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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 . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1964 M.A., U n i v e r s i t y of B r i t i s h C o l u m b i a , 1971  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF ED- D. in THE FACULTY OF GRADUATE ' %aeuit:y-i-S£ x  E  d  u  c  a  t  STUDIES i  o  n  We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1979 © ffames L e s l i e G a s k i l l \<VH }  In presenting t h i s thesis in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s thesis f o r s c h o l a r l y purposes may be granted by the Head of my Department or by his representatives.  It i s understood that copying or p u b l i c a t i o n  of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department of  Mathematics Education  The U n i v e r s i t y 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  relationships associated  variables of  the  a  control),  notion  measured  by  Besponsibility  Scale;  mathematics t o  society,  from  the  of  an  the  battery;  in  and  by an a u t h o r  achievement•variables Achievement T e s t  The  class into  scales  No  data  and c o n c e p t s  (locus  Achievement value to  of  learn  by s c a l e s  mathematics scale.  for  The t h r e e  measured  by  and p r o b l e m s o l v i n g  Skills.  hypotheses  were s u g g e s t e d  were  effects.  t o 1033 s t u d e n t s  standardized  by  The sample  difference  matrix  were s u b s e q u e n t l y  was  at t h e  within  each  was r a n d o m l y  split  one t o be r e t a i n e d f o r c r o s s  significant  Stepwise  independent  ability  of  in  Motivation.  The s c o r e s  variance-covariance The  Five  were c o m p u t a t i o n ,  were a d m i n i s t e r e d  t o remove c l a s s two s a m p l e s ,  of  constructed  and i n t e r a c t i v e  o f Achievement  grade s i x l e v e l .  block"  mathematics,  value  measured by t h e C a n a d i a n T e s t o f B a s i c  theory  the  variables,  "emotional  self-concept  dependent  the  affective  Intellectual  anxiety  measured  Nonlinear  study  e n j o y m e n t o f m a t h e m a t i c s , measured  Sandman  Stanford  of  to  achievement r e s p o n s i b i l i t y  oneself,  the  was  i n mathematics.  considered:  and  study group  and a c h i e v e m e n t  - were  mathematics  this  between  with  mathematics,  of  found  validation. between  o f m a l e s and t h a t o f t h e  the  females.  pooled.  regression  analysis  indicated  that  i i i  self-concept  alone  explained  achievement  variance;.  anxiety  also included  was  Principal of  the  set of  a  self-concept,  anxiety  from  value  factors Using  two  Factor  of  None  of  enjoyment), a  for  an  factor  or  2%,. rotation  factors.  These  (loadings  value  student  factor entering  non-linear  mathematics  orthogonal three  the  factor  from  (loadings  achievement r e s p o n s i b i l i t y  each  motivation  of  additional  factor  stepwise regression  value  the  the  and  scores  the  computation,  f o r an  motivational  s c a l e s ) , and  these scores,  exception  accounting  a f f e c t i v e scales revealed as  20%  case of computation*  component a n a l y s i s and  were i n t e r p r e t e d  the  In t h e  approximately  were  showed  that,  i n t o the  was  the  interactive  calculated. with  the  equation  only  one  for  retained.  hypotheses  were  significant. The validation  above samplei  It  was  self-concept should  be  that  findings  that  as as  in  the  repeated  group  enjoyment  studies  and  was  the  cognitive  the  e m o t i o n a l component.  alter  self-concept  and  that  component  anxiety  of  three  anxiety  dealing  suggested  using  the  cross  were c o n f i r m e d .  It  attempts to  altering  A l l the  of a b i l i t y ,  mathematics.  enjoyment  were  concluded  included  interpreted  analyses  with  variables,  i n mathematics motivation  self-concept of  anxiety  I t was  also  i n mathematics c o u l d  in  could and  be  that  suggested be  made  by  enjoyment. C h a i r m a n : Dr.  Gail  Spitler  iv  TABLE OF CONTENTS  Page List  of Tables  ..  ix  Acknowledgements  x i i  Chapter  '  1. THE FBOBLEM  ..  ,. . ; . i  BACK GBOUND  ....  Introduction  1  ...........  ............................, .  Emotional Block Variables  ,. 1  ... ... L  ,  Associated  2  W i t h An " E m o t i o n a l B l o c k " 1  Problem  ....  i ....... .  CASE FOB A NON—LINEAB Independent  MULTIVARIATE  1  APPBOACH  6 7  ' 8  Variables  8  Dependent V a r i a b l e s  11  Importance  13  Of The P r o b l e m  .RESEARCH HYPOTHESES  ...................  1.......  15  Summary Of The P r o b l e m  15  Generalization  16  Affective  A c r o s s Sex . . . . . . . . . . . . . . . . . . . . . . . . .  Inter-Scale  Affective-Achievement  C o r r e l a t i o n s ................. Scale  S T A T I S T I C A L HYPOTHESES . . . Significance  Versus Strength  Generalization Affective  Across  Inter-Scale  Affective-Achievement  Belationships  .........  i......... i ... i  Of B e l a t i o n s  .»  16 17  . . il 8 ...18  Sex  18  Belationships  19  Scale  Belationships  ,.i..;...19  V  2.  BELATED EESEABCH .,. INTRODUCTION  .. 21  ....................... i ..... i '. . i -. . 21  ATTITUDE VARIABLES  22  Number Of S t u d i e s  ................... . ..... . ...'....* 22  Typical Studies  23  ANXIETY I N MATHEMATICS . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . 25 General Anxiety  ...................................  S p e c i f i c Anxiety  29  VALUE ....  .  .  i  SELF—CONCEPT OF A B I L I T Y TO LEARN MATHEMATICS  .  .  .  ,  3  Self-Concept  32 .........  i.  i . . . . . . .  LOCUS OF CONTROL ... A  THE MODEL OF ACHIEVEMENT MOTIVATION  .......... 39  . , , i . . . . . . . . . . . . . . -  Achievement M o t i v a t i o n  40 40  V a r i a b l e s Of T h i s S t u d y R e l a t e d  To T h e ' M o d e l ...... 46  SUMMARY  50  3,. INSTRUMENTATION, DESIGN AND PROCEDURE ' INTRODUCTION ..... .. I. ......... .. INSTRUMENTATION ....  i ........ ... . 51 . . . . . i . . i . . . . - .i. . 51 .  ..  .... 52  Sandman S t u d y . , 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 I N MATHEMATICS ENJOYMENT VALUE  33 36  SUMMARY OF INDIVIDUAL A F F E C T I V E VARIABLES  The  1  ......... 32  Global Self-Ccncept Specific  25  .............. 58 .  i ... . 60 61  vi  Value Of Mathematics To S o c i e t y  ...  Value Of Mathematics F o r Oneself  61  ............ i . . . . . . . 61  SELF-CONCEPT OF ABILITY IN MATHEMATICS ...  w . i. .. i ....... . 64  LOCUS OF CONTROL ACHIEVEMENT  63  TESTS ..... i . . . . . . . . . . . . .  ,i . . . . . , i  TEACHEE RESPONSE SCALES ......  i..... .  .  65 67  AGE AND GRADE LEVEL CHOSEN . . . . . . . . . . . . . .  71  SUBJECTS  73  PILOT  75  MATERIALS ...................... A f f e c t i v e Scales  ................... 76  . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . .  Achievement Tests PBOCEDUBE  78  . . . . . . . . . . . . . . . . . . . . * L i . .......... 80  DATA DESCRIPTION ...........'............  i  .  Teacher Besponses  Data R e l i a b i l i t y  82  82  A f f e c t i v e S c a l e s ..  '...............  ............. 83  i .... . i . .  Achievement Tests PRELIMINARY  76  84 . i i i.. .4  ANALYSES . . . . . . . . . . . . . . . i . .  i a .  . . . . . . . . .  . i.i  . . . . . . . .  U n i t Of A n a l y s i s  85 85 86  I n c l u s i o n Or E x c l u s i o n Of TASC .. STATISTICAL PROCEDUBES .........  i ......... . 90 .  ,  ...94  S t a t i s t i c a l S i g n i f i c a n c e ..............±.......... . 94 Sex D i f f e r e n c e s  95  A f f e c t i v e Inter-*Scale R e l a t i o n s h i p s ............... 96 Affective-Achievement  R e l a t i o n s h i p s ,. i *  . , , ; t l . . . . . . . 98 ;  vii  Cross V a l i d a t i o n Cross 4.  ....101  V a l i d a t i o n Hypotheses  BESULTS  . . . . . . . . . . . . .  INTRODUCTION  ... .. i  i .... 102 ..i  i ................. . i . i . . . ; i. . ,i . .. 1 03  SEX DIFFERENCES  i ... i ., .i ...... i . 1 05 i .. 106  AFFECTIVE INTER-SCALE HYPOTHESES ., . . . . . . . . . . . . . . . . . . . . . .'.Vi. . . i . - .  Correlations Factor  Correlations  . . . . . . 1 1 1  ...... ............ .................... i ...111  CROSS VALIDATION  ........112  . . . . . . . . . . . . . . . . . . i . . i ....... . i . i i . . . 115  Analysis  ............. . . . . . . . . . . . i . . .  E q u i v a l e n c e , Of C o r r e l a t i o n s  . . . . . . . . . . i . . i . . . . 119  Analysis  SUMMARY 5. DISCUSSION  .^ . . . .  119  - i ...... L : . . . . . . 120  Analysis  Regression  06  .....109  Regression Analysis  Factor  1  Analysis  AFFECTIVE-ACHIEVEMENT RELATIONSHIPS  Factor  103  122 ^ ..... . .... . . . i . i . . . ; i . . . . i i . . . . 1 2 3  AND  INTRODUCTION  CONCLUSIONS . . . . . . . . . . . . . . . - , i I... i i . i ..... 1 26 . ....  .....  126  SEX DIFFEBENCES . . . . . . . . . . . . . . . . . . . . . . i .... i  I ....fl29  INTEB—BELATIONS OF THE "BLOCK" VABIABLES  130  THE BELATION OF THE "BLOCK" VABIABLES TO ACHIEVEMENT. .136 Correlations Multiple Factor  136  Begression Scores  Of  Standardized  . Scores  And  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139  LIMITATIONS OF THE S1U DY ......... ^.... i , . ,i. ..... i ..... i .. 1 41  viii  CONCLUSIONS  ..  FUTURE RESEARCH  ........  i....  ............................ i . .  Correlational Experimental  Studies  146  ........................149 i . '. i . i ..... 152  .,  APPENDICES  . . ....  A. INSTRUCTIONS FOR BEHAVIORAL B. INSTRUCTIONS FOR RANKING  BOOKLET  . . . . 1 . .... 4 166  CHECKLIST .  ......166  OF STUDENTS . ,i .... ,i  C. ADMINISTRATION BOOKLET D. QUESTIONNAIRE  ... .  ....................i147  Studies  REFERENCE L I S T  143  168  .. ,i ,,;  .170  .........  183  E. LAYOUT OF THE STUDENT RESPONSE FORMS . ; . . . . . . . '. . ^ .. 1 95 F. CLASS  MEANS  ACHIEVEMENT  AND  AND  STANDARD  AFFECTIVE  DEVIATIONS  OF  VARIABLES  G. DIFFERENCES BETWEEN MEANS FOR  MALES  THE 196  AND FEMALES  H. INTER—CORRELATIONS OF STUDENT—BEHAVIORS  i...  ...192 ..194  L I S T OF  TABLES  Table 1.  Page  P e r c e n t a g e s o f D i s s e r t a t i o n s and fieports Suydam  Dealing Reports  with  Affective Variables Listed i n  (1974-78)..  ......  2. C o r r e l a t i o n s Between G e n e r a l Scales  and  Several  Self-Concept  Social  Studies  Various  Anxiety  of  28  Ability,  Self-Concept,  Achievement...  35  4. C o r r e l a t i o n s Between an A c h i e v e m e n t and  22  M e a s u r e s o f A c h i e v e m e n t .. .> ..,  Mathematics S e l f - C o n c e p t , Mathematics  '.,  and S p e c i f i c  3. C o r r e l a t i o n s Between G e n e r a l  and  Journal-Published  Behaviors  Motivation  f o r I n t e r n a l and E x t e r n a l  Measure 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 t h e S u b - S c a l e s o f t h e Sandman  1  Inventory.  56  6. C l a s s T y p e , Sex 7. S c a l e s ,  and  Number o f S u b j e c t s . . . . .  Abbreviations,  74  Number o f I t e m s f o r t h e A f f e c t i v e  Scales. 8. S c a l e s , and  78 Abbreviations,  Number o f I t e m s *  Normed Means o f t h e A c h i e v e m e n t  9. P r e f e r e d  Sequence  and  Spacing  10. Means, S t a n d a r d D e v i a t i o n s , Reliability 11.  f o r the Achievement  Univariate Analysis of Variance Achievement  and  Tests.  of Scale  Maximum and  Reliabilities, i ......  79  Administration..  80  Score,  and  Hoyt  Affective Scales...  using  Each o f t h e  A f f e c t i v e V a r i a b l e s as Independent  86  X  Variables  and C l a s s  a s Dependent V a r i a b l e . . .,i  .. 88  12. R e s u l t s o f t h e B a r t l e t - B o x T e s t s o f H o m o g e n i e i t y o f Variance  on E a c h o f t h e A f f e c t i v e and A c h i e v e m e n t  Measures  89  13. C o r r e l a t i o n s Between A c h i e v e m e n t Variables Raw  using Scores Standardized  Variables  W i t h i n C l a s s , and  S c o r e s . ......... .........................  14. S q u a r e d C o r r e l a t i o n s Between Achievement •1.5. P a r t i a l of  and A f f e c t i v e  V  a  r  i  .. ... 91  MANX, TASC and t h e a  b  l  C o r r e l a t i o n s , and M u l t i p l e  e  Squared  s  .  93  Achievement  from a  Variables,  and MANX-.  M a l e s and F e m a l e s . . . . .  19. C o r r e l a t i o n s  20. F a c t o r L o a d i n g s Orthogonally  Variables;..>......i.107  Botated,  Polynomials  Three Achievement  BANK,  Checklist................  of the A f f e c t i v e Variables P r i n c i p a l Component  21. C o r r e l a t i o n s o f t h e F i r s t  and Second  Degree  108  on t h e F a c t o r s . 1 1 0 Terms o f  of the A f f e c t i v e V a r i a b l e s  with  Variables...............  Summary o f t h e S t e p w i s e A n a l y s e s Affective  .106  Between t h e A f f e c t i v e V a r i a b l e s ^  and t h e S t u d e n t - B e h a v i o r  Scores a s Independent  95  Scales  „  18. I n t e r - 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  Orthogoal  TASC,  . . i . . . . .  (17,i 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 A c h i e v e m e n t  22.  2  TASC when p r e d i c t i n g A c h i e vement S c o r e s , i  Behavioral Checklist, the  the  9  Correlations  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  for  .  Using  ....113  Standardized  Variables.....;........114  xi  23.  F a c t o r Score C o e f f i c i e n t  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 Standardized  25.  Regression  Achievement  Equations  Scores  ...................116 Factor  116 Factor  Regression  and F a c t o r S c o r e  Summary and  27.  I n t e r a c t i o n s as  Analyses  Usinq F a c t o r  F a c t o r Score I n t e r a c t i o n s as Independent  Scores Variables.118  and A c h i e v e m e n t  Scales  Sample 2  120  F a c t o r Loadinqs  From t h e A n a l y s e s  o f Sample  Sample 2., 29i  Using  ... ............ 117  Correlations of the Affective of  28.  of the Stepwise  Scores  Equations  Independent V a r i a b l e s 26.  S c o r e s and  Scores  of t h e Three  P r e d i c t i n g t h e Stepwise Faetor  Matrix  Error  Matrix  -. From a P r o c r u s t e a n  Sample 2 F a c t o r s t o a T a r q e t  1 and . . . . . . . . . . 121  Rotation of the  M a t r i x o f Sample 1  Loadinqs. 30.  ........121  Summary o f t h e S t e p w i s e Standardized  Scores  A n a l i s e s Usinq  as Independent  Sample 2  V a r i a b l e s . ........... 122  xii  ACKNOWLEDGEMENTS  To my d a u g h t e r  Kimberly,  from  whom  much  time  was  taken* To so  my  wife, Sheiagh,  committment  graciously. To G a i l  determination  Spitler, to f i n i s h  was i n s t r u c t i v e  through  several lo  Columbia  the  my a d v i s o r , whose  members  of  my  than  in  my  influence  directive.  committee  who  saw  me  revisions. Educational  Eesearch  which s u p p o r t e d t h e study  tests.  confidence  made i t p o s s i b l e , and whose  and s u p p o r t i v e r a t h e r  To t h e o t h e r  and  who a c c e p t e d my t i m e  Institute  of  British  with a grant f o r m a t e r i a l s  1  Chapter THE  1  PROBLEM  BACKGROUND Introduction If continued  a  pupil  "performs  frustration,  badly  he may d e v e l o p  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 . in  mathematics"  1965,  p. 4 7 ) .  establishment reduction be  major  associated anxiety, the  If  i s t r u e , then  concerns  of  i t s  (Marks,  block  to that  are not unusual  Purdy  &  Kinney,  the prevention  of the  It block"  will in  with repeated value  b l o c k " whenever i t o c c u r s ,  mathematics  behavioral be  educators*.  To  characteristics  argued  mathematics failure.  a n d enjoyment  mathematics t e a c h i n g  "block".  subjected  o f t h e " b l o c k " and t h e r e m o v a l , o r a t l e a s t  effectively,  "emotional  Such b l o c k s  added.j  this  is  an e m o t i o n a l  [Italics  o f the " e m o t i o n a l  ascertained;.  and  that i s  the a  should  do  this  should  concept  common  the  of  be an  one, o f t e n  Certain variables  such  as  o f m a t h e m a t i c s a r e o f t e n used i n  literature  to  characterize  such  a  2  For  the  purpose  c o n s i d e r e d synonymous w i t h in  terms of  scale  of  the  the  study  "affective".  s c o r e s o f one,  v a r i a b l e s a s s o c i a t e d w i t h an validate  this  "emotional  variables  and  between  mathematics achievement  were  examined.  the  presence  Research variables,  as  a  e d u c a t i o n , has and was  the  next  on  group,  chapter, and  its  t h a t the  other  affective  achievements examine between  the  Consequently,  mathematics,  Emotional  and  affective order  effects of be  o n l y one to  interact  to  of  and  these  mathematics shown, i n  o f the  this  variables  a g l o b a l measure is,  however,  with  each o t h e r  with  study  was  interactive an  designed  of  some  when s t u d i e d i n r e l a t i o n  the present  associated  and to to  relationships  "emotional  block"  in  t h r e e components o f m a t h e m a t i c s a c h i e v e m e n t ;  concepts,  and  problem  solving.  Block  Factors affecting (1972)  characterized  program  as one  1.  and  There  l i n e a r , n o n - l i n e a r , and  variables  computation,  variables  defined  variables  It will  examined.  In  was  t h e r e l a t i o n s h i p s among those  relationship  v a r i a b l e s might  block."  context  that t y p i c a l l y  mathematics achievement  with  the  been r a t h e r l i m i t e d .  selected  evidence  in  A " b l o c k " was  o r a number o f , t h e  pedagogical l i t e r a t u r e ,  "block"  "emotional"  the  success^ successful  who  f e e l s t h a t he  i s competent.  Crowder child  and  Wheeler  i n a mathematics  3  2. 3.  f e e l s t h a t he i s a c c e p t e d by h i s t e a c h e r . f e e l s t h a t h i s b e s t e f f o r t w i l l be a c c e p t e d by his teacher. knows t h a t h i s t e a c h e r w i l l p l a n work t h a t w i l l g i v e him s u c c e s s * knows t h a t e a c h d a y * s work w i l l be a challenge, (p. 4)  4. 5.  Characteristics way:  h i s past  to p r e d i c t  1, 4, and 5 may be summarized work e s t a b l i s h e d a s u c c e s s  success  at  a  current  task  i n the f o l l o w i n g  p a t t e r n a l l o w i n g him even  i f i t was  a  challenge. To  convince  teachers  that  there  among l e a r n i n g t h e o r i e s and t h a t t h e r e for  guiding  (1969) c i t e d  practice  in  Hilgard's l i s t  most t h e o r i e s o f l e a r n i n g .  the  was a c o m m o n a l i t y  were p r i n c i p l e s  useful  mathematics c l a s s r o o m  Fremont  of fourteen Of t h e s e ,  principles  common  three d e a l t with  to  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 yield more favourable outcomes t h a n f a i l u r e and p u n i s h m e n t . Tolerance for failure i s built by success experiences. Learning i s a i d e d by knowledge o f m i s t a k e s a n d successes. ( p . 43)  6. 12. Fremont of  (1969) r e i t e r a t e d t h e above  the  points i n  slow l e a r n e r i n mathematics;  The t e a c h e r  t o i n v o l v e t h e s t u d e n t s i n new e x p e r i e n c e s (p. 2 5 3 ) . student's  When  i s  the  r e a c t i o n as f o l l o w s :  mathematics  these!*"  Fremont  "After  years  t h a t cause t h e student (p. 5 2 4 ) .  success"  described of  failure  successes  t o exclaim,  He c o n t i n u e d ,  should " t r y  offering  case  ± t h e r e (J i s a s e r i e s o f q u i c k  of experiences do  such  h i s discussion  the in  - a series  'Hey, I  "These i n i t i a l  can  success  4  experiences  c a n n o t be o v e r e s t i m a t e d  the  steps  first  achievers" quite  on  (p. 5 2 5 ) .  the  road  i n importance.  hack  for  C o o n e y , D a v i s and  They  are  many o f t h e s e  Henderson  (1975)  low were  specific: Slow l e a r n e r s n e e d 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 to get correct answers. This is particularly t r u e f o r s t u d e n t s d o m i n a t e d by f e a r o f f a i l u r e or h o s t i l i t y . . . . They need confidence and encouragement more t h a n t h e y need t o know t h e basis f o r p a r t i c u l a r procedures. ( p . 334) The  was  importance  stressed  suggested readily succeed  that, i f  has The  directive  "interest  the  pupil  in has  They f e l t  o f t h e new  a  Kinney  new  (1965,  activity  some c o n f i d e n c e  p.  47).  They  develops  most  in his ability  m a t e r i a l so t h a t " t h e p u p i l  problems noted  (p.  associated ay  material  that the teacher should  a chance t o succeed"  were  when b e g i n n i n g new  M a r k s , P u r d y and  with i t . "  difficulty t h a t he  by  of success  always  the  feels  47).  with  B i g g s and  that determining the readiness of a  space  to  carrying  McLean  out  this  (1969) who  stated  child  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 experience. It is this kind of skill combined with the a r t of 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 child experiences some successes each day that d i s t i n g u i s h e s the t r u l y professional teacher from the t e c h n i c i a n . [ I t a l i c s a d d e d J (p. 8.) Running through of  success  child*s new  i s the  a l l these  statements  theme t h a t a s u c c e s s  assessment of the p r o b a b i l i t y  situation.  experience  is  experience  of being  I m p l i c i t i s the assumption motivating:  that  about the  the c h i l d  effects  changes  the  successful in a  that  the  success  w o u l d e x p e n d nrexre  5  e f f o r t i n t h e a c c o m p l i s h m e n t o f t h e new t a s k . hand, be  one  might expect  disabling  enabling  and  as  are  the  other  that the experiences of f a i l u r e  would  inhibiting the  effects are referred  rather  experiences  Learner  i n Mathematics  volume  stated  achievers  repeated  failures  school"  (p. 3 4 4 ) .  that:  "Students  is  (Lowry,  noted  presence and  fear  made  who  have  that  of mathematics"  Wilson  defensively  (1972)  of  had  worth  The panel  failure, at  least  (1970) i n t h e same characteristics  failure.  . . .  (1975)  difficulty  in  attitudes  understand  (p. 3 2 5 ) .  Dreger  report i n c l i n i c a l they  to  and n e a r  and H e n d e r s o n  t o have n e g a t i v e  nature"  classes  such  their  them s k e p t i c a l o f t h e v a l u e o f  Cooney, D a v i s  t h a t "Many p e r s o n s  academic  Indeed  preface  of f a i l u r e  be c o n v i n c e d t h a t t h e y c a n n o t mathematical  and  1972) t h e e d i t o r i a l  W e l l s and S h u l t e  their  have  mathematics are l i k e l y  a  In the  t h a t "One o f t h e most s t r i k i n g  low  and  success.  a l l o f them h a v e a l o w o p i n i o n o f t h e i r  as mathematics s t u d e n t s . "  of  motivating  t o i n the l i t e r a t u r e .  s t a t e d t h a t "because of a h i s t o r y almost  than  of  Factors affecting f a i l u r e . Slow  On  stated learning  toward  i t  o r do a n y t h i n g o f and Aiken sessions  (1 957) and  in  are emotionally disturbed i n the  (p. 344) .  distinguished  motivated learners.  I n t h e same  vein  Pikaart  b e t w e e n c o n s t r u c t i v e l y and  They s t a t e d ,  " c o n s t r u c t i v e l y " motivated students are those who have a h i g h l e v e l o f a c h i e v e m e n t m o t i v a t i o n and a low anxiety, whereas "defensively" motivated students a r e those who h a v e t h e 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 given with  task  would b e g i n  such a task  applied  who e x p e r i e n c e d  to  would  the  t o expect  tend  to  task,.  This  h e l p l e s s n e s s " by Weiner  (1972)  achievement motivation  syndrome,  (p. 2 1 0 ) .  In  responsibility achievement  this  oriented  Variables Associated In observed,  with  an  the  were:  outcome"  was a s s o c i a t e d of a c t i o n s  (1957)  cited  to i n t e l l e c t u a l  anxiety  factors"  taken  in  Schonel  who  that e f f o r t  "Emotional  a)  (M—ANXIETY) ,  lack of interest;  was  high  anxiety  return*  condensed in  to  opinion  For the  and a the  belief present  following  mathematical  five  situations  (M—ENJOYMENT) c )  (M—VALUE) , d) low s e l f ^-concept  mathematics  of  i n l e a r n i n g ; and t h e  b) low e n j o y m e n t o f m a t h e m a t i c s  learn  low  c h a l l e n g e s , low m o t i v a t i o n  of mathematics to  of c o n f i d e n c e  list  to  entitled  section  would n o t p r o d u c e any  this  variables:  accept  much  The f a c t o r s  and f e a r o f f a i l u r e ;  worth a s a l e a r n e r and l a c k to  with  (p. 3 4 4 ) .  low e s t i m a t i o n o f m a t h e m a t i c s and i t s v a l u e ;  inability  "low  achievement  " t h a t b a c k w a r d n e s s i n a r i t h m e t i c i s due as  above i n t h e p r e v i o u s  ability  "learned  influences  effect  summary, D r e g e r and A i k e n  identified  low v a l u e  as  effort  "Emotional_Blpck'|  as  study,  the  in  a  situations.  emotional  Block"  low  effort  the r e s u l t s  i t  at  confronted  labelled  who d e s c r i b e d  this  f o r accepting  reduce  was  persons  failure  and when  or  effect  that  study  failure  avoid  since  do n o t p e r c e i v e  repeated  (M—SELFCONCEPT),  of the  and  e)  7  unwillingness situations  to  accept  responsibility  in  achievement  (ACHIEVEMENT R E S P O N S I B I L I T Y ) .  It  s h o u l d be n o t e d  Internal-External  Locus  of  interchangeably  (Weiner,  Crandall  developed  (1965)  Responsibilty  Scale  internal-external  t h a t ACHIEVEMENT RESPONSIBILITY and  based  Control  1972).  Crandall,  the  an " e m o t i o n a l  used  Katkovsky  and  upon  Rotter's  Achievement  (1966)  theory of  locus of control.  domain  interchangeably;  been  Intellectual  S i n c e t h e above v a r i a b l e s affective  have  were  associated  the f o l l o w i n g phrases "block" variables,  b l o c k , " a.nd a f f e c t i v e  with  or terms w i l l  be  variables associated  the used with  variables.  Problem The  purpose  interrelationships students  when  of  this  study  was  'make c l e a r  in  which  construct be  i t  performing  mathematics.  