l e s and performinq an o v e r a l l t e s t of the e q u i v a l e n c e of the v a r i a n c e - c o v a r i a n c e matrices of the two samples. The t h i r d s t e p was to s u b j e c t the second sample to f a c t o r a n a l y s i s with a three f a c t o r s o l u t i o n f o l l o w e d by an orthogonal P r o c r u s t e s t r a n s f o r m a t i o n . The f o u r t h step was to s u b j e c t the v a r i a b l e s to stepwise r e g r e s s i o n a n a l y s i s . E quivalence of C o r r e l a t i o n s When the male and female v a r i a n c e - c o v a r i a n c e m a t r i c e s were compared u s i n g the Box t e s t , the r e s u l t i n g F r a t i o was 1.177 with degrees of freedom 55 and 868 095. The d i f f e r e n c e was not s i g n i f i c a n t a t the .10 l e v e l . T h i s confirmed the f i n d i n g s of no s i g n i f i c a n t sex d i f f e r e n c e s from the i n i t i a l a n a l y s i s . 120 The c o r r e l a t i o n s o f t h e a f f e c t i v e and achievement v a r i a b l e s a r e shown i n Table 27. The r e s u l t s may be compared t o t h o s e i n T a b l e s 18 and 20 f o r Sample 1* The o v e r a l l t e s t o f e q u i v a l e n c e o f t h e v a r i a n c e - c o v a r i a n c e m a t r i c e s r e s u l t e d i n an F r a t i o o f 0*987 w i t h degrees of freedom 55 and 3 429 430. T h i s was not s i g n i f i c a n t a t the .10 l e v e l . T a b l e 27 C o r r e l a t i o n s of the A f f e c t i v e and Achievement S c a l e s of Sample 2 COMP CONC PEOB IABS IAEF MANX VSOC SCON ENJOY CCNC .64 PEOB .65 ,67 IAES . 12 .06 .08 IAEF -.01 -.01 -.07 .25 MANX -.43 -.40 -.38 -.24 .03 VSOC . 17 .27 .21 .18 .07 -,38 SCON .44 .47 . 44 .27 -.09 -.72 ,37 ENJOY .32 .30 .29 .22 .03 -.72 .45 VSEL . 18 .23 .20 .17 . 1 1 -.37 .69 F a c t o r A n a l y s i s The n e x t s t e p was t o s u b j e c t the second sample t o component a n a l y s i s w i t h a t h r e e f a c t o r s o l u t i o n 1 . The same s t r u c t u r e appeared. The f a c t o r l o a d i n g s of the r e s u l t s from the a n a l y s e s o f both samples a re i n Tab l e 28. A t e s t of the s t a b i l i t y of the f a c t o r s was made u s i n g an o r t h o g o n a l P r o c r u s t e a n t r a n s f o r m a t i o n ( H a c k s t i a n & Bay, * The e i g e n - v a l u e s and sc r e e c o r r e s p o n d e d c l o s e l y t o t h o s e o f th e i n i t i a l sample. 121 T a b l e 28 F a c t o r L e a d i n g s from the A n a l y s e s of Sample 1 and Sample 2 F a c t o r 1 F a c t o r 2 F a c t o r 3 V a r i a b l e S1 * S2 S1 S2 S1 S2 IARS .321 .373 .737 .745 -.025 -.037 IARF -.144 -.215 .843 .822 .136 .165 MANX -.893 -.883 -.055 -,.032 -. 199 -.223 VALSOC .170 .257 .066 .057 .879 .858 SELFCON .867 .870 .013 .016 .110 .129 ENJOY .760 .729 .129 .064 .362 .408 VALSEL .259 .195 .054 .085 .866 .891 *S1 = sample 1; S2 = sample 2. 1973). T h i s t r a n s f o r m a t i o n uses a l e a s t s quares a p p r o x i m a t i o n p r o c e d u r e t o r o t a t e a q i v e n f a c t o r s o l u t i o n t o a " t a r g e t " m a t r i x o f f a c t o r l o a d i n g s . I n t h i s case the t a r g e t m a t r i x was th e s e t of f a c t o r l o a d i n g s c a l c u l a t e d w i t h t h e f i r s t sample. As t h e r e was no t e s t o f g o o d n e s s — o f - f i t f o r the a l g o r i t h m t h e e r r o r m a t r i x appears i n Ta b l e 29. As t h e r e were o n l y 3 e r r o r s T a b l e 29 E r r o r M a t r i x from a P r o c r u s t e a n R o t a t i o n of t h e Sample 2 F a c t o r s t o a Target M a t r i x o f Sample 1 L o a d i n g s F a c t o r 1 F a c t o r 2 f a c t o r 3 IARS .046 .011 -.023 IARF -.075 -.021 .025 MANX .006 .015 -.008 VALSOC .102 -.001 -.025 SELFCON .005 .011 .004 ENJOY -.026 -.056 *032 VALSEL -.049 .039 .021 g r e a t e r than .05 and as t h e s o l u t i o n accounted f o r 76.4% o f the v a r i a n c e of t h e seven a f f e c t i v e v a r i a b l e s the f a c t o r s o l u t i o n was c o n s i d e r e d t o be adequate. These r e s u l t s 122 i n d i c a t e a s t a b l e f a c t o r space. R e g r e s s i o n A n a l y s i s T i e f o u r t h s t e p was t o ge n e r a t e a s t e p w i s e r e g r e s s i o n e q u a t i o n f o r Sample 2. The r e s u l t s a r e d i s p l a y e d i n Ta b l e 30. T a b l e 30 Summary o f Stepwise A n a l y s i s Using Sample 2 S t a n d a r d i z e d S c o r e s as Independent V a r i a b l e s — — — — — — — — — — — — — — — ——T — — — — — — Dependent Independent P a r t i a l F F Squared M u l t i p l e V a r i a b l e s V a r i a b l e s C o r r e l a t i o n s 1 R a t i o 2 Prob C o r r e l a t i o n s COMP SELFCON .436 16.74 .000 .215 MANX -.177 22.82 .000 CONC SELFCON .468 107. .000 .229 VALSOC .113 6.76 *009 PROB SELFCON .446 38.6 .000 .» 194 i p a r t i a l c o r r e l a t i o n s a r e those j u s t b e f o r e t h e v a r i a b l e e n t e r e d t h e e q u a t i o n . V a r i a b l e s a r e l i s t e d i n the o r d e r t h e y e n t e r e d the e q u a t i o n * 2 F r a t i o s and p r o b a b i l i t i e s a r e those of the f i n a l e q u a t i o n . I n comparison w i t h the r e s u l t s of Sample 1 t h e o n l y change i n v a r i a b l e s i n c l u d e d was i n t h e case o f CONC where VALSOC e n t e r e d . The p r o p o r t i o n s of e x p l a i n e d v a r i a n c e were s i m i l a r e x c e p t f o r CONC which had a 3.9% d i f f e r e n c e . However, as was noted b e f o r e , t h e number o f t e s t s o f s i g n i f i c a n c e i n r e g r e s s i o n a n a l y s i s i s g u i t e l a r g e . Thus the n o t e d d i f f e r e n c e c o u l d bave been t h e r e s u l t o f random f l u c t u a t i o n . . As t h e squared c o r r e l a t i o n s w i t h t h e seven a f f e c t i v e v a r i a b l e s i n c l u d e d i n the e q u a t i o n were .219, ,245 and .207 123 the r e d u c t i o n o f e x p l a i n e d v a r i a n c e w i t h the s t e p w i s e s o l u t i o n was a t most 1.6%. T h i s d i f f e r e n c e was not s i g n i f i c a n t at t h e .01 l e v e l . The c r o s s v a l i d a t i o n a n a l y s i s s u s t a i n e d v i r t u a l l y a l l f i n d i n g s of the i n i t i a l a n a l y s i s . SUMMARY The e q u a l i t y o f c o r r e l a t i o n s between sexes was n o t r e j e c t e d and the d a t a were pool e d f o r a l l subsequent a n a l y s e s . The a n a l y s e s i n d i c a t e d t h e " b l o c k " v a r i a b l e s , w i t h t h e e x c e p t i o n o f IABS and IARF were i n t e r - r e l a t e d . The c o r r e l a t i o n s , w i t h IARS and IARF e x c l u d e d , ranqed from .296 t o .728. The t e a c h e r r e s p o n s e s c a l e s were c o r r e l a t e d w i t h the " b l o c k " v a r i a b l e s . SELFCON, ENJOY and MANX were t h e most s t r o n g l y r e l a t e d ; SELFCON w i t h c o r r e l a t i o n s o f .06 t o .23 wi t h i n d i v i d u a l S t u d e n t - B e h a v i o r s and .35 w i t h RANK; ENJOY, -.02 t o -.17 and .16; MANX, .04 t o *23 and -.29. These d a t a tended t o supp o r t t h e c o n s t r u c t v a l i d i t y o f the a f f e c t i v e v a r i a b l e s . I t was a l s o shown t h a t the " b l o c k " v a r i a b l e s , a g a i n w i t h IARF e x c l u d e d , were a l l s i g n i f i c a n t l y c o r r e l a t e d w i t h t h e achievement v a r i a b l e s ; .094 t o .518. There were no s i g n i f i c a n t n o n - l i n e a r c o r r e l a t i o n s ; the maximums were MANX w i t h PROB (.088) and VALSOC w i t h COMP (.097). The r e l a t i o n s h i p s between the " b l o c k " v a r i a b l e s and the achievement v a r i a b l e s were examined u s i n g m u l t i p l e and 124 stepwise r e g r e s s i o n . The m u l t i p l e c o r r e l a t i o n s with COMP, CONC and EBOE were .483, -537 and .468 r e s p e c t i v e l y . Stepwise r e g r e s s i o n r e v e a l e d t h a t SELFCON was the major c o n t r i b u t o r to the e x p l a i n e d v a r i a n c e of the achievement v a r i a b l e s . MANX, the o n l y other v a r i a b l e t o e n t e r , d i d so once. To see i f the seven "block" v a r i a b l e s could be i n t e r p r e t e d i n a more simple manner, p r i n c i p a l component a n a l y s i s f o l l o w e d by ort h o g o n a l r o t a t i o n r e v e a l e d three f a c t o r s a c c o u n t i n g f o r 76% of the varian c e of the i n i t i a l seven v a r i a b l e s . F a c t o r l o a d i n g s suggested a M o t i v a t i o n F a c t o r (MF) with s t r o n g l o a d i n g s from SELFCON, ENJOY, and MANX; a Value F a c t o r (VF) with l o a d i n g s from VALSOC and VALSEL; and an Achievement E e s p o n s i b i l i t y F a c t o r (AEF) with l o a d i n g s from IAES and IABF. The f a c t o r s were i n t e r p r e t a b l e and showed a well d e f i n e d s t r u c t u r e even though ENJOY loaded .36 on VF and IAES loaded .3 2 on MF. Factor s c o r e c o e f f i c i e n t s were used t o c a l c u l a t e MF, AEF and VF f a c t o r s c o r e s f o r each s u b j e c t . I n t e r a c t i o n terms were c a l c u l a t e d m u l t i p l i c a t i v e l y . Stepwise r e g r e s s i o n u s i n g those f a c t o r s c o r e s showed t h a t MF accounted f o r the major p r o p o r t i o n of e x p l a i n e d v a r i a n c e . C o n t r a r y to the e x p e c t a t i o n s of the Achievement M o t i v a t i o n model no i n t e r a c t i o n terms were i n c l u d e d i n the equations. The c r o s s v a l i d a t i o n s u s t a i n e d the f i n d i n g s above with minor e x c e p t i o n s . There was no s i g n i f i c a n t d i f f e r e n c e between the v a r i a n c e - c o v a r i a n c e matrices of the sexes, nor was there a 125 s i g n i f i c a n t difference between the variance-covariance matrices of the two samples. This was tested at the 10% l e v e l . Factor analysis of the second sample showed l i t t l e change i n the fac t o r structure. Procrustean rotation of the Sample 2 factors to the loadings of the rotated Sample 1 fac t o r s , accounted f o r 76.4% of the o r i g i n a l variance of the seven a f f e c t i v e variables. This suggested a stable factor structure. Stepwise regression analysis of the second sample showed l i t t l e differences in explained variance: approximately 20%. The analysis showed consistency i n the i n c l u s i o n of variables. 126 Chapter 5 DISCUSSION AND CONCLUSIONS INTRODUCTION In C hapters 1 and 2, i t was shown t h a t t h e r e was a l i t e r a t u r e which i n d i c a t e d t h a t a s i g n i f i c a n t p r o p o r t i o n of mathematics students appeared to have an "emotional b l o c k " i n h i b i t i n g t h e i r achievement i n mathematics. Anxiety, enjoyment, value, and s e l f ^ c o n c e p t of i n mathematics were i d e n t i f i e d as the components of the "block". The Achievement M o t i v a t i o n Model was used t o suggest p o s s i b l e i n t e r a c t i o n s among the components when r e l a t e d t o achievement motivation* A f u r t h e r v a r i a b l e , l o c u s of c o n t r o l or academic r e s p o n s i b i l i t y , was suggested by the model. In Chapter 3 i t was argued t h a t f o u r of the Sandman (1973) s c a l e s would be the most a p p r o p r i a t e measures of the f o l l o w i n g v a r i a b l e s : anxiety of mathematics (MANX) 1, enjoyment of mathematics (ENJOY), value of mathematics f o r s o c i e t y (VALSOC), and s e l f - c o n c e p t of mathematics achievement (SELFCON). A p r e l i m i n a r y a n a l y s i s , d e s c r i b e d i n Chapter 3, i l h e c a p i t a l i z e d terms i n the parentheses w i l l be used i n t h e f o l l o w i n g d i s c u s s i o n . 127 confirmed t h a t the Mathematics Anxiety s c a l e was more v a l i d than the Test Anxiety S c a l e f o r C h i l d r e n as a measure of mathematics a n x i e t y . I n a d d i t i o n , a Value o f Mathematics f o r Oneself Scale (VALSEL) was developed by the experimenter. The I n t e l l e c t u a l Achievement E e s p o n s i b i l i t y Scale was s e l e c t e d as the measure of Locus of C o n t r o l . T h i s s c a l e had two p a r t s : r e s p o n s i b i l i t y f o r success (IABF) and r e s p o n s i b i l i t y f o r f a i l u r e (IABF). Two forms of t e a c h e r response, a r a n k i n g of students on a d e s c r i p t i o n of behaviors t y p i c a l of an "emotional b l o c k " (BANK), and a check l i s t of s p e c i f i c b e h a v i o r s a s s o c i a t e d with the " b l o c k " were a l s o developed by the experimenter. Three achievement measures were s e l e c t e d ; the A r i t h m e t i c Computation S c a l e from the S t a n f o r d Achievement T e s t : Form W (COMP) and the Mathematics Concepts (CONC) and Mathematics Problem Solving S c a l e s ( L e v e l 12) (PBOB) from the Canadian Test o f B a s i c S k i l l s : Form 4,. The d e s i g n , procedure, and t e s t a d m i n i s t r a t i o n of the m a t e r i a l s used with a sample of 1033 s u b j e c t s were d e s c r i b e d i n Chapter 3. In a d d i t i o n , a p r e l i m i n a r y a n a l y s i s showed t h a t some c l a s s means were s i g n i f i c a n t l y d i f f e r e n t and t h a t homogeneity of c l a s s variance c o u l d be accepted. To remove the e f f e c t s of c l a s s d i f f e r e n c e s i n subseguent c o r r e l a t i o n a l a n a l y s e s , the s c o r e s were s t a n d a r d i z e d w i t h i n each c l a s s (mean of zero; standard d e v i a t i o n of one). A l l s c a l e s c o r e s used i n the analyses of Chapter 4 were s t a n d a r d i z e d i n t h i s manner,* In Chapter 4 the h y p o t h e s i s of e q u a l i t y of the 128 c o r r e l a t i o n s between sexes was n o t r e j e c t e d and t h e d a t a were p o o l e d f o r a l l subsequent a n a l y s e s . The a n a l y s e s showed, w i t h t h e e x c e p t i o n o f IARP, t h a t t h e " b l o c k " v a r i a b l e s were i n t e r - r e l a t e d . The c o r r e l a t i o n s w i t h the t e a c h e r r e s p o n s e s c a l e s were low but i n t h e h y p o t h e s i z e d d i r e c t i o n t h u s t e n d i n g t o v a l i d a t e the " b l c c k " v a r i a b l e s . Squared m u l t i p l e c o r r e l a t i o n s o f t h e a f f e c t i v e v a r i a b l e s w i t h achievement v a r i a b l e s showed modest i n c r e a s e s o f e x p l a i n e d v a r i a n c e and s t e p w i s e r e g r e s s i o n showed SELFCON to be t h e major c o n t r i b u t o r t o the e x p l a i n e d v a r i a n c e o f t h e achievement v a r i a b l e s . The s q u a r e d m u l t i p l e c o r r e l a t i o n s were between .219 and .288 f o r the f u l l e q u a t i o n s and .213 and .268 f o r t h e s t e p w i s e e q u a t i o n s . F a c t o r a n a l y s i s r e v e a l e d t h r e e i n t e r p r e t a b l e f a c t o r s a c c o u n t i n g f o r 76% of the v a r i a n c e o f t h e i n i t i a l seven v a r i a b l e s . The t h r e e f a c t o r s were i n t e r p r e t e d as