what s o m e t h i n g occurs"  in  methodological students  (p. 2 9 0 ) .  experience  I t was a l s o  constant  or  also  follows: the laws  assumed  belief  held that these constant  to  In short, the that  b l o c k " when c o n f r o n t e d  near  some  s t a t e d t h a t "a  (p. 2 8 3 ) . . the  the  and Meehl  as  of people,  expressed  an " e m o t i o n a l  problems.  procedure  They  performance"  literature  experience  mathematical who  test  Cronbach  i s ' means t o s e t f o r t h  i s some p o s t u l a t e d a t t r i b u t e  reflected  clarify  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  (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 "to  to  some with  students, failure  in  8  m a t h e m a t i c s , e v i d e n c e d c e r t a i n b e h a v i o r s and to reduce the  individual's ability  situations.  The  that  major  mathematics  function  of  the  function  hypothesis  achievement  above  to  beliefs  of  in  tending  mathematical  t h i s study, then,  (M—ACHIEVEMENT)  would  was  be  a  variables,  M—ACHIEVEMENT = f(M—ANXIETY, M-ENJOYMENT, M—VALUE, M—SELFCONCEPT, ACHIEVEMENT RESPONSIBILITY). This was  does n o t to  be  imply  validated.  variables  which  relationships  Independent  had  In identified  Neal that  "emotional  be  the  block" set to  validated  their  in  terms  of  an  A NON—LINEAR MULTIVARIATE APPROACH  d e f i n i t i o n s : ; of a t t i t u d e , ;  to  time of  extensively  increasingly  one  review of  anxiety  t h i s study* in  some c o m m o n a l i t i e s i n  in  and  and  critical  attitude studies the  scales  mathematics  Measures of  mathematics  intensive several  Separate  were  attitude  were  being  analysis. Aiken  d e f i n i t i o n s of  (H972)  attitude.  Attitude as used means a p p r o x i m a t e l y interest, and to (p. 229)  in the s t u d i e s r e f e r r e d to here the same thing as enjoyment, some extent, l e v e l of anxiety,  (1969) w h i l e  a list  the  of  achievement.  at the  used  subjected  an  been d e s c r i p t i v e l y l i n k e d  v a l u e , e n j o y m e n t , and  typical been  of  Variables  Multiple measuring  construct  often  were t o  with  CASE FOR  the  However, i t d o e s mean t h a t  have  "emotional block"  not  that  the  giving  definition  of  of  attitude  attitude  variables  " i s not  claimed  precise,  but  9  inventories or  that  disliking  of mathematics,  mathematical useless" such  measure i t i n c l u d e  activity,  (p. 6 3 2 ) .  as  study h a b i t s ,  academic  interest,  standardized  overall  score  and  attitude  motivation,  and  unidimensionally"  test  noncognitive  study  the  measure t h e composite scores  on  correlation scale> anxiety  Alpert w i t h two  (debilitating) variance that  of  hypothesis the  would  scales  flaber  scales, anxiety  achievement  a multiple  scale  that  postulation of  each  that  assumption t h a t can  a his  to  an  attitudes,  be  represented  suggestion  study  of  achievement  give  would  mathematics and  with  a s compared  the  was  positive  have  a  measured t h e  (facilitating) increase  when u s i n g  the  two  a multivariate  was  the  did  not  than  the  single  construct  of  and  negative  in  explained indicated  Therefore,  function  a  multiple  more i n f o r m a t i o n  linear  on  that  any  scales  productive;  would add  of  they  than  The  scale  effect  higher  scales..  a p p r o a c h was  a  more i n f o r m a t i o n  achievement  (1960)  of  based  A simple i n t e r p r e t a t i o n of t h i s  with  achievement,  noted  i n d i v i d u a l s c a l e s , i n s o f a r as  several  variables  teacher*  The the  upon  same c o n s t r u c t ,  score.  need  He  habits  to  variables the  several  or  219) .  approach  assumption t h a t  mathematics i s u s e f u l  subscore  Complex I n t e r r e l a t i o n s . multivariate  avoid  toward  of  d o u b t on  (p.  t o engage i n o r  score.  usefulness  cast  liking  achievement anxiety*  achievement  "suggest the  that  as  (1969) c o r r e l a t e d  and  results  a tendency  a belief  Khan  such i n g r e d i e n t s  led  such, a s ,  the to  10  M-ACHIEVEMENT = M—ANXIETY + M—ENJOYMENT + M—VALUE + M—SELFCONCEPT + ACHIEVEMENT RESPONSIBILITY However, particular  more complex r e l a t i o n s  i t could  be t h e c a s e t h a t  the  e f f e c t o f another v a r i a b l e .  an  interaction  locus of c o n t r o l achievement In  had a  Wolk a n d D u C e t t e  may  effect  on  the  a  may  construct  be that  measure  with  In  moderate  (il 973) , showed  w h i c h was c o r r e l a t e d  (1966) c o n c e i v e d  as a moderator  one v a r i a b l e  occur*  That i s t o say, there  moderating  motivation  f a c t , Rotter  control  effect.  might a l s o  of  achievement. of  locus  of  variable.  The e f f e c t o f r e i n f o r c e m e n t f o l l o w i n g some b e h a v i o r . . . depends upon whether or not the person perceives a causal relationship between h i s own b e h a v i o r and t h e r e w a r d . (p* 1) He  continues P e r h a p s one o f the major conceptions which bears some relationship to the b e l i e f i n i n t e r n a l versus external control of"reinforcement i s that o f need for achievement; . . . p e o p l e who a r e h i g h i n t h e need f o r a c h i e v e m e n t , i n a l l p r o b a b i l i t y have some belief i n their own a b i l i t y o r s k i l l t o d e t e r m i n e t h e 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 is probably not l i n e a r * ( p . 3) Silverblank  She  found  that  considered, majors  scores  the  towards  facilitate  the  variables  noted another i n t e r a c t i o n means  of  variable  appear s i m i l a r .  However,  extremes o f a n x i e t y ;  secure or severely  was a s i m p o r t a n t To  relate  when  groups c o u l d  tended  unusually  (1973)  anxious*  they  effect.  scores  were  mathematics were  either  The d i s t r i b u t i o n o f t h e  a s t h e mean..  the statement  o f h y p o t h e s e s which  of t h i s study, a t h e o r e t i c a l  would  framework  11  was c o n s i d e r e d  important.  Instrumentality  t o address the i n t e r r e l a t i o n s of value of  success,  failure.  motivation The  instance  432) ,  is  sufficient  will  was  of  each o t h e r  t o note here  relationship  and  motivation  to a  avoid  specific  (Mitchel S Biglan,  the  1971,  i n Chapter  2*  It  Achievement  Motivation  f a c t o r s , motivation  to succeed,  of success,  some n o n - l i n e a r  achievement  interacting  be d i s c u s s e d  present  i n Chapter  with  activity.  correlations  oriented  o f the v a r i a b l e s of the  factors will  found  expectation  i n the p r e d i c t i o n o f achievement o r i e n t e d  factors  three  that  and value  model a l s o p r e d i c t e d  its  and  i n some d e t a i l  of three  of success,  of success,  Achievement M o t i v a t i o n ,  be p r e s e n t e d  composed  probability  The  theory  succeed  of instrumentality theories  p.  model  to  t h e o r i e s were  between  activity.  The  study  the  and  2.  Dependent, V a r i a b l e s _,_E  ,  ,  ,,  Attitude confused That  measures  scales  different  constructs  measure  affect  mathematics.  of  a  been  limited  c o n s t r u c t s b u t a l s o by p o o r l y  i s , the  Higgins  have  have  and  towards  mathematics  enthusiastic  about  "something l e s s than  items  only  from  have  by  referents. several  been' u s e d  to  aspects  of  different  f i n d i n g s tended t o c o n f i r m  this.  o f a t t i t u d e changes i n the s e t t i n g  laboratory the  scales  several  Some u n e x p e c t e d  (1970) i n h i s s t u d y  delineated  contained  those  not  found  opportunity  e n t h u s i a s t i c about  that to  students participate  the c o n t e n t  were but  material"  12  (p. be  55).  Attitudes  considered Aiken  about t h e v e h i c l e  and t h e c o n t e n t  should  separately. (1969) p o i n t e d  out that  A t t i t u d e t o w a r d m a t e r i a l t o be l e a r n e d by r o t e , s u c h as the m u l t i p l i c a t i o n table, i s not the same variable as a t t i t u d e t o w a r d p r o b l e m s and a l g e b r a i c symbols. (p. 8) The  measurement o f m a t h e m a t i c s  broken  into  problem  solving.  affective of  three  variables  each  analyzed  of  having  variables,  the  separately.  variables  and t h r e e  Aiken  computation,  Because of the p o s s i b i l i t y  the achievement  study  components;  three This  (Aiken  i t was f e l t achievement  resulted  dependent  more h i g h l y  measures study that  "that  of  the  with  each  i n the  major  that  attitude and  t h a n i n males"  present be  independent  attitude  In  (1970) c a l l e d f o r  and  unpublished scale  scores  achievement  (p. 1 4 ) .  s o l v i n g Carey  h i g h e r f o r males t h a n  Aiken  each  and  components s h o u l d  ability  were c o n s i d e r a b l y summary,  of  1961) s t a t e d  i n problem  t h e c o r r e l a t i o n s between  concepts,  that  i n five  with both  i n the case o f females  o f sex d i f f e r e n c e s  often  variables*  & Dreger,  correlated  i s  different relationships  d a t a c o l l e c t e d by him d e m o n s t r a t e d are  achievement  (1978)  problem  In a found  solving  f o r females.  a research program . . . to investigate the i n t e r a c t i o n s among t h e e n t i r e domain of affective and cognitive variables in their effects on m a t h e m a t i c s l e a r n i n g . . Such a program should be multivariate i n terms of both input and o u t p u t variables, and would entail a composite of correlational and e x p e r i m e n t a l research methods, (p. 253)  13  The  present  Importance  study  was  of the  considered  of  potential  possible  p a r t o f such  of a construct.  non-Iineat o r i e n t a t i o n hypotheses  results  was  could  quite  Because  of t h i s  large*  A  h a v e been s t a t i s t i c a l l y Therefore,  formed  were  relationships  an  r e s e a r c h and  important  associated useful  based  set  accepted  aspect  w i t h an  of  then  not  should  be  study,.  number of  If  As  and were  suggested This  the  by was  variables  considered  a  r e l a t i o n s h i p of each  to  s t u d i e d but the r e l a t i o n s h i p s  elucidated.  the  hypotheses  b l o c k " were t o be  only s h o u l d the  the  spurious  t h e o r e t i c a l models..  this  "emotional  m a t h e m a t i c s a c h i e v e m e n t be themselves  upon  the  number  uninterpretable.  existing  program.  of  study  theoretically which  a  Problem  The - v a l i d a t i o n multivariate,  t o be  Nunnally  among  (1970) s t a t e d , a  construct i s something t h a t the s c i e n t i s t puts together from his 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 e r v a b l e d i m e n s i o n o f b e h a v i o r . A construct represents a hypothesis (usually half formed) that a v a r i e t y of b e h a v i o r s w i l l c o r r e l a t e w i t h one a n o t h e r i n s t u d i e s o f i n d i v i u a l d i f f e r e n c e s a n d / o r w i l l be s i m i l a r l y affected by experimental treatments. (p. 139) He  continued,  those alike  "determining  variables correlate by  validation It nomological  experimental process" may net  be as  to  with  what e x t e n t  one  treatments  another  a l l , or some, o f or  are  i s a necessary  affected  step i n the  (p. 141) . useful  here  d e f i n e d by  to  note  C r o n b a c h and  the Meehl  concept (1955).  of  a  14  1) t o forth  "make c l e a r what something t h e l a w s i n which i t occurs,.  i s " means t o s e t  2) The laws . . may relate (a) observable properties or quantities to each other; o r (b) theoretical constructs to observables; 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 t o one a n o t h e r . 3) a c o n s t r u c t £mustj . . . net, at least some of observables. ^  occur i n a nomoloqical whose laws involve  4) " L e a r n i n g 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 t h e n o m o l o g i c a l network i n which i t o c c u r s , 5) An e n r i c h m e n t 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 t o t h e o r y i s j u s t i f i e d i f i t generates nomologicals that are confirmed by observation or i f i t reduces the number of nomologicals required to predict the same observations. 6) " o p e r a t i o n s " which are qualitatively very different " o v e r l a p " o r "measure t h e same t h i n q " i f t h e i r p o s i t i o n s i n t h e n o m o l o g i c a l n e t t i e them to t h e same c o n s t r u c t v a r i a b l e * (pp« 290—291) If variables  the was  confirmed  would s u g g e s t then  be  complex  as having  interactive  variables  and  that  must be  of a This  by t h i s  nature  of the  study,  set of  then the  in  future  research  the " b l o c k " . relationship  If  any  for the  between was  experimental  done e x p e c t i n g d i f f e r e n t  affective  variables  counteracting experiences  mathematics achievement  suggest  variable levels  specific  examined  identified  would  multivariate  which  those  should subjects  hypothesis the  used  of  a  noncognitive  confirmed manipulation effects  at  then  i t  of  one  several  second* study  would d e l i n e a t e the  was  considered important  interrelations  of a  number  then  because i t  of  variables  15  currently also  of  i n t e r e s t i n d i v i d u a l l y and  considered  an.important  experimental  hypotheses.  the  degree of  complexity  the  establishment  complex  be  is  the  step  i n the  was  generation  of  It  would  provide i n s i g h t  the  a t t i t u d i n a l domain.  of  attitude  variables  theoretical contribution  elucidated  It  into  i n Chapter  in  of  the  Moreover,  a t h e o r e t i c a l framework a p p r o p r i a t e  conceptualization  education will  of  of  first  collectively*  to  a  mathematics  t h i s study  and  2.  RESEARCH HYPOTHESES Summary o f  the  The teaching  Problem  reviewed l i t e r a t u r e  in  mathematics  block" i s r e l a t e d to also  suggests  specific anxiety,  relation  to  indicated differently  T h e r e f o r e , the  solving* exist  attitude several "block"  achievment  that  an  of  typical and  of  control,  is  "emotional  The  literature several  attitude  self-concept. also  of  more  scales:  Achievement suggested  in  helplessness".  literature  to  are  value,  or l o c u s  that  states  methods  " b l o c k " i s composed o f  which  "learned  The  three  the  enjoyment,  responsibility,  education  with  mathematics achievement.  that  constructs  associated  on  attitude  variables different  toward  are  probably  referents  or a f f e c t i v e v a r i a b l e s  of  also  argued t h a t  between  the  variables,  complex and  mathematics.  and  interactions  that  related  were r e l a t e d  measures; c o m p u t a t i o n , c o n c e p t s ,  I t was  mathematics  the  to  problem might  achievement  16  motivation  model d e s c r i b e d  three  affective  interacted  i n achievement  related  activity.  Generalization  constructs  which  a c r o s s Sex  Nunnally  (1S67) d e c l a r e d  that:  if both sexes a r e 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 separately f o r t h e two before correlates a r e computed. I f that i s not done, s e x s h o u l d be i n c l u d e d a s a n o t h e r 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  which would l e a d study  scores  separately  f o r the two s e x e s  t o r e s u l t s w i t h e f f e c t s o f s e x removed,  included  an  analysis  for  there  would be  no  sex  effects*  hypothesized  that  correlations  among the a f f e c t i v e and a c h i e v e m e n t  males all  and  females*  the following  significantly  It  would be  tested  was  different  variables f o r  I f t h i s h y p o t h e s i s was n o t a c c e p t e d  hypotheses  this  separately  then for  males and females* Affective_Inter-Scale It  was  correlations It analysis factor  Correlations,  hypothesized  that  associated  was  that  hypothesized  solution as  which,  after  the  following  a  with t h e " b l o c k . " principal  would r e s u l t  component  in  a  three  o r t h o g o n a l r o t a t i o n , w o u l d be three  I h e word s i g n i f i c a n t when u n m o d i f i e d significant* 4  would be s i g n i f i c a n t *  among t h e v a r i a b l e s  of the a f f e c t i v e variables  interpretable  there  will  factors  mean  and  their  statistically  17  componentsFactor Factor Factor  1: M—ANXIETY, M-rENJOYMENT, EESPONSIBILITY 2: M—SELFCONCEPT 3: M—VALUE  Affective-Achievement It would  be  correlated  non-linear  each  would  Because  to  based  affective  i t  three  aspects  t h e achievement of  success  have a r e l a t i o n  may  o f the second  have  hypothesized  variables  would  a  that  degree  with  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  arguments r a t h e r than  was  of  motivation  o f s u c c e s s , t o be d i s c u s s e d i n C h a p t e r  on l o g i c a l  Therefore,  the  scales  a c h i e v e m e n t i t was h y p o t h e s i z e d  measures o f a c h i e v e m e n t . probability  of  that the probability  relation  self-concept  t h a t each o f the a f f e c t i v e  with  achievment.  model s u g g e s t e d  and  flelationships  was h y p o t h e s i z e d  mathematics  the  Scale  ACHIEVEMENT  be  was  on e m p i r i c a l f i n d i n g s .  that  also  2,  some  of  the  other  non-linearly related to  achievement. It by  was f u r t h e r h y p o t h e s i z e d  m u l t i p l e r e g r e s s i o n a sub-set  would  be  correlated  more w i t h  t h a t when g r o u p e d  of t h e independent each  of the t h r e e  variables achievement  measures than  any i n d i v i d u a l  hypothesized  that  significantly  t o t h e v a r i a n c e e x p l a i n e d by t h e v a r i a b l e  the  one o r more a d d i t i o n a l  maximum c o r r e l a t i o n It  derived  was  from  also the  independent  together  with  variables  t h e achievement  hypothesized  factor  variable'.  score  that  It  was  would add having  variables.  linear  coefficient  composites  matrix  of the  18  rotated  solution  achievement suggested it  was  would  scores.  As  interactions hypothesized  composites explained  correlate the  representing variance  to  Achievement  among t h e that  the  of  versus  wherever following  null  the  rate  sample to  of  size  sample  an  the  was  and  of  that  the  Thorndike  the  model,  the  add  linear further  scores.  Relations test  could at  t e s t s of degree or  (1971)  be  be  the  chosen to  I t should  as  would  model  HYPOTHESES  was  analyses.  large  size  most i m p o r t a n t .  level  of  achievement  appropriate  This  the  Motivation  factors  factors  h y p o t h e s e s were t e s t e d  significance. error  Strength  with  i n t e r a c t i o n terms of  STATISTICAL  Significance  three  those  that  significantly  made,  .01  level  r e d u c e the  noted  that  s i g n i f i c a n c e are s i z e of  the  the of  overall as  the  related  relation  was  stated:  The e m p h a s i s 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 e a c h r e l a t i o n r a t h e r t h a n m e r e l y on its statistical significance. Construct validation aims more a t comprehension than n u m e r i c a l r e s u l t s , (p. 465) In the II  addition .01 error  the  large  sample s i z e gave a d e q u a t e  alpha  level  would  inordinately  Generalization It (1)  There  was  make t h e  p r o b a b i l i t y of  that a  Type  between  the  large.  across  Sex  hypothesized  would be  not  power so  no  that:  significant  difference  19  variance-covariance  matrix  o f t h e males and t h a t o f t h e  females.  It should was  rejected  a  be u n d e r s t o o d  It (2)  the  null  hypothesis  s e p a r a t e t e s t f o r m a l e s and f e m a l e s  made f o r t h e f o l l o w i n g  Affective  that i f  w o u l d be  hypotheses.  Inter-Scale Relationships was h y p o t h e s i z e d  T h e r e would be "block"  no  that:  significant  variables,  correlations  M—ANXIETY,  among  M—ENJOY MENT,  the  M—V ALOE,  M-SELFCONCEPT, and ACHIEVEMENT RESPONSIBILITY. (3)  No s i m p l e  factor  component  analysis  M—SELFCONCEPT, (4)  s t r u c t u r e would emerge f r o m  I f a simple  of  M—ANXIETY,  a  M-ENJOYMENT,  principal M—VALUE,  and ACHIEVEMENT RESPONSIBILITY.  s t r u c t u r e emerged f r o m  analysis  the  orthogonal  following  loading  a principal  rotation  would  component  not r e v e a l the  pattern:  Variable  Factor  M—ANXIETY M—ENJOYMENT ACHIEVEMENT RESPONSIBILITY M—SELFCONCEPT M—VALUE  Loading  F1  F2  F3  high high high low low  low low low high low  low low low low high  Affective-Achievement,Scale,Relationships It (5)  was h y p o t h e s i z e d  Each o f M—ANXIETY,  that:  M-ENJOYMENT,  M—VALUE,  M—SELF C ONCE PT  20  and ACHIEVEMENT RESPONSIBILITY  (6)  correlated  with  computation,  c o n c e p t s , and problem  The  quadratic  M-ENJOYMENT,  each  would n o t be  of  component M—VALUE,  the  achievement  (7)  Linear  of  each  of  M—ANXIETY,  M-SELFCONCEPT,  and  ACHIEVEMENT  multiple reqression using M-ENJOYMENT,  ACHIEVEMENT increase  correlated  o f c o m p u t a t i o n , c o n c e p t s or problem  M—ANXIETY,  explained  the  M-VALUE,  BESPONSIBILITY  the  measures;  solving;  EES EONS IBILITY. would n o t be s i q n i f i c a n t l y measures  significantly  "block"  not  variance  solvinq. variables  M-SELFCONCEPT,  would  with  and  significantly  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 variables  regression beyond  not  the variable  each o f t h e achievement (9)  would  from t h e f a c t o r  the  measures  the  scores  achievement  then would  near  orthogonal  not c o r r e l a t e  with  of achievement.  from t h e f a c t o r  significantly  with  scores.  measures  (10) I n t e r a c t i o n s  additional  maximally c o r r e l a t e d  I f a s i m p l e s t r u c t u r e d i d emerge  three  include  scores  increase the-explained measures.  in  (9)  would  not  v a r i a n c e o f each o f  21  Chapter 2 BELATED RESEARCH  • "  INTRODUCTION  It may  be  was shown i n C h a p t e r  characterized  enjoyment, v a l u e , also  suggested  Achievement interact,  Motivation  responsiblility In  this  attitude of the  number  mathematics. (1956,  these  and with  when r e l a t e d t o  including anxiety,  in  used,  "emotional  of constructs;  Atkinson's  was  research  an  separate  individual  matter  measuring  the construct  theory detail  of  It  specifically enjoyment*  the c o n s t r u c t s the stronger  in  mathematics.  r e l a t e d t o mathematics value,  and s e l f - c o n c e p t I n each o f  be n o t e d *  and a model w i l l  to  be t h a t t h e more c l o s e l y t h e  are  related  the r e l a t i o n  and a c h i e v e m e n t i n  achievement  of  a measure, o f a c h i e v e m e n t  achievement  will  was  might  of t h e a r g u m e n t i n t h e s e c t i o n s d e v o t e d  constructs  i n question  anxiety*  variables  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 thrust  block"  1958) t h e o r y  m a t h e m a t i c s , and l o c u s o f c o n t r o l , i s r e v i e w e d .  scales  of  i f  themselves  chapter  The the  a  and s e l f - c o n c e p t that  among  by  1 that  motivation be i d e n t i f i e d  the  to  the  between  subject  on  measures  area.  w i l l be p r e s e n t e d based  subject  the  The  i n some theory.  22  Each o f t h e a f f e c t i v e the  three  variables will  c o n s t r u c t s o f t h e achievement ATTITUDE  Number o f —  As it  should  the  an i n d i c a t i o n o f t h e i m p o r t a n c e o f t h e s e be n o t e d t h a t and  b y Suydam  Journal  attitude*  years  may  model.  VARIABLES  9.4%  f o r the years of  and Weaver  for  1974-1978  variables  16.1%  the j o u r n a l - p u b l i s h e d  of  Research i n  Mathematics  Education  achievement  i n Table  included  responsibility  1.  Table  1  P e r c e n t a g e s 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 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 t h e Suydam R e p o r t s (1974-78) Reports  1974 1975 1976 1977 1978 Total  N 7 5 5 11 26 54  Total* 76 112 99 112 176 575  Dissertations %  9,2 4.5 5.0 9.8 14.8 9-: 4  i T o t a l number o f r e p o r t s T o t a l number o f d i s s e r t a t i o n s  2  in  The numbers and p e r c e n t a g e s f o r e a c h o f t h e f i v e  be f o u n d  Year  the  r e p o r t s as  (1974, 1975, 1976, 1977, 1978)  measures o f s e l f - c o n c e p t , a n x i e t y , or  one o f  -" —  dissertations listed  motivation  with  Studies T  1  be i d e n t i f i e d  N 44 44 37 52 56 233  Total* 299 264 266 273 343 1145  % 14.7 16.7 13.9 19.0 16.3 16. 1  23  Typical: Studies The belief, low  importance  of  the  present study  expressed i n the mathematics  a c h i e v e r s have some-form  certain  affective  teaching  stems f r o m  literature,  the that  of "emotional block" revealed  characteristics.  attempted  t o c h a n g e some o f t h e 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  multivariate (1970,  a p p r o a c h was  1976)  attitude  complex  were t o be  studied*  DuCette encountered achievement,  and  when using  Wolk  considered  emphasized  when  by  (1972) n o t e d  one  and  have  simultaneously. Wylie  (1974) and  The Aiken  phenomena s u c h a s s e l f — c o n c e p t  studying only  achievement  have  individual  v a r i a b l e s have n o t been  with  studies  correlated  the  variables  although  by  that  dependent  independent  difficulties  variables,  or  are  such  as  variable.  It i s also highly c h a r a c t e r i s t i c of such research [Internal—External 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 overall academic performance or social a c t i v i s m have been s t u d i e d . While such behaviors are undoubtedly more interesting than variables such as level of a s p i r a t i o n o r r i s k - t a k i n g , the problem in studying them i s t h a t t h e y a r e so h i g h l y o v e r d e t e r m i n e d t h a t t h e p r e d i c t a b i l i t y from any one specific variable w i l l be s l i g h t * (p. 494) Underlying positive student  the  concern  attitudes would  probability  that  for  would  attend  increase  t o mathematics  he would  learn.  (1964) s u p p o r t e d t h e n o t i o n s£udy  attitude  o f two  the  is  the  notion  likelihood  that  that  and t h e r e b y i n c r e a s e  K r a t h w o h l , Bloom and different  o f t h e r e l a t i o n s h i p between a c h i e v e m e n t  approaches and  a the  Masias t o the  attitude.  24  As viewed f r o m t h e c o g n i t i v e p o l e , the s t u d e n t may be t r e a t e d as an a n a l y t i c a l machine, a "computer" that s o l v e s problems. I n c o n t r a s t ; v i e w e d from t h e a f f e c t i v e p o l e , we t a k e g r e a t e r cognizance of the motivation, drives, and emotions that are the factors bringing about achievement of cognitive behavior. (p. 57) As  an  example  prevalence of learn  i t "  they  girls  (p,i  continued,  who  dislike  57) .  There  "Note  for  mathematics  is  an  instance and  implied  so  the  cannot  r e l a t i o n s h i p of  causality. Khan was  and  functional  successes help increases  the  Weiss  (1973) s u g g e s t e d  rather promote  than  causal.  satisfaction  possibility  of  that  the  relationship  They s t a t e d ,  with s c h o o l ,  future  successes"  "academic  which i n  turn  (p. 770) . i  It  should  were f o u n d upon  noted here t h a t  which i n d i c a t e d c a u s a l  c o r r e l a t i o n a l data.  (1959) s t u d i e d mathematics scales  parents*  and  and They  y e a r s and  result* De  concluded  difficult  of  statements  yet  were  not*  group  mathematics of  liked  a number parents  grade e x p e c t a t i o n s in  i n the  f o r even t h e The  that  They u s e d  self-concepts  best  implication  (1964) who  was  that  correlated  of  Lindgren, attitude  based Norton  of and  of  the  regard  to  early  school  teacher was  that  be r a i s e d t h e n a c h i e v e m e n t would r i s e  A n o t h e r example Rocha  did  a  well established  (p. 1 7 4 ) .  could  between  "that  are  number  example P o f f e n b e r g e r and  e n c o u r a g e m e n t and  i t i s very  self-concept  that  a  r e l a t i o n s and  a t t i t u d e toward  ability  them"  For  differences one  the  mathematical  change  the  such as t h e  siblings,  and  be  Silva, toward  as  to i f a  Faraco, problem  25  solving, tests.  and In  success i n arithmetic  their discussion  problem-solving achievement  that  was  poor a t t i t u d e s The  usually  school, very  low  but  contribution domain;  stability  the  some  of  between  of  Aiken  of  1372,  of  implication  achievement; with  achievement  noted  achievement  in  typically  As  one  the  instruments  (Aiken,  w i t h the of  1969,  (Aiken,  p.  maturity  have been s t u d i e d  1973, which  and  of the  in  the  affective  the- p r o b l e m s n o t e d  l i t e r a t u r e associated  not  problems have l i m i t e d  9),  230).  "the  elementary  the  inventory  are  that,  with  affective variables the  an  Again,  s e l f - i n s i g h t , conscientiousness  attitudes^ varying p.  was  are  arithmetic  45).  measures o f  measuring  "Why  in  s i g n i f i c a n t , are  power by  achievement  asked  (p;  (1969)  and  by  factor  others?"  A number o f  predictive  out  a  attitude  attitude  9),.  degree of fill  that  of  consistent;  (p.  of  cause poor a r i t h m e t i c  Limitations  416),  (Aiken,  than  although s t a t i s t i c a l l y  large"  pupils  more  they  c o r r e l a t i o n a l , there  correlations  correlations  p.  attitudes  study  measured  of. r e s u l t s  i n some c l a s s e s  a l t h o u g h the  as  the  pupils  above  was  isolation,  w i t b each v a r i a b l e  will  be  presented;  ANXIETY IN  General  MATHEMATICS  Anxiety There  are  anxiety;  Denny  measured  by  some c o n f l i c t i n g r e s u l t s on  (1966)  the  provided evidence that  Manifest  Anxiety  Scale,  the  effects  of  high  anxiety,  as  facilitated  the  26  achievement reverse  of s u b j e c t s with  was  t r u e f o r those  Goulet  (1969) , u s i n g t h e  found  that-  inferior given of  ego-stress  results  anxiety  indicated  whereas  a  with  of the  two  Mazzei  Denny u s e d  the  low  Manifest  that the  sets  of o b j e c t s , s i t u a t i o n s ,  Sarasoh  be  used  Anxiety  case  The  two  intelligence.  Goulet  behind  Mazzei  and  when  However, b o t h  sets  interaction low  to are  with  high  anxiety for students than  The  the T e s t  low  anxiety  differences  i n the  the  fact  that  Anxiety  Scale  (TAQ)  (MAS).  It  a n x i e t y toward  may two  be  the  different  or conditions* this  possibility  was  stated  (1975):  Our behavior is determined in part by information available to us* Information at disposal i s , in turn, i n f l u e n c e d by whether attend to i t * (p. 175) He  (TAQ) ,  Ss  e x p l a i n e d by  Scale  s c a l e s measured  theory  anxiety)  more i n h i b i t i n g  s t u d i e s may  and  than  the  unequivocally lead  (p. 6 0 2 ) .  disordinal  i n t e l l i g e n c e , and  students  results  t o low  that  Questionnaire  d i d not  instructions"  but  intelligence.  Anxiety  (TAQ)  (relative  intelligence low  b e i n g more f a c i l i t a t i n g  with high for  with  Test  "high anxiety  performance  high  the our we  continued In my v i e w , a p e r s o n ' s l e v e l o f t e s t a n x i e t y i s , t o a s i g n i f i c a n t degree a p r o d u c t o f experiences that influence what he attends to i n h i m s e l f and t h e world . . . . Two response components .have been e m p h a s i z e d by w r i t e r s who e s p o u s e t h i s v i e w . One i s emotional and autonomic reactivity sweating, accelerated heart rate, etc* The other concerns cognitive events e.g., saying to oneself 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)  by  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  specific  example. In T e s t a n x i e t y Type A, a p e r s o n g e t s u p s e t b e f o r e , during, and after tests because of relatively isolated unfortunate experiences ( f o r example, a traumatizing teacher in the third grade). 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 in other areas and (b) conflict and ambivalence over achievement and b e i n g e v a l u a t e d , (p. 175) That  the  to  two  related  the r e s u l t s  of  TAQ  and  different  a study to  related  testing  situation)  from  unrelated source  displayed Similar found  Gibby  t h a t they and  passed  decrement  Eating and  out  fail  in  word  different such  as a note  the  test  performance, from  Gibby  had  (1967)  who  five  of  Schedule  Along  as  analysis  from  the The  the  six  which  asked  same l i n e by  the  that  similar  resulting  school  office  former  group not.  academic f a i l u r e  were  teachers  Tiiey a l s o of  tell  English "a  the  marks  significant  stress" o f  found  s t u d e n t how  students  the  significant Intelligence  parents,  peers,  intelligence.  Dreger  O'Connor  a  by  did  They f o u n d  categories  on  latter  f l u e n c y score f o l l o w i n g the  the  are  found  stress  the s t u d e n t s '  well';  would r a t e t h e i r this  He  than  student*  stress resulting  grades  anxiety,  (failure  effects  c o n d i t i o n s " (p. 3 7 ) .  themselves  factor  and  of  (1954),;  performance  were d i s a p p o i n t e d w i t h  experimental c h a n g e s on  of  measures  s e t s of c o n d i t i o n s i s s u p p o r t e d  against  depressed  effects  by  task had  about a complaint  MAS,  done by O s i e r  stress  an  the  of  and  Aiken  (1957)  the T a y l o r M a n i f e s t  cited  a  Anxiety  28  Scale which argued  displayed five  that  constructs studied  attempts  Test,  c o l l e g e grade  psychology  anxiety  scales  They  more  between  were t y p i c a l l y  the  anxiety  they  anxiety (1960)  s c a l e s and  Scholastic  Aptitude in a  t h a t c o r r e l a t i o n s among t h e among g e n e r a l  scales as  scales.  Further,  s c a l e s and t h e c o g n i t i v e t e s t s  lower than those  the cognitive tests.  general  and s p e c i f i c  general  specific  A l p e r t and Haber  than those  between g e n e r a l  this  (GPA) , and g r a d e s g i v e n  found  s c a l e s were h i g h e r  as t h o s e  with  point average  course.  correlations  and  measure  the r e l a t i o n s h i p s o f three  specific  well  to  f a c t o r s . . From  would he more p r o d u c t i v e .  three  specific  distinct  between  the  specific  scales  (See T a b l e 2 ) .  Table  2  C o r r e l a t i o n s Between G e n e r a l and S p e c i f i c Anxiety S c a l e s and S e v e r a l M e a s u r e s o f A c h i e v e m e n t Bel  *-  MAS AI AS TAS AATAAT+  . 89 .84 .73 . 82 .87 .83  AS  AI  .39  i  —  T  n  TS  AAT-  .32 .28 .38  .38 .37 .30 .64  AAT+  GPA  —— ^— i  .32 .34  -.33 -.25 -.24 -. 40 -.48  .01 -.04 -. 06 -. 24 -;35 .37  Psych  -.08 -.05 .14 -.21 -i26 .23  SAT  . 10 . 13 -.24 -. 18 -. 29 .21  T a y l o r M a n i f e s t A n x i e t y S c a l e (MAS) ; Welsh A n x i e t y I n d e x (AI) ; Freeman A n x i e t y S c a l e ( A S ) ; M a n d l e r - S a r a s o n T e s t A n x i e t y S c a l e (TAS); Achievement Anxiety Test-Debilitating (AAT-); A c h i e v e m e n t A n x i e t y T e s t - F a c i l i t a t i n g (AAT+) ( A l p e r t & H a b e r , 1 9 6 0 , p. 209.)  They  concluded, S p e c i f i c a n x i e t y s c a l e s and g e n e r a l anxiety scales measure, to a significant extent* something  29  different* Furthermore, i t appears that the variable which the specific scales measure, and w h i c h g e n e r a l s c a l e s do n o t , i s i n v o l v e d i n a c a d e m i c p e r f o r m a n c e t o such an extent that the specific 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 t h a n a r e the g e n e r a l a n x i e t y s c a l e s . (p,. 209) Alpert between that  and  facilitating  an  absence  measure o f  sampling  should  be  groups  of  =  facilitating  93,  response to  multiple  to  the  scale  anxiety  the  difference They  item  present  may  not  and  They  found  .32,  -.08,  c o r r e l a t i o n s with and  and the  .50  that  and  -.40. two  be  a  therefore anxiety  in  c o r r e l a t i o n s between GPA  -.45,  stated  p o s i t i v e e f f e c t s of  were .36,  were ,*50* .32,  anxiety*  is  scale.  96)  the  a negative  wien s t r e s s  92,  debilitating  considered  debilitating  in a  anxiety  p r e d i c t i n g GPA  also  responses  included  (N  combined  and  motivation  items  and  Haber  three and  the  between  GPA  However,  the  anxiety  scales  .54.  Specific Anxiety c  Suin, earlier  Edie,  publication  Nicpletti, (Suin,  1970)  and  Spinelli  (1972) c i t i n g  an  stated.  O v e r one t h i r d of the s t u d e n t s who actively sought help through a c o u n s e l l i n g center behavior therapy program d e s c r i b e d t h e i r p r i m a r y problem as c o n n e c t e d with mathematics. (p* 373) On  the  Rating  basis Scale  "describing e.g*, monthly  of t h i s  they  (MARS). practical  'working  on  an  bank a c c o u n t * '  The  developed scale  situations income t a x or  a was  that form,'  'figuring  the  Mathematics composed o f involve  98  items  mathematics  'checking sales  Anxiety  over  tax.'"  your (p.  30  373). of  They  .78  found  and  a  Aptitude  Test.  therapy  for  norming  t h a t the  correlation The  mean  g r o u p was  a  scale  e x a m i n e d and aiken  syndrome o f e m o t i o n a l  subjects replaced  by  subjected and  the  The found  the  t h a t the  three items  "endeavor t o  females.  that  of  the  of anxiety  suggested  measure.  detect  Dreger  the  Anxiety  of  most  and  presence  of  relatively  They  !(TMAS) low  to  704  reliability  t o number a n x i e t y .  They  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 *  three items On  sex  the had  a  scale  c l u s t e r e d together.  correlation  of  other hand, S z e t e l a a strong  relation  They  -.44  with  (1973) to  found  the  Test  (p < .0001) .  differences anxiety  correlations Szetela  had  Taylor  then  of  items  t-he  a  mathematics  (p. 3 4 4 ) .  Scale  be  items  achievement  intelligence  256.9 and  seeking  valid  Questionnaire  • The  Differential  students  anxiety'"  relating  Mathematics Anxiety  correlated  was  a more g e n e r a l  items  grade*  Some  the  the  specificity  t h r e e mathematics a n x i e t y  Anxiety  SCAT.  the  'Number  fourteen  three  for  anxiety  Taylor Manifest  three  mathematics that  the  with  with  r e a c t i o n s t o a r i t h m e t i c and  called  administered  -.35  reliability  m e a s u r i n g a n x i e t y i n a mathematcs s i t u a t i o n  began t h e  tentatively  a test—retest  187.3.  compared t o  (1957)  of score  mathematics  T h e s e r e s u l t s on that  s c a l e had  have with  were  (1973)  c o r r e l a t e d -.24  found  been n o t e d . attitude  .305  for  that  f o r males and  Kahn  scores  m a l e s and test -.11  (1969) on  the  .509  for  anxiety for  and  females.  31  In  summary  achievement  anxiety  more g e n e r a l evidence  these are  studies indicated that  better  p r e d i c t o r s of  measures of a n x i e t y .  that  tests of  achievement  possible  sex  anxiety;  achievement  However, t h e r e  mathematics a n x i e t y  scales  The  measures  was  studies  also  than  no  were s u p e r i o r  of  clear to  the  indicated  differences. VALUE  The  value  sub-constructs; another,  the  was  that  be  found the  most  achievement*  one, value  component the of  of  for  However,  for  would be  a generalized  divided  into at l e a s t  mathematics  for  mathematics f o r o n e s e l f * .  important  motivation  stated  value  be  i n d i c a t e d which of  achievement oneself  may  these  the  value  suggested the  theory  more  that  from the  of the  value  appropriate.  of expectancy  society, literature  constructs  prediction  information  No  of  would  mathematics theory  h i s s t u d y he  found  of  mathematics  Baynor  (1974)  value:  the strength of tendency t o a c t i n a c e r t a i n way depends upon t h e strength of expectancy that an activity w i l l r e s u l t i n a c o n s e q u e n c e and t h e v a l u e o f t h a t c o n s e q u e n c e t o t h e i n d i v i d u a l summated oyer all expected consequences of the activity. (p. 126) In  two  that  College students c l a s s i f i e d high in n-Achievement i.need for a c h i e v e m e n t (J and low in Test Anxiety (Ms > Maf) r e c e i v e d h i g h e r g r a d e s i n an i n t r o d u c t o r y psychology course, and were relatively more concerned about doing well t h a n a n x i o u s when t h e g r a d e was s e e n as h i g h l y related to future goals t h a n when i t was not* (p. 132)  32  W r i t i n g a b o u t t i e same s t u d y Raynor  (1970)  i n a different  article  concluded,  that a student's ciaracteristic aciievement motivation f o r t i i s particular course i s revealed only when i m m e d i a t e performance i s important f o r future career success. (p. 32) It  appeared necessary  t h a t some a c c o u n t  s h o u l d be made  of  t h e p e r c e p t i o n s t u d e n t s have o f t h e i n c e n t i v e s t h a t  in  m a t h e m a t i c s m i g h t h a v e f o r them.  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  possibly  be  students.  appropriate Career  f o r upper grade,  goals,  as  i m p o r t a n t t o some e l e m e n t a r y perceive  success  Although  Raynor  i n mathematics as having  future l i f e ,  although not n e c e s s a r i l y career  might  that  success student value  feel  success  in  i n other courses being valued might  those  have  an  future effect  which  would  elementary  school  might  They m i g h t a l s o  oriented.  They  was i m p o r t a n t f o r  concurrently*  I f the  o u t c o m e s and c o u r s e s t h e n on  be  an e f f e c t o n t h e i r  mathematics taken  the possible set  suggested,  school students.  success  their  that  orientation  to  mathematics. Aiken for  use a t  (1974)  the  developed  college  level.  a Value of Mathematics s c a l e The  scale  correlated  ( P e a r s o n r ) w i t h t h e SAT-M a n d .40 w i t h h i g h s c h o o l SELF-CONCEPT OF A B I L I T Y TO LEARN Global  .27  grades.  MATHEMATICS  Self-Ccncept As  with  the  c o n s t r u c t o f a n x i e t y i t w i l l be  argued,  33  w i t h somewhat more c o n s i s t e n t  evidence*  self-concept  in  predict  of  achievement  achievement  more  Self-concept self-worth  dynamic s y s t e m himself, 1970,  strongly  has  been  (Anderson, of beliefs  each  belief  a  specific  in  a  measure  subject  than a g e n e r a l  used  such a s " i n t e g r i t y  self-structure"  a  that  would  measure*  global  sense  o f t h e whole o r any p a r t  1965, p. 9 ) , o r a s " a  a corresponding  complex  value"  of  of h i s  w h i c h an i n d i v i d u a l h o l d s t r u e with  of  and .about  (Purkey,  p. 7). On t h e o t h e r  adjectives  into  hand. S m i t h  five  (1960)  analyzed  f a c t o r s : self-esteem,  i n d e p e n d e n c e , e s t r a n g e m e n t , and body image. findings  helped  self-concept likely  investigators dealt  unwittingly 191).  the  same  global  confounded The n o t i o n problems  attitude.  self-concept  most a p p r o p r i a t e Specific  anxiety—tension, He n o t e d t h a t h i s  of a g l o b a l  The  for this  with  "It  seems  measures which may  self-concept self-concept  have  variables"  a p p e a r s t o have  with i t as d i d t h e n o t i o n  argument  related  of adjustment.  will  be  made  of a  that  t o mathematics achievement  a  i s the  study.  ..Self-Concept The  basis  several  associated  scale  bipolar  t h e p o o r r e l a t i o n s h i p between t e s t s o f  and e x t e r n a l c r i t e r i o n  that  (p.  explain  70  in  restriction, the  (13967) d e f i n e d  or narrowing, o f the c o n s t r u c t  literature*  Brodkover,  self-concept  of  academic  Erickson ability  has  a  and J o i n e r as  being  34  symbolic their  behavior  academic a b i l i t y ,  self-concept out  such t h a t  of  i f this  an  correlated  a  observe  and  specific  adequate  qeneral  achievement*  may  academic a b i l i t y  was  several  we  "when i n d i v i d u a l s p u b l i c l y  He  we  behavior"  subject  of  refer  (p*  restriction  self-concept  found  what  to  9).  To  Patterson  academic  oriented  define  scales  as find  (1967)  ability with  (SCA)  subject  that  the specific SCA S c a l e s were, w i t h one exception, s i q n i f i c a n t l y better predictors of achievement in t h e p a r a l l e l s u b j e c t t h a n was t h e q e n e r a l SCA s c a l e , (p.. 163) However, in  the  same  achievers, predictor SCA  of  was  qeneral  specific  not  true  of  achievement b e t t e r studies  that  SCA  "Amonq  scale  for  except  males. Bachman  ability  f o r males, than d i d  girls,  the  mathematics  the:  In  study  a  (1970) f o u n d  better specific  (p.  163).  related that  predicted  a  to  general  mathematics  mathematics self--concept  or  intelligence controlled mathematics  general  self-concept  were e q u a l l y  the  studies"  However, w i t h  better,  'uniform'  social  scale  than e i t h e r the  scales.  scale  female  (1967),  is a significantly  mathematics s e l f - c o n c e p t -predicted  self-concept  Patterson  grade achievement than are  achievement  self-concept  the  found  in a l l subjects  mathematics  social  d i f f e r e n c e s occurred.  study,  the  Scales  This  sex  achievement  self-concept*  scale  and  good p r e d i c t o r s .  the  For general  (See  Table  3.) One  problem  associated  w i t h Bachman's s t u d y i s  that  35 Table 3 C o r r e l a t i c n s between G e n e r a l S e l f - C o n c e p t 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 M a t h e m a t i c s A c h i e v e m e n t 1  Zero-Order Correlations Variables Correlated w i t h Math A c h i e v e m e n t  Males  Females  Males  Females  .45 .48 .32  .60 -55 .46  .20 ;29 .03  .37 .36 .20  General Self-Concept Math S e l f - C o n c e p t Social Studies Self-Concept 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 results the  of  desired  IQ Controlled  was  a "cognitive" character variance  insofar  as  to  partial  i tpartialled the  numerical  achievement  was c o n t r o l l e d t h e c o r r e l a t i o n between  females using (1964)  superiority  general  p, 1 7 7 ) .  self—concept  the  evidence  a consistent  and  cited  o f a mathematics  a general scale.  indicated Piers  1970,  It  mathematics mathematics  and  should  scale  scale  -.16  for  be n o t e d  that  Piers  and  Harris  f o u n d no s e x d i f f e r e n c e s , . From  over  when  and i n t e l l i g e n c e was .05 f o r males  (Bachman,  a more  Indeed,  out  o u t some o f  intelligence  contains  self-concept  items.  used  Harris  self-concept  scale,  achievement  was  Self—Concept  Scale,  self-concept  is of  However, t h e f i n d i n g s trend  i n that  (1964), found  .32.  there  that Koch  another  using  no  clear-cut  ability  of other  direction.. For their  own  scale studies  example.  wide  i t s c o r r e l a t i o n with grade (1972)  wide  correlated  range s c a l e ,  range six  the Tennessee  with  mathematics  36  achievement  and  quite  compared  low  Moreover* the covariate  found  use  may  a relation to  the  of  results  o f a measure o f  have  masked  been  demonstrated.  Finally,  the  construct  was  i t  mathematics s e l f - c o n c e p t  .25.  a  These  o f Bachman n o t e d  general  stronger  of  were above*  intelligence  as  r e l a t i o n s h i p than  i n terms o f the  considered  results  a has  face v a l i d i t y  of  more a p p r o p r i a t e t o u s e  the  ability  scale  than  a  general  scale.  LOCOS OF Although context  of  o f a c h i e v e m e n t , the  individuals  attributed  control  educators* to the  construct  Some of  seemingly  had  work a p p e a r e d  i n t e r e s t e d i n the  mathematics  of  locus  CONTBOL  the  been  studied i n  t o have been done  itself  r a t h e r than  l a c k of i n t e r e s t  conflicting  f i n d i n g s of  could  the by by be  a  number  r e l a t i o n s h i p between  quality  studies. Hjelle  point  averaqe  (1970) (QPA)  found  no  cf grades given a t u n i v e r s i t y  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 possible.explanations.  (I-E).  and He  Botter's gave  First  there may be an o v e r abundance o f 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 t h e w o r l d as a d e f e n s e a g a i n s t f a i l u r e b u t who a r e i n i t i a l l y h i g h l y competitive. Thus, e x t e r n a l s would s t i l l maintain comparatively strong achievement motivation in clearly structured competitive s i t u a t i o n s . . ... Second, the I-E dimension is probably not generalizable across s i t u a t i o n s , and i n t h e 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 is probably more specificity d e t e r m i n i n g QPA t h a n i n other kinds of competitive s i t u a t i o n s . (p. 326)  two  37  If  the  grades  first and  explanation  locus  of  However, Weston  with  styles  learning,  on  the  Questionnaire  were  achievement at  grade  and  achievement  f o r low  the  in  for related  g r a d e s 6,  locus  of  achievement large  problem  noted  described  at  grade  solving  the is  Rotter  younger  achievement  found  that  Responsibility six  and  between  intellectual  mathematics  total  Crandall, found  8,  that  in  scales 10,  block",  and  by  age*  DuCette  Thus  arithmetic  Iowa  the  3,  4,  and  California  enough be  of  5 but  only  Achievement that  mathematics  relationship  is  considered  an  more c o m p l e x t h a n  can  to  the  to  and  Test  I t would a p p e a r t h e n , related  to  (1965)  scales  m i g h t be  with  appeared  Crandall  of t h e  to  second  positively  be  correlations.  (1973) s t u d i e d  scale  specific  i t correlated  13,.  order  Achievement  Hjelle's  and  grades  on  more  with achievement  s i t u a t i o n may  simple f i r s t  motivation  scale  However, as  consistent the  a  Katkovsky  children, to  Intellectual  scale.  correlations  a younger  Wolk and achievement  that  contrdl variables  enough n o r  "emotional be  to  at  He  to  related  w i t h a l m o s t a l l the  Skills  occasionally  not  attitudes*  not  same s c a l e  significantly  the  for  Achievement  the  unsatisfactory*  Test  parental  at  arithmetic  responsibility  Questionnaire  than  explanation  Basic  studied  Intellectual  only  s h o u l d be  Responsibility  using  he  relationship  four* It  be  the  (1968) c o r r e l a t e d  a c a d e m i c a c h i e v e m e n t , and measures  then  control should  age-  of  i s true  an  the  r e l a t i o n s h i p of  estimate  of  success  an at  38  "pursuit  rotor  difficulty  preferred  percentage subject and  on  of a  an  by  fellow  estimate  the  exams  students  in  Aptitude  who  correlations  were  V e r b a l and  calculated  Locus of C o n t r o l .  one  only  exception  significant  the  scale  of  That  the  DuCette,  moderator  1973,  p.  variable*  a c h i e v e m e n t and subjects  who The  as  a  This  variable  for  a third  explanation  between of  this Lintner  control, On  males  showed a s m a l l , task,  locus  say,  locus  two  4 shows  the  on  the The  the  different  control  correlations  the  of  of  and  the  I—E  (Wolk was  and  may  be  between  failure  and  control  Gates-McGintie  and  and  response  acting  inconsistent  (1974)  who  Another studied  student response  praise,  Reading T e s t ,  to  interaction  whereas,  to  of  variables.  achievement.  DuCette  a  dimension.  control  low  on  with  with  groups"  task they found a d i s o r d i n a l of  the  midterm  that  is  of  by  demonstrated  moderated locus  the  levels  other noncognitive  non-significant the  the  "significantly  the  of  scales.  subjects  that  variable  academic  a coding on  Table  d i f f e r e n t l e v e l s on  moderator be  of  task  m e a s u r e s d i f f e r e d among g r o u p s  that  of  second  studied  were a t  example i s t h a t  for  Tbat i s t o  suggested  relations  praise*  the  for  on  performance  each  of  surpassed  Quantitative  The  suggested  data  may  locus  66)  estimate  exception  SAT.  c o r r e l a t i o n s between v a r i a b l e s &  and  internal  correlations,.  quantitative  an  level  performance  for  Internal-External  the  would be  psychology,  Test  of  subject,  psychology examination,  final  Scholastic  tasks",  praise.  females On  they found  a sex  Table  4  39  C o r r e l a t i o n s between an A c h i e v e m e n t M o t i v a t i o n Measure and V a r i o u s B e h a v i o r s f o r I n t e r n a l and E x t e r n a l L o c u s o f C o n t r o l S u b j e c t s Internals Ps e s t T a s k Ps e s t T e s t Preference T e s t P e r f Midterm Test Perf F i n a l SAT Verbal SAT Quantitative  Externals  -.28** _,29**  2  3  Z (int-ext)  + .01 + .04 + . HO -* V4 -*04 -.09 -. 27*  •.44*** + * 39*** +.37*** +.41*** +.33**  1  1.24 1.65** 1.81** 2;70*** 2*09** 2.18** 3*02***  *p < .10 **p < .05 ***p < .01 Z statistic of the difference between the s c o r e s of the I n t e r n a l s and t h e Externals* E s t i m a t e d p r o b a b i l i t y ox s u c c e s s a t t h e p u r s u i t r o t o r t a s k . [ ^ E s t i m a t e d p r o p o r t i o n of fellow students surpassed by the subject* 4  2  differences but  no  the  main f a c t o r s o f  interaqtions  appeared Stevens  within  (1976) u s i n g  Hotter s 1  locus  variable  of  interactions  i n the only  control  (1964) who  variables  and  factor*  interactions  the  I-E  found  i t was  same s t u d y .  scale  sex  that  summary,  was  there  found  praise,  Daniels a  and  disordinal  T h e r e f o r e , because of  control  deemed i m p o r t a n t  and  to  of the  include  study.  information to  Again  between l o c u s  present  SUMMARY OF In  prior failure,  w i t h i n s t r u c t i o n a l methods.  potential  The  sex  within  other a f f e c t i v e v a r i a b l e s this  the  inconsistently  interaction the  on  found  that  Crandall, were no  specifically  Crandall  and  significant  related  Katkovsky  differences.  INDIVIDUAL A F F E C T I V E VARIABLES the  showed t h a t  mathematics achievement  the was  literature relation  dealing of  the  s i g n i f i c a n t but  with a f f e c t i v e variables  low.  However,  with the  40  literature  outside  particularly  that  an  alternative  variables acting one of  as  area  approach  to  (1976).  An  example  She f o u n d  relation  the  This  more  that  line  this  with  function  Chapter  could  Motivation  1  therefore  not  Model  Achievement  i t  affective  was  relationships  provide  such  following  might  that  w i t h no  of  a  relate this  looking f o r theoretical  However, t h e A c h i e v e m e n t a  framework  and  will  detail.  MODEL OF ACHIEVEMENT  ,  —-r^-  discussion  MOTIVATION  1  I t should  be u n d e r s t o o d i n  r—  t h a t . i n the l i t e r a t u r e o f Achievement  t h e words " m o t i v e " and " m o t i v a t i o n "  synonymously;  Feather  disposition  personality  depended  that  Motivation =  Motivation  study  with l e v e l of  variables  suggested  of  c h i l d r e n the  t h a n h a d been t e s t e d  i n some  the  levels  Marjoribanks*  12 y e a r o l d E n g l i s h  A s s u m p t i o n s of: t h e .model. the  was  be . j u s t i f i e d .  did  be p r e s e n t e d  THE  of  some o f t h e v a r i a b l e s  and achievement v a r i e d  i n t e r a c t i o n s and h o n - r l i n e a r framework  conceptualization  of argument l e d t o t h e h y p o t h e s i s  complex  In  suggested  That i s , the r e l a t i o n s h i p  mathematics achievement t o the study;  education,  may b e d i f f e r e n t a t s e v e r a l of  between a t t i t u d e  ability.  mathematics  an i n t e r - r e l a t e d s e t w i t h  with a second  a third*  of  r e l a t e d t o achievement motivation,  as moderators o f o t h e r s .  variable  much  the  of  upon  level  (1966 b) d e s c r i b e d  of  whereas expectation  not  used  motive a s a l a t e n t  strength and  are  of  motivation  incentive  value.  41  Atkinson  and E e i t m a n  (1956) were q u i t e  specific:  we c o n c e i v e a m o t i v e as a latent d i s p o s i t i o n to strive for a p a r t i c u l a r g o a l - s t a t e o r aim, e.g.; achievement, a f f i l l i a t i o n , power* . . . The t e r m m o t i v a t i o n c a n t h e n be u s e d t o d e s i g n a t e t h e a r o u s e d state o f t h e p e r s o n t h a t e x i s t s when a m o t i v e h a s been engaged b y t h e a p p r o p r i a t e e x p e c t a n c y , i . e . ; an expectancy that performance of some act i s instrumental t c attainment of the goal of that motive. (p 361) Achievement exemplified Feather  are  the  (1966),  Eeitman It  by  Motivation works  Atkinson  (1956),  i s a specific  Atkinson Eaynor  of  behavior  evaluation p.  432).  will  of  literature  (1958), (1974),  Atkinson Atkinson  and and  (1970).  theories  which  t h e h y p o t h e s i s t h a t t h e b e h a v i o r o f an  lead  those  Differences  large  instrumentality  i n d i v i d u a l i s i n part determined the  a  (1972), and Weiner and K u k l a  instance by  of and  Weiner  "distingushed  has  to  outcomes  b y a) h i s e x p e c t a t i o n s  various 11  outcomes  (Mitchell  between t h e s e t h e o r i e s  &  and  that  b)  Biglan,  his 1971,  concern  the way i n w h i c h 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 in the d i f f e r e n t analyses. The d i s c r e p a n c y concerns whether o r n o t c o n c e p t s w h i c h a r e a k i n t o u t i l i t y i n various models a r e taken t o be i n d e p e n d e n t of subjective probability. ( F e a t h e r , 1966, p. 32) Atkinson's independent  status  utility  of  strength  of motive  p.  The  35)  an  model and  gives he  incentive and  theory  suggests  evaluation  of that  value  Achievement  both the i n d i v i d u a l ' s expectation his  that  "the  may be c o n s i d e r e d  incentive  of  m o t i v e s and i n c e n t i v e  valence  or  as a function of  ..(Feather,  Motivation  o f s u c c e s s and  s u c c e s s and f a i l u r e  values  1966  a,  proposes  that  failure  and  be a s s e s s e d .  42  Atkinson's really  (1974)  cne o f r e s u l t a n t  model o f A c h i e v e m e n t  achievement  oriented  Motivation i s tendency.  He  assumes, that a l l individuals have acquired a motive t o a c h i e v e (Ms) and a m o t i v e t o avoid failure (Maf) . That i s to s a y a l l p e r s o n s have some c a p a c i t y f o r interest in achievement and some c a p a c i t y for anxiety about failure* . . . One o f t h e s e m o t i v e s produces a tendency to undertake a c t i v i t y . . . . It i s assumed t h a t t h e two o p p o s e d t e n d e n c i e s combine additively and yield a resultant achievement o r i e n t e d t e n d e n c y (p* 18) Algebraically, resultant the  tendency,  failure  component task  in  by  the  by  The  task.  accrue  task  i t  t o expend  component i s m o d i f i e d Again,  T-f  success,  Ps,  probability  success. avoid of  and  Maf>  failure,  failure.  Pf  = Maf  Is of and  probability  The  six  and  the  T-f  success  of s u c c e s s a t the upon  successful  to succeed i s  also  be  somewhat  e n e r g y on an  in a parallel  easy  way  but  and,  x Pf x I f  are, respectively, success If  for  algebraically;  Ts = Ms x Ps x I s  Ms,  may  stands  tendency  Although motivation  the opposite d i r e c t i o n .  where  Tr  However,  may  the reduced i n c e n t i v e  failure  where  the e x p e c t a t i o n  by t h e e a s e o f t h e  decreased task.  modified  of  T-f  tendency.  t h e i n c e n t i v e s which  completion enhanced  +  Ts f o r s u c c e s s o r i e n t e d  avoidance  is  and by  T r = Ts  and  motivation  incentive  are, respectively,  of f a i l u r e ,  independent  value  are  of  motivation  and t h e i n c e n t i v e  variables  toward  to  value  reduced  in  43  number  by  postulating  that  success  and  the p r o b a b i l i t y  of  o t h e r p o s t u l a t e s reducing the sum  of  success is  the  i s one  the  these  incentive  assumptions  The tested  value  and  n e g a t i v e o f the  Is =  associated  He  is  one  number o f v a r i a b l e s of s u c c e s s  and  incentive  probability  of  (1.0).  Two  are t h a t  the  the.probability value  of  of success.  with  and.  that estimated  f u n c t i o n (1 had  (1 - Ps)  If =  e m p i r i c a l support*  hypothesis  success.  of t h e . p r o b a b i l i t y  failure  that the  (1 - Ps) , P f =  linear  sum  of  failure  Symbolically  are:  model and  the  negative of  (1.0)  the  Ps)  of  —Ps  L i t win value of  success  the e s t i m a t e d  s u b j e c t s d e s i g n a t e a monetary  v a r i o u s r i n g s on  a ring  (1 966) was  a  probability value  t o s s game.  to  He  be  found  that t h e e s t i m a t e s were l i n e a r , and t h e a v e r a g e s l o p e of all the v a l u e e s t i m a t e s was a p p r o x i m a t e l y e q u a l t o the 1 - Ps line* However, the slope of the a c h i e v e m e n t - o r i e n t e d Ss v a l u e e s t i m a t e s was somewhat l a r q e r t h a n t h e 1 - Ps l i n e . (p. 114) Combining  t h e above e x p r e s s i o n s :  T r = Ms  x Ps =  This of  Ms  this  -  Maf  x  (Ms - Maf)  + Maf x Ps  x  x  (1 - Ps)  (1 -  x  with  Ps .  T h e r e was  2  some  (-Ps)  Ps)  l a s t expression l e d to a q u a d r a t i c empirical  interaction support  for  interaction. Probability  their  (1 - Ps)  perception  (Atkinson  &  of  of  success i s assessed  their  Feather,  potential 1966;  by  level  Moulton,  askinq s u b j e c t s of  1974).  achievement This  was  44  considered  similar  to  ability  to  positive  self-concept  condition  learn.  the  measurement  Brookover was  a  of  self-r-concept  and E r i c k s o n (1969) h e l d necessary  but  not  of that  sufficient  f o r achievement.  Although a s i g n i f i c a n t proportion 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 level ( a p p r o x i m a t e l y 50 p e r c e n t ) p r a c t i c a l l y none o f t h e s t u d e n t s w i t h low s e l f - c o n c e p t s o f ability achieved at a high l e v e l . ( p . 106) When  graphed  with achievement a s t h e a b c i s s a and s e l f - c o n c e p t  as t h e o r d i n a t e capital  this  r  three sets.  paired  associate  and  learning  on  difficulty.  The  intermediate,  or hard.  group.  respective  Youseff  much  mean  (1968) g r o u p e d were  task.  difficulty  the c o l o r s .  to  and  on  t h r e e g r o u p s were r a n d o m l y Different  The'subjects  The r e s u l t s  an  inverted  relation* p a i r s o f words be  used  in a  The t h r e e g r o u p s o f words  colors  The words were p r e s e n t e d colors.  like  a guadratic  The s e t s o f words  were e q u a t e d  each  appear  " L " ( ) which would s u g g e s t Karabenick  into  would  variance , of  designated  were a s s o c i a t e d  easy, with  t o the s u b j e c t s i n t h e i r  were t o l d  of t h e s t u d y  the  the significance of  showed  that:  persons f o r whom Ms > Mf £ M f i s e q u i v a l e n t t o M a f J p e r f o r m e d b e t t e r t h a n t h o s e f o r whom Mf > Ms a t tasks designated as being of intermediate d i f f i c u l t y , but t h e performance o f these groups d i d not differ when t a s k s were e a s y o r d i f f i c u l t . I n a d d i t i o n , whereas p e r s o n s f o r whom Ms > Mf t e n d e d t o perform b e t t e r at intermediate difficulty tasks, t h a n a t e a s y o r d i f f i c u l t t a s k s , p e r s o n s f o r whon Mf > Ms p e r f o r m e d better on easy o r d i f f i c u l t t a s k s than a t those designated as being of intermediate difficulty. ( p . 418) This  was  supported  by F e a t h e r  (1961) who f o u n d  that  45  s u b j e c t s w i t h Ms > Mf t e n d e d  to  persevere  longer  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 were  perceived  as  being  easy  or hard.  at  than those which  On  the o t h e r hand,  s u b j e c t s w i t h Mf > Ms t e n d e d t o p e r s e v e r e a t e a s y o r tasks.  tasks  difficult  I t m i g h t be e x p e c t e d t h a t i f s u b j e c t s t e n d e d t o b e h a v e  as Feather found then achievement  would  be  higher  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 that  summary, t h e a c h i e v e m e n t  the  Success,  levels and  attention the  in  Motivation  Value  of  to  Success  perseverance.  school situation  variations may  and  of  m o t i v a t i o n model s u g g e s t e d Succeed, P r o b a b i l i t y  influenced  The  the  degree  of  present author held that i 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  academic  of  achievement.  These r e l a t i o n s ,  be r e p r e s e n t e d a s f o l l o w s , w i l l s e r v e as  the  to  which  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 S u c c e e d 2.  P r o b a b i l i t y o f Success  3.  Value of Success  Attention > -—> Perseverance  Achievement  The a r r o w s a b o v e 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 . not the  intended  that they imply a c a u s a l r e l a t i o n s h i p , nor  d i r e c t i o n i s only as T h e r e were f i v e  the  "emotional  value,  block"  self-concept  Achievement  It is that  indicated* variables identified in  mathematics;  and a c h i e v e m e n t  M o t i v a t i o n model  i s  i n the s e c t i o n  anxiety,  responsibility*  tripartite;  The  of  enjoyment, Yet the following  46  discussion the t h r e e  will levels  i n d i c a t e d i n the flexible  in  relate of  the  Achievement  above  this  each of the  diagram.  five  v a r i a b l e s t o one  M o t i v a t i o n model w h i c h That  the  respect i s supported  by  model Moulton  is  of are  quite  (1974)  who  stated i t i s r e c o g n i z e d t h a t the t o t a l s t r e n g t h of tendency to perform a task requiring skill includes tendencies associated with other incentives contingent upon successful performance. An important fact about many of these "extrinsic" i n c e n t i v e s s u c h as s o c i a l a p p r o v a l , p r e s t i g e , money, etc., i s that the more difficult the task is p e r c e i v e d t o be by o t h e r s , t h e g r e a t e r the m a g n i t u d e and/or quality 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"  achievement following  motivation  Level mathematics dimension  test  Study B e l a t e d  one,: , m o t i v a t i o n was,  in  (Ms - M a f ) . by  is  c a t e g o r i e s , as  using the  somewhat  this  unreliable  produce  marked  changes  typically  the  worded, i n  the  used t o  succeedi.  to  Test  Anxiety  related  to the  succeed  has  sufficiently  groups Anxiety  using  level as  of a  about  Motivation  usually  Test.  t h a t "the  the  measure t h e  some s t u d i e s r a t h e r t h a n  in  be  in  i m a g e r y f o r the The  Model  Thematic Aperception  i s done may  p. 3 5 ) .  to  Motivation  testing  affiliation  to-the  study,  which t h e  1958,  presently  each o f  way.  V a r i a b l e s of t h i s  assessed  v a r i a b l e s were a s s o c i a t e d w i t h  However,  conditions  the  under  motivating  to  achievement  or  whole"  (Atkinson,  Questionnaire  motivation  been  has  to avoid f a i l u r e .  t h e d i f f e r e n c e between  been In  measures  47  of  Ms and  Maf  the present suggest  a measure of.Maf has  been used  by  itself.  study the achievement motivation model was  possible  interactions  v a l i d a t e the model i t s e l f . Mathematics  Anxiety  Questionnaire  and  between  Therefore  therefore  used to  v a r i a b l e s and not  it  c l o s e l y corresponded  was  In  related  was  proposed  t o the Test to  the  to  that  Anxiety  motivation  dimension of the model. Enjoyment  of  mathematics was  opposite of anxiety.' -.76  Sandman  considered  (1973) found  a  somewhat the  correlation  of  between anxiety and enjoyment of mathematics, tending  confirm  this  supposition;  Therefore,  enjoyment  was  to  also  a s s o c i a t e d with M o t i v a t i o n to Succeed,.  closely Weiner  Achievement  Eesponsibility,  or  related  the  Achievement  (1972)  to  held  theory that  of  persons  l o c u s of c o n t r o l , i s  with  low  m o t i v a t i o n f e l t t h a t e f f o r t d i d not i n f l u e n c e t h e an  activity  high  and  achievement  represented  t h a t the opposite motivation.  was  . As  Motivation. achievement outcome  true f o r persons this  dimension  of with was  by achievement r e s p o n s i b i l i t y i t was  proposed t h a t  achievement r e s p o n s i b i l i t y would a l s o correspond  to m o t i v a t i o n  to of  succeed.  Woulk and DuCette  ( 1973)  commented on the  degree  correspondence o f the two t h e o r i e s . Both t h e o r i e s , f o r example, make p r e d i c t i o n s about the type of risk that c e r t a i n subjects prefer, . . . . p e r s i s t e n c e , s h i f t s i n l e v e l of aspiration, and success e s t i m a t i o n . . . . Even more than t h i s , both t h e o r i e s make very s i m i l a r p r e d i c t i o n s about the performance of c e r t a i n subjects on these dependent v a r i a b l e s ; . . Indeed, t h e r e i s so much  48  overlap in these theories in both theoretical structure and predictions that a q u e s t i o n can be r a i s e d as t o 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) Level mathematics  of  probability own  (Moulton, the  value  from  success  (Ps)  probability  of  1974,  o r an  p*  79)  estimate  of  to  reasonably  strength  of  was in of  close  asked  i s hard;"  to  do  mathematics,  with  estimate  task.  to  assessing  t o ask  As  this  i n assessing  self-concept  was  the  was  Ss  often  to  students  c l o s e to  associated  state tasks"  a  or  population  the  appeared  evaluate  task  is  of h i s  with  the  easy"  what t h e  self-concept  the  task  to  "This  to  i n f e r r e d from  at  o f the  to  These p r o c e d u r e s  asking  of  related  respect  was  items such as,  student ability  probability  success. —L, .e v— e. l . ,- t - h.-.r .. e•e— : — • 'v a l u e  was  for  "simply  proportion  the  agreement w i t h  or "This task  was  be  at a certain level  the  would s u r p a s s a t  to  technique  success  to a c h i e v i n g  Self-concept  considered  The  subject be  was  Success*  of  give  an  p r o b a b i l i t y , of-:: s u c c e s s ;  achievement  Probability  their  two:  considered  Motivation  c l o s e to  model  of,^-—s u c c e s s—.  Value  and  of  Value  Success  therefore  was  in  of the  associated  Mathematics Achievement with  that  dimension; The  hypothesized  levels  of  and  five  the  summarized  variables variables  as  Motivation  relationships  of  the  of  theory  of  interest  between Achievement  in  this  Succeed =  Anxiety  in  Mathematics  three  Motivation  study  follows: to  the  may  be  49  + Achievement R e s p o n s i b i l i t y + Enjoyment o f Mathematics Probalility  o f Success = Self-Concept  of A b i l i t y i n  Mathematics Value o f Success = Value o f Mathematics It  was  distinction Motivation between Kempler he  among  expected  these  model  solvers  that  three  there  levels  some o f t h e c o n s t r u c t s o f (1962) a d m i n i s t e r e d  students.  He i d e n t i f i e d  and 30 as n o n r i g i d .  this  problem  less  30 s t u d e n t s  and t h e 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  self-confidence to r i g i d i t y "  (p. 5 1 ) .  Intellectual 12%  should  of the variance  This  corresponded  (1973) c l a s s e d Scale,  the  the Test  Moreover,  of to  this  a  were  was .32  (p <  .01)..  that  • low  that  the  Scale  of  for  and  accounted f o r  Self-Esteem .35.  Achievement  results  was  jar  (1977) f o u n d  Coopersmith  Scale  water  lead  to Achieve Scale  conflicting  students  will  correlation  Anxiety  problem  which i n t u r n  Responsibility the  107  questionnaire  Luchin's  study  DeAnda  Intellectual  Gumpgookies' M o t i v a t i o n Because o f these  for  on t h e  arouse anxiety  Achievement  which  to  as r i g i d  riqid  test  rationale  example  t h a n n o n r i q i d and t h a t t h e r a n k  between r e s u l t s  "the  scale  t h a t on a  correlation  stated  For  water j a r t e s t  order  He  Achievement  solving  He f o u n d  confident  the  study.  s e l f - c o n f i d e n c e i n mathematical a b i l i t y  significantly  be a c l e a r  identified relations  the Luchin's  on  would  of  because of the a l r e a d y  termed a m e c h a n i z a t i o n  college  of  not  Scale.  However, S i u  Responsibility  Children  as m o t i v a t i o n  and  the  scales.  interpretations  the  50  above r e l a t i o n s h i p s a r e  deemed a r e a s o n a b l e  hypothesis.  SUMMABY In "emotional presented closely the  this  chapter  block" that  t o the  constructs,  this respect. included. reasonably  of the  was  used  also  hypotheses. related  In  consideration*  a l s o argued  t h a t the  with  Achievement justify  general the which  to the  and  five  evidence  c o n s t r u c t s should  be  considered,.  of  One  somewhat ambiguous e v i d e n c e  specific  to  effects  those  both  associated  constructs  had  related  examined  subject area being  Therefore  be  was  measuring  anxiety,  I t was  literature  variables  scales  related  the  one  and  testing evidence would  g e n e r a l s c a l e s were  five of the  Motivation  variables three  model,.  pointed to  to  model  interactive  potential be  could  independent This  n o n - l i n e a r and  have  in  taken  sex into  51  3  Chapter  INSTfiUMENTATION, DESIGN AND  PEOCEDOEE  INTBODUCTION in indicating  Chapter  1 i t was shown t h a t t h e r e  - that  a  significant  proportion  s t u d e n t s - a p p e a r s t o have an " e m o t i o n a l achievement  i n mathematics.  self—concept of  the "block".  suggest  possible  related of  among  motivation.  c o n t r o l o r achievement  literature mathematics their  value,  and  as t h e c o m p o n e n t s  M o t i v a t i o n model was u s e d  interactions  t o achievement  of  enjoyment,  were i d e n t i f i e d  The A c h i e v e m e n t  a  block" i n h i b i t i n g  Anxiety,  o f mathematics  is  the  components  when  A further variable,  responsibility,  was s u g g e s t e d  to  locus by t h e  model* In attitude  Chapter  2  i t was a r g u e d  s c a l e was r e l a t e d  correlated  i t would  t o a s u b j e c t area  be w i t h  achievement  further  suggested  that although  anxiety  in  mathematics  is  mathematics  achievement  than  general  measure s h o u l d  effects  occurs  design  there  more  i n that area.  correlated  Evidence  was that with  measure, t h a t of  sex  and t h e r e f o r e t h e  accordingly.  It  was some e v i d e n c e  highly  an  t h e more s t r o n g l y  a more g e n e r a l  be i n c l u d e d *  i n the l i t e r a t u r e  was c o n s t r u c t e d  t h a t t h e more c l o s e l y  a  related  statistical  52  In  this  procedure w i l l  chapter,  he d e s c r i b e d *  a n a l y s i s concerning the  testing  of  p r o c e d u r e used also  be  the  instrumentation,  The  results  of  design  a  and  preliminary  t h e d e c i s i o n t o i n c l u d e o r e x c l u d e TASC i n  t h e major h y p o t h e s e s w i l l  for eliminating  be p r e s e n t e d .  The  differences  will  inter-class  described. .INSTBUMENTATIQN As  study  four  the  seven  affective  were t a k e n f r o m t h e Sandman  description associated the  of  of with  sections  Following  his  battery,  be  presented.  scales  w i l l be  be  achievement  scales  a  general  The  details  described  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  that the three  The.Sandman  will  each o f the f o u r  response s c a l e s w i l l  and  in  constructs. the  teacher  discussed.  Study  Sandman reviewed  study  (1973)  s c a l e s used i n t h i s  11  s review.  the c o n s t r u c t i o n  In  his  study  Sandman  and v a l i d a t i o n p r o c e d u r e s  (1973)  used  for  some o f t h e mere p r o m i n e n t m a t h e m a t i c s a t t i t u d e s c a l e s s u c h as Dutton's  (1954)  Thurstone  Scale,  A i k e n and Dreger«s  Mathematics A t t i t u d e Scale,  (which  has  similar  t c those  (1958)  scale,  used on a n x i e t y and  Pupil Opinions Scale. study  in  Hoyt's He  number  s c a l e s ) , Hoyt  (1960) f i f t e e n also  a  reviewed  of  (1961) items  and M c E a c h e r n ' s  sub-scale  Minnesota  Ericksen's  (1962)  which t h e H o y t - M c E a c h e r n s c a l e was d i v i d e d i n t o s i x  53  sub-scales,  and  Antonnen's  longitudinal  study  study  factor  l o a d i n g s of  were  used  general. formed  to  on  was  made,  administered  a semantic  single  on  the  the  and  common,  achievement  The  and  the  slightly  Hussen  of  had  cited  than  several  i n Mathematics.  and  that  i n the  (1971)  Likert-type Opinions  Antonnen, Skills.  .07  .66  and  and  with  and  .25,  measure  an The  achievement  and  something  mathematics  scales  International  sub-scales  views about the  validity.  multi-dimensional  The  were  intelligence.  a process, attitude  in society,  IQ  between  tended to  with  other  a  Basic  relationship  (1967) u s e d one  However, Sandman n o t e d  between  with  Pupil  with  were factor  and  d e v e l o p e d by  were  In  item  Antonnen  Minnesota  scales  scales a  at  Scale,  attitude  stronger  toward mathematics as  attempt  Iowa T e s t o f  attitude  Antonnen  sub-scales  only convergent  scale  the  attitude.  correlations  Hoyt's  attitude  they  for  the  Thurstone  in  p r i n c i p a l component  c i t e d M a s t a n t i i o n o and  and  the  achievement  ranged, r e s p e c t i v e l y ,  Achievement  mathematics  only  scales,  correlations  Sandman attitude*  that  differential  among the  .14.  