M o t i v a t i o n (MF), Achievement R e s p o n s i b i l i t y (AEF) and Value (VF). The p o s t u l a t e d s t r u c t u r e was n o t observed. However, t h e f a c t o r s were c l e a r l y i n t e r p r e t a b l e . R e g r e s s i o n a n a l y s i s showed MF to be the major e x p l a n a t o r y component* I t s h o u l d be noted t h a t s e l f - c o n c e p t was t h e major component o f t h i s f a c t o r . C r o s s v a l i d a t i o n s u p p o r t e d the f i n d i n g of no sex d i f f e r e n c e s among th e c o r r e l a t i o n s o f t h e a f f e c t i v e and achievement v a r i a b l e s . The f a c t o r s t r u c t u r e was shown t o be s t a b l e . The s t e p w i s e r e g r e s s i o n i n the c r o s s v a l i d a t i o n sample t y p i c a l l y s e l e c t e d the same v a r i a b l e s as done w i t h 129 Sample 1. The o n l y d i f f e r e n c e found i n the c r o s s v a l i d a t i o n a n a l y s i s was t h a t VALSOC was i n c l u d e d i n t h e . e q u a t i o n f o r CONC. The p r o p o r t i o n o f e x p l a i n e d v a r i a n c e o f t h e achievement v a r i a b l e s was c o n s i s t e n t l y between 19% and 23%; s i m i l a r t o t h a t i n Sample 1. In t h i s c h a p t e r d i s c u s s i o n o f r e s u l t s w i l l c e n t r e on t h r e e a r e a s : the l a c k of sex d i f f e r e n c e s ; t h e i n t e r c o r r e l a t i o n s o f t h e " b l o c k " v a r i a b l e s and f a c t o r a n a l y s i s ; and t h e m u l t i p l e and s t e p w i s e a n a l y s e s o f t h e a f f e c t i v e v a r i a b l e s , f a c t o r s c o r e s and i n t e r a c t i o n s w i t h the achievement v a r i a b l e s . L i m i t a t i o n s of the s t u d y , c o n c l u s i o n s and f u t u r e r e s e a r c h w i l l a l s o be d i s c u s s e d . SEX DIFFEEENCES When the i s s u e of sex d i f f e r e n c e s i n mathematics i s r a i s e d i t i s o f t e n i n terms o f average performance. T h a t i s q u e s t i o n s such as "Do boys, on t h e av e r a g e , p e r f o r m b e t t e r t h a n g i r l s or v i c e v e r s a ? " a re asked. Although t h i s approach was c o n s i d e r e d p a r e n t h e t i c a l l y i n t h i s s t u d y (see Appendix 6 ) , another a s p e c t of sex d i f f e r e n c e was o f more i n t e r e s t . The g u e s t i o n here was, " I s the r e l a t i o n s h i p between a g i v e n p a i r o f v a r i a b l e s t h e same f o r boys as f o r g i r l s ? " A t e s t of e q u i v a l e n c e of the v a r i a n c e - c o v a r i a n c e m a t r i c e s showed no o v e r a l l d i f f e r e n c e s s i g n i f i c a n t a t the 10% l e v e l . T h i s c o u l d c a s t some l i g h t on t h e i n c o n s i s t e n t f i n d i n g s of sex r e l a t e d d i f f e r e n c e s i n c o r r e l a t i o n s o f 130 a f f e c t i v e v a r i a b l e s found i n the l i t e r a t u r e , p a r t i c u l a r l y i f u n i v a r i a t e comparisons were made. For example, i t c o u l d be t h a t items worded t o tap i n f o r m a t i o n a s s o c i a t e d with enjoyment may e l i c i t more i n f o r m a t i o n a s s o c i a t e d with value f o r the boys than they would from the g i r l s . Thus other s t u d i e s may f i n d the c o r r e l a t i o n o f enjoyment with mathematics achievement may be d i f f e r e n t f o r boys than f o r g i r l s . However, i f value items are s p e c i f i c a l l y i n c l u d e d w i t h i n the s c a l e or i n a s e p a r a t e s c a l e the d i f f e r e n c e s may disappear. T h i s c o u l d be another reason f o r choosing a m u l t i v a r i a t e approach t o the r e l a t i o n of a f f e c t i v e s c a l e s with achievement. That i s not to say t h a t sex d i f f e r e n c e s should be ignored i n f u t u r e r e s e a r c h . I t should be determined i f changes i n value change enjoyment i n a d i f f e r e n t manner f o r the two sexes, and whether or not those changes, i n t u r n , a l t e r achievement i n a d i f f e r e n t manner, INTERRELATIONS OF THE "BLOCK" VARIABLES The "emotional b l o c k " was c h a r a c t e r i z e d i n the pe d a g o g i c a l l i t e r a t u r e as being a s s o c i a t e d with high a n x i e t y i n mathematics, low value of the worth o f mathematics t o s o c i e t y and s e l f , low enjoyment, low s e l f - c o n c e p t , and an u n w i l l i n g n e s s t o accept r e s p o n s i b i l i t y f o r e i t h e r f a i l u r e or success i n achievement s i t u a t i o n s . Other l i t e r a t u r e p o i n t e d out t h a t a n x i e t y could, i n f a c t , f a c i l i t a t e achievement provided a student was motivated to achieve or had high 131 i n t e l l i g e n c e * T h e r e f o r e , i t was h y p o t h e s i z e d t h a t t h e v a r i a b l e s would be c o r r e l a t e d and y e t show t h a t they tapped d i f f e r e n t d i m e n s i o n s . I n g e n e r a l t h i s h y p o t h e s i s was a c c e p t e d . I t s h o u l d be r e c a l l e d t h a t t h e model of Achievement M o t i v a t i o n , o u t l i n e d i n C h a p t e r 2, h e l d t h a t t h e b e h a v i o r of an i n d i v i d u a l was determined by h i s e x p e c t a t i o n t h a t t h e b e h a v i o r would l e a d t o v a r i o u s outcomes, h i s e v a l u a t i o n of t h o s e outcomes, and h i s s u b j e c t i v e p r o b a b i l i t y t h a t he c o u l d behave i n t h e g i v e n way. I t would appear r e a s o n a b l e t h a t a s t u d e n t c o u l d b e l i e v e t h a t p a y i n g a t t e n t i o n i n a mathematics c l a s s l e d t o b e t t e r marks and, t h a t b e t t e r marks were i m p o r t a n t . Y e t , he might a l s o b e l i e v e t h a t h i s a t t e n t i o n would n o t l e a d t o h i s i n c r e a s e d achievement** The r e s u l t of t h i s might be t h a t the s t u d e n t would not a t t e n d . A l g e b r a i c a l l y the Achievement M o t i v a t i o n model, as d e s c r i b e d by A t k i n s o n (1958), A t k i n s o n and F e a t h e r (1966), and A t k i n s o n and Raynor (1974), l e d t o a t h r e e p a r t e g u a t i o n o f a r e s u l t a n t tendency (Tr) t o a c t which i s Tr = (Ms - Maf) x Ps x (1 - Ps) , where (Ms - Maf) was t h e r e s u l t a n t m o t i v a t i o n t o succeed, l e s s t h e m o t i v a t i o n t o a v o i d f a i l u r e . Ps was t h e s u b j e c t i v e p r o b a b i l i t y o f s u c c e s s and (1 - Ps) was t h e i n c e n t i v e v a l u e o f s u c c e s s . The l a t t e r was a r e s u l t o f t h e model's assumption of an i n v e r s e r e l a t i o n between Ps and Is,. The t r i p a r t i t e e q u a t i o n s u g g e s t e d t h a t a f a c t o r a n a l y s i s would be 132 a p p r o p r i a t e . P r i n c i p a l component a n a l y s i s y i e l d e d t h r e e e i g e n - v a l u e s g r e a t e r t h a n 1.00, s a t i s f y i n g the Kaiser-Guttman c r i t e r i o n ( C a t t e l l , 1966, p. 206). The " s c r e e " o f the e i g e n - v a l u e s ( C a t t e l l , 1966, p. 206) a l s o s u g g e s t e d t h r e e f a c t o r s . These t h r e e f a c t o r s accounted f o r 76% o f the v a r i a n c e of the o r i g i n a l s e t of seven v a r i a b l e s . I n t h e l i g h t of the Achievement M o t i v a t i o n model a t h r e e f a c t o r s o l u t i o n of t h e a f f e c t i v e v a r i a b l e s was p a r t i c u l a r l y i n t e r e s t i n g . i n o r t h o g o n a l r o t a t i o n o f t h e f a c t o r s t o i n c r e a s e i n t e r p r e t a b i l i t y l e d t o a M o t i v a t i o n F a c t o r (MF) w i t h l o a d i n g s from MANX, ENJOY and SELFCON, a V a l u e F a c t o r (VF) w i t h h i g h l o a d i n g s from VALSEL and VALSOC, and an Achievement E e s p o n s i b i l i l i t y F a c t o r (AEF) w i t h l o a d i n g s from IAES and I AEF.. SELFCON by the t h e o r y s h o u l d have appeared as a s e p a r a t e f a c t o r . However, as Maf i n o t h e r r e s e a r c h had been t y p i c a l l y measured w i t h t h e T e s t A n x i e t y S c a l e , and as i t has been argued by t h e p r e s e n t a u t h o r t h a t ENJOY s h o u l d be c o n s i d e r e d t h e o p p o s i t e o f a n x i e t y , i t was d e c i d e d t o c a l l t h e f i r s t f a c t o r the M o t i v a t i o n F a c t o r (MF) . A comparison o f t h e h y p o t h e s i z e d and t h e a c t u a l l o a d i n g p a t t e r n s from the component a n a l y s e s f o l l o w s . 1 3 3 Hypothesized A c t u a l F a c t o r Loadings F a c t o r Loadings V a r i a b l e F1 F2 F3 F1 F2 F3 MANX hig h low low high low low ENJOY hi g h low low high low low IAES high low low low high low IAEF h i g h low low low high low SELFCON low high low high low low VALSEL low low high low low h i g h VALSOC low low high low low high The Achievement E e s p o n s i b i l i t y F a c t o r (AEF) was composed of IAES and IAEF. The i n d i v i d u a l s c a l e s had c o r r e l a t i o n s of a t most -.251 with the other v a r i a b l e s . T h i s may be because the s c a l e s were t r u l y independent or t h a t the s c a l e s had low i n t e r n a l c o n s i s t e n c i e s ; ,52 and .61. I t might be suggested t h a t the s c a l e s , developed i n the e a r l y 1960's, may have had reduced v a l i d i t y f o r the students of 1977, or t h a t the s c a l e s were a g e n e r a l measure of achievement r e s p o n s i b i l i t y r a t h e r than being s p e c i f i c a l l y a s s o c i a t e d with mathematics. T h i s l a t t e r was a p o s s i b i l i t y i n l i g h t of the evidence, presented i n Chapter 2, showing b e t t e r c o r r e l a t i o n s between measures o f anxiety and s e l f - c o n c e p t and measures of achievement when the a f f e c t i v e s c a l e s were d i r e c t l y r e l a t e d to achievement i n the s p e c i f i e d content a r e a , Thus i f a mathematics o r i e n t e d measure of achievement r e s p o n s i b i l i t y were developed i t i s p o s s i b l e f u t u r e s t u d i e s may show IAES and IARF to be c o r r e l a t e s of other a f f e c t i v e measures i n mathematics. I t was i n d i c a t e d i n Chapter 2 t h a t the theory of Achievement M o t i v a t i o n and Locus of C o n t r o l theory correspond 134 and t h a t a measure o f locu s o f c o n t r o l would i n t e r a c t with a measure of achievement m o t i v a t i o n . Woulk and DuCette (1973) presented evidence f o r t h i s r e l a t i o n . What was not c l e a r was to which o f the t h r e e c o n s t r u c t s of the Achievement M o t i v a t i o n model l o c u s cf c o n t r o l , or achievement r e s p o n s i b i l i t y , s h o u l d be r e l a t e d . Locus of c o n t r o l i s the degree t o which an i n d i v i d u a l accepts r e s p o n s i b i l i t y f o r the r e s u l t s of an a c t i o n or a t t r i b u t e s i t t c some cause e x t e r n a l t o h i m s e l f . A b e l i e f i n s e l f r e s p o n s i b i l i t y c o u l d suggest t h a t the i n d i v i d u a l would, i n an achievement s i t u a t i o n , attend to the task thus i n c r e a s i n g the p r o b a b i l i t y of s u c c e s s . A l t e r n a t i v e l y , a b e l i e f i n an e x t e r n a l cause of l e v e l of achievement would suggest i n d i f f e r e n c e , thus reducing the p r o b a b i l i t y of success* Because, i n t h i s study, MF has been i n t e r p r e t e d as the m o t i v a t i o n to succeed and avoid f a i l u r e , and VF as the value of success, the most l i k e l y correspondence o f AEF was with t h e s u b j e c t i v e p r o b a b i l i t y o f success. The components of the M o t i v a t i o n F a c t o r , MANX, SELFCON and ENJOY, were s t r o n g l y i n t e r c o r r e l a t e d . MANX c o r r e l a t e d -.728 and -.702 with ENJOY and SELFCON r e s p e c t i v e l y and ENJOY c o r r e l a t e d .56 with SELFCON. I t should be noted that the negative c o r r e l a t i o n s are an a r t i f a c t of the s c o r i n g of MANX. Sandman (1973) found s i m i l a r c o r r e l a t i o n s -.76 and ^.72. The degree o f o v e r l a p was a l s o i n d i c a t e d by the r e s u l t s o f Sandman's f a c t o r a n a l y s i s o f the s c a l e s . For example. Sandman's (1973) study showed that item 4 135 on t h e ENJOY s c a l e , " I don't l i k e a n y t h i n g about mathematics," l o a d e d on t h e a n x i e t y f a c t o r . Whereas i t e m s 2 and 8 on the MANX s c a l e l o a d e d -^51 and .61 on t h e enjoyment f a c t o r . The i t e m s were: "2. When I hear the word mathematics, I have a f e e l i n g o f d i s l i k e , " and "8. I have a good f e e l i n g toward mathematics." Both i t e m s tapped an e m o t i o n a l domain w i t h o u t c h a r a c t e r i z i n g a p a r t i c u l a r form of f e e l i n g o t h e r t h a n a " d i s l i k e " o r "good" f e e l i n g . I t would appear t h a t i n t h e case of i t e m number 2 t h e i n t e n t was t o get a r e s p o n s e a s s o c i a t e d w i t h s t r e s s w i t h o u t u s i n g the word a n x i e t y . The i n t e n t o f t h e e i g h t h i t e m l i k e l y was t o get a r e s p o n s e o p p o s i t e t o a n x i e t y . As a f u r t h e r example, i t e m s 4, 5 and 8 o f t h e SELFCON s c a l e l o a d e d - . 