Hoyt s c a l e In  score  v a l i d i t y , no  scale,  test,  intelligence  of  a  Dutton's  of D u t t o n ' s  correlations  in  and  example, he  intelligence  .03  scales  These d a t a e s t a b l i s h e d  For  .79;  the  of f a c e  attitude  presented*  Scale,  the  mathematics a t t i t u d e .  generate  a basis  mathematics  version  of  Sandman's c r i t i c i s m s were t h a t  analysis  who  of  (1967) use  were  toward the mathematics  reliabilities  were so  of  Study attitude  place  of  teaching. low  that  54  Johnson  (1970) was  permission  to  use  A second that  used  in  advised  the  National  sub-scales  is vs.  Wilson,  Dull, Ideal  scale  Math  They  Easy  the  scales  stated  i n t e r m s cf t h e  relationships  between  variables  Sandman's  was  review  of  constructs  It  Scale  the  vs*  Non-Math,  was  Math Anxiety,  to  but  the  seven  Actual  attempt  validate  some e v i d e n c e  preliminary quite  forms  clear  from  scale, construction  proceeded r a t h e r  a somewhat u n s o p h i s t i c a t e d Sandman  Each  was  Mathematics  Facilitating  no  attitude  had  of  Hard,  r e s u l t s on  noted.  that  mathematics e d u c a t i o n  The  asked  Sandman  Study  were Math  Math S e l f — C o n c e p t , T h e r e was  other  when he  n o t e d by  vs*  D e b i l i t a t i n g Anxiety.  and  scales  1969).  and  from  the  Longitudinal  a Likert scale.  Self—Concept,  use  multi—dimensional  (Eomberg &  Fun  to  them.  Achievement  Math  not  h a p h a z a r d l y and  in at  level. Construction.  Attitude  measures  h a v e been l e s s t h a n a d e q u a t e b e c a u s e o f c o n f o u n d e d  constructs  as  1,  well  (1973)  as  confused  was  scales.  His  quite  referents. critical  a l t e r n a t i v e was  already  cited  attitude  assigning  them t o  one  Mathematics Mathematics,  of  Teacher Value of  As of  noted the  i n Chapter  construction  t o t a k e i t e m s from instruments,  eight by  Perception  Student*  Perception  Mathematics  Materials,  of  of  of  the  many  and  of  the  Toward  Self-Concept  Mathematics C l a s s ,  Enjoyment  attitude  Anxiety  Mathematics i n S o c i e t y ,  Mathematics,  seven  rewriting  constructs:  the  of  Sandman  Perception  Mathematics,  in of and  55  Motivation  i n Mathematics.  Although the  National  t h e s c a l e s were s i m i l a r  Longitudinal  Sandman n o t e d t h a t appear  to  be  selected items)  measuring  was  scales, left  because  and  on  eight  correlation  of  which  constructs  questionable  matrix  and t h a t  for  younger  construct  p o s i t i v e and  were  negative  to persons s k i l l e d i n  education.  The  Materials other  of the items.  eachw.  the  be  items  The  California  rotation.  identified  instrument  not  load  were  administered  was s u b j e c t e d  by v a r i m a x  could  that  in  items of the Perception  scales  identified t o 2547  This were  and  Indiana.  to p r i n c i p a l  The  component  Seven f a c t o r s emerged, with  the  was d e s i g n e d  six  attitude  t o measure.  of t h e Mathematics C l a s s  between t h e s i x r e m a i n i n g  and  students  scales  are  As  scale did  on t h e s e v e n t h f a c t o r , t h e s c a l e was e l i m i n a t e d .  correlations 5.  each  not  t h e b a s i s o f c o r r e l a t i o n s between t h e i t e m s  the  Table  (equal  items  The s c a l e s were t h e n  analysis followed six  of  did  a s were two i t e m s from e a c h o f t h e  g r a d e s e i g h t and e l e v e n  item  for  o f a l a c k of c o n s i s t e n c y  the scales four  reworded. in  items  and m a t h e m a t i c s  seven s c a l e s  scales  inappropriate  t h e s c a l e s were d i s t r i b u t e d  eliminated,  piloted, and  Ten  for a preliminary scale and  Achievement,  the c o n s t r u c t s of i n t e r e s t  u s e d seemed  students.  test construction Scale  Study o f Mathematics  many o f t h e i t e m s i n t h o s e  some o f t h e v o c a b u l a r y secondary  t o t h e s c a l e s used i n  shown  The in  56 Table 5 C o r r e l a t i o n s Between t h e S u b - s c a l e s of t h e Sandman I n v e n t o r y 1 1 2 3 4 5 6  Basis  Teacher Anxiety Value Self-Concept Enjoyment Motivation  of,Scale It  of  1.00 -.40 -.72 -.76 -.64  1.00 ;33 . 45 .45  is  The  four  on t h e b a s i s  o f the s c a l e s  Teacher  teacher  by  related  o f t h e more r i g o r o u s  an  used  because  not  block"  used  on t h e m o t i v a t i o n  and s e l f - c o n c e p t  be  given  f o r - each  general  considerations  Sandman  scales  (1)  The  constructs Longitudinal constructs  that  for this  development  of  the  of  Thus, s c a l e s  from t h e  the  the  The  of eight measuring value  of  were a l l  reasons  selection  of  that some the  were:  the  scales  was b a s e d  similar  to  that  Study  of  Mathematics  had a p p e a r e d  three  scales s p e c i f i c a l l y ,  governed  study  of  mathematics.  mathematics,  Apart  study.  the l i t e r a t u r e t o  of mathematics a b i l i t y  t a k e n f r o m t h e Sandman b a t t e r y . will  structure  perception  in  factor; of  construction  factor  because only  i n mathematics, enjoyment  mathematics,  1.00 .76  f o r use i n t h i s  d i d n o t a p p e a r from  "emotional was  identifiable  were s e l e c t e d  not  the student  scale  items loaded anxiety  s c a l e was  to  Motivation  1. 00 . 66 .59  Selection  t h e Sandman s c a l e s and t h e i r  that  be  1.00 -.46 .36 .34 .41 .36  5  3  2  in  used  other  in  upon a s e t o f the  National  Achievement. various,  often  These used  57  mathematics  attitude •scales.  these c o n s t r u c t s  I t was a p p a r e n t  were o f r e c o g n i z e d from  number  attitude scales, construct  popular  was f u r t h e r Sandman  scales:  face  v a l i d a t i o n by e x p e r t s ,  and  then  of items contained  construct  empirical  identification, pretest  validation  of  a n a l y s i s o f t h e Sandman  items could  factor  scales could  that  the s c a l e s  be shown t o l o a d  be an a i d t o  present  study*  s h a r e d common v a r i a n c e  on f a c t o r s  v a r i a b l e s , an e x p l a n a t i o n  and  associated  of various  with  f i n d i n g would  enhanced.  The  length  of  consideration. mathematics  for  Children,  the  Sandman  Together  scales  likely fatigue.  have  and t h r e e  greater  of  the  Anxiety  Although  reliability,  time o f a number caused  important  a c h i e v e m e n t t e s t s some two  of  reduced  scales  longer the  longer  reliability  I n a d d i t i o n i t was f e l t  homogeity  an  f o r s o c i e t y s c a l e , the Test  have  administration  was  with the a d d i t i o n o f the value  t e s t i n g t i m e was r e p r e s e n t e d .  often  of  by  of the items*  the extent  of  selection,  scales  To  of  of  analysis, re-writing,  i n t e r p r e t a t i o n o f the r e s u l t s o f the  be  in a  similarity  item  the  other  the  a c r e d i b l e procedure i n c o n s t r u c t i o n  his  Factor  As  ensured.  followed  analysis  that  importance.  i t e m s were s e l e c t e d of  the pool  then  that  (.77  the to  Scale hours scales  increased  tests  would  because  of  coefficients  .86) were  quite  58  acceptable. For the  further justification  scales refer  t o the  of  the  corresponding  inclusion  of each  s e c t i o n i n the  of  following  more d e t a i l e d a n a l y s i s . ANXIETY I N From concluded relate  the  that  more  evidence  specific  MATHEMATICS presented  scales  were  more  not  clear  strongly  mathematics than  a more g e n e r a l  anxiety  were i n c l u d e d  scales  anxiety in this  Toward M a t h e m a t i c s S c a l e  Anxiety  Scale  for  Sandman  the  factor The  enjoyment  the  follows; and  of  the  tended  1  anxiety  achievement  in  Therefore  two  scale. study;  to  anxiety  mathematics to  was  Sandman's  (1973)  Sarason's  (1958)  Test  items of t h i s  scale  along  items.  The  anxiety  s c a l e on  .20,-.31, .54, eighth  factor.  correlations  and  f a c t o r analysed  attitudinal  second  scales  i t  Children.  i t e m s from as  that related  Anxiety  of  2  s t r o n g l y to achievement than d i d general  However, i t was  other  Chapter  achievement a n x i e t y  scales.  with  in  This the  scale i s reproduced  items  -.34, loaded  accounts  anxiety below.  at ease i n a  and The  1.  I feel  2.  When I h e a r the word f e e l i n g of d i s l i k e .  analyis  to  the  produced identified  .58,  .62,  -.59 some  .61  extent  n u m b e r i n g i s not  anxiety  .58,  and  enjoyment s c a l e s  mathematics  loadings  -.24. on  for  the  (-.76).  The  the  original;.  class.  mathematics,  I  the  have  a  59  3.  I feel tense mathematics.  4.  It doesn't problems*  5.  Working  6.  It makes me mathematics.  7.  I t s c a r e s me  8.  I have a  there  scale,  .82  scale  correlated  identified  the  o v e r l a p , thus The Davidson, general age  that  Test  the  the  of the  doing  mathematics. mathematics* of  this  scale.  w e l l as n e g a t i v e i t e m s by  Alpert  s h o r t y e t had compared  with  1960).  another,  the  in  and  the  existing  the  Haber  a moderately  high  reliability  Third,  items accounting  S Waite,  for college  test  t h i n k about  although factor  f o r the  Anxiety Scale f o r Children  i n A p p e n d i x D.)  results  mathematics  of the  analysis  degree  of  interpretation.  achievement  developed  the  aiding  was  about  me.  important  & Haber,  individual  of  work  toward  as  (-86)  with  Lighthall  analog  items  shown t o be  (Alpert  t o me  l e d to the s e l e c t i o n  positive  consistency  p f t h e TAQ  to  t o have t o t a k e  good f e e l i n g  were  talks  nervous t o even  Second, the s c a l e  internal  me  w i t h numbers u p s e t s  which was  (1960)*  someone  disturb  Several reasons First,  when  1958)  anxiety Test age  was  students.  as can  selected  s c a l e because  Anxiety  be  A l p e r t and  seen Haber  (TASC) as  the  i t was  Questionaire  the  Table  (1960)  more school  which  (See t h e f i r s t from  (Sarason,  set of  2 i n Chapter  study  was 30 2  indicated  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  w i t h a c h i e v e m e n t measures t h a n  were t h e  more g e n e r a l  measures  60  of  anxiety.  with  The  TASC was a r e l a t i v e l y  a f o u r month t e s t - r e s t e s t  Davidson,  Lighthall,  Waite &  reliability  fiubush,  s h o r t * 30 i t e m , of  .666  test  (Sarason,  1960)  ENJOYMENT S c a l e s measuring enjoyment mathematics scale  were  i t  was  felt  felt  item  scale  from  this  together analysis  the  .32 and .32. on  the  loaded  loadings  The n u m b e r i n g  on  Test and.23 for  scale f i l l e d  college students  this  need.  c o n s i s t e n c y o f .85 f o r an e i g h t  a  study,: single  items.  Again factor  the  items  when a n a l y s e d  According t o the  Sandman  on t h e a n x i e t y f a c t o r  factor.  and  item  The s c a l e i s r e p r o d u c e d  1.  Mathematics i s much.  something  2.  Working m a t h e m a t i c s  3.  I would l i k e mathematics.  4.  I don't l i k e  5.  I  which  I  enjoy  anything  like  a  very  problems i s fun. .  t o spend l e s s . t i m e i n s c h o o l about  job  doing  mathematics.  which  doesn't  use  8  below.  i s not the o r i g i n a l .  would  with  were .73, .62, -.55, - . 4 7 , -.49, .47,  4 loaded  self-concept  *38 w i t h t h e  developed  Sandman's  other a t t i t u d e  Item  Aptitude  was  was a c c e p t a b l e f o r t h i s  with  The e n j o y m e n t  t h a t one w r i t t e n f o r y o u n g e r  t h a t an i n t e r n a l  scale  (1974),.  .95 and c o r r e l a t e d  As t h e s c a l e  would be more a p p r o p r i a t e . was  Aiken  scale of the Scholastic  s c h o o l grade.  students  It  by  h a d an A l p h a C o e f f i c i e n t  mathematics high  developed  o f m a t h e m a t i c s and v a l u e o f  any  61  mathematics. 6*  I enjdy talking mathematics.  to  other  7.  I like  8.  M a t h e m a t i c s i s more o f a game t h a n work.  t o p l a y games t h a t  use  people  about  numbers. it  is  developed  a  hard  VALUE Value  of Mathematics t o Although  Aiken  mathematics s c a l e written  independence  the  was  factor  value  .64,  factor;  Scale;  l o n g , had  Sandman  the  .61, and  -.45  The  items  i n the  value  a  with item  I t s h o u l d be  noted  Value of  that the  consistency of  study.  The  of  item  were  8 loading  are reproduced  5.),  degree  scale.  a The  present  indicated  the  was  (See T a b l e  of m a t h e m a t i c s f o r s o c i e t y  an i n t e r n a l  scale  instrument.  of the s c a l e s  analysis  of  more a p p r o p r i a t e .  documented  of  value  Sandman's s e t o f s c a l e s  t o g e t h e r with the i t e m s from  Oneself  8 items  the s h o r t e r  grades  that  well  validity  the  .58,  anxiety  section for  and  on  -,.45, .41,  that  would a i d i n t e r p r e t a t i o n  Sandman's  loadings  had  inter-relationships  argued,  However,  felt  secondary  constructed,  established was  (1974)  has b e e n a r g u e d  carefully  it  i t was  f o r the lower It  Society  .55,  ;31  i n the  on next  Mathematics  Sandman  scale,  .77.  Value of Mathematics f o r Oneself It  has  been argued  that  t h e measures o f t h e  value  of  62  mathematics to  used i n t h i s  incentives  related  study  should  directly  Sandman's  (1974)  Motivation  i n Mathematics s c a l e s f i t  felt  that,  Scale,  i n addition  a scale  accomplish  Value  of  to  was  end,  scales  comprehension  a scale  scale.  Sandman the  and  levels  Society nor h i s  s h o u l d be  i t e m s of t h a t  It  d e v e l o p e d by t h e  to  suit  parallel  of  the  scale*  The  two  t o those  established  scales  V a l u e o f Math t o S o c i e t y  Society  included.  present  the  i t e m s were c h o s e n t h a t  was  To  t o measure V a l u e o f  of grade 6 students.  Because  value scale,  Neither  this criterion*  purporting  reworded  i t e m s were c o n s t r u c t e d  value  to  d e v e l o p e d f r o m a number o f i t e m s s e l e c t e d  attitude  the  student.  t o t h e Value of Mathematics t o  M a t h e m a t i c s f o r O n e s e l f was It  the  Mathematics  more s t u d e n t — o r i e n t e d  this  include items pertaining  author.  from  various  reading  Wherever of  possible  the  Sandman  validity closely  and  of the  paralled  a r e compared  below.  V a l u e of Math f o r O n s e l f  1. M a t h e m a t i c s i s u s e f u l f o r the problems o f everyday life*  1. M a t h e m a t i c s i s u s e f u l f o r my p r o b l e m s i n e v e r y d a y life.  2. T h e r e i s l i t t l e need f o r m a t h e m a t i c s i n most j o b s .  2. T h e r e i s l i t t l e need f o r mathematics i n t h e j o b s I would want.  3. Most p e o p l e s h o u l d some m a t h e m a t i c s .  3. D o i n g w e l l i n m a t h e m a t i c s h e l p s me i n o t h e r s u b j e c t s .  4.  study  Mathematics i s . h e l p f u l i n understanding today's world.  4. M a t h e m a t i c s h e l p s me understand today's world.  5. M a t h e m a t i c s i s o f g r e a t i m portance to a country's development.  5. I f I g o t b e t t e r marks i n m a t h e m a t i c s I would e n j o y m a t h e m a t i c s more.  6. I t i s i m p o r t a n t  6.  t o know  I t i s important  f o r me  to  63  mathematics i n order g e t a good j o b *  know m a t h e m a t i c s i n t o g e t a good j o b .  to  order  7.  You can g e t a l o n g p e r f e c t l y well i n everyday l i f e without mathematics:  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 without mathematics.  8.  Most o f t h e i d e a s i n mathematics aren't very u s e f u l *  8.  Most of t h e : i d e a s i n mathematics a r e n ' t very u s e f u l to me,.  SELF-CONCEPT OF Although  Patterson  s c a l e s o f s e l f ^-concept the  scale  reason the to  i n the  was  factor  factor  along  2 loaded  and  8  factor.  with other  .31  loaded The  repreduced  The  -.62,  Item  (1973)  Sandman s c a l e  analysis.  were  (1967)  of a b i l i t y  Sandman  t h a t the  items,  ABILITY IN  .46,  below.  The do  in  b a t t e r y was  used*  appeared  -.49,  .39  numbering  1.  I don't  2.  Mathematics -is easy  3.  I in  4.  No m a t t e r how mathem a t i c s .  5.  I often think, mathematics problem  as  items, items  -.31,  enjoyment f a c t o r and  (1970)  to achieve  . 69,  a  The  major  factor  when  were s u b j e c t e d on  the  - 38,  anxiety and  items  respectively  on t h e  was  i s not  .83. the  The  -.17. 4,  usually understand mathematics c l a s s .  scale  original.  hard  me. what we  I try,  I  are t a l k i n g cannot  "I can't do seems h a r d .  about  understand  i t , " when  5,  anxiety  w e l l i n mathematics. for  used  mathematics,  while  consistency  very  Bachman  attitudinal  .56,  .32,  internal  and  l o a d i n g s of the  .68,  on t h e  MATHEMATICS  a  is  64  6.  I am  good a t w o r k i n g  mathematics  7.  I remember most mathematics.  8.  I f I d o n ' t see how t o work a m a t h e m a t i c s r i g h t away, I n e v e r g e t i t .  of  the  LOCUS OF The  scale selected to  Intellectual  Achievement 1965).  no  far  control 0  are  (p.  As  93).  they  so  developed  (1966) I-E Test  of  scale, Battle Internal  (1961) L o c u s o f other  scales  number  of  Second, the  scale  External  Control  "contain  such  was  items  (Crandall,  "there  has  [in  locus  been of  of  experience"  school  achievement Botter's  (1963) C h i l d r e n ' s  Picture  of  Control,  and  i n several respects. describing and  the  d i f f e r e d from  Bailer's  First,  reinforcement  behavioral  dominance, a c h i e v e m e n t and other  that  areas  with  which  Locus  Scale  in  problem  Scale  beliefs  all  6 Botter's  motivational  affiliation,  They s t a t e d  across  IAB  learn  measure l o c u s o f c o n t r o l was  major c o n c e r n  the  I  CONTBOL  that  consistent their  things  Besponsibility  Katkovsky & C r a n d a l l , demonstration  problems.  areas  dependency"  the  in such (p.  a as  93).  scales  include a variety of sources and a g e n t s s u c h as l u c k , f a t e , impersonal s o c i a l f o r c e s , more-personal "significant ethers," etc., the IAB limits the s o u r c e o f e x t e r n a l c o n t r o l t o t h o s e p e r s o n s 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 w i t h 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 p e e r s . (p. 93) In found scale,  a two no  their  initial  administration  month t e s t - r e t e s t r e l i a b i l i t y significant  sex  of  the  o f ,.69  scale  they  f o r the  whole  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 and  (.26 a t g r a d e s 3, 4, 5: .16 a t g r a d e s 6,  socio-economic status  8,  Children's  the  (Crandall,  scores  total only  two  lAfi  scale.  Crandall & Katkovsky,  on t h e n e g a t i v e  scale  S c a l e and  P i c t u r e T e s t had a much s t r o n g e r r e l a t i o n s h i p  to socio-economic s t a t u s than the study  12)  (.08 a t g r a d e s 3,4, 5: .11 a t g r a d e s  6, 8, 10, 1 2 ) . They n o t e d t h a t t h e L o c u s o f C o n t r o l the  10,  items,  In  a  second  1965) t h e y f o u n d  the p o s i t v e items,  and  that the  f o r b o t h 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  significant  Desireability  correlations  Questionaire  children give s o c i a l l y  with  the  Children's  (a measure o f t h e d e g r e e t o w h i c h  desired  responses):  -.26  for  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 a n d -.15 f o r o l d e r c h i l d r e n on the  positive  items*  I t should  be n o t e d t h a t  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 separately. DuCette  This  (1974).  procedure  was  also  the used  this  Achievement Intellectual  failure  items  They f e l t t h a t a s t h e p o s i t i v e  correlation study.  latter  by L i n t n e r and and  s c a l e s c o r r e l a t e d * 45 t b e y w o u l d c o m b i n e them* low  i n this  t h e two s c a l e s  They  were  Responsibility Achievement  Because o f the  were c o n s i d e r e d  referred  to  Scale  -  as  separately i n  the  Success  Responsibility  negative  Intellectual (IARS) a n d t h e  Scale  -  Failure  (IAJBF). ACHIEVEMENT TESTS The  set  of  achievement  scales  Mathematics C o n c e p t s and M a t h e m a t i c s  was  Problem  made up o f t h e Solving  scales  66  (level the  12)  from the  Canadian  Test  of  Basic  a r i t h m e t i c Computation t e s t from  (1964).  The  Canadian Test o f  Basic  because  it  was  and  subjects. Skills, (e.g.,  standardized  Further, o f t e n had  antonnen, In  a  Professor of  1974;  of  Education,  Skills  the  : Form 4  achievement  (CTBS) was 30  Iowa  000  Test  the  1971;  CTBS  and  Birch  and Test  selected Canadian of  i n a t t i t u d e - achievement  Mastantuono,  review  Stanford  v a l i d a t e d on  i t s precursor, been u s e d  Skills  Basic studies  Weston, 1 968),. (1972),  McDonald  McGill University stated,  Unless a user is able to s e l e c t an a p p r o p r i a t e sample o f s u b j e c t s , c a r r y o u t h i s own i t e m analysis and reliability and validity studies, he must . a c c e p t , on t h e r e p u t a t i o n o f t h e t e s t d e s i g n e r , many o f t h e b a s e s upon which h i s conclusions are made. It i s t h u s r e a s s u r i n g t o be a b l e t o 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 . It i s in fact* simply a Canadian version o f t h e w e l l known Iowa Test of Basic S k i l l s . (p. 16) Form  4,  although  curricular teachers  changes  had  been  mathematics the the  British  of  the  metricated,  made using  in the  c l a s s e s i n the system  community and  earlier  not  grades.  of  British metric  three  measurement  system  years was  still  Moreover, o n l y  two  items  1)  gallon  1 pint;).  Thus i t was  was  valid  the  effect  and  that  would be  i f students  5 quarts  could  consistent across  that  Which o f t h e  greatest?  3 quarts  the  required  measurements i s t h e 4)  Even  not the  2) felt  though  6  use system  in  following  t h a t the  sample.  in  knowledge  pints  answer t h e  in  testing,  i n common  been t a u g h t  (e.g.,  recent  exclusively  preceding  had  between u n i t s  some  Columbia.  students  .relation  the  reflected  3)  1  scale  questions  67  There  was  no  Canadian T e s t of B a s i c scale  of  void.  the  SAT:  Biedesel's.  Achievement  test  was  was  Further,  the  as  version still  had  only  that  used  by  content  In  of  emphasis. for  was  the  this  Stanford  been  use  no  well  school  as  a  guestiohs  an  However, an reviewed, district  the  advantage. format  the e a r l y  versions  as.  of  computational  change i n the  more r e c e n t  i t was  However,  considered  reduced.  the  Computation  selected to f i l l  criticism  the  t h e e m p h a s i s on c o m p u t a t i o n i n l i g h t  had  been  The  (1964) was  of computational  was  present  W  criticism  deemed s i g n i f i c a n t * questions  arithmetic  selected  there  presentation  Skills.  (1965)  being  instrument,  s c a l e included with  Form  changes i n mathematics scale  computational  date  the  of was  not  number  advantage t o  widely  the  of this  accepted  participating  and  in  this  study.  TEACHEB EESPONSE SCALES In order validation  of  to the  characteristics  give  teachers'  may  blocks.  to a check  student  as  that students  a  referent* with  an  the  construct the  block"  in  o p i n i o n s were s o u g h t a b o u t p u p i l s  who  Two  list  to  to  associated  response  strength  chosen a f f e c t i v e  mathematics, have s u c h  some  with  scales i n relation  the  "emotional  methods were used*  of n i n e The  "emotional  The  characteristics characteristics block"  might  first using  were  was  a  each  behaviors  exhibit.  This  68  was  similar  Lighthall Test to  to  the  a n d Waite  Anxiety  respond  used  (1958) i n t h e i r  Scale f o r Children  to a  included items  procedure  17 such  item  by  initial  (TASC),;  scale  Sarason,  of  Davidson,  validation They a s k e d  anxiety  of  the  teachers  behavior  which  as  Does t h e c h i l d e x h i b i t unwarranted f i d g e t i n g (e.g., s q u i r m i n g , r e s t l e s s b e h a v i o r ) when called upon t o recite i n class? Does t h e c h i l d become u p s e t o r a n x i o u s when a t e s t i s announced i n c l a s s o r he i s called upon t o recite? (p. 106) In  the  "emotional of  block"  behavior  achievement. of  affective  items.  existed  in  with  taxonomy.  study which  response  The K r a t h w o h l ,  i t  an  to  "emotional  forms  thus  reducing  (1964)  taxonomy  to c o n s t r u c t the check of  block"  could f a l l  t h a t an  negative  mathematics  level  L e v e l 2.3, S a t i s f a c t i o n  "block."i  hypothesized  Bloom and M a s i a s  that the  a t which r e s p o n s e s  was  would l e a d t o  o b j e c t i v e s was used  I t was f e l t  students  level  current  affect would  and s t i l l  displayed be  i n Besponse,  list  high  by  i n the  was t h e l o w e s t  be c o n s i d e r e d  a  Krathwohl e t a l s t a t e d that  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 o f s a t i s f a c t i o n involves two m a t t e r s : (1) d e c i d i n g which b e h a v i o r s  They noted that " t h e c a t e g o r i e s o f t h e a f f e c t i v e domain s t r u c t u r e a r e developed t o handle primarily positive values rather than aversions* f e a r s , and d i s l i k e s . " However, t h e y continued, "It i s believed that, with very little interpretation..., t h e framework c a n be used f o r those • n e g a t i v e t y p e s o f o b j e c t i v e s one i s l i k e l y t o 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 ) . 