4 6 , .32 an a n x i e t y f a c t o r . The i t e m s were: "4. No m a t t e r how h a r d I t r y I cannot u n d e r s t a n d mathematics," "5 . I o f t e n t h i n k , ' I c a n ' t do i t , » when a mathematics problem seems h a r d , " and "8. I f I don't see how t o work a mathematics problem r i g h t away, I never get i t . " There i s an u n d e r l y i n g sense o f f r u s t r a t i o n i n t h e s e i t e m s which would e x p l a i n the r e l a t i o n s h i p w i t h a n x i e t y . I n t u r n , i t e m 8 of the ENJOY s c a l e , "Mathematics i s more o f a game t h a n i t i s hard work," l o a d e d on t h e s e l f - c o n c e p t f a c t o r , and gave a sense o f degree of d i f f i c u l t y . These comments are not meant as c r i t i c i s m of the s c a l e c o n s t r u c t i o n b u t r a t h e r a s an o b s e r v a t i o n o f t h e d i f f i c u l t y o f d e a l i n g w i t h a b s t r a c t i d e a s and b e i n g l i m i t e d , by the age o f th e s u b j e c t s , t c a s m a l l v o c a b u l a r y . A l t h o u g h one c o u l d argue 136 on the b a s i s of t h e s e d a t a t h a t the i t e m s c o u l d be p l a c e d i n more a p p r o p r i a t e s c a l e s , i t c o u l d a l s o be argued t h a t the c o m p l e x i t i e s of language t o g e t h e r w i t h t h e complex d e t e r m i n a n t s o f t h e a f f e c t i v e domain make c o n s t r u c t i o n o f c o m p l e t e l y i ndependent s c a l e s i m p o s s i b l e . B a t h e r than t r y i n g t o o p t i m i z e on the arrangement of the i t e m s , t h e components of v a r i a n c e may be b e t t e r accounted f o r by f a c t o r a n a l y s i s f o l l o w e d by o r t h o g o n a l r o t a t i o n . Indeed t h a t was t h e approach t a k e n i n t h i s s t u d y . The r e ason f o r t h e o v e r l a p of the s c a l e s i n the Value F a c t o r (VF) was c l e a r : the a u t h o r c o n s t r u c t e d t h e VALSEL s c a l e t o be p a r a l l e l t o the Sandman s c a l e . The o n l y major d i f f e r e n c e was t h a t t h e s t u d e n t was t o respond i n terms of b e n e f i t s t o h i m s e l f r a t h e r t h a n s o c i e t y . The argument f o r c o n s t r u c t i n g t h e s c a l e i n t h i s manner was p r e s e n t e d i n Chapter 3. I t i s s u f f i c i e n t here t o note t h a t t h e c o r r e l a t i o n between t h e two s c a l e s was .67, A l t h o u g h t h i s was moderately s t r o n g , a degree o f independence was suggested. However, t h e r e l i a b i l i t i e s o f t h e two s c a l e s , VALSOC .68 and VALSEL .69, suggest t h a t the "independence" might be e r r o r v a r i a n c e . Indeed when c o r r e c t e d f o r a t t e n u a t i o n due t o t h e r e l i a b i l i t i e s o f the t e s t s ( N u n n a l l y , 1967, p. 204) t h e c o r r e l a t i o n was .98. THE RELATION OF THE "BLOCK" VABIABLES TO ACHIEVEMENT C o r r e l a t i o n s 137 The i m p o r t a n c e ox" t h e " e m o t i o n a l b l o c k " was the common b e l i e f t h a t i t had u s u a l l y been a s s o c i a t e d w i t h poor achievement. T h e r e f o r e , i t was h y p o t h e s i z e d t h a t the v a r i a b l e s were c o r r e l a t e d w i t h achievement. a p a r t from IABF the a f f e c t i v e v a r i a b l e s were s i g n i f i c a n t l y c o r r e l a t e d w i t h achievement. MANX c o r r e l a t e d -.410, -.387, and -.331 wi t h COMP, CONC and PBOB r e s p e c t i v e l y . These c o r r e l a t i o n s compared w i t h t h o s e of A l p e r t and Haber (1960) who c o r r e l a t e d f a c i l i t a t i n g a n x i e t y and GPA on t h r e e samples of d a t a and found c o r r e l a t i o n s of .36, .32 and .50. Note t h a t t h e d i f f e r e n c e i n s i g n i s an a r t i f a c t o f s c o r i n g . A s i m i l a r p r o c e d u r e w i t h d e b i l i t a t i n g a n x i e t y r e v e a l e d c o r r e l a t i o n s of -.45, -.08 and -.40. The c o r r e l a t i o n s o f t h i s s t u d y were a l s o c o n s i s t e n t w i t h Kahn (1969) who found c o r r e l a t i o n s of . 305 f o r males and .509 f o r f e m a l e s . The s t r o n g e s t c o r r e l a t i o n s were between SELFCON and achievement .457, .518, and .462 which compared w i t h Bachman's (1970) c o r r e l a t i o n s o f .48 f o r males and .55 f o r f e m a l e s when r e l a t i n g mathematics s e l f - c o n c e p t and mathematics achievement. I n terms o f t h e t h r e e achievement v a r i a b l e s , MANX and ENJOY were more s t r o n g l y r e l a t e d t o COMP t h a n t o CONC and PBOB. Whereas, VALSOC and VALSEL were more s t r o n g l y r e l a t e d t o CONC and PBOB tha n t o COMP. SELFCON was h i g h e s t f o r CONC and s i m i l a r f o r COMP and PBOB. I t was i n t e r e s t i n g t o c o n j e c t u r e about the p o s s i b l e r e a s o n s . Mathematics may be 138 thought of as d e a l i n g w i t h numbers and a g r e a t p r o p o r t i o n o f mathematics c l a s s time i n middle and upper elementary s c h o o l was spent on c a l c u l a t i o n . As MANX was c o r r e l a t e d h i g h e s t w i t h COMP a p o s s i b l e i m p l i c a t i o n was t h a t mathematics a n x i e t y b e g i n s i n t h e e a r l y y e a r s o f s c h o o l . The h i g h e r c o r r e l a t i o n s o f VALSOC and VALSEL t o CONC and PEOB appeared r e a s o n a b l e because o f t h e a p p l i e d n a t u r e o f t h e c o n t e n t i n those achievement a r e a s . The low c o r r e l a t i o n s of IAES and IARF w i t h achievement, t h e l a r g e s t was .190, were unexpected i n the l i g h t o f t h e l i t e r a t u r e . I t was ex p e c t e d t h a t s u c c e s s f u l s t u d e n t s would be w i l l i n g t o a c c e p t r e s p o n s i b i l i t y f o r t h e i r s u c c e s s , as i f a c c e p t i n g a due reward, and poor s t u d e n t s t o want t o r e j e c t r e s p o n s i b i l i t y f o r f a i l u r e as a defense t o r e t a i n s e l f - r e s p e c t * The o n l y c o r r e l a t i o n of a q u a d r a t i c component t h a t was expected from t h e o r y was t h a t o f SELFCON w i t h t h e achievement v a r i a b l e s . The h y p o t h e s i s stemmed from the t h e o r y o f Achievement M o t i v a t i o n which had s u b s t a n t i a l e x p e r i m e n t a l s u p p o r t f o r a q u a d r a t i c term f o r the s u b j e c t s ' ' p e r c e i v e d p r o b a b i l i t y of s u c c e s s . I n t h e p r e s e n t study i t was argued t h a t t h e s e l f — c o n c e p t of mathematics co r r e s p o n d e d c l o s e l y t o t h a t d i m e n s i o n . However, a l l t h r e e c o r r e l a t i o n s o f the q u a d r a t i c term of SELFCON were not s i g n i f i c a n t . The s t r o n g e s t g u a d r a t i c r e l a t i o n s were VALSOC w i t h COMP (.097) and MANX w i t h PBOB (.088) (p < . 0 5 ) . However as t h e maximum e x p l a i n e d v a r i a n c e was .9% and t h e v a r i a b l e s were n o t 139 c o n s i s t e n t t h e f i n d i n g was c o n s i d e r e d t o be o f no i m p o r t a n c e . M u l t i p l e B e q r e s s i o n c f S t a n d a r d i z e d Scores and F a c t o r S c o r e s The p e d a g o g i c a l l i t e r a t u r e has a s s o c i a t e d s e v e r a l v a r i a b l e s w i t h an " e m o t i o n a l b l o c k " i n mathematics. As i n d i c a t e d above, t h e s c a l e s measuring those v a r i a b l e s were a s s o c i a t e d w i t h each o t h e r y e t showed some degree of independence. I f the c o n s t r u c t of " e m o t i o n a l b l o c k " has v a l i d i t y then t h o s e v a r i a b l e s s h o u l d a l l c o n t r i b u t e t o the p r e d i c t i o n of achievement. I n o t h e r words t h a t p o r t i o n o f ind e p e n d e n t v a r i a n c e s h o u l d e x p l a i n some a d d i t i o n a l v a r i a n c e o f t h e achievement v a r i a b l e s . When a l l seven v a r i a b l e s were p r e s e n t i n t h e r e g r e s s i o n e g u a t i o n t h e r e was an i n c r e a s e , a l b e i t r a t h e r s m a l l , i n the m u l t i p l e c o r r e l a t i o n ; .483, .537 and .468 compared w i t h SELFCON by i t s e l f ; .457, .518 and.462. These d i f f e r e n c e s had .01 < p < .05 f o r COMP and CONC and p > .05 f o r PBOB. I n d e e d , from th e s e r e s u l t s one would a n t i c i p a t e t h a t one o r two o f t h e measures would e x p l a i n n e a r l y as much a s the whole s e t . Stepwise r e g r e s s i o n c o n f i r m e d t h i s . SELFCON appeared i n a l l t h r e e r e g r e s s i o n e q u a t i o n s w i t h MANX a p p e a r i n g o n l y i n t h e e q u a t i o n f o r COMP. I n the c r o s s v a l i d a t i o n a n a l y s i s t h e f i n d i n q s were s i m i l a r . Most o f t h e v a r i n c e was e x p l a i n e d by SELFCON. The othe s i x measures were weak e x c e p t f o r MANX f o r COMP and VALSOC f o r CONC. 140 The q u e s t i o n to be r a i s e d here i s whether the other v a r i a b l e s were excluded because the c o n s t r u c t s they measure would add no s i g n i f i c a n t e x p l a i n e d v a r i a n c e or whether stu d e n t s responding to SELFCON were i n f l u e n c e d by more than one c o n s t r u c t . The i s s u e i s one o f u n i d i m e n s i o n a l i t y of the measures. T h e r e f o r e , f a c t o r s c o r e c o e f f i c i e n t s c a l c u l a t e d from the o r t h o g o n a l r o t a t i o n of the p r i n c i p a l components were used to generate f a c t o r s c o r e s . The a n a l y s i s i n c l u d e d the f a c t o r s c o r e s and t h e i r i n t e r a c t i o n terms. This was a t e s t o f the Achievement M o t i v a t i o n theory t h a t i n t e r a c t i o n terms would i n c r e a s e e x p l a i n e d v a r i a n c e . The hypothesis was not supported. Indeed, cnl y one f a c t o r , MF, e x p l a i n e d 19.1%, 19.5%, and 16.1% of the variance of COMP, CONC, and PEOB, r e s p e c t i v e l y . Most of t h i s v a r i a n c e c o u l d be accounted f o r by SELFCON. I t should be r e c a l l e d t h a t one of the major c o n t e n t i o n s of t h i s study was t h a t a p o s s i b l e reason f o r the low c o r r e l a t i o n s between a f f e c t i v e v a r i a b l e s and achievement was the m u l t i v a r i a t e nature of the a f f e c t i v e domain and the p o t e n t i a l i n t e r a c t i o n s among the variables.. The present a n a l y s i s lends support to the m u l t i v a r i a t e nature o f the a f f e c t i v e domain i n that t h r e e f a c t o r s were needed to span the seven a f f e c t i v e measures. However, a t l e a s t with r e s p e c t to the seven v a r i a b l e s i n t h i s study, l i t t l e support c o u l d be found f o r the h y p o t h e s i s that the v a r i a b l e s i n t e r a c t i n the 141 p r e d i c t i o n of achievement. Moreover, the a n a l y s i s of the i n d i v i d u a l s c a l e s c o r e s suggested t h a t SELFCON was the s i n g l e most important v a r i a b l e of the t h r e e grouping under MF. As w i l l be noted l a t e r i n the s e c t i o n on f u t u r e r e s e a r c h t h i s should not mean t h a t t h e other v a r i a b l e s be d i s m i s s e d f o r they may be u s e f u l i n e i t h e r more s p e c i f i c achievement s i t u a t i o n s or at e a r l i e r grade l e v e l s . LIMITATIONS OF THE STUDY Before drawing c o n c l u s i o n s and s u g g e s t i o n s f o r f u r t h e r r e s e a r c h , some l i m i t a t i o n s o f the study should be emphasized. A major l i m i t a t i o n of t h i s study was i t s c o r r e l a t i o n a l n a t u r e . Because of t h i s no c a u s a l i n f e r e n c e s c o u l d be drawn. However, i t was u s e f u l f o r s u g g e s t i n g probable d i r e c t i o n s f o r c a u s a l r e s e a r c h . A second l i m i t a t i o n of t h i s study was the s e t o f measures used. The achievement v a r i a b l e s , although i n t h r e e p a r t s , computation, concepts and problem s o l v i n g , may s t i l l have been too g l o b a l f o r the p s y c h o l o g i c a l model chosen. I t may be the case t h a t the Achievement Motivation model operates a t the i n t r o d u c t i o n of new m a t e r i a l or new t e a c h i n g u n i t s . Thus while these t e s t s were summative i n nature spanning the m a t e r i a l of s e v e r a l y e a r s , q u i z z e s o r i e n t e d t o a r e c e n t l y taught t o p i c may produce d i f f e r e n t r e s u l t s . The a f f e c t i v e v a r i a b l e s i n c l u d e d here were only a subset of p o s s i b l e a f f e c t i v e s c a l e s . A t t i t u d e Toward Teacher 1 4 2 and M o t i v a t i o n i n Mathematics were two examples of s c a l e s not i n c l u d e d here. The l a t t e r , as i n t e r p r e t e d by Sandman (1973) , i s the degree t o which the student chooses t o work with mathematical m a t e r i a l s o u t s i d e c l a s s by c h o i c e r a t h e r than need. The i n d i v i d u a l s c a l e s themselves may e i t h e r have been too l i m i t e d i n the sampling of the c o n s t r u c t domain, i n some cases, or too g e n e r a l i n e t h e r s . Although t h i s was not l i k e l y t o be the case i n the Sandman s c a l e s because the t e s t s were c o n s t r u c t e d from a pool o f items i n c l u d e d i n many p r i o r s c a l e s , i t may w e l l have been the case t h a t the author c o n s t r u c t e d s c a l e Value o f Mathematics (VALSOC) was too l i m i t e d . As was i n d i c a t e d i n Chapter 3, t h i s s c a l e was made the same l e n g t h as the Sandman s c a l e s i n order t o keep the t o t a l a d m i n i s t r a t i o n time t o a minimum, and the items were, wherever p o s s i b l e , made p a r a l l e l to the Value of Mathematics f o r S o c i e t y s c a l e * On the other hand the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y S c a l e s , (IARS and IARF) may have been too g e n e r a l . They were c o n s t r u c t e d to measure w i l l i n g n e s s to take r e s p o n s i b i l i t y f o r success and f a i l u r e i n achievement s i t u a t i o n s , r a t h e r than i n the more r e s t r i c t e d s e t of mathematics achievement s i t u a t i o n s . Age l e v e l was the t h i r d l i m i t a t i o n . Although t h e Achievement M o t i v a t i o n model c o u l d be operant a t the i n t r o d u c t i o n of new m a t e r i a l i t may a l s o be the case t h a t students had formed major s e t s of a f f e c t i v e o r i e n t a t i o n s by the time they had reached s i x t h grade. T h e r e f o r e , i f more 1 4 3 g l o b a l measures o f achievement were t o be used then perhaps e a r l i e r grades would be more a p p r o p r i a t e . A f o u r t h l i m i t a t i o n was the p o p u l a t i o n from which the sample was drawn. I n s o f a r as socio-economic l e v e l and c u l t u r a l elements d i f f e r , the i n t e r r e l a t i o n s h i p s d e s c r i b e d may not h o l d . CONCLUSIONS I t would appear t h a t there was an a f f e c t i v e f a c t o r , MF (motivation f a c t o r ) , which was r e l a t e d to achievement a t the grade s i x l e v e l . T h i s f a c t o r was composed of the v a r i a b l e s c a l l e d , i n t h i s study, mathematics anxiety (MANX), s e l f - c o n c e p t o f a b i l i t y i n mathematics (SELFCON) and enjoyment of mathematics (ENJOY). These three v a r i a b l e s tend to c o r r e l a t e more s t r o n g l y with teacher rankings of students and a teacher-response Student-Behavior c h e c k l i s t than do the other a f f e c t i v e v a r i a b l e s . T h i s gave some evidence of the v a l i d i t y of these components as a measure of what co u l d be d e s c r i b e d as an "emotional b l o c k " i n mathematics. In the stepwise r e g r e s s i o n s SELFCON was always the f i r s t to be i n c l u d e d i n the a n a l y s i s of both Sample 1 and 2. In the a n a l y s i s of f a c t o r s c o r e s only MF, which had SELFCON as a component, was i n c l u d e d . From the Achievement M o t i v a t i o n model i t was p r e d i c t e d t h a t s e l f - c o n c e p t of a b i l i t y i n mathematics would correspond t o s u b j e c t i v e p r o b a b i l i t y of s u c c e s s . Since the p r e d i c t e d 144 r e l a t i o n s d i d not appear i n the analyses the correspondence was questioned. As SELFCON formed a f a c t o r together with ENJOY and MANX a more p l a u s i b l e correspondence was with the m o t i v a t i o n f a c t o r . In t u r n the achievement r e s p o n s i b i l i t y f a c t o r (AEF), p a r t i c u l a r l y the IAES component, showed evidence of independence from MF (motivation f a c t o r ) . I n the l i g h t of i t s i n t e r p r e t a t i o n as the student's b e l i e f i n h i s a b i l i t y t o c o n t r o l h i s achievement, a p o s s i b l e c o n c l u s i o n i s t h a t I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y may be i n t e r p r e t a b l e as s u b j e c t i v e p r o b a b i l i t y of success. ARF, however, d i d not d i s p l a y the i n t e r a c t i o n s p r e d i c t e d by the Achievement M o t i v a t i o n model. T h i s may have been because of the c o r r e l a t i o n a l , as opposed t o experimental, nature • of the study. As the achievement r e s p o n s i b i l i t y s c a l e s f o c u s on the a t t r i b u t e s of achievement such as l u c k , e f f o r t , i n t e r n a l c o n t r o l or e x t e r n a l c o n t r o l , the c o n f i r m a t i o n of the above i n t e r p r e t a t i o n , through f u t u r e r e s e a r c h , c o u l d l e a d to q u i t e s p e c i f i c programs f o r changing a student's s u b j e c t i v e p r o b a b i l i t y of success. Meichenbaura (1975) s t a t e d that For some r e s e a r c h e r s S's sense of c o n t r o l over the t h r e a t e n i n g s i t u a t i o n seems most c r i t i c a l . Presumably a person w i l l a p p r a i s e a p o t e n t i a l l y a v e r s i v e s i t u a t i o n as l e s s t h r e a t e n i n g i f he p e r c e i v e s h i m s e l f as having some measure of c o n t r o l over the a v e r s i v e s t i m u l u s . (p. 239) S e l f - c o n c e p t was found to be a c o r r e l a t e of achievement as were mathematics a n x i e t y and enjoyment. However, the v a r i a n c e of achievement scores accounted f o r by 1 4 5 a n x i e t y and enjoyment was v i r t u a l l y t h a t accounted f o r by s e l f - c o n c e p t as was evidenced by the e x c l u s i o n of the former two v a r i a b l e s i n the stepwise r e g r e s s i o n a n a l y s i s . There was an e x c e p t i o n i n the case of computation when anx i e t y was a l s o i n c l u d e d . T h i s was confirmed i n the c r o s s v a l i d a t i o n a n a l y s i s . The f a c t o r a n a l y s i s was another piece of evidence as the three v a r i a b l e s loaded on the same f a c t o r and ag a i n , with the e x c e p t i o n o f the equation f o r computation where t h e value f a c t o r was i n c l u d e d , the m o t i v a t i o n f a c t o r was the s o l e s e l e c t e d f a c t o r . Parsimony, then, would i n d i c a t e t h a t s e l f - c o n c e p t be accepted as the major explanatory component. However, i t i s the c o n t e n t i o n of the present author t h a t the focus of a t t e n t i o n should be on these t h r e e v a r i a b l e s as a group. When the c o r r e l a t i o n s between the th r e e were c o r r e c t e d f o r a t t e n u a t i o n s e l f - c o n c e p t was found t o c o r r e l a t e - . 8 7 and . 6 9 with mathematics a n x i e t y and enjoyment and mathematics a n x i e t y - . 9 0 with enjoyment. In a d d i t i o n S a r a s o n f s ( 1 9 6 5 ) a n a l y s i s of t e s t a n x i e t y i n d i c a t e d a c o g n i t i v e component* Meichenbaum ( 1 9 7 5 ) noted that some r e s e a r c h had demonstrated t h a t the s p e c i f i c emotion experienced by a person depends not o n l y upon h i s s t a t e o f p s y c h o l o g i c a l a r o u s a l , but a l s o on the way i n which s i n t e r p r e t s or l a b e l s t h i s s t a t e . They a l s o found t h a t t h i s l a b e l i n g process i t s e l f i s i n f l u e n c e d by what the person a t t r i b u t e s as being the o r i g i n of t h i s s e l f a r o u s a l * (p. 2 3 9 ) T h i s r e s e a r c h e r h o l d s t h a t the c o n s t r u c t o f s e l f - c o n c e p t should be i n t e r p r e t e d as the c o g n i t i v e component 146 of a n x i e t y . The lower c o r r e l a t i o n , c o r r e c t e d f o r a t t e n u a t i o n , of s e l f - c o n c e p t and enjoyment (-.69) could i n d i c a t e a l e s s e r c o g n i t i v e component i n enjoyment of mathematics. The d i s a t t e n u a t e d c o r r e l a t i o n of -.88 of enjoyment with a n x i e t y may suggest an emoticnal counter to a n x i e t y . Of c o n s i d e r a b l e note was the very minor r o l e of value o f mathematics i n p r e d i c t i n g achievement. However, i n r e t r o s p e c t , i t was reasonable i n that the i n c e n t i v e s a s s o c i a t e d with the value of mathematics tend to be delayed r a t h e r than immediate f o r grade s i x students. Compared with the immediate e f f e c t s of a n x i e t y and enjoyment i t was l i t t l e wonder t h a t value was of l i t t l e importance i n p r e d i c t i n g achievement i n mathematics. I t should not be thought t h a t value o f mathematics i s o f no importance. I t may be the case t h a t i t should be an important and d e s i r a b l e a f f e c t i v e outcome i n and o f i t s e l f . The r e s u l t s of t h i s study, however, do suggest t h a t i n c r e a s e d achievement not be expected as a r e s u l t o f t e a c h i n g towards value of mathematics as an a f f e c t i v e outcome. FUTURE BESEABCH As i n d i c a t e d i n the s e c t i o n on l i m i t a t i o n s c o r r e l a t i o n a l s t u d i e s cannot imply c a u s a l r e l a t i o n s . However, one advantage c o r r e l a t i o n a l s t u d i e s have over c a u s a l s t u d i e s i s t h a t o f t e n they can d e a l with more v a r i a b l e s or measures and suggest a p p r o p r i a t e c o v a r i a t e s and p o t e n t i a l 147 i n t e r r e l a t i o n s f o r c a u s a l a n a l y s i s . The d i s c u s s i o n of f u t u r e r e s e a r c h w i l l be d i v i d e d i n t o two s e c t i o n s ; c o r r e l a t i o n a l and expe r i m e n t a l . C o r r e l a t i o n a l S t u d i e s In t h i s study i t was argued t h a t Self-Concept of A b i l i y i n Mathematics was the e g u i v a l e n t to an assessment o f the s u b j e c t i v e p r o b a b i l t i y of suc c e s s . S e l f - c o n c e p t was found, though, t o c o r r e l a t e h i g h l y with anxiety and enjoyment which are c l o s e r to mo t i v a t i o n measures. T h i s f i n d i n g and s e v e r a l other c o n s i d e r a t i o n s l e d to an a l t e r n a t i v e i n t e r p r e t a t i o n o f s e l f - c o n c e p t . I t could be t h a t a student's answers on the s e l f - c o n c e p t s c a l e were t r u t h f u l and t h a t they were e s t i m a t e s of the mark he thought he would r e c e i v e . Yet t h i s may not correspond t o h i s p e r c e p t i o n of success i n mathematics. For a "D" student success might w e l l be an i n c r e a s e to a "C" i n which case a l a r g e p r o p o r t i o n of students would s t i l l surpass him. I t i s a l s o i n t e r e s t i n g t h a t the Achievement M o t i v a t i o n model p r e d i c t e d c o r r e l a t i o n s between the q u a d r a t i c term of s u b j e c t i v e p r o b a b i l i t y o f success and achievement and yet only two marqinal (.01 < p < .05) c o r r e l a t i o n s of qu a d r a t i c terms were found: VALSOC with COMP and MANX with PROB. These c o n s i d e r a t i o n s suggest t h a t one p o s s i b l e d i r e c t i o n f o r f u t u r e research i s the development of a Mathematics I n t e l l e c t u a l R e s p o n s i b i l i t y s c a l e . I t cou l d then 148 be v a l i d a t e d i n comparison with the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y S c a l e and then have i t s c o n s t r u c t v a l i d a t i o n t e s t e d as a measure of the s u b j e c t i v e p r o b a b i l i t y of success. As suggested i n the l i m i t a t i o n s s e c t i o n , more r e s e a r c h might be done with a view to the expansion of the Value of Mathematics f o r O n e s e l f s c a l e . I t may be the case t h a t VALSOC was not r e p r e s e n t i v e enough f o r young s t u d e n t s . Thus two stages of r e s e a r c h are i n d i c a t e d . The f i r s t i s t o s o l i c i t from youngsters the reasons why mathematics i s important f o r them* For example, an open ended q u e s t i o n c o u l d be used such as "Mathematics i s important to me because ?" The responses to such a question c o u l d form the b a s i s of a L i k e r t s c a l e which c o u l d be used i n a manner s i m i l a r t o t h a t i n t h i s study. I t was a l s o pointed out i n the l i m i t a t i o n s s e c t i o n t h a t the Achievement M o t i v a t i o n model may be v a l i d a t the i n t r o d u c t o r y staqe f o r new m a t e r i a l . The experience of the present author teaching a year long course i n geometry bears t h i s out. At the f i r s t of f o u r r e p o r t i n g s e s s i o n s many good al g e b r a students were a l e t t e r grade or two lower than expected and t h e i r p l a c e s were taken by students who had t y p i c a l l y performed a t a lower l e v e l in. a l g e b r a . However by the second r e p o r t i n g s e s s i o n i t was an e x c e p t i o n a l case t h a t had not r e v e r t e d t o a ranking s i m i l a r t o t h a t i n the p r e v i o u s algebra course. I f t h i s i n f o r m a l o b s e r v a t i o n has any f o r c e then an a p p r o p r i a t e study would take account of the change 149 over time of a group of students i n a new mathematics s i t u a t i o n . Such a study w i t h p e r i o d i c t e s t i n g c o u l d be used t o answer some c a u s a l guestions i f c r o s s — p a n e l c o r r e l a t i o n technigues were used. I t may be the case t h a t i f samples c o u l d be i d e n t i f i e d t h a t were, f o r example, more or l e s s achievement o r i e n t e d , then t h e i n t e r r e l a t i o n s d e s c r i b e d above might be q u i t e d i f f e r e n t . E x p e r i m e n t a l S t u d i e s . The major f i n d i n g of t h i s study was t h a t the m o t i v a t i o n f a c t o r which c o n s i s t e d of s e l f - c o n c e p t o f mathematics, anxiety i n mathematics, and enjoyment of mathematics was t h e only c o n s i s t e n t f a c t o r p r e d i c t i n g achievement and t h a t was a l s o c o n s i s t e n t a c r o s s sex groups. F u r t h e r , SELFCON formed the b a s i s of t h a t f a c t o r . A q u e s t i o n t h a t should be asked i s "Are these measures r e l a t e d because responses t o them are based on s i m i l a r c o n s t r u c t s , or are they r e l a t e d because one of them causes the other two or two of them cause the t h i r d , or i s t h e r e yet another cause u n d e r l y i n g the t h r e e . I n s o f a r as achievement l e v e l causes s t r e s s then s e l f - c o n c e p t of achievement should be r e l a t e d t o a n x i e t y and, as noted i n the previous s e c t i o n , may be i n t e r p r e t e d as the c o g n i t i v e component of a n x i e t y . In t u r n , an i n c r e a s e i n enjoyment, as the "emotional" aspect of anxiety, would be expected to reduce a n x i e t y . The hypothesis t h a t t h i s 150 e x p e r i m e n t e r would h o l d i s t h a t as l o n g as enjoyment i s s u s t a i n e d , t h e n a n x i e t y w i l l he reduced and s e l f - c o n c e p t o f achievement w i l l he i n c r e a s e d . I t s h o u l d be noted t h a t the r e s u l t s o f t h i s s t u d y do n o t show IABS and IABF as i m p o r t a n t v a r i a b l e s i n the p r e d i c t i o n of mathematics achievement. However, s e v e r a l p o s s i b i l i t i e s have a l r e a d y been suggested* The f i r s t i s t h a t the measures may i n v i t e r e s p o n s e s not n e c e s s a r i l y r e l a t e d s p e c i f i c a l l y t o achievement i n mathematics,. The second i s t h a t t h e i m p o r t a n c e of t h e two v a r i a b l e s may be i n t h e i n t r o d u c t o r y s t a g e o f m a t e r i a l . The t h i r d i s t h a t r e l a t i o n s not showing up i n c o r r e l a t i o n a l s t u d i e s may show up i n e x p e r i m e n t a l s t u d i e s . Thus i t i s p o s s i b l e t h a t f o c u s s i n g on t e c h n i q u e s t o change the a t t r i b u t i o n o f s u c c e s s and f a i l u r e may i n c r e a s e l e a r n i n g . I t i s j u s t t h i s p o s s i b i l i t y t h a t B a r - T a l d i s c u s s e s (1978) i n h i s a r t i c l e on a t t r i b u t i o n t h e o r y and achievement. In summary one c o u l d c o n c e i v e of d e s i g n i n g e x p e r i m e n t a l p r o cedures t o (a) change s e l f - c o n c e p t of a b i l i t y , (b) i n c r e a s e enjoyment and, (c) a l t e r the a t t r i b u t i o n o f s u c c e s s and f a i l u r e * A p o t e n t i a l l y i n f o r m a t i v e study would use each o f the p r o c e d u r e s i n a t h r e e f a c t o r , f u l l y c r o s s e d d e s i g n w i t h two l e v e l s i n each. The two l e v e l s o f each f a c t o r would c o r r e s p o n d t o t h e p r e s e n c e or absence of t h e p r o c e d u r e . A p r e t e s t o f mathematics a n x i e t y c o u l d be i n c l u d e d as a f o u r t h f a c t o r w i t h two or t h r e e l e v e l s . Again t h i s f a c t o r would 151 f u l l y c r o s s the other t h r e e . 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J o u r n a l of E d u c a t i o n a l Psychology, 1958, 49, 173-181,. P a n i a s i g u i , I . , & Knight, F. B. The e f f e c t of awareness of success or f a i l u r e * In F. B. Knight ( E d i ) , Twenty-ninth yearbook of the N a t i o n a l S o c i e t y f o r the Study of E d u c a t i o n : r e p o r t of the s o c i g t y ^ s committee on a r i t h m e t i c . Chicago: U n i v e r s i t y of Chicago P r e s s , 1930. P a t t e r s o n , A. R e l i a b i l i t y and v a l i d i t y o f s e l f - c o n c e p t s c a l e s . In W. Brookover, E. E r i c k s o n , and L. J o i n e r (Eds.). S e l f - c o n c e p t of a b i l i t y and s c h o o l achievement, I I I : r e l a t i o n s h i p of s e l f - c o n c e p t to achievement i n high s c h o o l . E d u c a t i o n a l Research S e r i e s , 36, C o - o p e r a t i v e Besearch P r o j e c t , 2831. E a s t L a n s i n g , Michigan State U n i v e r s i t y , 1967, P i e r s , E. V., & H a r r i s , D. A. Age and other c o r r e l a t e s of s e l f - c o n c e p t i n c h i l d r e n . J o u r n a l of E d u c a t i o n a l  Psychology, 1964, 55, 91-95. P i k a a r t , L., & Wilson, J . W. The r e s e a r c h l i t e r a t u r e . In W. C. Lowry (Ed.), The slow l e a r n e r i n mathematics, Beston, V i r g i n i a : The N a t i o n a l C o u n c i l of Teachers of Mathematics, 1972. Poffenberger T. M., & Norton, D A. F a c t o r s i n the f o r m a t i o n of a t t i t u d e toward mathematics. J o u r n a l of E d u c a t i o n a l  Besearch, 1959, 52, 171-177. Purkey, W. W. S e l f - c o n c e p t and s c h o o l achievement. Englewood C l i f f s , N.J.: P r e n t i c e - H a l l , 1 970 . 162 Baynor, J . 