1  1  69  are i n d i c a t i v e method of manifestations  of  satisfaction; (2) developing a systematically recording the 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  the  c o n s t r u c t o f an  "emotional  A  negative  a  statement  "satisfaction"  positive  at  replaced  block"  the with  voluntary  statements,  Krathwohl et  laughing,  level  i n the  al description  of  affect  and  whereas  neqatively oriented. level  would  dissatisfaction*  Examples i n t h e taxonomy  next  was  same  dislike*  The  statement  aversion  included behaviors v a r i o u s body  taxonomy was  have or  such  as  movements.  3,  Valuing,  The  was,  At t h e l o w e s t l e v e l of Valuing, he is at least willing t c p e r m i t h i m s e l f t o be so p e r c i e v e d and a t t h e h i g h e r l e v e l s he may behave so as to further t h i s impression a c t i v e l y . (p. 139) For  example  t h a t he  a  hated  Preference physical  student  a  remarked d i r e c t l y  m a t h e m a t i c s would be  for  a  Value.  r e a c t i o n s would be  Commitment, b e c a u s e be  who  considerable  considered  Avoidance behavior  t o the at  level  and  involuntary  i n t e r p r e t e d as b e i n g  of  energy  in  3.2,  at l e v e l  Krathwohl e t a l s t a t e d , "there investment  teacher  the  must  3;3, also  object  or  phenomenon". T h e r e was of a f f e c t i v e  no a t t e m p t  responses  Conceptualization  t o have t e a c h e r s  above l e v e l 3.  of a Value,  gather  evidence  For example, l e v e l  required  evidence that the s t u d e n t has d e v e l o p e d e v a l u a t i v e j u d g e m e n t s w i t h r e g a r d t o t h e o b j e c t he v a l u e s ; (2) evidence of a b s t r a c t o r s y m b o l i c t h i n k i n g about t h e v a l u e o b j e c t ; (3) e v i d e n c e o f g e n e r a l i z a t i o n a b o u t a s e t o r c l a s s o f v a l u e s of which the object is a member. (p. 157)  4. 1,  70  Apart  from  such  all  behavior,  unacceptably  both of  list cited  v e r b a l and  Sarason  et a l  short otherwise, number  of  reduce The  list  of  i n Chapter  1.  An  physical  behaviors  (1S58) .  The  list  for a class  responses  appears used  would  observe  have  of  and  was  become  t o f o l l o w the  i n parentheses  had  students,  would i n c r e a s e r a p i d l y qiven  from  made t o  of b e h a v i o r s 30  characteristics  i n the  were i d e n t i f i e d  attempt  t h e amount o f c o n s i d e r a t i o n  be  o p p o r t u n i t i e s to  behaviors  of c h a r a c t e r i s t i c s  f o l l o w i n g nine  label will  the  having  long.  The literature  teachers not  and  to  examples  thus tend  A short  These  labels  s u b s e q u e n t t a b l e s and d i s c u s s i o n . doings-mathematics  have  you  1.  t e n d s to g i v e random a n s w e r s t o q u e s t i o n s mathematics c l a s s ? (Eandom Answers)  2.  appears (Appears  3.  expresses mathmetics?  4.  tends to increase mathematics c l a s s ?  5.  says that no matter c a n ' t do m a t h e m a t i c s ?  what he/she does he/she (Expresses I n a b i l i t y )  6.  has hands t h a t (Hands Shake)  when  7.  says t h a t mathematics i s u s e l e s s ? (Says M a t h e m a t i c s U s e l e s s )  8.  sometimes  tense Tense)  during  mathematics  disruptive (Disruptive  shake  refuses  to  behavior Behavior)  doing  answer  during  lessons?  anxiety or nervousness (Expresses Anxiety)  about during  mathematics?  questions  to  response.  upon.  f o l l o w i n g e a c h one;  While the student is observed t h a t he/she  kept  required  each  were d e c i d e d  sample  t o be  the  the  during  71  mathematics p e r i o d ? 9.  f i d g e t s more d u r i n g ( F i d g e t s More)  Appendix  A has  teachers  the  for  behaviors as  the  mathematics  use  of  this  Answer) lessons?  scale.  student-behavior  entered the  to  complete s e t o f i n s t r u c t i o n s  teacher-response,  to  (Refuses  the  set  As  student  to  this  checklist,  analysis individually of  given  this  behaviors  the  was  and was  a the  referred  or  simply  Student-Behaviorsi The rank  the  second  students as  students  f i t  characteristics.  form  of teacher  t o the  degree  response to  was  which  a  description  based  The  description follows;  t o have  they  upon  them  felt the  the above  A student with the block may give random a n s w e r s t o q u e s t i o n s o r may r e f u s e t o answer them a t all* He/she may a p p e a r t e n s e , have h a n d s t h a t s h a k e as he/she writes, fidget or increase disruptive behavior i n the mathematics c l a s s . The s t u d e n t may tell you t h a t he/she f e e l s a n x i o u s o r n e r v o u s a b o u t mathematics or t h a t mathematics i s u s e l e s s . He/she may state that no m a t t e r how h a r d he/she works i t seems t o make no d i f f e r e n c e . The  procedure  names  of  the  f o r ranking.was a simple grade s i x s t u d e n t s  above c h a r a c t e r i s t i c s .  The  was  r e f e r r e d t o as  AGE  AND  i n the  a l l  the  c l a s s i n terms o f  the  set of i n s t r u c t i o n s  t e a c h e r s f o r the above s c a l e measure  ordering  may  be  found  of  given  to  i n A p p e n d i x B.  RANK.  GRADE LEVEL CHOSEN  the This  72  Antonnen between  1017  students  grades  sharply.  who  likelihood  12.  suggested  He  that  this  the  ability  be  chosen  from  written  been  successfully  administered  Intellectual  Achievement  school children  eight.  would  But b e c a u s e ,  t i e present study  Grade that  seven  students  at the time  concerned  the  about  manner  8  was  o f the t e s t i n g , their  to  answer that  students  The  and  had  group* was  The  developed  secondary  levels.  level  was  grade  o f t h i s s t u d y , t h e r e was  split  not  326).  i f possible.  optimum g r a d e  done  were  and  the the  suggested  Scale  between with  grades  grade  selected  seven  six  because  move  to  an and  subjects.  i t was  s p r i n g , t h e y would  forthcominq  of  with  of  p.  students  .Responsibility  school  of  scores  done  view  1970,  that  i n the l o c a l e  elementary-secondary eight  (Hjelle,  f o r grade  the  be  external  to  that  same g r o u p  i n order to reduce  i n both e l e m e n t a r y  appear  attitudes  i n the d i s c u s s i o n  o l d e r group  Sandman i n v e n t o r y was  in  attitude  study  a t an  of  an  the  that  earlier  items i n a d i s c r i m i n a t i n g  sample  It  found  against f a i l u r e "  However,  for  6 and  were a s young a s p o s s i b l e  world as a defense  the  11 and  of students "arriving  self-report  the d i f f e r e n c e s  Evidence c i t e d  locus of control students  studied  s t u d e n t s i n g r a d e s 5 and  in  declined  (1963)  be  the  felt quite  secondary  school. It  was  elementary particularly  and  also  noted  early  by  Aiken  junior-high  (1976)  that  "The  q r a d e s a r e viewed  i m p o r t a n t to the development  of  attitude  late  as b e i n g toward  73  mathematics."  (p* 269)  Because to  grade  6  of  there  was  t o compensate f o r lower  tape  some  was t h e n  by  about  the  i n the items.  comprehension  on t a p e  administered  concern  o f t h e l a n g u a g e and p h r a s i n g  a l l s c a l e s were r e c o r d e d  The as  Sandman s c a l e s had n o t been  students,  appropriateness order  the  levels,  the  the  present  In  items  author.  d u p l i c a t e d and p l a y e d b a c k t o t h e s t u d e n t s  t h e s c a l e s were b e i n g  presented  i n written  form.  SUBJECTS The district schools The  subjects  in  British  industry  Columbia.  bridged  or b u s i n e s s .  population  residential  areas  There  rural  The l a r g e s t  administrative  into five  farmland  both  areas:  from  a  large  were  approximately  commuted t o a n e a r b y  For  64  areas  proportion of  urban  elementary  14 000  and urban  school  students. with  the  little working  center.  convenience  the  district  two r e s i d e n t i a l - c o m m e r c i a l a r e a s ,  interspersed  with  small  farms,  and  was two one  area. As  students,  there i t  questionnaires each area take  selected  and a n n e x e s e n r o l l i n g  district  divided  were  part  materials  was  were possible  to  for  approximately  administer  t o 14 t o 16 c l a s s e s a t a t i m e .  were c o n t a c t e d in  materials  the  i n order  study.  was c o m m i t t e d ,  This  i n this  of s i z e was manner  and  the  tests  Schools were  450 and within  asked  to  done u n t i l t h e s e t o f some 63 c l a s s e s  from  74  29  schools  were  c o n s i d e r a t i o n s such  contacted*  as s p o r t s d a y s and  number o f c l a s s e s was from  the  study  requested classes  As sets  of  in  Some o f t h e and  the  final  six, These  1186  who the  camping  s i x and  splits text.  takinq  Only  five  and  the  tests  c l a s s type,  Table  the teacher's  sex  and  request.  of  test  were  subjects  from  o f C l a s s Type, Classes 11 33 J2 56  6  Sex  and  Boys 53 410 66 529  of  Such c l a s s e s were to  as  "class  grade s i x s u b j e c t s  study  Table  although  Number o f  grade  a d m i n i s t r a t i o n of 6 summarizes  number o f s u b j e c t s *  Table  56  complete  were composed  were i n c l u d e d i n t h e  at  5- 6 s p l i t 6 only 6- 7 s p l i t Total  the  a  1033  referred  t h e s e c l a s s e s Were i n c l u d e d i n t h e students  of  study  from  seven  done w i t h  seven*  are  a l l the  participatinq.  t o be  missed  final  eliminated  consisted  was  minute  the  sample  c l a s s e s i n the  following  trips  to supply  final total  or  last  failed  students  analysis  subjects  "splits".  types"  o f the  thus q i v i n g  five  The  of  more c l a s s e s were  teachers  s c h o o l s with  data,  grade s i x .  called  26  Three  because  much  eliminated,  grades  59.  information*  from  Because  Subjects  Girls  Total  63 380 M 504  116 790 127 1033  the  75  PILOT A pilot the  written  handling  for  of t h e experimenter  Scale*  The two t e a c h e r r e s p o n s e  procedures.  of  the  two  number o f t e a c h e r s  No  the  i n the  as  pilot  i n t h e same d i s t r i c t  total  of  50 s t u d e n t s , u n d e r t o o k  with  the p a r t i c i p a t i n g  convey  the  purpose o f t h e p i l o t *  as c r i t i c a l o f t h e f o r m a t  to indicate during the  materials  may  description found  included  made  responses,  sample  was  teachers  be  found  of  the  too  small.  was h e l d i n  The t e a c h e r s  with a  order  i n Appendices  They  to  sheets  also  or c o n f u s i o n  final  A  were a s k e d t o  b o o k l e t s , response  The  A  administration.  of d i f f i c u l t y  administration.  or  Two c l a s s e s ,  the p i l o t  of t e s t  any s o u r c e s  to gather  i t was c o n s i d e r e d t h a t t h e  the a d m i n i s t r a t i o n booklet as possible*  arose  and  o f Mathematics f o r  was  was s e l e c t e d *  meeting  asked  tapes,  s c a l e s were  attempt  scales  school  be  and t e a c h e r s , t h e  of  made V a l u e  f o r the r e l i a b i l i t y o f teacher  validity  and  students  of  o f e v a l u a t i n g t h e 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  response  evidence  be  t o a s s e s s t h e adequacy  of the m a t e r i a l s , the a u d i b i l i t y  purposes  the  was c o n d u c t e d  i n s t r u c t i o n s f o r both  reliability Oneself  study  forms  were that  of the  A, B, C, D, and E.  o f t h e s e t o f m a t e r i a l s g i v e n t o each t e a c h e r  A  will  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  eight  Oneself  Scale  selected  items  items  of  the  were a d m i n i s t e r e d from  Value  of  Mathematics  t o g e t h e r with  for  e i g h t randomly  the achievement r e s p o n s i b i l i t y  scale  and  76  six  items  from  the  from  three  response  the  a  and  r e o r g a n i z e d and  of  the  the the  of the  large  of  w h i c h was  variance  effect  of  considered  was  scores  items  had  mean  was  were  positive 17.56  the  Items  different  administration booklet  of  error  correlations for  the  p o s s i b l e o f 40  and  estimate  would t e n d in  light  (unless  the  to balance  the  standard  of  after  the  A l l the  t o .56.  d e v i a t i o n was  a minimum o f  the  testing  reverse polarity. .17  of that  were c a l c u l a t e d  from  Onself  be n o t e d  reliability  c o r r e l a t i o n s ranging and  the  I t should  the but  Hoyt  Mathematics f o r  variance  corrected  The  adequate i n  main s t u d y .  increased)  Item-scale  item  the  Value  not a f f e c t  increased  hypotheses.  maximum  the  sample o f the  l a r g e s a m p l e would  test  pilot  some w o r d i n g s c h a n g e d .  reliability .63  Scale f o r Children.  administration instructions*  result  was  S c a l e was  Anxiety  s c a l e s were i n c l u d e d b e c a u s e o f  formats As  Test  5*15  The with  a  8,  MATERIALS Af f...,e c•..-,t i— v e  S c ..a •l e s^  Each t e a c h e r outlined  the  order  administered, instructions students  was  the  in  q i v e n an which  timinq of  t h a t were t o be  were  to  begin  the read  a d m i n i s t r a t i o n booklet the  materials  test  to  a d m i n i s t r a t i o n , and  t o the  responding.  were  which  students See  before  Appendix C f o r  be the the the  complete a d m i n i s t r a t i o n b o o k l e t . The  affective  s c a l e s were  split  into  three  parts  each  77  characterized Children  by  (TASC),  respond  yes  Achievement  response the f i r s t  or  no,;  one  c f two  thought  b e s t completed  placed  Crandall,  in  The  Katkovsky,  required  the  students  part,  the  Intellectual  required  the  students  second  Scale,  possible  the  The T e s t A n x i e t y S c a l e f o r  part,  Besponsibility  select  were  style;  alternative  a sentence. same  and  Items from  Crandall  (1965)..  the f o u r a f f e c t i v e  the  (Anxiety  Mathematics  battery i n Society,  for  i t e m s was a f i v e don't  see Chapter The  for  the  reproduced order  from  Value of Enjoyment Value  were  randomly  of  s e t of  agree,  of the s c a l e s  For a fuller  were  placed  c o m p l e t e l y i n Appendix in  selected  agree, each  ordered.  together with  i n the t e x t can  description  o f each  of the  3.  students  noted  was  mode f o r t h i s  three parts together with d i r e c t i o n s  specifically toward  o f each  scales  d i s a g r e e . . I t e m s from  part  they  three  scale  strongly  to  study of  Mathematics,  and t h e a b b r e v i a t i o n s used  f o u n d i n T a b l e 7.  scales  scale;  i n the t h i r d  o f items  scales  The r e s p o n s e  Likert  reported r e l i a b i l i t i e s  t h e number be  used  Part  constructed  know, d i s a g r e e , and s t r o n g l y  of the scales The  Toward  author  Oneself. point  t h e two  S e l f - C o n c e p t i n Mathematics,  o f M a t h e m a t i c s ) , and an Mathematics  which  o r d e r as i n the o r i g i n a l  composed o f i t e m s f r o m Sandman  statements  to  Table  7  t o mathematics  mathematics  would  was  into D. that  a  be  examples  booklet  which  An added b e n e f i t the  scales  were p l a c e d l a s t ; not  and  of  is the  pertaining  Thus,  a  bias  p r e s e n t when t h e s t u d e n t s  78  Table 7 Table  o f S c a l e s , A b b r e v i a t i o n s , Number o f Items f o r the A f f e c t i v e S c a l e s Scale  Abbr*  Test Anxiety Scale f o r C h i l d r e n I n t e l l e c t u a l Achievement Responsibility: Success I n t e l l e c t u a l Achievement Besponsibility: Failure A n x i e t y Toward M a t h e m a t i c s Enjoyment i n Mathematics Value o f Mathematics S e l f - C o n c e p t i n Mathematics Value o f Mathematics for Oneself  a n s w e r e d t h e more because and  the  response  therefore  affective  a  was  felt  that  differing  responded  sheet,  to  a c a s s e t t e tape the  items.  consistency  17 8 8 8 8 8  was  to  placed  responding  reading  the was  Twenty of  the  of understanding items.  first  to  an  abilities  of  prepared copies oral  The  sheet  was d e v e l o p e d key-punching  on  with  the  with which t h e  I n order t o reduce the  these  experimenter  were made o f t h e t a p e t o  delivery.  were, f o r a l l t h e above s c a l e s ,  order t o f a c i l i t a t e sheets.  IARF MANX ENJOY VALSOC SELFCON  t h e number o f g u e s t i o n s a n s w e r e d  students  responses  17  TASC  introduction  s c a l e s and the l e v e l  ensure  IARS  mode was c o n s i d e r e d t o be t h e s i m p l e s t  good  might a f f e c t  reading  30  VALSEL  scales.  affective  effects  TASC  scale*  It students  general  Items  The  made on one  student response  especially  f o rthis  study i n  of t h e data  directly  from t h e  See A p p e n d i x E f o r an example o f t h e answer  sheets.  79  Achievement  Tests  The the  following  Concepts,chosen be  three achievement order:  and  because  t h e most f a m i l i a r  problem booklet  solving and  were t o be a d m i n i s t e r e d i n  Arithmetic  Mathematics i t was  tests  Computation,  Problem  Solving.  also  and s h o u l d be  scales  were  first;  thought anxiety  anxiety  was  the  more t h a n  one  word  the  tests,  would  concepts  and  concepts  the  problem  they  appeared.  administration*  p r o b l e m s may  of the c h a r a c t e r i s t i c s of  scale  was  c o n t a i n e d i n t h e s t a n d a r d CTBS  the  eliminate i t s effect The  the  that  s t u d y , the p l a c i n g  would  The  were a d m i n i s t e r e d i n t h e o r d e r t h a t  increase  this  This order  thought t h a t the computation  T h i s tended to reduce complexity of was  Mathematics  It  have t e n d e d t o  questions under  and,  as  examination i n  solving  scale  last  on t h e o t h e r s c a l e s .  names,  a b b r e v i a t i o n s used  number o f i t e m s , r e l i a b i l i t y ,  and  the  in this  publisher's  study, normed  means f o r g r a d e s i x a p p e a r i n T a b l e 8.  Each format;  of  the  had  Again s t u d e n t s responded  facilitate  key-punching.  l e v e l i n t h e CTBS was the  tests  problem  accordingly.  solving See  As  i t e m 52 scale  Appendix  a  1  multiple  on a s p e c i a l  the f i r s t  items  choice  response  answer s h e e t t o for  this  grade  f o r t h e c o n c e p t s c a l e and  40 f o r  t h e r e s p o n s e s h e e t s were numbered  E for  an  example  of  the  answer  sheets. T a b l e 9 summarizes  t h e s e q u e n c i n g o f t h e t e s t s and  the  Table 8  80  S c a l e s , A b b r e v i a t i o n s , Number o f I t e m s , E e l i a b i l i t i e s , a n d Normed Means o f t h e A c h i e v e m e n t T e s t s Scale  Number o f Items Eel*  Abbr.  S t a n f o r d Achievement Test: A r i t h m e t i c Computation Canadian l e s t of Basic S k i l l s : Mathematics Concepts Problem S o l v i n g  Norm Mean  COMP  39  .87  24,3  CONC PBOB  45 31  .86 .83  20. 1 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  administration*  Table 9 Prefered  Sequence and S p a c i n g Mon.  Tues.  TASC  MANX VALSEL VALSOC SELFC ENJOY  break  Morning  of Scale  IABS IABF  Administration*  Wed.  Thur.  no tests  COMP  Afternoon  F r i .  PEOB  CONC  *In a l l cases t h e seqiiencinq a n d t h e two d a y s e p a r a t i o n between a f f e c t i v e a n d a c h i e v e m e n t t e s t s were t o be m a i n t a i n e d * T i m i n q c o u l d be a l t e r e d to suit the school orqanization. Timing here r e f e r s t o time a t w h i c h t h e t e s t s s h o u l d be administered, not t h e time allowed f o r the t e s t i n g session*  PBOCEDUBE Materials assembled* the the  fcr  This  approximately  s e t was s u f f i c i e n t l y  s t u d e n t s o f one g e o g r a p h i c r e g i o n . tests  each o f  was  375  students  large t o administer to The a d m i n i s t r a t i o n  done i n 5 s e s s i o n s , e a c h a week l o n g ,  the five  geographic  regions.  were  After  the  of  one f o r initial  81  contact  had  schools, study' and of  been made w i t h  a l l teachers  were  invited  d e s c r i p t i o n of the  results,  of  the  p r i n c i p a l s of  a region  with  materials  the  were g i v e n *  confidentiality  participating  classes involved  at  to a meeting.  the  of the  meeting the  in  the  purpose  Q u e s t i o n s about  data,  and  time  use  required  were a n s w e r e d . a  s e t of  teacher* cards who IBM  materials  I t i n c l u d e d an  f o r ranking might  the  have an  the  booklets, three  a  affective  arithmetic Test and  a  class  and  the  because absolute  scales  the  affective  school  oh  upon  number the  tape,  c f the  attitude scales.  Test  set a  set  which and  they  scale for  two  the  Stanford  Skill  booklets,  administered  I t was be  before  and  mornings*  platooning  order  qroupinqs of  suggested to  administered  consecutive  test  the  tests.  session. scales  of  observed  answer s h e e t s of  of  student  to reduce p o s s i b l e e f f e c t s of  were t h e  three  a  affective  of Basic  were  organization  requirements  between e a c h  student,  achievement  testing  preferably of  booklet,  i n mathematics, a  of  cassette  Canadian  f o r the  affective  that the  sessions;  block"  set  participating  d e s c r i p t i o n of  identification  o f the  achievement  teachers  the  f o r each  achievement s c a l e s i n order longer  to each  s c a l e s , a c l a s s s e t of each  answer s h e e t s The  one  students  copy  on  "emotional  Student-Behaviors,  provided  administrative  students  mark-sense c a r d s ,  recorded  was  and  the  in  the the the two  However, the  only  rest  period  scales; lasc,  iaE,  and  82  The two  day  a c h i e v e m e n t t e s t s had  l a p s e between t h e  achievement  scales,.  administration  s i m i l a r requirements  a d m i n i s t r a t i o n of the  See  9  Table  above  with  affective  a  and  f o r the p r e f e r r e d  schedule. DATA DESCRIPTION  For  each s t u d e n t  gathered: behaviors  the  identification from  description  the  of  number,  Student  that  "emotional  block"  scores,  and  eight affective  Teacher  Responses Sex  were a s k e d to  an  Blank  was  cards  t e a c h e r s put students  on  o r d e r from then  The  names  the  cards  down t h e  t h a t they  instructions numbers  were a l l o w e d *  most t o l e a s t  copied  the o r d e r  from  given  were t h e n  t h e c l a s s by  and  IBM  the  Student  rank  the  was  on t h e  the  numbered f r o m  the experimenter.  The  which  on  the  with  an  test  teachers  corresponded  Behavior  checklist.  o b t a i n e d by h a v i n g numbers  the  of  the  They p l a c e d t h e c a r d s i n  description  identification  to  cards  provided.  appeared  rank  achievement  identification  like  identified  associated  three  were  scores.  number on  behavior  the  be  data  teacher  1 f o r male, 0 f o r f e m a l e *  t o mark the  observed  may  test  of  checklist,  mathmatics,  coded  pieces  sex,  Behavior  behaviors in  followinq  provided*  They  numbers o f t h e s t u d e n t s cards.  teachers.  Appendix B has The  in the  identification  1 t o t h e number o f s t u d e n t s  in  A rank  by  score  was  obtained  83 - ••;) '.*'•'!  giving  a l l students  TASC s c a l e , which c o n s i s t e d 1  coded  i f  yes  and  IARF s c a l e s  were made up  statement.  The  negative  Strongly  0 i f no.  of two  alternatives  were  were 5 l e v e l L i k e r t  2.  MANX, and scales  1 to Strongly Disagree with  For  each  eight  affective  scales  the  o f t h e items,.  calculated  by  adding  items  up  value  were o m i t t e d ,  the  the f o l l o w i n g  author  developed  replacing  missed  items  the  the  answered  (N +  M)  denotes the Thus  a  responses heavily  responses.  with a  N £  coded  were  the  reversed.  s c o r e on e a c h  was  Because  some  were a d j u s t e d by  using  w h i c h had  the e f f e c t  value e g u i v a l e n t t o the  of  mean  Xi  above N d e n o t e s t h e  number o f o m i t t e d  student  who  would  have  than  formula  with  i=1  N formula  scores  Items  items,*  Y =  In the  polarity the  given  F o r each o f  items  o f the  negative  and  to a  which were  5.  =  answers,  VALSOC, SELFCON,  s c a l e s those  of  those  o f t h e IARS  five  the  and  no  endings  1,  coded  VAISEL  and  items  alternative  were r e v e r s e d .  Agree =  of yes  The  polarity  ENJOY, and  of  (1),  a one  Scales  The was  median r a n k  (0).  below a z e r o  Affective  above t h e  items,  typically the  number o f and  chose  unanswered  would a s t u d e n t  who  Xi  answered i t e m s , the  item  higher items  c h o s e the  M  score.  valued  item  weighted  more  lower  valued  item  84  Data  Beliability The  clata  university several for  computer  computer  through  center.  errors.  answers,  a  out  dropping  or the adding  scales*  set  of  random  A  scores  The  on  negative  was  with  the  affective  loadings or  which  scoring.  (-.0 1).  polarity  and  further  The found  might Only  i t e m was correct.  analyses  Sandman s c a l e s and  for  program, scales  number  error  thus  finishing  had the  a set  written of  the  answer  original  the  i t e m by  item  scores  scanned.  Any  checked.  affective with  the  A and  the e d i t e d  0.5%. LEBTAP,  and  (Nelson,1974)  each item  indicate one  check  was  was  of  column o f each  both  item  checked  study  of  on one for  the  used  was  were  IABF  was  selection calculated  shortness  subjects  for  coding,  scale,  proper  was  checked  incorrect  Reliabilities  because  because t h e  check  records that  d i v e r g e n t was  e r r o r r a t e was  item a n a l y s i s  to  written to c a l c u l a t e the  were c h e c k e d  resulting  data,  program  last  widely  answer s h e e t s  scales  reversing,  before  checked  volume o f  written to  student  o r two  of the  program was  which  s e t o f 50  extreme  and  was  A computer  the  a limited  key-punching  of an i t e m  at  the a u t h o r  i t e m had  those  Another  number  staff  t h r e e a c h i e v e m e n t t e s t s w h i c h were t h e n  An run  the  third  achievement data.  range.  