0. B e l a t i o n s h i p s between a c h i e v e m e n t - r e l a t e d m o t i v e s , f u t u r e o r i e n t a t i o n , and academic performance. J o u r n a l of P e r s o n a l i t y and S o c i a l P s y c h o l o g y . 1970, 15, 28-33. Baynor, J . 0. F u t u r e o r i e n t a t i o n i n t h e s t u d y o f achievement m o t i v a t i o n . In J . W. A t k i n s o n and J,. 0. Baynor ( E d s . ) , M o t i v a t i o n and achievement. Washington: Winston & Sons, 1974. B i e d e s e l , C. A. S t a n f o r d Achievement T e s t : a r i t h m e t i c t e s t s . In 0. K Buros ( E d . ) . The s i x t h mental measurements  yearbook. New J e r s e y : Gryphon P r e s s , 1965* Bomberg, T. A., & W i l s o n , J . W. The development o f t e s t s . NLSMA B e p o r t s , No. 7. S t a n f o r d * C a l i f . : S c h o o l Mathematics Study Group, 1969. B o t t e r , J . B. G e n e r a l i z e d e x p e c t a n c i e s f o r i n t e r n a l v e r s u s e x t e r n a l c o n t r o l o f r e i n f o r c e m e n t . P s y c h o l o g i c a l Monographs. 1966, 80, 1-28,. Sandman, B. S. The development, v a l i d a t i o n , and a p p l i c a t i o n o f a m u l t i - d i m e n s i o n a l mathematics a t t i t u d e i n s t r u m e n t . ( D o c t o r a l D i s s e r t a t i o n , U n i v e r s i t y o f M i n n e s t o t a , 1973). D i s s e r t a t i o n A b s t r a c t s I n t e r n a t i o n a l , 1974, 34, 7054A-7055A. ( U n i v e r s i t y M i c r o f i l m s No. 74-10,626) Sarason I . G. T e s t a n x i e t y , a t t e n t i o n , and the g e n e r a l problem of a n x i e t y . I n C. D. S p i e l b e r g e r and I . G. Sarason ( E d s . ) . S t r e s s and a n x i e t y ( V o l , 1),.New Y o r k : John W i l e y , 1975. S a r a s o n , S. B., Davidson, K. S., L i g h t h a l l , F. F., & W a i t e , B-. B. A t e s t a n x i e t y s c a l e f o r c h i l d r e n . C h i l d Development, 1958, 29, 10 5-113. S a r a s o n , S. B., Davidson, K. S., L i g h t h a l l , F. F., Waite, B. fi,, S Bubush, B. K. A n x i e t y i n e l e m e n t a r y s c h o o l c h i l d r e n . New York: John Wiley and Sons, I n c i , 1960. S c h u l t z , B- W. C h a r a c t e r i s t i c s and needs o f t h e slow l e a r n e r . In W. C. Lowry, (Ed.), The slow l e a r n e r i n mathematics. B e s t o n , V i g i n i a : The N a t i o n a l C o u n c i l o f T eachers o f Mathematics, 1972. S i l v e r b l a n k , F. A s e l e c t i o n of s e l e c t e d p e r s o n a l i t y f a c t o r s between s t u d e n t s t a l e n t e d i n E n g l i s h and s t u d e n t s t a l e n t e d i n M a t h e m a t i c s , C a l i f o r n i a J o u r n a l o f E d u c a t i o n a l B e s e a r c h , 1973, 24, 61-65. 163 S i u , P. K. B e i a t i o n s h i p s between m o t i v a t i o n a l p a t t e r n s and academic achievement i n C h i n e s e and P u e r t o R i c a n second and t h i r d grade s t u d e n t s . ( D o c t o r a l d i s s e r t a t i o n , Fordham U n i v e r s i t y , 1972). D i s s e r t a t i o n A b s t r a c t s I n t e r n a t i o n a l . 1973, 33, 407A. ( U n i v e r s i t y M i c r o f i l m s No. 73-1519) ~ S m i t h , P. A. A f a c t o r a n a l y t i c s t u d y o f t h e s e l f - c o n c e p t . J o u r n a l o f C o n s u l t i n g P s y c h o l o g y , 1960, 24, 191. Sowder, L. High v e r s u s low geometry a c h i e v e r s i n the NLSMA Y - p o p u l a t i o n . J o u r n a l f o r B e s e a r c h i n Mathematics E d u c a t i o n . 1974, 5, 20-27. Spear, P. S. M o t i v a t i o n a l e f f e c t s of p r a i s e and c r i t i c i s m on c h i l d r e n ' s l e a r n i n g . D e v e l o p m e n t a l P s y c h o l o g y , 1970, 3, 124-132. S u i n , R. M. The a p p l i c a t i o n o f s h o r t term v i d e o - t a p e t h e r a p y f o r t h e t r e a t m e n t o f t e s t a n x i e t y of c o l l e g e §tu dents,. P r o g r e s s r e p o r t . C o l o r a d o "Sra te U n i v e r s i t y , 19 70. S u i n , B. M., E d i e , C* A., N i c o l l e t t i , J . , & S p i n e l l i , P. B. The MABS, a measure o f mathematics a n x i e t y : p s y c h o m e t r i c d a t a . J o u r n a l of C l i n i c a l P s y c h o l o g y , 197 2, 28, 373-375. Suydam, M. N., & Weaver, J . F. Be s e a r c h on mathematics e d u c a t i o n (K-12) r e p o r t e d i n 1973. J o u r n a l f o r B e s e a r c h i n Mathematics E d u c a t i o n . 1974, 5, 283-2721 Suydam, M. N., & Weaver, J . F. Besearch on mathematics e d u c a t i o n (K-12) r e p o r t e d i n 1974. J o u r n a l f o r B e s e a r c h i n Mathematics E d u c a t i o n . 1975, 6, 253-282. Suydam, M. N., & Weaver, J . F. Besearch on mathematics e d u c a t i o n r e p o r t e d i n 1975. J o u r n a l f o r B e s e a r c h i n  Mathematics E d u c a t i o n , 1976, 7, 193-257. Suydam, M. N., . & Weaver, J . F. B e s e a r c h on mathematics e d u c a t i o n r e p o r t e d i n 1976. J o u r n a l f o r Besearch i n Mathematics E d u c a t i o n . 1977, 8, 242-316: Suydam, M. N., & Weaver,- J . F„ Besearch on mathematics e d u c a t i o n r e p o r t e d i n 1977. J o u r n a l f o r Bes e a r c h i n Mathematics E d u c a t i o n . 1978, 9, 242-311. S z e t e l a , W. The e f f e c t s o f t e s t a n x i e t y and s u c c e s s / f a i l u r e on mathematics performace i n grade eight,* J o u r n a l f o r Besearch i n Mathematics E d u c a t i o n . 1973, 4, 152-160. Thorn d i k e , B. L. E d u c a t i o n a l measurement. Washington: American C o u n c i l on E d u c a t i o n , 1971. 164 T a f f e l , S. J . , & O'Leary, K. D. B e i n f o r c i n g math with more math: choosing s p e c i a l academic a c t i v i t i e s as a reward f o r academic performance. J o u r n a l of E d u c a t i o n a l Psychology, 1976, 68, 579-587. Tulock, M. K. Emotional b l o c k s i n mathematics* Mathematics Teacher, 1957, 50, 572-576. Weiner, B. a t t r i b u t i o n t h e o r y , achievement m o t i v a t i o n and the e c u c a t i o n a l p r o c e s s . Beview of E d u c a t i o n a l Research, 1972, 42, 2032 203-214. Weiner, B., Heckhausen, H., Meyer, W. U* , S Cook, B. E,. Causal a s c r i p t i o n and achievement behavior: a c o n c e p t u a l a n a l y s i s of e f f o r t and r e a n a l y s i s of l o c u s of c o n t r o l . J o u r n a l o f P e r s o n a l i t y and S o c i a l Psychology, 1972, 2 J , 239-248. Weiner, B., & Kukla, A. An a t t r i b u t i o n a l a n a l y s i s of achievement m o t i v a t i o n . J o u r n a l of P e r s o n a l i t y and S o c i a l  Psychology, 1970, 15, 1-20. Wells, D. w. , & S h u l t e , A. P. An example of p l a n n i n g f o r low a c h i e v e r s . I n M, Bosskopf (Ed.), ffhe t e a c h i n g of secondary s c h o o l mathematics. Washington: the N a t i o n a l C o u n c i l of Teachers of Mathematics, 1970. Weston, D. 1. An e x p l o r a t i o n of the i n t e r r e l a t i o n s h i p s among c h i l d r e n ' s a r i t h m e t i c achievement, t h e i r s t y l e s of l e a r n i n g , t h e i r r e s p o n s i b i l i t y f o r i n t e l l e c t u a l academic , achievement and t h e i r parents' a t t i t u d e s . ( D o c t o r a l d i s s e r t a t i o n , Wayne State U n i v e r s i t y , 1968),* D i s s e r t a t i o n A b s t r a c t s I n t e r n a t i o n a l , 196 9, 30, 1087A-1088A. ( U n i v e r s i t y M i c r e f i l a s ~ N o . 69-14,690) Whitlock, C., & B u s h e l l , D., J r . Some e f f e c t s of "back-up" r e i n f o r c e r s on r e a d i n g behavior. J o u r n a l of Experimental C h i l d Psychology, 1967, 5, 50-57. ~ Wine, J . Test a n x i e t y and d i r e c t i o n of a t t e n t i o n . P s y c h o l o g i c a l B u l l e t i n , 1971, 76, 92-105* Winer, B. J . S t a t i s t i c a l p r i n c i p l e s i n experimental d e s i g n , (2nd ed.). New York: McGraw-Hill, 1971. Wolk, S., & DuCette, J. The moderating e f f e c t of l o c u s of c o n t r o l i n r e l a t i o n to achievement-motivation v a r i a b l e s . J o u r n a l of P e r s o n a l i t y , • 1 9 7 3 , 4J, 5S-70. Wylie, E. C. The s e l f - c o n c e p t : a review of methodological c o n s i d e r a t i o n s and measuring instruments (Vol* 1). U n i v e r s i t y of Nebraska Press, 166 Appendix A INSTRUCTIONS FOR BEHAVIORAL CHECKLIST On the BACK cf the mark-sense cards provided (one f o r each student) w r i t e the i n d e n t i f i c a t i o n number of each o f your grade s i x s t u d e n t s . DO NOT MARK IN THE COLUMNS UNDEB THE HEADING "IDENTIFICATION NUMBER" on the f r o n t of the card mark the o v a l with 1 i n i t under the a p p r o p r i a t e item number i f you have n o t i c e d the student e x h i b i t i n g t h a t behavior i n your mathematics c l a s s during the year,. Some of the students w i l l have a blank card, or you might have only checked o f f one o f the behaviors. However, pl e a s e i n c l u d e even blank cards with an i d e n t i f i c a t i o n number on t h e i r back. While the student i s doing mathemtics have you observed t h a t he/she 1,. tends to give random answers to questions d u r i n g mathematics c l a s s ? 2. appears t e n s e during mathematics l e s s o n s ? 3. expresses a n x i e t y or nervousness about mathematics? 4. tends to i n c r e a s e d i s r u p t i v e b e h a v i o r d u r i n g the mathematics c l a s s ? 5. says t h a t no matter what he/she does he/she c a n ' t do mathematics? 167 6. has hands t h a t shake when doing matematics? 7. says that mathematics i s u s l e s s ? 8. sometimes r e f u s e s to answer q u e s t i o n s d u r i n g mathematics period? 9. f i d g e t s more during mathematics l e s s o n s ? When you have f i n i s h e d please put the cards i n the envelope with the YELLOW t a b . 168 Appendix B INSTRUCTIONS FOR RANKING OF STUDENTS On the s e t of cards p r o v i d e d , write the names of each o f your grade s i x students one to a card. Order t h e cards from most l i k e the d e s c r i p t i o n below to l e a s t l i k e i t . The name of the student most l i k e the d e s c r i p t i o n should appear on the top of the deck, O B the piece of paper provided, l i s t the i d e n t i f i c a t i o n numbers of the students i n the same order as the names appear on the c a r d s : from most l i k e the d e s c r i p t i o n to l e a s t l i k e i t . Beside each i d e n t i f i c a t i o n number i n d i c a t e male or female. The f o l l o w i n g i s a d e s c r i p t i o n of o b s e r v a b l e c h a r a c t e r i s t i c s of students who may have an "emotional b l o c k " i n mathematics. Try not to c o n s i d e r achievement or a b i l i t y . Very good s t u d e n t s may e x h i b i t the b l o c k and very poor students may not. A student with the b l o c k may give random answers to g u e s t i o n s or may r e f u s e to answer them at a l l . He/she may appear tense, have hands t h a t shake as he/she w r i t e s , f i d g e t s or i n c r e a s e d i s r u p t i v e behavior i n the mathematics c l a s s . The student may t e l l you t h a t he/she f e e l s anxious or nervous about mathematics or t h a t mathematics i s u s e l e s s . He/she may s t a t e t h a t no matter how hard he/she works i t seems t o make no d i f f e r e n c e . When you have f i n i s h e d please put the paper i n the envelope 169 with the YELLOW tab. 170 Appendix C ADMINISTRATION BOOKLET Thank you f o r v o l u n t e e r i n g your time and t h a t o f your students to enable me to gather the data I need f o r my d i s s e r t a t i o n . I hope the t e s t r e t u r n s and the r e s u l t s of my study w i l l be o f help and i n t e r e s t t o you. There are three aspects to t h i s study: 1. A student g u e s t i o n n a i r e about a t t i t u d e s and f e e l i n g s towards mathematics. The q u e s t i o n a i r e i s i n 3 twenty minute p a r t s . 2. A s e t of achievement t e s t s a l s o i n t h r e e p a r t s , each o f which i s t h i r y - f i v e minutes long; 3. A s e t of m a t e r i a l s f o r you t o f i l l out about your s t u d e n t s . T h i s can be done d u r i n g the t e s t p e r i o d s so that your time commitment i s not i n c r e a s e d . lo r e t a i n the anonymity of the student and to p r o t e c t the c o n f i d e n t i a l i t y o f your r e p l i e s and those of your s t u d e n t s , I have asked you, i n the encl o s e d m a t e r i a l s , t o g i v e them an i d e n t i f i c a t i o n number. The numbers should be c o n s e c u t i v e beginning at 1 and i n the same order as your c l a s s l i s t . When I r e t u r n the r e s u l t s of the achievement t e s t s , o n l y the student number w i l l appear. Although the study i s about mathematics THESE IS NO NEED TO DO ALL THE TESTING DURING SCHEDULED MATHEMATICS PERIODS. In f a c t , f o r at l e a s t the f i r s t two q u e s t i o n n a i r e s i t would be p r e f e r a b l e t o g i v e them i n some other p e r i o d . DO NOT MENTION THAT THE QUESTIONNAIRES HAVE ANYTHING TO DO I 1 7 1 WITH MATHEMATICS AS THE FIRST TWO QUESTIONNAIRE SECTIONS CONCERN SCHOOL IN GENERAL. Please r e f r a i n from making ANY e v a l u a t i v e comments about the q u e s t i o n n a i r e or the use of r e s u l t s u n t i l AFTER ALL TESTING IS DONE. In p a r t i c u l a r sudents w i l l want to know what use you i n t e n d to make o f the mathematics achievement t e s t r e s u l t s : Are you qoing t o use then f o r grading? Are they going to count toward the r e p o r t ? The best answer t o give i s t h a t the t e s t r e s u l t s are going t o be used by you to f i n d out areas of s t r e n g t h s and weaknesses so t h a t you can plan f u t u r e work. Try t o a v o i d a d e n i a l o f the use of the t e s t r e s u l t s f o r g r a d i n g u n t i l AFTER the l a s t t e s t . I want t o encourage the s t u d e n t s to work as hard as p o s s i b l e ; j u s t as they would do f o r you on a c l a s s t e s t . I f you have any questions please c o n t a c t me at t h e s c h o o l or at my home. Thanks a g a i n . Jim G a s k i l l 172 TEACHER'S ADMINISTRATION INSTRDCTIONS STUDENT QUESTIONNAIRE From your c l a s s l i s t a s s i g n each. student an i d e n t i f i c a t i o n number by numbering your l i s t i n order* Each sheet f i l l e d i n by the student and ca r d s f i l l e d i n by you t h a t r e l a t e t o i n d i v i d u a l s t u d e n t s must have the same number. T h i s number r e t a i n s c o n f i d e n t i a l i t y of student i n f o r m a t i o n , a l l o w s me t o c o r r e l a t e a l l the i n f o r m a t i o n about each student, and enables me t o communicate student r e s u l t s back t o you. Before you begin a d m i n i s t e r i n g the q u e s t i o n a i r e s , p l e a s e make sure you have 1. a c a s s e t t e tape r e c o r d e r with speaker (from your school) . 2. a cassete tape l a b e l l e d SIDE ONE-3. an answer sheet f o r each student* 4. ten e x t r a p e n c i l s (Just i n case some students don't have one.) 5. an envelope with a BLUE tab. 6. a q u e s t i o n n a i r e f o r each student. P l e a s e attempt t o a d m i n i s t e r the q u e s t i o n n a i r e s i n the morning on two c o n s e c u t i v e days. I suggest the f i r s t two before r e c e s s , separated by f i v e t o t e n minutes and the t h i r d on the second day b e f o r e r e c e s s . 173 For purposes of s t a n d a r d i z a t i o n the above seguence would be p r e f e r a b l e . However, i f p l a t o o n i n g or other c o n s i d e r a t i o n s make i t i m p o s s i b l e , I w i l l l e a v e i t to your d i s c r e t i o n . But please have the q u e s t i o n n a i r e s administered d u r i n g the two days s p e c i f i e d on the envelope with the BLUE t a b . Would you a l s o be sure t h a t a l l m a t e r i a l s are c o l l e c t e d and returned to the o f f i c e when you are f i n i s h e d because other c l a s s e s w i l l be u s i n g the same p e n c i l s , tapes and q u e s t i o n n a i r e s . 1. Set up the tape r e c o r d e r with the tape c a s s e t t e SIDE ONE f a c i n g up* 2. Hand out the answer s h e e t s . T e l l the s t u d e n t s not to w r i t e on them u n t i l you t e l l them. 3. T e l l the students to write the number t h a t you w i l l g ive them i n the space i n the upper l e f t hand corner marked IDENTIFICATION NUMBER. Bead the numbers from your c l a s s l i s t . i 4. Say; • I am going to hand out some b o o k l e t s . Do not w r i t e i n them, and do not open them u n t i l I t e l l you. 5. Hand out the b o o k l e t s . Say: The teacher who has sent you these b o o k l e t s has asked me t o read t h i s l e t t e r to you. Eoys and g i r l s : I am i n t e r e s t e d i n h e l p i n q other boys and g i r l s to do b e t t e r i n s c h o o l . I w i l l be asking you some q u e s t i o n s — - q u e s t i o n s t h a t have no r i q h t or wrong answers. They are q u e s t i o n s about how you f e e l . You can answer h o n e s t l y because I w i l l not know your name. Your teacher w i l l g ive you a number th a t you w i l l w r i te on each of your answer sh e e t s . Your teacher w i l l not know your answers because your 174 answer sheets w i l l he p l a c e d i n an envelope, s e a l e d and d e l i v e r e d to me. However, even though we won't know who your are, your answers are very important so please answer c a r e f u l l y . On the answer sheet t h a t has been handed out, your answers to the f i r s t s e t of questions w i l l go under the columns with the heading QUESTION SET #1. Try not to chanqe any of your answers. Make your d e c i s i o n before you mark your sheet; I f you have to make a chanqe erase the o l d mark as well as ycu can. Each o f the f o l l o w i n q questions needs a yes or no answer. I f your answer i s yes, c i r c l e the YES beside the question number. I f your answer, i s no, c i r c l e the NO. Each q u e s t i o n must have one answer. Pl e a s e look a t the example at the bottom of the f i r s t page. Are there any questions? (Pause.) Open your b o o k l e t s and answer the q u e s t i o n s as they are read from the tape; 6. Turn on the tape. 7. Say: C l o s e your b o o k l e t s and t u r n them over. 8. Give them a 5 - 10 minute break* 9. Say: Open your b o o k l e t s to the second s e t of q u e s t i o n s . (Pause.) The answers to the next set of questions w i l l go i n the column- headed QUESTION SET #2. For the f o l l o w i n q q u e s t i o n s you must s e l e c t one of the two p o s s i b l e statements t h a t complete the sentence. Remember, each question must have one and only one answer. Look at the example; (Pause.) Are t h e r e any q u e s t i o n s ? (Pause,) Turn over your answer sheets. Answer the questions as they are read from the tape. 175 10. Turn on t h e t a p e . 11. At t h e end of the second s e t o f q u e s t i o n s STOP THE TAPE. DO NOT EEWIND. IT IS IN THE COERECT POSITION TO START THE NEXT SESSION. 12. COLLECT THE ANSWER SHEETS, THE BOOKLETS, AND THE EXTRA PENCILS. SECOND SESSION 1. S e t up t h e t a p e r e c o r d e r w i t h the c a s s e t t e SIDE ONE f a c i n q up. I f you have n o t rewound the tape i t s h o u l d be i n the c o r r e c t p o s i t i o n * Turn t h e t a p e on t o see i f QUESTION SET #3 i s announced. 2. Hand o u t t h e answer s h e e t s . Make sure t h a t t h e answer s h e e t s get back t o the c o r r e c t c h i l d e r n by u s i n g your c l a s s l i s t . 3. Hand out e x t r a p e n c i l s i f needed, 4. Hand out t h e b o o k l e t s . 5. Say: Open your b o o k l e t s t o the i n s t r u c t i o n s f o r t h e t h i r d s e t o f questions,. I n t h i s n e x t s e c t i o n you w i l l be g i v e n a number o f s e n t e n c e s * I f you agree w i t h t h e s tatement t r y t o d e c i d e i f ycu f e e l s t r o n g l y about i t , I f so you would c i r c l e t h e 1. I f you j u s t a g r e e , i- you would c i r c l e t h e 2. Or you might d i s a g r e e w i t h t h e s t a t e m e n t . I f so t r y t o d e c i d e i f you f e e l s t r o n g l y about i t . I f you do, c i r c l e t h e 5. I f you j u s t d i s a g r e e c i r c l e the 4. I f you c a n ' t make up y o u r mind or don't u n d e r s t a n d t h e s e n t e n c e , t h e n c i r c l e t h e 3. Look a t the example i n your b o o k l e t . (Pause.) Do you have any q u e s t i o n s ? (PAUSE). Answer each q u e s t i o n as i t i s r e a d from the t a p e . 6. Turn on the tape* 176 7. At the end of the t h i r d s e t of qu e s t i o n s STOP THE TAPE. REWIND THE TAPE 8. C o l l e c t the b o o k l e t s , answer sheets and e x t r a p e n c i l s . 9. Place the answer sheets i n the envelope with the BLUE tab on i t . 10. Return the cassete, b o o k l e t s , and answer sheets to the o f f i c e t o be picked up. Keep the p e n c i l s f o r the achievement t e s t s t h a t you w i l l give i n the next few days. THANK YOU FOR YOUR EEFORT AND ASSISTANCE. 177 TEACHES 1S ADMINISTSATION INSTBUCTIONS ACHIEVEMENT TESTS Before you begin a d m i n i s t e r i n g the achievement t e s t s make sure you have: 1. A c l a s s s e t of Stanfo r d Achievement Te s t s (SAT) . 2. A c l a s s s e t of Canadian T e s t s of Basic S k i l l s (CTBS). 3. An answer sheet f o r each student* 4. Ten e x t r a p e n c i l s . 5. An envelope with a BED tab. The t e s t s should be administered on two c o n s e c u t i v e days. The SAT on the morning of the f i r s t day, the CIBS-mathematics concepts t e s t on the afternoon of the f i r s t day, and the CTBS-problem s o l v i n g t e s t on the morning of t h e second day. For purposes of s t a n d a r d i z a t i o n the above sequence must be maintained. However, although the t i m i n g suggested i s p r e f e r a b l e , p l a t t o c n i n g or other c o n s i d e r a t i o n s may make i t i m p o s s i b l e . T h e r e f o r e , the t i m i n g w i l l be l e f t t o your d i s c r e t i o n . I f the t e s t s HAVE to be administered on one day then one should be given before r e c e s s , one a f t e r r e c e s s and the l a s t one a f t e r lunch. In a l l cases though, please have the t e s t s administered d u r i n g the two days s p e c i f i e d on your envelope with the BED t a b . Before you hand out any m a t e r i a l s please ask your s t u d e n t s not to w r i t e on the bo o k l e t s and to mark the sheets only as d e s c r i b e d . 178 Would you a l s o be c o l l e c t e d and r e t u r n e d t o t b e because o t h e r c l a s s e s w i l l t e s t s . sure t h a t a l l m a t e r i a l s a re o f f i c e when you are f i n i s h e d be u s i n g the same p e n c i l s and 1. Hand out answer s h e e t s and f o o l s c a p . 2. T e l l t h e s t u d e n t s t o w r i t e the number you are g o i n g t o g i v e them i n the space i n the upper l e f t hand c o r n e r marked IDENTIFICATION NUMBEB. Bead the number from the same c l a s s l i s t t h a t you used t o a s s i g n numbers f o r t h e q u e s t i o n n a i r e s . 3. Say: T h i s i s t h e f i r s t o f a s e t o f t h r e e mathematics t e s t s t o f i n d out how much you have l e a r n e d . These t e s t s a r e s e n t by t h e same person t h a t s e n t t h e q u e s t i o n n a i r e s . However, he w i l l r e t u r n t h e r e s u l t s of the t e s t s t o me, so be sure you do your b e s t . I s h a l l g i v e you a^  t e s t b o o k l e t . Do n o t open i t u n t i l I t e l l you t o do so. 4. Hand out b o o k l e t s . 5. Say: Now open your b o o k l e t s t o t e s t 5: A r i t h m e t i c C o m putation, which s t a r t s on page 16,. Look a t t h e top o f t h e page o f y o u r t e s t b o o k l e t where i t s a y s "DIBECTIONS". The d i r e c t i o n s say; "Work t h e example i n each box. Then l o o k a t the p o s s i b l e answers a t t h e r i g h t s i d e o f t h e box and see i f your answer i s g i v e n . I f i t i s , c i r c l e t he l e t t e r on your answer s h e e t which i s the same l e t t e r as t h e l e t t e r b e s i d e t h e answer t h a t you have chosen. I f your answer i s NOT g i v e n , c i r c l e t h e l e t t e r which i s the same as the l e t t e r b e s i d e NG which means n o t g i v e n . Use t h e f o o l s c a p f o r your work." Look a t t h e sample q u e s t i o n . 64 minus 23 l e a v e s what? The c o r r e c t answer, 41 , has been w r i t t e n below t h e l i n e . The l e t t e r b e s i d e t h e 41 i n the 179 p o s s i b l e answers a t the r i g h t s i d e of the box i s " c " so you would c i r c l e the " c " on your answer sheet. When I t e l l you to s t a r t , behin with example 1 and do as many examples on pages 16 and 17 as you can. Do not spend too much time on any one example, i f you cannot do an example, go on to the next one. When you f i n i s h page 17, example 39, go back and check your work on t h i s t e s t . Do not work on any other test,. Use the s c r a t c h paper f o r f i g u r i n g . BEADY, GOJ 6. Becord the STABTING TIME. Add t h i r t y f i v e minutes to i t ; When t h i s time i s reached say: STOP! Close your booklet and put your p e n c i l down,. 7. C o l l e c t the b o o k l e t s , answer s h e e t s , and e x t r a pencils,. 1. At the next s e s s i o n , hand out the answer sh e e t s , making sure that the students get t h e i r own answer sheets. 2. Hand out any p e n c i l s i f needed, and s c r a t c h paper. 3. Say: I s h a l l give you a t e s t b o o k l e t again* Do not open i t u n t i l I t e l l you to do so. 4. Hand out the booklets f o r the Canadian T e s t s of B a s i c S k i l l s . 5. Say: Now we are ready f o r the second mathematics t e s t ; Open your t e s t b o o k l e t to page 77. (Pause.) F i n d the s e c t i o n o f your answer sheet f o r t e s t M-1, Mathematics Concepts. (Pause.) The d i r e c t i o n s I w i l l read t o you are a l i t t l e d i f f e r e n t , so l i s t e n c a r e f u l l y . This i s a t e s t of how well you understand the number system and the terms and o p e r a t i o n s used i n mathematics. Four answers are given f o r each e x e r c i s e , but only 180 one o f t h e s e answers i s r i g h t . You a r e t o choose t h e one answer t h a t you t h i n k i s b e t t e r t h a n t h e o t h e r Then, on the answer s h e e t , f i n d t h e row o f answer numbers t h a t i s numbered the same as t h e e x e r c i s e . C i r c l e t h e number on t h e answer s h e e t t h a t i s the same as t h e number b e s i d e t h e answer t h a t you t h i n k i s b e s t . DO NOT MAKE ANY MABKS ON THE TEST BOOKLET. Use your s c r a t c h paper f o r f i g u r i n g . You w i l l have 30 minutes f o r t h i s t e s t . I f you f i n i s h e a r l y , c l o s e your t e s t b o o k l e t and w a i t q u i e t l y . Don't l o o k a t t h e o t h e r t e s t s i n the b o o k l e t . I f you have any q u e s t i o n s , r a i s e your hand. I w i l l h e l p you a f t e r t h e o t h e r s have bequn. Turn t o page 81 and b e q i n w i t h e x e r c i s e 52. Stop when you reach paqe 83 e x e r c i s e 96. (Pause.) Does everybody have t h e r i g h t p l a c e ? (pause*) Eeady, go. 6. fiecord t h e t i m e . Add 30 m i n u t e s . When t h i s t i m e i s reac h e d say: STOP; C l o s e your t e s t b o o k l e t . 7. C o l l e c t t h e b o o k l e t s , answer s h e e t s , and p e n c i l s . At t h e l a s t s e s s i o n 1. Hand out the answer s h e e t s , making s u r e t h a t t h e s t u d e n t s get t h e i r own answer s h e e t s . 2. Hand out any p e n c i l s i f needed, and s c r a t c h paper. 3. Say: I s h a l l g i v e you a t e s t b o o k l e t again,. Do not open i t u n t i l I t e l l you t o do so. 4. Hand out t h e b o o k l e t s f o r t h e Canadian T e s t of B a s i c S k i l l s . 5. Say Now we a r e ready f o r t h e t h i r d mathmematics t e s t . Open your t e s t b o o k l e t t o page 87. F i n d t h e s e c t i o n o f your answer s h e e t f o r T e s t M-2, Mathematics Problem S o l v i n g . (Pause.) As t h e d i r e c t i o n s I w i l l r ead are d i f f e r e n t f r om those i n t h e b o o k l e t l i s t e n c a r e f u l l y . 181 This i s t e s t of how w e l l you can s o l v e mathematics problems. The e x e r c i s e s i n the t e s t are l i k e the samples shown a t the r i g h t . A f t e r each e x e r c i s e are t h r e e p o s s i b l e answers and a "not g i v e n " meaning t h a t the c o r r e c t answer i s not given. Work each e x e r c i s e and compare your answer with t h e t h r e e p o s s i b l e answers. I f the c o r r e c t answer i s g i v e n , c i r c l e the number t h a t i s the same as the number b e s i d e the r i g h t answer. I f the c o r r e c t answer i s not given, c i r c l e the f o u r t h number. The sample e x e r c i s e s show you what to do. Now read t h e f i r s t sample e x e r c i s e . (Pause.) What i s the r i g h t answer f o r t h i s e x e r c i s e ? (Pause f o r r e p l y . ) Yes, the second answer, 3, i s the c o r r e c t answer. You would c i r c l e the two on you answer sheet t o show t h a t the second answer i s the c o r r e c t one. Sometimes the c o r r e c t answer i s not g i v e n . Now read the second sample e x e r c i s e . (Pause.) What i s the c o r r e c t answer f o r t h i s problem? (Pause f o r reply.) Yes, 1, i s the c o r r e c t answer. Since 1 i s not one o f the suggested answers, you would c i r c l e the f o u r on your answer sheet t o show t h a t the c o r r e c t answer i s not g i v e n . Work a l l o f the e x e r c i s e s i n the t e s t i n t h i s way. Do not rework an e x e r c i s e when your answer i s not l i k e any of the three suggested answers. Instead, c i r c l e the number 4 and go on to the next e x e r c i s e . I f you cannot work an e x e r c i s e , leave i t and go on to the next one. I f you have time, you may r e t u r n to i t l a t e r . Do your work on the s c r a t c h paper. Do not w r i t e on the t e s t b o o k l e t . You w i l l have 30 minutes f o r t h i s t e s t . Now f i n d ycur place t o begin* Turn to page 91 and begin with e x e r c i s e 40. Stop when you reach page 93 e x e r c i s e 70. (Pause.) Does everyone have the r i g h t place? (Pause.) Heady, go. Eecord the time. Add t h i r t y minutes. When t h i s time s reached say: Stop! Time i s up. Please c l o s e your t e s t booklet at once. 182 7. C o l l e c t answer sheets, b o o k l e t s , and p e n c i l s . Put answer sheets i n the envelope with the RED tab. Return m a t e r i a l s t o the o f f i c e . THANK YOU ALL FOR YOUR TIME AND PATIENCE. 