T h e s e were t h e n  sheets. the  of  out  the  program  select  i n t h e wrong c o l u m n .  print  for  As each  a l l t h e d a t a and  of data  by  Because of t h e  computer  responses  to  key-punched  programs were w r i t t e n by  key-punching  possible  were  two  of  the  years  85  younger  than  the  sample Sandman used f o r d e v e l o p m e n t .  was  a slight  was  VALSOC w h i c h s h o w e d a d r o p f r o m .77  concern .74  attentuation  of r e l i a b i l i t y ,  were t h e d r o p s of I A B S , f r o m  to  .59.  However,  the  .69.  t o .52  reliabilities  a d e q u a t e , p a r t i c u l a r l y as t h e s a m p l e s i z e a d e g u a t e power f o r t h e  the l a r g e s t o f  to  .66  There  Of and  which  greater  IABF, from  were  considered  (1033)  would  give  analyses.  A c h„—,. i e v e m e n t, T e s t s A s i m i l a r procedure scales.  E a c h i t e m was  was  c a r r i e d o u t on t h e  examined f o r e x t r e m e l y  c o r r e l a t i o n s w i t h t h e whole  test  i n c o r r e c t coding, reversing,  or  Only distractor whole  one  w h i c h had  scale  checked  item  than  on  which  achievement  low o r  may  have  f o r k e y i n g and  the coding  indicated  scoring.  t h e t h r e e a c h i e v e m e n t t e s t s had  an e q u a l o r h i g h e r c o r r e l a t i o n did  negative  correct and  response.  found  with  The  e s t i m a t e s of r e l i a b i l i t y  f o r t h e t e s t s were c a l c u l a t e d  reported  together  in  deviations,  Table  10  maximums and  preliminary of  analysis  included  the  issues and  t o be  Hoyt  and  are  standard  scales.  models  addressed:  t h e s e c o n d was  i n the ensuing  means,  was  ANALYSES  hypothesized had  the  minimums o f t h e  PEE L I MI N A BY Before  with  the  This item  correct.  a  analyses.  were  the f i r s t  tested was  the  two unit  w h e t h e r o r n o t TASC s h o u l d  be  86  T a b l e 10 Means, S t a n d a r d D e v i a t i o n s , Maximum S c o r e , And H o y t B e l i a b i l i t y f o r t h e A c h i e v e m e n t and A f f e c t i v e S c a l e s N = 1033  l 2  Scale  Mean  S.D,  COMP CONC PBOE TASC IABS IARF MANX VALSOC SELFCON ENJOY VALSEL  18.76 23.94 16. 3 3 12.55 29.52 27. 54 18.89 31. 91 28.33 24.95 29.81  7.33 8.54  Min  6.23 5.78 2.39  2.83  Max  Hoyt B e l .  0 0 0 0 17 17  39 45  .88 * 88  32 30  8 8 8 8 8  40 40 40 40 40  .85 i 84 ,*52 .61 . 81 .69 . 81 .82  5.94  4.91 5.94  6.81 5.23  34 34  Bep.  Reli  .87 . 86  .83  .672 .66 .74 . 86 .77  . 83 .85 .69  . 68  Beported r e l i a b i l i t y , 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 .  Unit of Analysis The invariably analysis. on  upon which  used  i n d i v i d u a l as the unit of d i s c u s s i o n or  the  However, t h e m a j o r i t y  studies  could  in  experimental  be randomly  subjects to  literature  were p a r t  remove  environment example,  effects  f o r example,  literature  on  achievement,  and  sex  stated  spotty  was  In this  a n d i t was h e l d  the  case  was n o t f o r m e d  that  a  independently o f the  (1978), i n t h e i r differences  the  study  student's  in  finding  of  For  review o f t h e mathematics  that of  based  desirable  t h e s t u d e n t found h i m s e l f *  Sherman  nature  based  p s y c h o l o g y i n which i n d i v i d u a l s  in  related  were  of the literature  groups  o r c l a s s i n which  Fennema  hypotheses  t o t r e a t m e n t groups.  of i n t a c t  class  self—concept,  The  assigned  the  superior  87  m a t h e m a t i c s £for m a l e s J w h i c h was a l w a y s f o u n d i n conjunction with a host of l e s s favourable a t t i t u d e s by females, suggests that important negative 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 themselves, (p. 202) The  unit  first  of  analysis  issue  was r e s o l v e d i n t w o s t e p s ; t h e  dealing with differences  among  s e c o n d w i t h d i f f e r e n c e s among c l a s s In  the f i r s t  each o f t h e eleven level  split)  step u n i v a r i a t e analyses  computer  hypothesis TASC, in  &  Bent,  each  programs  Package f o r t h e S o c i a l S c i e n c e s Steinbrenner  means,  (SPSS)  1975).  and t h e  variances*  variables within  using  class  Of  were done f o r  class  type  (grade  from t h e S t a t i s t i c a l (Nie, Hull,  the  Jenkins,  33 a n a l y s e s t h e n u l l  was n o t r e j e c t e d a t t h e .05 l e v e l  i n only 9  I A B S , AND I A B F i n t h e g r a d e 5-6 s p l i t ,  cases:  MANX and SELFCON  t h e g r a d e 6 c l a s s e s , and TASC, MANX, SELFCON, and ENJOY  the  grade  results,.  6-7 A  deviations  split;  table may  of  be  See  Table  t h e 56  found  in  11 f o r a summary o f t h e s e  class  means  i n A p p e n d i x F*  and  standard  The g r a n d  means f o r  t h e a f f e c t i v e s c a l e s were: TASC, 1 2 . 5 ; I A B S , 2 9 . 5 ; I A B F , 2 7 . 5 ; MANX, 1 8 . 9 ; VALSOC, 3 1 . 9 ; VALSEL,  2 9 . 8 . The g r a n d  SELFCON,  (20.1);  decided  different  with  w e r e : COMP, 18.8 ( 2 4 . 3 ) ; CONC,  and PBOB, 16.3 ( 1 3 . 3 ) .  were s i g n i f i c a n t l y  25.0; and  means f o r t h e a c h i e v e m e n t t e s t s  t h e normed means i n p a r e n t h e s e s 23.9  2 8 . 3 ; ENJOY,  Because t h e c l a s s  i n most i f n o t a l l c a s e s  means  i t was  t o a d j u s t t h e raw s c o r e s b y t a k i n g d e v i a t i o n s f r o m t h e  c l a s s means. For  the  second  step  a  Bartlett-Box  tests  of  88 Table  ill  U n 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 U s i n g Each o f t h e A c h i e v e m e n t and A f f e c t i v e V a r i a b l e s a s I n d e p e n d e n t V a r i a b l e s and Class a s Dependent Variable Variable  MSB  df Between  MSW  Grade 5-6 COMP CONC PEOB TASC IARS IABF MANX VAL SOC SE1FC0N ENJOY VAL SEL  116. 1 117.5 66.7 24. 7 7.3 9.3 10 3. 2 54.5 55.8 135.6 77.2  10 10 10 10 10 10 10 10 10 10 10  42. 94 59.04 31.06 25. 15 4.67 8. 10 29.11 21.18 26.41 43.23 29.06  df Within  F ratio  F prob  split 105 105 105 105 105 105 105 105 105 105 105  2.71 1,99 2.15 .98 1.56 1,15 3.55 2.57 3, 14 2:66  .005* .041* .027* .463 . 129 .333 .001* .008* .030* .002* *006*  7.41 7.0 2 5.08 2.83 1.94 2,42 1. 16 2.62 1.31 1.96 2*92  .000* .000* .000* .000* i002* .000* .254 .000* ,118 ,001* .000*  4. 79 8*93 10,77 1i45 2,33 3,70  .000* .000* .000* . 160 .013* .000* :490 .008 i073* .252* .020  2.11  Grade 6 o n l y C CM E CONC PEOE TASC IAES IARF MANX VALSOC SELFCON ENJOY VALSEL  318.3 422.7 172. 2 93.0 11.0 18. 1 41.6 60. 1 47.5 87.0 74. 1  32 32 32 32 32 32 32 32 32 32 32  42.97 60.24 33.89 32.89 5.67 7.47 35.98 1 22.96 1 36.23 44.49 25.38  756 756 756 756 756 756 756 756 756 756 756  G r a d e 6-7 s p l i t COMP CONC PROB TASC IARS IARF MANX VALSOC SELFCON ENJOY VALSEL *p < .05  179.4 355. 5 204.6 39.2 11.8 25.6 28.7 48. 0 57.0 54,. 8 44. 8  11 11  11 11 11  11 11 11 11 11 11  37.46 39.80 18.99 29.01 5.07 6.92 , 30.03 19.46 32.71 43.23 20.52  115 115 115 115 115 115 115 115 115 115 115  196  2.47 1.74 1.27 2, 19  89  homogeneity  of  calculated. according This  variance  This  t o grade  analysis  two  type,  done  class  with  and a l s o  12 when  Table  variables  CONC  variances  were  t h e c l a s s e s grouped on  a l l classes  was a l s o done by a computer  As can be s e e n f r o m only  was  f o r the  program  a l l classes  and  IARS  together. from  were  showed  again  SPSS.  grouped  significant  d i f f e r e n c e s i n v a r i a n c e between c l a s s e s .  Table 12 Table  o f the R e s u l t s of the Bartlet-Box T e s t s o f H o m o g e n i e i t y Of V a r i a n c e on Each o f t h e A f f e c t i v e And A c h i e v e m e n t Measures Grade  5-6  Split  Scale  STAT  PEOB  STAT  CALC CONC PEOB TASC IARS IARF MANX VALSOC SELFCON ENJOY VALSEL  1.11 1.52 .37 .95 a. 20 .92 1.04 .77 .94 1.04 .41  .35 . 12 .96 .49 .29 .51 .41 .66 .50 .40 .94  1.45 1.55 1.02 1.34 1.11 1, 17 1.25 1. 12 1.45 .75 1.56  Since  moderate  *p  Organization  6 Only  6-7  PROB .05* .02* .44 . 10 .31 .23 . 16 .29 .05* .84 .02*  Split  STAT 1. 18 1.09 .61 1. 4 3 2.45 1.96 1. 2 5 .66 . 86 .95 .66  Combined  PROB  STAT  .30 .36 ,83 .15 .005* ,03* ,*25 ,:78 ,i58 .49 .78  PROB  1*30 1.54 1 .04 1*32 1.39 1 .26 1.22 ,95 1.26 .82 1.17  .07 ,.01* ,40 . 06 .03* . 10 . 12 .58 . 09 , 83 L18  <.05  departures  homogeneity  of  distribution  of the F - s t a t i s t i c  decided  from  v a r i a n c e do n o t s e r i o u s l y  not to r e j e c t  (Winer,  the  assumption  of  affect  the sampling  1 9 7 1 , p,  2 0 5 ) i t was  the n u l l hypothesis  t h a t t h e r e would  be  90  no  significant  d i f f e r e n c e s among  analyses  proceded  of  same p o o l e d  the  standardized deviation  it  variance  extreme net  whether  may  or  deviation scores  variance  of c l a s s grade  Therefore,  of the  he  a  were  standard  and  homogeneity  organizations  (splits)  groupings  was  grade type  groupings  s t a n d a r d i z a t i o n on  seen i n Table  with  13.  The  any  more were  within  class  the  inter-scale  differences  are  word " s c o r e s " , when u s e d  achievement or a f f e c t i v e  Exclusion of second  included or  different  with  scales, will  mean z e r o and  mean  standard  classroom.  Test  Anxiety  TASC  Anxiety tc  could  measurement  All  be  shown  greater of  correlational  considered  This decision  i n Mathematics have  t o be  Scale f o r C h i l d r e n  in further analyses.  shewn i n the  TASC  preliminary question  the  not  from  be  validity  estimates  in further analyses.  or not  whether  were  The  one.  The  could  types  other*  standardized  Inclusion  be  of a n a l y s i s o f  separate  effects  conjunction  deviation  variances  Thus t h e  I n a l l f u t u r e d i s c u s s i o n the  scores  to  tests  the  considered  correlations  in  on  than  slight.  variance.  t h a t none of t h e  The  class  variances.  1.  of  appeared  class  e a c h c l a s s t o a mean o f 0 and  within  From t h e of  as i f a l l the  the  and  linear  was  rested  on  in  the  something  which  p r e d i c t i v e and  anxiety  (TASC)  t o measure  (MANX) and  was  scale  concurrent mathematics  regression  analyses  91  T a b l e 13 T a b l e o f C o r r e l a t i o n s Between A c h i e v e m e n t and A f f e c t i v e V a r i a b l e s Using Scores S t a n d a r d i z e d W i t h i n C l a s s , and Baw S c o r e s * COMP  CONC  PBOB  TASC IABS IABF MANX VSOC SCON ENJOl  1. 00  COMP CONC  S '.64 .70 E  PBOB  S E  TASC  IAES  1.00  .66 .72  1.00  S - . 23 E -.24  -.33 -.33  -,.28 -.31  1.00  S E  . 16 .16  .09 .13  .10 .13  - . 14 -.14  1.00  IABF  S B  .01 .03  -.03 .01  -,06 -.03  .08 .09  .26 .28  1.00  MANX  S - . 42 B -.36  -.39 -.33  -i35 -.32  .33 .32  -.25 -.24  .02 .01  VALSOC  S B  . 18 . 16  .25 .21  .17 .15  -.09 -,.03  .16 .18  SELFCON S B  .45 .41  .49 .46  .45 .43  -.43 -.44  .26 ,27  ENJOY  S B  . 32 .25  . 27 .21  .27 .22  -.11 -.09  .22 .21  .07 - .72 . 10 - . 72  .41 , 42  1.00 .55 . 55  VALSEL  S B  . 17 .15  .19 .16  .14 .12  -.03 ,02  . 16 . 16  . 10 - . 3 7 ,. 12 - . 37  .67 .70  .30 - 29  .66 .69  *S = S t a n d a r d i z e d correlations were p e r f o r m e d written  and  computing  .09 - . 3 6 . 12 - . 3 6  -.07 -.04  -.71 - , 72  correlations,  supported  staff  indicated  by t h e U n i v e r s i t y  (Le S T e n i s c i , the correlation that  1.00  .34 .32  1.00  E = Baw  using the Triangular Begression  First, This  score  1.00  score  Package  of British  .49 * 51  (TBP)  Columbia  1977). between MANX and TASC was . 3 2 .  t h e two s c a l e s were m e a s u r i n g  different  92  constructs.  Moreover from Table  accounted  for a  greater  14 i t c a n be s e e n  proportion  a c h i e v e m e n t v a r i a b l e s t h a n d i d TASC.  of  that  variance  Although  MANX  MANX  i n the and  TASC  T a b l e 14 S g u a r e d C o r r e l a t i o n s Between MANX, TASC and t h e A c h i e v e m e n t V a r i a b l e s  MANX TASC MANX • TASC  combined variance  to  CONC  PEOB  MANX  .17 .05 .18  .15 .11 .20  .13 .08 .16  1.00 .10  contribute a significant  (p < , 0 0 1 ) , t h e a d d i t i o n a l  variance CONC.  COMP  attributable  to  proportion of explained  proportion  of  1ASC was a t most 5% i n t h e c a s e o f  However, when c o m p a r e d w i t h t h e p r o p o r t i o n o f  explained  by  substantial. when  into  account  achievement  MANX  alone  (15%) ,  t h e 5%  On t h e o t h e r h a n d t h e d a t a  that  t h e other  i n Table  mathematics a f f e c t i v e  the increase  was  i n explained  construct  concurrent still  considered 15  showed  variance  taken  of the  v a r i a b l e s when TASC was added was a t most 2%. I t  validity  MANX  c r n o t MANX validity  terms  of  appropriate  However, t h e  issue  c o u l d be shown t o h a v e a d e g r e e o f  a s a measure o f  t o be a d d r e s s e d *  In  a p p e a r e d t o be t h e most  measure t o u s e i n t h e f o l l o w i n g a n a l y s e s . whether  variance  s c a l e s were  a p p e a r e d t h a t t h e i n f l u e n c e o f TASC was s m a l l *  of  explained  mathematics  anxiety  was  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 S q u a r e d 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 A c h i e v e m e n t S c o r e s Squared Partial Correlation of TASC*  F  -.0341 -.1218 -. 1597  COMP CONC PEOB  2  Multiple E  Without TASC  prob  .446 .006 .0004  With TASC  .2192 .2447 .2069  .2193 .2560 *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 . A11 other 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 equation*  2  T h e r e were two v a l i d a t i n q these  was  BANK  (the r a n k i n g  description  of behaviors  "emotional  block"),  by  which  The  measures used.  t e a c h e r s o f s t u d e n t s on a  may  second  The f i r s t o f  be was  associated  with  an  the s e t of observed  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  teachers  the  dichotomized  mathematics classroom.  within and of  The BANK s c o r e s were  each c l a s s , t h e lower h a l f h a v i n q  t h e upper h a l f consistency  calculated  zero  a s c o r e o f one ( 1 ) . To q i v e some  point  between  characteristics.  a score of  biserial BANK  and  They r a n g e d  correlations each  of  in  (0)  evidence  were  then  the behavioral  between .09 a n d . 2 3 .  See  Table  16. A  table  cf  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 f o u n d  i n A p p e n d i x H.  an i t e m  a  of  calculated. use by  test,  The  a  result  T r e a t i n g each o f t h e b e h a v i o r s a s  Hoyt  estimate  was .70.  of  Although  was  T h i s was n o t a l e g i t i m a t e  o f t h e H o y t e s t i m a t e a s t h e 1033 r e s p o n s e o n l y 56 t e a c h e r s .  reliability  i t d i d suggest  sets  were  made  that the teacher  94  report  variables  were c o n s i s t e n t w i t h  have been a r e s u l t  of the "halo  e a c h o t h e r , i t may a l s o  effect."  Typically a strong initial positive or n e g a t i v e impression o f a person, group, o r event tends t o influence ratings on a l l s u b s e q u e n t observation. ( I s a a c S M i c h a e l , 1971, p. 58.) In  turn,  o n l y one o f t h e t e a c h e r  Shake, c o r r e l a t e d with  MANX.  the  correlations  scoring  validity  than  behaviors  with  In a d d i t i o n  the  achievement  of the  behavioral  may  be  characteristics;  found  i n Table  above, s u g g e s t e d  to retain  one  and z e r o f o r i t s a b s e n c e .  validity, i naddition noted  a l lin  did  The n e g a t i v e c o r r e l a t i o n s a r e an a r t i f a c t the  are  i t  expected  data  concurrent  TASC  was n o t s i g n i f i c a n t .  not high,  o f the behavior  these  variable  the  with  #6, Hands  the  of  presence  of  although  direction.  of  more s t r o n q l y w i t h  The d i f f e r e n c e  variables,  report variables,  to  16*  that  A  f o r the summary  This evidence of  of  the construct  MANX was t h e most a p p r o p r i a t e  f o r t h e analyses o f t h e hypotheses  o f the  study,. STATISTICAL PBOCEDOBES Statistical The .01.  This  Significance level  of significance  level  was  chosen f o r  chosen i n order t o reduce  error rate f o r the entire s e t of analyses. this  was  necessary  tests  of significance  this  because  of  I t was  study  was  the overall felt  that  t h e l a r g e number o f i m p l i e d  i n regression analysis.  Indeed,  f o r any  95 T a b l e 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 Characteristic 1 BANK TASC MANX COME CONC PBOB  2  4  3  -.33 -. 40 .13 . 14 .20 . 23 -.34 -. 24 -.32 -,.24 -.30 - .25  -.34 .16 .23 25 -.26 -.25  5  -. 18 .04 .13 -. 17 -.14 - .13  7  6  -.26 .09 . 18 -.19 -.21 -.22  - . 16 . 10 .09 -.10 -. 12 -. 10  8  -.18 .07 ,16 -.14  -.17 .08 .09 -.14  -.15  -.11  -.in  -.15  9  BANK  -.26 1.00 . 13 -.22 .18 -.36 -.29 .40 r.25 .42 -,25 .41  Answers Appears Tense 3. 1. Bandom Expresses 2. Anxiety 4. Disruptive Behavior 5. Expresses I n a b i l i t y Shake 7. Says M a t h e m a t i c s U s e l e s s 8. B e f u s e s 6. Hands F i d g e t s More t o Answer 9. single  selection of a variable  amongst k i n d e p e n d e n t (1976) s u g g e s t t h a t level  variables,  alpha d i v i d e d  w i t h which t o c o n t r o l  this  would i n c r e a s e  may  be j u s t a s s e r i o u s  chosen  "when  anticipated independent were  considered of  priori"  three  reasonable.  and t h a t  rate  be an  They a l s o  a more l i b e r a l  significant  (p.  f o r the t e s t s and  from  appropriate note  error  that which  alpha could  relationships  be  are  1 4 ) . T h e r e f o r e , as t h e number o f  seven,  of an  In addition,  t o an a c c e p t a b l e  this  study  typically  alpha  level  o f .01 was  because o f t h e l a r g e  t h e s a m p l e , t h e power was c o n s i d e r e d  Type I I e r r o r  Sex  by k would  t h e p r o b a b i l i t y o f a Type I I  variables  between  predictor  Kupper, S t e w a r t , and W i l l i a m s  Type I e r r o r ,  specific  a  as t h e strongest  adequate t o  keep  size the  level.  Differences The  difference  null  h y p o t h e s i s was t h a t  t h e r e was no s i g n i f i c a n t  between 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 x o f t h e m a l e s  96  and  t h a t of the  females.  A l t h o u g h sex  differences  n o t e d i n t e r m s o f d i f f e r e n c e s b e t w e e n means, t h e the  present  case  of  study the  factor  analysis,  dependent  matrix.  little  However, f o r i n t e r e s t , t h e  importance*  Differences  d i f f e r e n c e s were e x a m i n e d and  the  event that  analyses  by  the  sex  and  this  Stanley  hypothesis  .10,  ...  (p.  287).  p.  595)  to  was  insure  The  Bex  used and  a n a l y s i s of v a r i a n c e of  description and  a  was  should i t was  females  was  variance-covariance b r e v i t y the  be  product-moment  separate  with  p =  of .10.  as  power  as d e s c r i b e d a one  for by way  (OWMAB) d e v e l o p e d by  a  test"  Winer  (1971,  multivariate the  Faculty  Columbia;  that  in  the  following  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  to  equal  be done i f t h e  matrices  Affective Inter-Scale null  In  o f a Type I e r r o r as l a r g e  understood  description will  The  means  in  c a l c u l a t e d by  program  score  of  adviseable  reasonable  procedure  the  reduce the r i s k  tested  Psychology at the U n i v e r s i t y of B r i t i s h It  raw  (1970) n o t e t h a t " I t m i g h t be  some c i r c u m s t a n c e s t o r u n a r i s k  the  upon  rejected  To  was  as i n  i n A p p e n d i x G.  was  undertaken.  of  b e t w e e n means w e r e  included  hypothesis  were t o be  a Type I I e r r o r Glass  null  often  hypotheses  were c o r r e l a t i o n a l i n n a t u r e o r ,  variance-covariance  and  are  was  not  n u l l hypothesis accepted.  be o f one  of  However,  for  test.  Belationships hypothesis  correlations  of between  no  siqnificant  affective  Pearson  scales  was  97  tested  p = .01.  with,  calculated Package  by  the  The  computer  study  component f a c t o r  orthogonal  varimax  factor  and p r o b a b i l i t i e s Triangular  were  Regression  1977)  the independence of the a f f e c t i v e  principal  the  ratios  program,  (TRP) (Le & T e n i s c i , To  F  analysis  rotation,.  variables a  was p e r f o r m e d  The r e s u l t s  were  f o l l o w e d by  compared  with  s t r u c t u r e p r e d i c t e d by t h e a c h i e v e m e n t M o t i v a t i o n  model. all  factor  coefficient  analyses,  generations  rotations  were  General  F a c t o r a n a l y s i s Program  British  Columbia  Hakstian  f o r using  component a n a l y s i s (1)  desired,  the f a c t o r  1973,  p.  (3)  there  coefficient  criteria  were  t o be r e t a i n e d  retained 1.00  alberta  University  of  was a u t h o r e d by  of  the  principal  t h e r e s u l t s o f a common  orthogonal  criterion  should  as " t h i s  in and  Kaiser-Gutman c r i t e r i o n  than  the  or  factor  was c o n s i d e r e d t o be one  near  orthogonal  was no i n d e t e r m i n a c y computation  measures present i n  (Hakstian  &  Bay,  42-3.)  eigen-value  be  at the  results  t h e c u r r e n t study  and  score  Two factors  score  with  The program  the  r a t h e r than  o f e x p l o r a t i o n , (2) were  (aGFaP)  factor  (1973).  Reasons  were  performed  computer c e n t r e .  and Bay  analysis  and  used the the  to  determine  analysis; Cattell  t h e number o f  the  Kaiser-Gutman  "scree"  s t a t e d t h a t t h e number o f  test. factors  e q u a l t h e number o f e i g e n - v a l u e s  marks  the  last  factor  with  The to  greater  significant  98  alpha  coefficient  cf  homogeniety" ( C a t t e l l ,  The " s c r e e " t e s t s u g g e s t e d retained  t h a t t h e number o f  s h o u l d be d e t e r m i n e d  bottom of t h e curve  1966, p.  207).  factors  to  by t h e " s c r e e " r e m a i n i n g  when t h e e i g e n - v a l u e s  were  be  a t the  plotted  from  highest to lowest. Typically the curve 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 then becomes absolutely straight (except, sometimes, f o r minor, i r r e g u l a r d e p a r t u r e s ) . . . . In large samples there are usually clear representations o f two n o t o n e , s u c c e s s i v e s t r a i g h t scree slopes. I n t h i s c a s e one t a k e s the l i n e of t h e upper s l o p e . ( C a t t e l l , 1966, p. 206) To  study  orthogonally (1966)  noted  the  rotated using  Nunnally  of  structure  the  varimax  t h a t a l l a n a l y t i c methods  s i n g l e mathematical rotation  factor  f u n c t i o n ) of f i n d i n g  factors  were  t h e c o m p o n e n t s were procedure.  Cattell  (methods m a x i m i z i n g simple  structure  subject to limitations.  a by  However,  (1967) s t a t e d  The v a r i m a x method h a s p r o v e d v e r y s u c c e s s f u l as an analytical a p p r o a c h t o o b t a i n i n g an orthogonal r o t a t i o n of factors. E v e n i n t h o s e c a s e s where t h e results 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 o f a simple s t r u c t u r e , the s o l u t i o n usually i s close enough to greatly reduce t h e l a b o r of f i n d i n g a satisfactory solution. (p. 333) Affective-achievement Relationships T h i s a n a l y s i s was done i n two s t a g e s . of  analyses  used  first  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  The s e c o n d s e t used f a c t o r s c o r e s w i t h i n each  The  set  class.  w h i c h were a l s o s t a n d a r d i z e d  class.  Standard  score analysis.  The  hypothesis  of  no  99  significant  Pearson  p r o d u c t moment c o r r e l a t i o n s b e t w e e n  a f f e c t i v e v a r i a b l e and e a c h a c h i e v e m e n t with  p = .01  using  variable  was  t h e c o m p u t e r p r o g r a m TEP.  The  tested  quadratic  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 a c h i e v e m e n t v a r i a b l e s was by  correlating  with  variables.  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 tested  usinq  R e g r e s s i o n Packaqe  the  Le  and  (TEP) c o m p u t e r  A multiple regression of  affective  given  effects  selected below with  with  variable  variables  e q u a t i o n h a v i n q a minimum number  the  largest  of  with  the  selected  are  then  reqression.  selecting  correlation  again  until  no  new  of  dependent v a r i a b l e h a v i n g the variables held constant. scanned  i n  case  any  The of the reduced  b y t h e a d d i t i o n o f t h e new member.  non-significant partials  an  significant partial  v a r i a b l e s have h a d t h e i r p a r t i a l c o r r e l a t i o n  significance  begins  Triangular  proqram.  The p a r t i a l c o r r e l a t i o n i s t h e  of the already  selected  (1977)  a n a l y s i s i s the process  variable  correlation. the  Tenisci  correlations  v a r i a b l e s was d e v e l o p e d by s t e p w i s e  Stepwise regression independent  tested  t h e squared scores of t h e a f f e c t i v e v a r i a b l e s  t h e scores of the achievement  was  each  are  deleted  variables  and  have  the  a  Those process  significant  partial* The difference and  hypothesis between  the  t h a t produced with  usinq  formula  from  that E  2  there  was  no  significant  of the r e s u l t i n g minimal  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 Kerlinger  and  Pedhazur  equation tested  (1973, p.  71)  100  where k^_ e q u a l s t h e number smallest of  B  and k^  2  the l a r q e s t  score analysis,.  were  related  of  student  affective  variables  interactions  their  equations.  affective  scale  of  Achievement among  analyses  i t s three  The  using stepwise  using  The i n t e r a c t i o n  hypothesis  affective regression.  factor.  