183 Appendix D QUESTIONNAIRE BOOKLET1 DC NOT OPEN THIS BOOKLET UNTIL YOUR TEACHES TELLS YOU Beys and g i r l s : I am i n t e r e s t e d i n h e l p i n g o t h e r boys and g i r l s t o do b e t t e r i n s c h o o l . I w i l l be a s k i n g you some q u e s t i o n s — q u e s t i o n s t h a t have no r i q h t or wrong answers. They a r e q u e s t i o n s about how you f e e l . You can answer h o n e s t l y because I w i l l not know your name; Your t e a c h e r w i l l q i v e you a number t h a t you w i l l w r i t e on each o f your answer s h e e t s . Your t e a c h e r w i l l n o t know your answers because your answer s h e e t s w i l l be p l a c e d i n an e n v e l o p e , s e a l e d and d e l i v e r e d t o me. However, even though we won't know who you a r e , your answers a r e v e r y i m p o r t a n t so p l e a s e answer c a r e f u l l y . On t h e answer sheet t h a t has been handed out w r i t e the number t h a t the t e a c h e r has g i v e n you i n the space marked IDENTIFICATION NUMBER;. Your answers t o t h e f i r s t s e t of q u e s t i o n s w i l l qo under t h e columns w i t h t h e h e a d i n g QUESTION SET #1. T r y n o t lThe f i r s t s e t o f 30 i t e m s make up the Te s t A n x i e t y S c a l e f o r C h i l d r e n . The second s e t of 34 i t e m s make up the I n t e l l e c t u a l Achievement R e s p o n s i b i l i t y S c a l e . The Achievement R e s p o n s i b i l i t y S c a l e was s c o r e d and the i t e m s s p l i t i n t o two s u b - s c a l e s as d e s c r i b e d i n C r a n d a l l , Katkovsy and C r a n d a l l (1965). 184 to change any of your answers. Make your d e c i s i o n b e f o r e you mark your sheet. I f you have to make a change er a s e the o l d mark as w e l l as you can* Each o f the f o l l o w i n g guestions needs a yes or no answer. I f your answer i s yes, c i r c l e the YES beside the gue s t i o n number. I f your answer i s no, c i r c l e the NO beside the q u e s t i o n number. f o r example i f question 5 was 5. Do you l i k e dogs? And your answer was yes, then beside number 5 c i r c l e YES. 4. YES NO 5. YES NO 6. YES NO I f you have any ques t i o n s please ask your teacher.* 185 You must answer every q u e s t i o n YES or NO. 1. Do you worry when the t e a c h e r says t h a t she i s going t o ask you qu e s t i o n s to f i n d out how much you know? 2. Do you worry about being promoted, t h a t i s , p a s s i n g from the s i x t h grade t o the seventh grade at the end o f the year? 3. When the teacher asks you to get up i n f r o n t of the c l a s s and r e a d a l o u d , a r e you a f r a i d ycu are going t o make some bad mistakes? 4. When the te a c h e r says she i s going to c a l l upon some boys and g i r l s i n the c l a s s to do a r i t h m e t i c problems, do you hope t h a t she w i l l c a l l upon someone e l s e and not on you? 5. Do you sometimes dream a t n i g h t t h a t you are i n s c h o o l and cannot answer the t e a c h e r * s guestions? 6. When the tea c h e r says t h a t she i s going t o f i n d out how much you have l e a r n e d , does your heart begin t o beat f a s t e r ? 7. When the tea c h e r i s t e a c h i n g you about arith-metic, do you f e e l t h a t other c h i l d r e n i n the c l a s s understand her b e t t e r than you? 8. When you are i n bed at n i g h t , do you sometimes worry about how you are going to do i n c l a s s the next day? 9. When the teacher asks you to w r i t e on the blackboard i n f r p n t of the c l a s s , does the hand you wr i t e with sometimes shake a l i t t l e ? 10. When the tea c h e r i s te a c h i n g you about r e a d i n g , do you f e e l t h a t other c h i l d r e n i n c l a s s understand her b e t t e r than you? 11. Do you t h i n k you worry more about s c h o o l than other c h i l d r e n ? 12. When you are a t home and you are t h i n k i n g about your a r i t h m e t i c l e s s o n f o r the next day, do you become a f r a i d t h a t you w i l l get the answers wronq when the tea c h e r c a l l s upon you? 13. I f you are s i c k and miss s c h o o l , do you worry t h a t you w i l l do more poorly i n your schoolwork than other c h i l d r e n when ycu r e t u r n . 186 14. Do you sometimes dream a t n i g h t t h a t o t h e r boys and g i r l s i n your c l a s s can do t h i n g s you cannot do? 15. When you a r e home and you a r e t h i n k i n g about your r e a d i n g l e s s o n f o r the n e x t day, do you worry t h a t you w i l l do p o o r l y on t h e l e s s o n ? 16. When the t e a c h e r says t h a t she i s g o i n g t o f i n d out how much you have l e a r n e d , do you get a funny f e e l i n g i n your stomach? 17. I f you d i d v e r y p o o r l y when the t e a c h e r c a l l e d on you, would you p r o b a b l y f e e l l i k e c r y i n g even though you would t r y not t o c r y ? 18. Do you sometimes dream a t n i g h t t h a t the t e a c h e r i s angry because you do not know your l e s s o n s ? I n t h e f o l l o w i n g q u e s t i o n s the word " t e s t " i s used. What I mean by " t e s t " i s any time t h e t e a c h e r asks you t o do something t o f i n d o u t how much you know or how much you have l e a r n e d . I t c o u l d be by your w r i t i n g on paper, o r by your s p e a k i n g a l o u d , o r by your w r i t i n g on the b l a c k b o a r d . Do you un d e r s t a n d what I mean by " t e s t " - - i t i s any time the t e a c h e r a sks you t o do something t o f i n d out how much you know. 19. Are you a f r a i d o f s c h o o l t e s t s ? 20. Do you worry a l o t b e f o r e you t a k e a t e s t ? 21. Do you worry a l o t w h i l e you a r e t a k i n g a t e s t ? 22; A f t e r you have t a k e n a t e s t do you worry about how w e l l you d i d on t h e t e s t ? 23. Do you sometimes dream a t n i g h t t h a t you d i d p o o r l y on a t e s t you had i n s c h o o l t h a t day? 24. When you are t a k i n g a t e s t , does the hand you a r e w r i t i n g \11 with shake a l i t t l e ? 25. When the te a c h e r says t h a t she i s going to gi v e the c l a s s a t e s t , do you become a f r a i d t h a t you w i l l do poo r l y ? 26. When you are t a k i n g a hard t e s t , do you f o r g e t some t h i n g s you knew very w e l l before you s t a r t e d t a k i n g the t e s t ? 27. Do you wish a l o t of times t h a t you d i d n ' t worry so much about t e s t s ? 28. When the te a c h e r says t h a t she i s going to g i v e the c l a s s a t e s t , do you get a nervous or funny f e e l i n g ? 29*. While you are t a k i n g a t e s t do you u s u a l l y t h i n k you are doing po o r l y ? 30* While you are on your way to s c h o o l , do you sometimes worry t h a t the teacher may g i v e the c l a s s a t e s t ? DO NOT TORN THE PAGE UNTIL THE TEACHER TELLS YOU 188 The answers to the next s e t of questions w i l l qo i n the column headed QUESTION SET # 2 . F o r the f o l l o w i n q q u e s t i o n s you must s e l e c t one of the two p o s s i b l e statements t h a t complete the sentence. For example 6 . I f you were given a choice of pie would you choose 1. apple, or 2 . c h e r r y ? I f you p r e f e r c h e r r y then b e s i d e number 6 . You would c i r c l e the 2 . I f you have any questions please ask your teacher. I f a teacher passes you to the next grade, would i t probably be 1. because she l i k e d you, or 2 . because of the work you d i d ? When you do w e l l on a t e s t a t s c h o o l , i s i t more l i k e l y to be 1. because you s t u d i e d f o r i t , or 2 . because the t e s t was e s p e c i a l l y easy? When you have t r o u b l e understanding something i n s c h o o l , i s i t u s u a l l y 1. because t h e teacher d i d n ' t e x p l a i n i t c l e a r l y , or 2 . because you d i d n ' t l i s t e n c a r e f u l l y ? When you read a s t o r y and can't remember much of i t , i s i t u s u a l l y 1. because the s t o r y wasn't well w r i t t e n , or 2 . because you weren't i n t e r e s t e d i n the s t o r y ? Suppose your parents say you are doing w e l l i n s c h o o l . I s t h i s l i k e l y to happen 1. because your s c h o o l work i s good, or 2 . because they are i n a good mood? Suppose you d i d b e t t e r than usual i n a s u b j e c t at s c h o o l . Would i t probably happen 1. because you t r i e d harder, or 2 . because someone helped you? 189 7. When • you l o s e a t a game o f c a r d s o r c h e c k e r s , does i t u s u a l l y happen 1. because t h e o t h e r p l a y e r i s good a t the game, o r 2. because you don't p l a y w e l l ? 8. Suppose a person d o esn't t h i n k you are v e r y b r i g h t or c l e v e r . 1. can you make him change h i s mind i f you t r y t o , or 2. a r e t h e r e some people who w i l l t h i n k y o u r ' r e not ver y b r i g h t no matter what you do? 9. I f you s o l v e a p u z z l e g u i c k l y , i s i t fl. because i t wasn't a very hard p u z z l e , o r 2. because you worked on i t c a r e f u l l y ? 10. I f a boy or g i r l t e l l s you t h a t you are dumb, i s i t more l i k e l y t h a t they say t h a t 1. because t h e y a r e mad a t you, or 2. because what you d i d r e a l l y wasn't very b r i g h t ? 11. Suppose you s t u d y t o be a t e a c h e r , s c i e n t i s t , o r d o c t o r and you f a i l ; Do you t h i n k t h i s would happen 1. because you d i d n ' t work h a r d enough, or 2. because you needed some h e l p , and o t h e r p e o p l e d i d n ' t g i v e i t t o you? 12; When you l e a r n something q u i c k l y i n s c h o o l , i s i t u s u a l l y 1,. because you p a i d c l o s e a t t e n t i o n , o r 2. because t h e t e a c h e r e x p l a i n e d i t c l e a r l y ? 1 3 . I f a t e a c h e r says t o you, "Your work i s f i n e , " i s i t 1. something t e a c h e r s u s u a l l y say t o encourage p u p i l s , o r 2. because you d i d a good job? 14; When you f i n d i t hard t o work a r i t h m e t i c o r math problems a t s c h o o l , i s i t 1. because you d i d n ' t s t u d y w e l l enough b e f o r e you t r i e d them, o r 2. because the t e a c h e r gave problems t h a t were t o o hard? 15. When you f o r g e t something you heard i n c l a s s , i s i t 1. because t h e t e a c h e r d i d n ' t e x p l a i n i t v e r y w e l l , or 2. because you d i d n ' t t r y very hard t o remember? 16. Suppose you weren't s u r e about the answer t o a q u e s t i o n your t e a c h e r asked you, b u t your answer t u r n e d out t o be r i g h t . I s i t l i k e l y t o happen 190 1. because she wasn't a s p a r t i c u l a r as u s u a l , o r 2. because you gave t h e b e s t answer you c o u l d t h i n k o f ? 17. When you r e a d a s t o r y and remember most of i t , i s i t u s u a l l y 1. because you were i n t e r e s t e d i n the s t o r y , o r 2. because t h e s t o r y was w e l l w r i t t e n ? 18. I f your p a r e n t s t e l l you you're a c t i n g s i l l y and not t h i n k i n g c l e a r l y , i s i t more l i k e l y t o be 1. because o f something you d i d , o r 2. because they happen t o be f e e l i n g c r a n k y ? 19. When you don't do w e l l on a t e s t a t s c h o o l , i s i t 1. because t h e t e s t was e s p e c i a l l y h a r d , o r 2. because you d i d n ' t study f o r i t ? 20; When you win a t a game of c a r d s or c h e c k e r s , does i t happen 1. because you p l a y r e a l l y w e l l , or 2. because t h e o t h e r person doesn't p l a y w e l l ? 21. I f people t h i n k you're b r i g h t o r c l e v e r , i s i t 1. because they happen t o l i k e you, o r 2. because you u s u a l l y a c t t h a t way? 22. I f a t e a c h e r d i d n ' t pass you t o t h e next grade, would i t pr o b a b l y be 1. because she "had i t i n f o r you," o r 2. because your s c h o o l work wasn't good enough? 23. Suppose you don't do as w e l l as u s u a l i n a s u b j e c t a t s c h o o l ; Would t h i s p r o b a b l y happen 1. because you weren't as c a r e f u l as u s u a l , o r 2. because somebody b o t h e r e d you and ke p t you from working? 24. I f a boy o r g i r l t e l l s you t h a t you a r e b r i g h t , i s i t u s u a l l y 1. because you tho u g h t up a good i d e a , or 2. because t h e y l i k e you? 25. Suppose you became a famous t e a c h e r , s c i e n t i s t o r d o c t o r . Do you t h i n k t h i s would happen 1. because o t h e r p e o p l e h e l p e d you when you needed i t , or 2. because you worked v e r y hard? 26. Suppose your p a r e n t s say you a r e n ' t d o i n g w e l l i n your s c h o o l work. I s t h i s l i k e l y t o happen more 191 1. because your work i s n ' t v e r y good, o r 2. because they a r e f e e l i n g c r a n k y ? 27. Suppose you a r e showing a f r i e n d how t o p l a y a game and he has t r o u b l e w i t h i t . Would t h a t happen 1. because he wasn't a b l e t o u n d e r s t a n d how t o p l a y , or 2. because you c o u l d n ' t e x p l a i n i t w e l l ? 28. When you f i n d i t easy t o work a r i t h m e t i c o r math problems a t s c h o o l , i s i t u s u a l l y 1. because t h e t e a c h e r gave you e s p e c i a l l y easy problems, or 2. because you s t u d i e d y o u r book w e l l b e f o r e you t r i e d them? 29. When you remember something you heard i n c l a s s , i s i t u s u a l l y 1. because you t r i e d h a r d t o remember, o r 2. because the t e a c h e r e x p l a i n e d i t w e l l ? 30. I f you can't work a p u z z l e , i s i t more l i k e l y t o happen 1. because you are not e s p e c i a l l y good at w o r k i n g p u z z l e s , o r 2. because the i n s t r u c t i o n s weren't w r i t t e n c l e a r l y enough? 31. I f your p a r e n t s t e l l you t h a t you are b r i g h t or c l e v e r , i s i t more l i k e l y 1. because t h e y a r e f e e l i n g good, o r 2. because o f something you d i d ? 32. Suppose you a r e e x p l a i n i n g how t o p l a y a game t o a f r i e n d and he l e a r n s q u i c k l y . Would t h a t happen more o f t e n 1. because you e x p l a i n e d i t w e l l , o r 2. because he was a b l e t o u n d e r s t a n d i t ? 33. Suppose you're not sure about the answer t o a q u e s t i o n your t e a c h e r asks you and t h e answer you g i v e t u r n s o u t t o be wrong. I s i t l i k e l y t o happen 1. because she was more p a r t i c u l a r t h a n u s u a l , o r 2. because you answered too q u i c k l y ? 34. I f a t e a c h e r says t o you, "Try t o do b e t t e r , " would i t be 1. because t h i s i s somethinq she miqht say t o g e t p u p i l s t c t r y h a r d e r , o r 2. because your work wasn't as good as us u a l ? DO NOT TOBN THE PAGE UNTIL YOUB TEACHEB TELLS YOU 192 I n t h i s next s e c t i o n you w i l l be g i v e n a number o f s e n t e n c e s ; I f you agree w i t h t h e statement t r y t o d e c i d e i f you f e e l s t r o n g l y about i t . I f so you would c i r c l e t h e 1„ I f you j u s t a g r e e , c i r c l e t h e 2. Or, you might d i s a g r e e w i t h t h e s t a t e m e n t . I f s o , t r y t o d e c i d e i f you f e e l s t r o n g l y about i t . I f you do c i r c l e t h e 5. I f you j u s t d i s a g r e e c i r c l e t h e 4. I f you c a n ' t make up your mind o r don't u n d e r s t a n d t h e sen t e n c e t h e n c i r c l e t h e 3. Fo r example, i f the statement was 8. I l i k e i c e cream. I f you l o v e i t you wculd c i r c l e t h e 1. I f you j u s t l i k e i t you would c i r c l e t h e 2. I f you c a n ' t make up your mind o r don't c a r e you would c i r c l e t h e 3. I f you don't l i k e i t you would c i r c l e t h e 4. I f you hate i t you would c i r c l e t h e 5. I f you have any q u e s t i o n s p l e a s e ask your t e a c h e r . Turn t h e page when your t e a c h e r t e l l s you . The answers f o r t h e s e q u e s t i o n s w i l l go under t h e column headed QUESTION SET #3. 193 1. I enjoy t a l k i n g t o other people about mathematics. 2. Mathematics i s more of a game than i t i s hard work. 3. I t makes me nervous to even t h i n k about doing mathematics. 4. Mathematics i s something which I enjoy very much. 5. Doing w e l l i n mathematics h e l p s me i n o t h e r s u b j e c t s . 6. When I hear the word mathematics, I have a f e e l i n g of d i s l i k e . 7. I am good a t working mathematics problems. 8. I f I don't see how t o work a mathematics problem r i g h t away, I never get i t ; 9. Mathematics i s u s e f u l f o r my problems i n every day l i f e . 10. Most people should study some mathematics. 11. I f e e l tense when someone t a l k s t o me about mathematics. 12. I don't do very w e l l i n mathematics. 13. I have a good f e e l i n g toward mathematics,; 14. You can get along p e r f e c t l y w e l l i n every day l i f e without mathematics. ,15. Mathematics i s h e l p f u l i n understanding today's world. 16. I would l i k e t o spend l e s s time i n school doing mathematics. 17. Mathematics i s u s e f u l f o r the problems of every day l i f e . 18. I can get along p e r f e c t l y w e l l i n every day l i f e without mathematics. 19. No matter how hard I t r y , I cannot understand mathematics. 20. Working mathematics i s fun. 21. I f I got b e t t e r marks i n mathematics I would enjoy mathematics more. 22. Mathematics helps me understand today's world. 1 94 23. Mathematics i s easy f o r me. 24. I l i k e t o play games t h a t use numbers. 25. There i s l i t t l e need f o r mathematics i n most jobs. 27- I f e e l a t ease i n a mathematics c l a s s . 28. There i s l i t t l e need f o r mathematics i n the jobs t h a t I would want. 2S. I t s c a r e s me t o have to take mathematics. 30. I would l i k e a job which doesn't use any mathematics. 31. Mathematics i s o f great importance t o a c o u n t r y ' s developaent. 32. Most of the i d e a s i n mathematics aren't very u s e f u l f o r me* 33. I t i s important f o r me t o know mathematics i n order to get a gccd j o b. 34. I don't l i k e a n y t h i n g about mathematics. 35. I remember most of the t h i n g s I l e a r n i n mathematics. 36. I t doesn't d i s t u r b me t o work mathematics problems. 37. I t i s important t o know mathematics i n order t o get a good job. 38. Working with numbers upsets me. 39. I o f t e n t h i n k , "I can't do i t , " when a mathematics problem seems hard, 40. Most o f the ide a s i n mathematics a r e n ' t very u s e f u l . THANK YOU FOE ANSWERING ALL THESE QUESTIONS 195 Appendix E IAY OUT OF THE STUDENT ANSWEE FORMS Eeproduced below a r e the f i r s t few l i n e s of the answer s h e e t s f o r t h e achievement t e s t s . I d e n t i f i c a t i o n Number Keypunch C a r d #1 I n f o Only - — — — " ' •"• - • — — T — ~ Card #2 Card #3 Computation Test T e s t M-1 Math Concepts T e s t M-2 Math Problem S o l v i n g 1. a b c d 2. f g h i 3. a b c d e j e 52. 1 2 3 4 53. 1 2 3 4 54. 1 2 3 4 40. 1 2 3 4 41. 1 2 3 4 42. 1 2 3 4 Reproduced below a r e t h e f i r s t few l i n e s o f the resp o n s e s h e e t s f o r the a f f e c t i v e s c a l e s . I d e n t i f i c a t i o n Number Keypunch C a r d #4 Car d #5 Card #6 I n f o Only Q u e s t i o n Q u e s t i o n Q u e s t i o n Set 3 Set 1 S e t 2 S t r o n g l y Don«t S t r o n g l y Agree Know Disagree Agree Disagree 1. yes no 1. 1 2 1. 1 2 3 4 5 2. yes no 2. 1 2 2. 1 2 3 4 5 3. yes no 3. 1 2 3. 1 2 3 4 5 196 Appendix F CLASS MEANS AND STANDARD DEVIATIONS OF THE ACHIEVEMENT VARIABLES AND AFFECTIVE VARIABLES C l a s s COMP CONC PROB TASC IABS IARF MANX VSOC SCON ENJOY VSELF 1 16.9 20.5 12.6 14.6 30.0 27.4 19.6 31.0 26.6 25.2 30.0 6.66 8.63 7.01 5.06 2.10 3.01 5.55 5.28 6,49 6. 18 6.01 2 20.0 25.7 16.3 14.5 28.0 26.9 17.4 34.1 29.4 25.7 31.1 6.36 7. 94 5,49 5.01 3.01 2.49 6.26 3. 97 5.84 8, 20 4.48 3 20.4 29.5 21.1 9.9 29.9 29.3 20.8 31.9 27.9 24.5 29.8 7.53 8.35 6.03 6,06 2.4 7 2.02 8. 56 3. 98 7.30 8. 22 3.57 4 18.7 22.6 15.0 11.7 30.0 28.1 21.8 30.4 27.7 20.7 27.2 8. 14 9.38 6.21 6.29 2.17 2.81 6.41 5:. 40 6. 12 5.68 5. 45 5 25.1 32.8 22.8 13.9 29.8 29.7 18.3 34.2 28.3 26.4 31.3 5. 04 5.70 3.83 8,49 1.72 1.32 5. 22 3.80 5. 43 6. 29 2.87 6 26.2 33. 1 21.7 9.63 29.5 27.2 17.2 32.4 29.5 26,0 30.7 4.24 5.62 5.04 4. 19 2.42 3.47 6.89 4.88 5.51 6. 57 4.61 7 19.4 26.5 17.3 11.3 30.7 27.7 18.4 32.3 28.7 24.1 30,8 5. 76 6.28 5.41 5.16 1.74 2.69 5.04 4,94 5.78 6.68 5.46 8 14.2 20.6 13. 4 15.2 30.0 27.3 18.2 32.9 29.0 24.0 29.8 3.85 7.02 4.43 5,21 2.37 2.69 5.00 4.67 6. 27 5.83 4.35 9 20.2 29.2 20. 1 13.8 29.8*26.8 17.2 32.7 30.2 25,1 29.4 7.06 6.58 5.78 3.37 2.79 3.1 1 5.30 5. 45 5.66 7.99 4.27 10 22.5 35.3 25.0 8.5 31.8 29,3 21.7 33.2 30.8 18.3 28.8 2.88 3.50 2.61 1,97 0.98 2.25 2.73 2.32 3.92 2.42 3. 49 11 18.3 24.4 15.9 11.3 30.1 26.4 16.8 30.9 29.3 24.1 27.0 7.54 8.S5 6.00 4.11 1.78 2.70 5.06 4.58 4. 92 6.67 5.63 13 23.9 28. 1 20. 1 13.0 29.8 28.7 17.9 32,9 27.6 26,0 31.9 6. 92 8.04 6.35 6.82 2.19 2.70 6.00 4.48 6. 24 5.81 4.44 14 17.4 23.6 14.7 12.0 28.2 26.8 19.3 31.3 27.5 26.2 30.0 6.05 6.79 5.50 5,93 2.94 2.66 5.22 5.27 3. 86 5. 12 5.83 15 18.2 23.6 15.0 11.9 29.9 29.1 19.4 33.6 27.4 25.8 31.0 7.77 7.52 5.72 5.88 2.37 2.59 7.34 4.56 7. 25 6.51 5,39 16 24.8 27.5 20.2 11.0 29.7 27.4 20.0 33.5 28.6 24.4 30.4 5. 34 6.78 5.35 5.96 2.31 3. 16 4.23 4. 19 3. 22 6.09 5.02 17 14.4 23.0 14.0 11.2 28.8 27.7 19.6 32.6 29.6 26.3 29.5 5.62 9.29 6.64 7. 17 2.66 2.39 7. 10 4.67 6. 76 6.09 5.71 18 15.2 20.2 12.8 12.2 29.7 28.0 18,3 30.8 28,7 24.8 27.9 6.03 6.70 5. 11 5.78 1.95 2.55 7. 10 4.36 5. 95 7.59 5.15 19 23.7 26.4 18.7 12.3 29.9 29.2 18.3 33.6 28.3 25.2 33,4 6.63 7.65 3.35 4.30 2.26 2.68 3.81 5.61 4.36 5.70 4.36 20 18.0 27.5 20.3 11.4 29.8 26.6 21.3 30.2 26.4 22,6 28.6 7.47 6.76 4.59 5,25 2.66 2.93 5. 46 5.26 6.25 6.51 4,54 21 19.4 26.6 19.2 13.1 29.8 27.2 27.7 26.9 23.4 13,8 22.1 7- 21 6.31 5.61 4,94 1,86 3.67 5.29 5.21 5.85 4.41 6.66 197 22 18 . 1 16. 8 5.64 3.77 23 23.0 25-3 7.71 9.52 24 20.9 27.1 7.56 7. 86 25 15. 1 22.0 6. 50 8. 22 26 19.8 22.8 7.52 8,03 27 16. 1 20.7 5.00 5.68 28 15.3 21.5 9.78 7.72 29 12.3 17. 9 6. 38 5. 34 30 17.7 25.8 5.40 7.23 31 15.0 18.0 4.47 10. 5 32 23.9 25.3 7. 95 9-05 33 12.7 19.9 4.76 7.53 35 19.9 20.1 7. 58 7.36 36 25.6 22.4 3. 20 5.76 37 18.1 25.0 5. 61 5.71 38 17. 1 19.8 7.09 8.98 39 21.4 23.8 7. 92 7,58 40 27.0 35.0 5. 24 3. 54 41 26.3 27.9 5. 82 5.74 42 15.5 23.0 5. 99 8. 31 43 17.7 20.1 4. 15 5. 05 44 14.7 17.7 7. 17 6. 28 45 16.8 23.3 5.73 5.32 46 20.6 24.9 7. 02 10. 3 47 19.6 24.1 4. 22 8.29 51 12.8 19.3 14. 1 14.9 28,0 3.79 4.65 1.32 17.5 12.8 29.0 6.87 6.98 2.37 17.0 13.5 29.7 6.97 5.58 2.30 15.4 16.0 29,9 5. 36 5.26 2.32 18.3 11.7 30.2 6.17 6.81 2.50 13.6 15.2 30.3 3.92 5.01 1.49 16.9 11.1 28.4 5.61 5* 93 2.63 13.7 14.3 29.7 5.21 6.05 2.67 17.0 12.5 30,7 5.07 5.93 1.90 12.0 14.1 31.3 4.50 4.39 1.04 17.6 12.2 29.4 6.72 6.77 1,54 11.1 12,3 30.6 5.05 5.55 1.69 15.4 11.3 29.3 6.24 5.78 3.34 18.8 10,4 31.5 5.04 2.72 1.513 19.5 11.6 30.0 3.93 3. 14 2.45 14.6 13.4 29.4 7.09 5.94 2.36 17.5 13.3 29.0 6.06 5.62 2.27 24.2 16.8 30.2 3.90 6.06 0.45 18.1 14.6 29.1 7.08 5.50 2.30 16.3 13.1 29.0 6. 84 5.63 1.97 14.4 13.7 29.0 3.87 3.73 1.63 11.2 11.8 28.8 4. 24 5.07 2.95 14.7 12.9 2 9.4 4.76 5.69 2.17 16.8 16,0 28.7 6. 24 5.68 2-87 16.4 6.3 28.3 5.39 4.23 2.11 15.3 11.9 29.2 26.1 21.7 31.8 3.66 7.16 5.31 26.4 19.1 31.7 3.19 6.62 4.86 28.0 20.9 29.7 2.50 6. 93 5.34 28.5 18.9 34.3 2.70 5.84 3.60 27.6 16.4 31.2 3.02 5.90 4.90 27.7 19.0 34.5 3.15 5.42 3.72 26.7 17.0 30.3 1. 16 6.53 4. 85 27.3 18.3 31.6 2.58 3.51 5.27 28.8 17.4 31.4 2.27 6. 13 4.75 30.5 17.8 35.6 1.93 8.28 4.14 28.4 17.3 33.3 2.36 5.49 3.82 28.8 19.2 30. 1 1.78 4.17 3.67 26.8 17.2 32.2 2.55 5.68 7.13 27.9 13. 9 35.1 3.52 3.56 4.85 28.4 16.5 31.2 2.06 3.96 4.77 26.5 18.2 30.6 3.42 5.95 4.85 27.8 18.5 32.5 2.43 6.00 3.52 25.8 18.2 34.6 3.35 8.35 4.04 27.6 20.0 30.0 2.33 4.78 4.34 26.5 17.7 31.8 3.78 5.36 4.51 28. 1 19.7 29.9 3.24 4. 35 6,99 25.2 21.0 29.0 3.19 5.73 4,71 28.6 19.3 33.5 2.21 5.60 3.81 28.4 20.3 32.4 2.19 6.87 4.19 26.5 19.8 25.4 3.24 5.S8 6.63 26.3 18.4 31.0 25.7 22,3 32.4 4.27 7.30 5.25 28. 4 26.5 29.7 6.22 7.37 5.12 28. 1 24. 1 27. 9 4.59 7.05 5.97 27.9 27.3 33.4 6.75 6.76 3.85 30.6 27.9 29.8 6.62 6.52 5.53 28.6 26.9 32.7 6.64 8.20 4.30 31. 3 26.8 29.7 5.68 5.01 3.56 27.3 24.4 30.6 5.75 6.40 4.47 29. 2 26,9 28.1 5.16 6.62 4.76 29.0 27.8 31.0 5. 15 5.70 6.07 31.3 26.8 29.4 4.89 6.35 3.84 28.0 23.8 27.0 6.87 5.53 4.15 31.6 25.2 30.1 5.33 7.64 7.04 31.6 28.3 33.5 4.63 9.68 6.95 32. 6 26.4 28.9 4.01 6.99 5.36 27.4 24.1 28.3 6.91 8.12 5.61 26.6 26. 1 31.0 6.15 6.92 4.89 29. 8 29.2 33.6 8. 11 6.22 4.88 25,0 23.9 27.9 5.45 6.08 4.64 29. 4 24.8 28.7 5.66 5.14 4.26 28.3 25. 1 28.5 5.47 6.31 5.99 25.4 24.4 29.5 6.48 6.47 5.38 29. 3 28.4 33.9 4.02 6.07 4.24 25. 9 26.8 29.4 5.82 7.28 5.08 29.4 20.6 24.4 7.57 6.35 6.05 26.3 26.9 27.9 198 4.90 8.37 4.73 7,45 3.00 3.28 6.81 4, 17 7. 68 6.54 4.79 52 28.9 38. 5 24.3 9.7 30.4 27.4 19, 9 32.6 30.3 21.5 29.9 5.34 3.26 3. 97 5,08 2.22 1.97 5.87 4.45 3. 98 7. 67 4.58 53 16.8 20.9 14.4 12.8 28.6 27.1 19.6 32.7 27.2 22.1 28.8 6. 03 7.97 5.25 4.94 2.30 2.48 4. 54 3.86 4.66 6.87 4.44 54 17.3 25. 2 15.2 13.3 30.0 28.4 18.6 33.8 29.3 25.8 30.6 6. 16 4.84 4.82 4.80 1.73 1.81 3.81 3.49 3. 50 3.70 5.66 55 14.6 20.3 13.3 12-6 30.0 28.7 18.1 33.7 26.3 26.0 31.4 6.47 7.93 5.59 3.84 2.44 2.03 5.49 4. 17 5.63 5. 51 5. 10 56 17.3 20.0 15.3 12. 8 28.8 27.8 17.7 32.3 30.5 26.3 31.3 5.79 9.49 5.68 4.17 2.93 3.37 3.27 5.32 3.78 5. 13 5.67 57 17.0 24.7 15.4 8.7 28.8 27.2 19.9 30.3 27.3 24.3 28.9 7.52 8,05 6.27 4.98 2.35 2.57 4.58 4.63 5. 61 6.43 3.73 58 17.3 17. 6 12.4 14.0 28. 1 26.3 19.5 32.9 26.8 22.4 29.7 6.00 6.23 5.98 7.98 2.50 2.05 7.90 5. 13 8. 48 8.00 5.87 59 16.0 20.2 16.3 14.4 28.3 28.8 18.9 34.2 27.0 26.6 31.3 5.57 6.02 4.79 5.10 2.66 2.33 6. 19 3.89 5. 76 7.69 3.99 62 21.9 26.8 15.5 15.9 29.6 27.4 18.8 32.4 27.6 24.7 3,1.0 5. 93 8.17 5.68 4.63 2.37 2.32 4.52 3.58 5. 95 5. 25 2.60 63 22.4 28.8 20.5 12.8 30.1 26.8 16.8 32.4 29.6 25.9 29.1 8. 33 10. 1 5.29 5.57 1.73 3.33 5. 18 5. 18 4. 44 5.33 5.26 OVERALL MEANS FOR EACH TEST 18.7 23.9 16.3 12.5 29.5 27.6 18.9 32.0 28,3 25.0 29,8 OVEBAL S.D.«S FOR EACH TEST 7.3 8.5 6.2 5.7 2.4 2.8 5.9 4.9 6,0 6.8 5.2 199 Appendix G DIFFERENCES BETWEEN MEANS FOR MALES AND FEMALES U n i v a r i a t e A-nalyses of V a r i a n c e w i t h Sex as a Dependent V a r i a b l e and t h e Three Achievement and Seven A f f e c t i v e S c a l e s as independent V a r i a b l e s N = 1033 V a r i a b l e Mean S.D. MSW MSB F R a t i o F Prob COMP M 17.5 7.24 52.2 1728.3 33. 1 .0000 F 20.1 7.21 CONC M 23.7 8.51 73. 1 64,3 .9 .348 F 24, 2 8.58 PROB M 15.8 6.32 38.4 287.4 7.5 .006 F 116.9 6. 06 IARS M 29.4 2.51 5.7 24.0 4. 2 .041 F 29.7 2.26 I ARF M 27.3 2-89 8.0 46.9 5.9 .016 F 27.8 2.76 MANX M 18.9 6. 21 35.3 1.6 .04 . 834 F 18.8 5.65 VALSOC M 32.0 5.05 24.1 5.7 . 24 .627 F 31. 8 4. 76 SELFCON M 28.8 6.08 35.4 203.3 5. 7 .017 F 27.9 5.81 ENJOY M 24.9 7.05 46.5 13.0 . 28 .597 F 25.1 6.57 VALSEL M 29.8 5.40 27.5 .3 .01 .922 F 29.8 5.08 A n a l y s i s o f v a r i a n c e showed a s i g n i f i c a n t d i f f e r e n c e (p < -01) f a v o r i n g the f e m a l e s i n both COMP and PROB. Only 200.. three o f the seven a f f e c t i v e v a r i a b l e s , IABS, IABF and SELFCON showed s i g n i f i c a n t d i f f e r e n c e s (p < .05). Females tended to accept r e s p o n s i b i l i t y f o r f a i l u r e and success more than males and males had a somewhat high e r s e l f - c o n c e p t i n mathematics than d i d the females. The t a b l e above summarizes the one-way a n a l y s i s of v a r i a n c e f o r males and females c a l c u l a t e d from raw sco r e s on each s c a l e and over the complete 1033 cases; 529 males and 50 4 females. Although the d i f f e r e n c e s between males and female means are s i g n i f i c a n t on some of the s c a l e s , there are onl y two p a i r s of means which d i f f e r by more than one s c a l e p o i n t : COMP at 2.6, and PBOB at 1.1- When these d i f f e r e n c e s are t r a n s l a t e d i n t o p r o p o r t i o n s of ex p l a i n e d variance the d i f f e r e n c e s become l e s s important. When sex i s c o r r e l a t e d with the achievement v a r i a b l e s the squared c o r r e l a t i o n s show t h a t sex accounts f o r only 3.8% of the va r i a n c e of COMP and 2,1% of the v a r i a n c e of PBOB, 201 Appendix H INTEE—CORRELATIONS OF STUDENT-BEHAVIORS 1 2 3 4 5 6 7 8 1 1.00 2 .19 1.00 3 .23 .51 4 .30 .06 5 .33 .19 6 .12 .26 7 .30 .02 8 .33 .11 9 .09 .16 1. Tends t o g i v e random answers t o q u e s t i o n s d u r i n q mathematics c l a s s . 2. Appears t e n s e d u r i n g mathematics l e s s o n s . 3. E x p r e s s e s a n x i e t y o r n e r v o u s n e s s about mathematics. 4. Tends t o i n c r e a s e d i s r u p t i v e b e h a v i o r durng the mathematics c l a s s . . 5. Says t h a t no matter what he/she does he/she c a n ' t do mathematics. 6. Has hands t h a t shake when d o i n g mathematics. 7. Says t h a t mathematics i s u s e l e s s . 8. Sometimes r e f u s e s t o answer q u e s t i o n s d u r i n g mathematics p e r i o d . 9. F i d g e t s more d u r i n g mathematics. 1,00 .01 .27 .23 .12 ,04 .23 1.00 .12 -.02 .36 .35 .37 1.00 .06 .31 .16 .28 1.00 .00 .01 .07 1.00 .22 .31 

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