the  seven  factors. were i n t e r r e l a t e d and model  suggested  several  the f a c t o r  multiple  s c o r e s and  t e r m s were c a l c u l a t e d  variables  in  factor the  variables  score  corresponding  across  of the f a c t o r s  that  to  the score o f each  components,  were p e r f o r m e d  each  the  Motivation  scores as independent  the  by  f o r each o f t h e t h r e e  used  The f a c t o r  to  and summing  would n o t s i g n i f i c a n t l y i n c r e a s e each  variables  were  by m u l t i p l y i n g  the product o f the scores  resulting  the  c o e f f i c i e n t s which  variables  the a f f e c t i v e v a r i a b l e s  interactions.  taking  factors  regression  affective  f o r a given factor  the  regression  the  each  Because because  The  the multiple  were c a l c u l a t e d  on  coefficient  of  of independent  scores c o e f f i c i e n t matrix.  coefficients  scores  e q u a l s t h e number  variables  2  generate a f a c t o r  Factor  independent  E .  factor  each  of  explained was  and u s i n g t h e  the  score  tested,  by  regression interactions variance  of  w i t h p = .01,  101  Cross  Validation Cross v a l i d a t i o n  results  of  comparison In  an  analysis  sample.  The  i d e a l because s p l i t t i n g not  the  process  of  confirming  substantially  B e c a u s e i t was  i t i s often large  difficult  initial  sample  t h e sample i n two  reduce  the  the i n t e n t i o n select  of t h i s  equal  power t o t e s t  t o examine  a number  was  randomly  two  sample,  would be u s e d a s t h e s e t f r o m which t h e b e s t  procedure  would t e n d  sample  random  number  the  solely  models  number was  found.  above  and  model  qenerated  Thus  the  was this  second  All  random was  the  F  = 236)  f o r the n o r m a t i v e sample  F  = 268)  f o r the  cross-validation  subjects  one q r o u p  number,  N's  (Sample sample  f o l l o w n g c o m p a r i s o n s were made between  assiqn  with  a  and a l l above  number was  assigned  The r e s u l t i n g  to  then f o r each c l a s s the  A s e c o n d random  w i t h the median  below, t o t h e o t h e r .  was  normative  t h e s a m p l e s was  were p u t i n t o  .5 t h e s u b j e c t  the  for cross-validation.  number  the other.  sample,  on c h a n c e .  random  subject  number was if  a  below t h e median  were p u t i n t o to  of  p r o c e d u r e used t o s e l e c t  subject  median  number  t o maximize  would be r e s e r v e d The  each  larqe  would  possible  into  a  was  of  divided  If  one, t h e s a m p l e  first  study  the hypotheses.  to  The  second  parts  and  chosen.  the b e s t  sample.  t o get a  models  parts.  the  p e r f o r m e d on one sample t h r o u g h t h e  o f t h e same a n a l y s e s p e r f o r m e d on a s i m i l a r  educational research  similar  is  assigned  I f the second  to one g r o u p  and  were 511  (M =  275,  1) and 522  (M =  254,  (Sample  Sample  2).  1 and Sample  The 2.  102  Cross  V a l i d a t i o n Hypotheses It  was  difference and  was h y p o t h e s i z e d  was no s i g n i f i c a n t matrix  o f t h e males  Sample  1. . T h i s  The  factor  factors  Procrustean second The Sample 2.  t h a t the  correlations  among  and a c h i e v e m e n t v a r i a b l e s would be s i m i l a r was t e s t e d  variance-covariance  the  there  that of the females.  affective  of  that  between t h e v a r i a n c e - c o v a r i a n c e  It  in  hypothesised  found  using the  Box  t o those  for  equal  matrices* a n a l y s i s was r e p e a t e d in  the  initial  u s i n g t h e same number  analysis.  t r a n s f o r m a t i o n was made r o t a t i n g solution  test  the  to the factor  stepwise  regression  &n  the  orthogonal factors  of  space of the f i r s t * analysis  was  repeated f o r  103  Chapter 4 BESULTS INTEODUCTION I n C h a p t e r s 1 a n d 2, indicated  students.  the  literature  was  cited  which  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 m a t h e m a t i c s  achievement  ability  a  of  a  significant  Anxiety,  proportion  enjoyment,  value,  i n m a t h e m a t i c s were i d e n t i f i e d  "block",*  The  Achievement  motivation.  and  as  components  mathematics  self-concept of  the  Motivation  p o s s i b l e i n t e r a c t i o n s among t h e achievement  of  components  model when  of  suggested related  to  A further variable, locus of control  o r a c h i e v e m e n t r e s p o n s i b i l i t y , was s u g g e s t e d by t h e m o d e l . I n C h a p t e r 3 i t was a r g u e d t h a t f o u r (1973)  scales  following of  would  (VALSOC),  and  (SELFCON). Children  Also  the  Sandman  be t h e most a p p r o p r i a t e m e a s u r e s o f t h e  v a r i a b l e s : anxiety o f mathematics  mathematics  of  (ENJOY),  value  self-concept included  of of  were  ( T A S C ) , a more g e n e r a l  (MANX) , 1  mathematics mathematics  the  enjoyment  f o rsociety achievement  Test Anxiety  Scale f o r  measure o f a n x i e t y , t h e  ilhe capitalized terms i n the parentheses 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 t h e t a b l e s .  will  be  Value  used  104  of  Mathematics  experimenter) scale, into  a  two  for  and  for  and  with  "block."  the  checked  for  (IABF).  a list  of  success  o f an  specific  Three achievement  Form  W  Mathematics Canadian  Problem  Test of The  materials  Basic S k i l l s ;  design,  in  showed t h a t  some c l a s s  z e r o and  the  a standard A  construct  second validity  Mathematics achievement was  eliminate  to  TASC from  statistical  from  the  Form 4  (PBOB).  and of  12)  administration  1033  subjects  variance  with  also  two  be  accepted. mean  of  concurrent  and  performed forms  of  with  may  the  using  found  in  three  response.  Scale  A summary o f be  Sandman  the  teacher  Mathematics Anxiety  used  and  one.  further analyses.  procedures  were  a class  a n a l y s i s of the  was  r e t a i n the  the  different  could  TASC i n c o m p a r i s o n  the  of  addition, a preliminary analysis  preliminary  m e a s u r e s and  decided  (Level  were s t a n d a r d i z e d  Scale  Achievement  scales  class  of the  selected;  and  d e v i a t i o n of  Anxiety  Stanford  block"  associated  were  means were s i g n i f i c a n t l y  of  scores  In  students  (CONC)  sample  C h a p t e r 3.  behaviors  and  Mathematics Concepts  procedure a  homogeneity  Therefore,  the  Solving  used w i t h  described  that  (COMP) and  split  (IARS)  "emotional  measures  the  Responsibility  Teachers ranked  typical  by  T h i s s c a l e was  A r i t h m e t i c C o m p u t a t i o n s c a l e from t h e  Test;  and  failure  (developed  Achievement  of Locus of C o n t r o l *  a d e s c r i p t i o n of behaviors  the  (VALSEL)  components; r e s p o n s i b i l i t y  (BANK),  It  Scale  the I n t e l l e c t u a l  measure  responsibility on  Oneself  and  to  hypotheses the  last  105  section  of C h a p t e r In  3.  t h i s c h a p t e r t h e r e s u l t s o f t h e a n a l y s e s and  validation  p e r t a i n i n g t o the h y p o t h e s e s SEX  The affective  of  to sex,  more  differences  may  be  between  interest  the  relationship  than  corresponding differences  s c o r e s c a l e means,  between  A p p e n d i x G.  sexes  was  v a r i a b l e s t o the achievement v a r i a b l e s .  H o w e v e r , t h e raw  in  presented.  DIFFERENCES  focus of t h i s study  d i f f e r e n c e s , due were  are  The  found  cross  correlations means*  deviations may  hypothesis  between the of  found  c o r r e l a t i o n s among t h e v a r i a b l e s f o r  both  i n Winer of  17.  (1971,  falsely  798  from  was  no  matrix  significant differences  was  t e s t e d u s i n g t h e Box  p,  595).  procedure  I n order t o reduce  the  and as  The  F ratio  For The  t h e male  was  p < .10  1.245  and  probability  f o l l o w i n g hypotheses  female  corresponding degrees of  data  was  w i t h degrees of freedom  n u l l h y p o t h e s i s was and  that  outlined  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  277.  F = 1.25.  there  v a r i a n c e - c o v a r i a n c e m a t r i x of the males  s e t a t .10. and  that  the females  and  be  i n Table  females  Because of the redundancy of i n f o r m a t i o n i n the the  the  Therefore,  between  standard  means f o r m a l e s and  of  not r e j e c t e d ,  sets  were  were t e s t e d u s i n g o n l y t h e  freedom  and t h e  pooled pooled  55  and  data the  data.  106 T a b l e 17 Correlations  o f t h e a f f e c t i v e and A c h i e v e m e n t f o r M a l e s and F e m a l e s  Scales  Males COMP  CONC  PBOB  IABS  IABF  MANX  VSOC  SCON  ENJOY  .64 CONC PBOB .66 . 15 IABS -.03 IABF -.40 MANX .19 VALSOC SELFCON .51 .34 ENJOY .12 VALSEL  1.00 -64 . 13 -.07 -.39 ,.19 .54 .26 . 12  1 .00 . 13 1.00 -.12 .20 -.29 -.33 .11 .15 .33 .48 .26 .25 .06 ,19  1.00 -.04 .11 -.05 .02 .07  1.00 -.35 -.68 -.73 -.37  1. 00 .34 :37 . 59  1.00 .56 .34  1.00 .51  1.00 -.33 -.74 -.73 -.38  1, 00 .241.00 .35 .57 .71 .26  Female CONC PBOB IABS IABF MANX VAL SOC SELFCON ENJOY VALSEL  .70 .67 .24 .08 •.43 .23 .44 .30 .24  1.00 .69 . 10 -.02 -.39 .25 ,49 .21 ,19  1.00 .12 .02 -.33 .15 -45 .22 .14  AFFECTIVE  1.00 .37 -.19 .15 .15 .18 .14  1.00 -.06 .11 -.03 .23 . 10  INTEB-SCALE HYPOTHESES  Correlations In  the following  correlations, correlations, correlation correlation. multiple of  multiple  correlations,  squared  multiple  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 .  will  be used to. d e n o t e a Note  correlation  variance  a n a l y s e s r e f e r e n c e w i l l b e made t o  that  when  Pearson  either  by t h e i n d e p e n d e n t v a r i a b l e Correlations  product  moment  the correlation  i s squared the r e s u l t i s the  o f t h e dependent v a r i a b l e  The t e r m  explained or  or  proportion predicted  or variables.  between  each  pair  of  the  affective  107  variables  were  correlations tested  calculated*  The  hypothesis  were n o t s i g n i f i c a n t l y d i f f e r e n t  a t the , 0 1 level*  The r e s u l t s  that  the  zero  was  from  a r e shown  i n Table 1 8 .  Table 1 8 Inter-correlations IARS I A R F  . 2 7 6 * *  MANX VALSOC SELFCON ENJOY VALSEL *p <  IAEF  - . 2 5 1 * *  1 . 0 0 0  - . 7 0 2 * *  . 2 9 6 * *  1 . 0 0 0  . 3 6 0 * *  . 5 6 4 * *  - . 3 7 2 * *  . 6 5 2 * *  . 3 0 7 * *  <  were with  Except  of  t h e IARF  significant IARS  f o r four  different  frcm  of  correlations  Table  . 2 7 6 , the  This  Excepting  the  maximum was . 1 1 6 w i t h  o f t h e IARF c o r r e l a t i o n s ,  a l l others  zero  or  at  1 8 suggests  variables;  variables.  . 5 1 1 * *  with t h e other  (p < . 0 1 ) .  the  * 0 1level  i n 1 7 out of 2 1 c o r r e l a t i o n s  of  1 . 0 0 0  . 0 1  two  not accepted.  the  - . 0 4 3  - . 3 4 1 * *  - . 7 2 8 * *  * * F  ENJOY  1 . 0 0 0  . 1 0 4 *  . 0 7 7 *  correlation  groups  - . 0 0 4  . 1 1 6 * *  variables  Therefore  SELFCON  . 1 6 2 * *  Only  were  VALSOC  . 2 2 0 * *  . 0 5 ;  ENJOY.  MANX  Variables  1 , 0 0 0  . 1 4 3 * * . 2 4 4 * *  o f the Affective  that  t h e n u l l h y p o t h e s i s was t h e r e were a t l e a s t  t h e IABS and IARF p a i r was  born  better.  out  two  and t h e r e s t o f  i n subsequent  factor  analyses. Althouqh study,  net  part  of  the a f f e c t i v e variables  the  were  formal hypotheses correlated  r a n k i n g s o f s t u d e n t s a n d the S t u d e n t - B e h a v i o r that  as t h e absence o f a b e h a v i o r  was coded  with  of the teacher  checklist.  Note  0 and t h e p r e s e n c e  108  1,  positive  ability  correlations  t o accept  correlations summary weak only  i n Table  out o f  direction. different of  expected  ( t h e maximum seven  Of from  expected  responsibility  were  appears  were  was 70  f o r failure  with  the  Although  .23 between  correlations  those  zero  19.  seven,  (p < ; 0 1 ) .  the construct v a l i d i t y  with a n x i e t y and t h e  only  and  negative  other v a r i a b l e s .  the correlations MANX a n d Eandom  were one  in  the  was  were  Answers) unexpected  significantly  The r e s u l t s gave some  of the a f f e c t i v e  The  evidence  variables.  T a b l e 19 C o r r e l a t i o n s between t h e A f f e c t i v e V a r i a b l e s , and t h e S t u d e n t - B e h a v i o r Checklist  Behavior  IAES  IARF  MANX VALSOC SELFCON ENJOY  BANK,  VALSEL  -. 10** .04 .23** -. 13** -.20** - . 1 3 * * -,06 Random Answers - . 2 1 * * - . 1 1 * * -.07 -. 13**-.04 .15** - , 09* Appears Tense -.05 .06* .20** -. 10** -.23** -, 16** -,i06 Expresses Anxiety - . 0 8 * - . 0 7 * -.06 -.10** .02 .09* - . 02 Disruptive Behavior -.22** -.14** -.05 -.06 -.01 .19** -. 09* Expresses Inability 05 -.06 .02 -06 -.04 .02 ,05 Hands Shake .20** - .11** -.17** - . 1 7 * * - . 1 1 * * -,09* .03 States Mathematics Useless .04 03 - . 0 9 * -.03 .00 -.05 .03 Refuses t o Answer -.22** -.16** -.07 - . 1 1 * * .03 .16** - . 05 Fidgets More .16** .09* .07 -.03 - .29** , 18** .35** RANK *p < , 0 5 ; **p < .01  109  Factor  Analysis A  principal  variables  was  eigen-values: 0.210.  component  performed  analysis  of  the  affective  which g e n e r a t e d t h e f o l l o w i n g s e t o f  3.068, 1.206, 1,077, 0.683,  See t h e g r a p h b e l o w f o r t h e p l o t  0.446, of the  0.310,  and  eigen-values.  "Scree" of the Eigen-Values from t h e P r i n c i p a l Component A n a l y s i s o f t h e A f f e c t i v e V a r i a b l e s  3  Eigen-  2  Values  1  1  It  was c l e a r f r o m  retained  of  the  according  Kaiser-Guttman greater  2  than  factors  graph  4 Factors  that  since there  I t should  predicted  by  5  three  t o the "scree" t e s t .  criterion,  1.0.  3  be n o t e d  6  factors This  t h e Achievement  should  be  agreed with t h e  were t h r e e that t h i s  7  eigen-values was t h e number  Motivation  theory*  110  The  three  factors  affective further  variables.  f o r 76% o f  This  was  the  variance  considered  of the  acceptable  for  analysis. In o r d e r  three  accounted  factors  procedure.  to a i d the interpretation  were The  orthogonally factor  rotated  o f t h e f a c t o r s , the using  the  l o a d i n g s a r e shown i n T a b l e  varimax 20. The  T a b l e 20 F a c t o r l o a d i n g s o f t h e a f f e c t i v e V a r i a b l e s on t h e O r 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 F a c t o r s Factor  three the the of  1  IABS IABF MANX VALSOC SELFCON ENJOY VALSEL  .3206 -.1441 -.8927 .1695 .8672 .7603 .2589  factors  were r e a d i l y  highest  loadings  were a r t i f a c t s from was  (ABF).  Factor  called 3  because o f t h e h i g h With  IABS l o a d e d  Factor 3  .7372 ,8427 -.0554 .0662 .0130 .1290 .0544  -.0252 .1358 -.1992 .8794 ,1096 .3621 .8657  interpretable-  Factor  (MF) .  1,  Note t h a t t h e n e g a t i v e  of the s c o r i n g .  Factor  2  t h e two I n t e l l e c t u a l A c h i e v e m e n t  scales,  Scales.  2  having  l o a d i n g s f r o m MANX, SELFCON and ENJOY, was c a l l e d  Motivational Factor MANX  Factor  the was  Achievement  identified  loadings  respect  from  loadings  having  Eesponsibility  Eesponsibility  as  high  Factor  t h e V a l u e F a c t o r (VF)  the  VALSOC  to the hypothesized  .321 on F a c t o r 1 and ENJOY l o a d e d  simple .362  and  VALSEL  structure, on  Factor  111  2.  However, i n t h e l i g h t  main  components,  complexities  o f t h e much s t r o n g e r  the  structure  that occurred  may  requirement of orthogonality Cattell  (1966)  says  be  (p.  186).  theory  but  a  result  on  a  The  of  present  i n Chapter  factor  the  study.  structure are to  a n a l y s i s d i d not support the 1 which  of Achievement M o t i v a t i o n .  loaded  defined.  and s i m p l e  was e x p e c t e d IARS a n d I A E F d i d n o t l o a d factor  of the  r a r e c a s e s do f a c t o r s h a p p e n This  f a c t o r s t r u c t u r e hypothesized the  been  "orthogonality  Only i n very  from  have  well  maintained i n t h i s  contradictions. orthogonal"  was  loadings  on  of t h e i r  was  derived  Contrary  t o what  the  motivational  own.  In addition  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 o f i t s own  loaded  with  MANX a n d ENJOY, The  c o r r e l a t i o n s among t h e 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)  analysis  of  the items of f o u r of t h e a f f e c t i v e scales  known t h a t t h e s c a l e s a r e n o t p e r f e c t r e p r e s e n t a t i o n s constructs.  The  interpretation by  definition  correlation  orthogonal  of  the various  orthogonal  rotation,  then,  are  i t was  of their  allowed  components o f v a r i a n c e  factors  factor  independent  an  because  and  have  zero. AFFECTIVE-ACHIEVEMENT RELATIONSHIPS  Correlations To non-linear  test  the  hypotheses  that  r e l a t i o n s between each o f t h e  there  were l i n e a r a n d  affective  variables  112  and  t h e achievement  variables,  orthogonal  polynomials  d e g r e e 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 d e g r e e  were  with  s i g n i f i c a n t l y correlated  therefore  only  considered.  the f i r s t  terms  t h e achievement s c o r e s and  second  degree  terms  were  Of t h e s e c o n d d e g r e e t e r m s two c o r r e l a t i o n s  m a r g i n a l , MANX w i t h significant  at  PBOB and VALSOC w i t h  t h e ,*01 l e v e l .  a t most .097 t h e p r o p o r t i o n 0.94%.  and  of  COMP, a n d  Further,  with  none  were were  correlations of  o f e x p l a i n e d v a r i a n c e was a t  The s e c o n d d e g r e e t e r m s were n o t r e t a i n e d  most  for further  analysis. In  17 o f  hypothesis for  was  the  21  first  degree  n o t a c c e p t e d a t t h e .01 l e v e l .  a summary o f t h e c o r r e l a t i o n s  second  degree  achievement  relations  terms  of  of  linear  the affective  the  ,.01  level  or  better.  None  of  i nthe analysis.  with the  t h e IABF  variable.  Thus i t was r e t a i n e d  linear  However, t h e  The t h e o r e t i c a l i m p o r t a n c e  of 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 a s a  t o test possible  t h e other a f f e c t i v e variables i n p r e d i c t i n g  Regression  orthogonal  were s i g n i f i c a n t  were s i g n i f i c a n t a t t h e .01 l e v e l .  I A B F was r e t a i n e d  moderator  interactions achievement.  Analysis  A series of regression first  and  variables*  correlations  with  null  See T a b l e 21  variables  T h r e e o f t h e IABS l i n e a r c o r r e l a t i o n s at  the  model  to  be t e s t e d  a n a l y s e s were  was t h a t  performed.  of simple l i n e a r  The  multiple  113 Table 21 C o r r e l a t i o n s o f t h e F i r s t and Second Degree Terms o f Orthogonal Polynomials of the Affective Variables with t h e Three Achievement Variables COMP V a r i a b l e and De g r e e  Batio  F Prob  F  r  PBOB  CONC  r  F Batio  F Prob  F F B a t i o Prob  r  1 .190 2 -.006  19.1 .021  .000 .856  .121 .203  7.57 .269  .006 ,611  IABF  1 .030 2 -.003  .451 .005  .560 .901  -.049 .002  1.24 .002  .265 ,919  - . 0 5 4 1. 48 . 2 2 2 .03 9 .791 .378  MANX  1 -.410 2 .049  103. 1.23  ,000 .267  -.387 .069  89.7 2.40  ,000 .117  - .331 .088  VALSOC  1 . 194 2 .097  19.9 ;000 4 . 7 9 .. 0 2 8  .222 .079  26.3 .317  .000 .072  SELFCON  1 .457 2 .075  135, 2.87  .000 .087  .518 .006  ENJOY  1 .320 2 .083  58.1 3.51  .000 i059  VALSEL  1 . 157 2 .034  12.9 5.97  .001 ,446  F o r each  regression. affective multiple  scales;  correlations. of  in  parentheses.  and  PBOB w e r e : . 4 8 3  respectively. variables the It  The  would  187. -000 .016 .868  .462 .028  .000 .533  .236 .03 9  30.4 .777  , 241 3 1 . 5 . 0 0 0 . 0 6 0 1.87 . 1 6 9  . 151 .017  11.8 .001 . 153 , 6 9 7  as  the  s h o u l d be n o t e d  .537  (.233),  4.57 -542  .031 .469  variables  all  the  variables.  The  independent  hypothesis  null  that t h i s  (.288),  138. ,403  .094 .033  the a f f e c t i v e v a r i a b l e s  variables  between  ,000 .382  s q u a r e d im u l t i p l e  n o t account f o r a  achievement  correlations  .005 . 171  used with  62.6 .000 3. 94 . 0 4 5  *124 7 . 9 6 .060 1.85  o f the achievement  were  . 128 8 . 5 1 *025 . 3 2 9  .004 .574  I ABS  correlations  w i t h COMP, CONC,  and  that  significant  .468 the  affective  proportion  was n o t a c c e p t e d a t t h e ,. 0 1 i s not a large  SELFCON  and  the  ( . 219)  level.  i n c r e a s e over  achievement  of  the  variables  114  (.457, . 5 1 8 , . 4 6 2 ) . A s e r i e s o f s t e p w i s e a n a l y s e s was p e r f o r m e d a  minimal  sub-set of a f f e c t i v e  the achievement s c o r e s . variables  were  added  The c r i t e r i o n to  one  The  affective  was  would  s e t so  select predict  that  no  the regression equation unless t h e  i n c r e a s e i n v a r i a n c e accounted level.  v a r i a b l e s which  to  f o r was s i g n i f i c a n t a t t h e .01  v a r i a b l e s SELFCON and MANX  e g u a t i o n a n d o n l y SELFCON i n t h e o t h e r s .  The  appeared-in summary  of  t h e a n a l y s e s a p p e a r s i n T a b l e 22.  T a b l e 22 Summary o f t h e S t e p w i s e 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 Variables  Independent Partial Variables Correlations  1  F Ratio  F Squared M u l t i p l e Prob C o r r e l a t i o n s  2  COMP  SELFCON MANX  .457 -.140  37.2 .000 10.2 . 0 0 2  .225  CONC  SELFCON  .518  187. 0 0 0  .268  PROB  SELFCON  .462  138. *000  .213  A  *This i s the p a r t i a l prior t o entry i n the equation. V a r i a b l e s a r e i n t h e order o f e n t r y f o r each equation F R a t i o s and F Probs a r e those a s s o c i a t e d with t h e Beta c o e f f i c i e n t s of thef i n a l eguation.  2  In comparison  w i t h t h e maximal e q u a t i o n s t h e l o s s  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 ; the  Kerlinger  and  Pedhazur  a maximum o f 2.08%.  eguation  (1973,  Usinq  71)  this  d i f f e r e n c e was s i g n i f i c a n t a t t h e .05 l e v e l b u t n o t 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 n o t r e j e c t e d .  p.  of  115  It to  the  would a p p e a r t h a t  prediction  students  of  the  MANX and SELFCON c o n t r i b u t e achievement  may have been r e s p o n d i n g  influenced  by  mathematics.  how t h e y  In other  dimensional.  Thus  have r e s u l t e d from  However,  t o t h e i t e m s on t h o s e  responded  words,  scores.  to other  stimuli  the scales  the equations  may  most  scales  related to  n o t be u n i -  o u t l i n e d above c o u l d  MANX and SELFCON  accounting  for  well  variance  common t o o t h e r v a r i a b l e s .  Factor  Analysis By  correlating  achievement  variables  identification contribution developing three  the  of  through  independent  This  effects  identified  The generate for the  rotated  student  classes  achievement  statistical  way  the  of  As t h e  component  analysis  factors  of the  three  the hypothesized  inter-raction  p r i n c i p a l component f a c t o r s were  raw  standardization  matrix.  Factor  from the s t a n d a r d i z e d  weights i n T a b l e  within  the  be t e s t e d .  a f a c t o r score  each  a  i n the p r i n c i p a l  model,  the  regression  measures t o a i d i n t e r p r e t a t i o n .  Motivation  could  with  o r f a c t o r making t h e maximal was  c o u l d be i n t e r p r e t e d i n terms o f Achievement  factors  multiple  the construct  was a c h i e v e d .  factors  orthogonal  as  23.  The s c o r e s  was  done i n i t i a l l y  scores. was  I t  done u s i n g  to  were c a l c u l a t e d  affective  were  should only  scores  used  again  scores  using  standardized  f o r t h e a f f e c t i v e and be  noted  that  t h e s u b j e c t s from  the Sample  116 T a b l e 23 Factor Score  Coefficient  Factor 1  Factor 2  Factor 3  .1267 -.1736 -.4224 -.1490 .4357 .3024 -.0965  .5801 .6852 .0354 -.0339 -.0604 -.0199 -.0487  -. 1679 *0652 .0980 .5923 -. 1531 .0503 . 5594  IARS IARF MANX VALSOC SELFCON ENJOY VALSEL 1.  The c o r r e l a t i o n  scores  i s shown  correlations  matrix of f a c t o r i n Table  24.  Matrix  scores I t can  and be  achievement  seen t h a t t h e  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  zero.  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 A c h i e v e m e n t S c o r e s 1  COMP CONC PSOB MF ARF VF  COMP  CONC  PROB  1.00 .66** .67** .43** .07 .09*  1.00 .66** . 44** -.04 .08  1.00 .40** -.02 ,01  MF  ARF  1.00 .00 .01  1.00 .0 1  VF  *p <".05 **p < .01 *As t h e t h r e e factor scores are virtually orthogonal 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 with t h e achievement scores a r e qood estimates o f the proportion of variance a c c o u n t e d by a n y 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 the  order t o e s t a b l i s h the proportion  achievement v a r i a b l e s accounted  regression equations independent  were q e n e r a t e d  variables.  were a s f o l l o w s w i t h  of  variance  f o r by t h e t h r e e  variance  factors,  with the three f a c t o r s  The p r o p o r t i o n s o f e x p l a i n e d accounted  f o r by  of  as  variance  the  seven  117  affective .196  v a r i a b l e s shown i n p a r e n t h e s e s f o r c o m p a r i s o n : COMP,  (.233);  eguations are proportion as  .202(.288);  shown  in  of  a reduction  three  CONC,  explained  25.  Table  variance  accounted  seven  a f f e c t i v e measures.  could  have been e r r o r  reduction  was n o t o f g r e a t  I t should  be  noted  due t o s c a l e  The  i n the  importance  because  76% o f t h e v a r i a n c e  f o r only  variance  The  24% was e x p e c t e d  of approximately  factors  and PROB, . 1 6 2 ( . 2 1 9 ) .  the  ofthe  t h e 24%  that  reliabilities  less  than 1 . 0 0 . Table 25 R e g r e s s i o n E g u a t i o n s o f t h e Three F a c t o r Scores P r e d i c t i n g t h e Three a c h i e v e m e n t S c o r e s Dependent Independent R e g r e s s i o n We i g h t s Variable Variable  Squared M u l t i p F Correlations Prob  F Ratio  COMP  MF ARF vr  .4359 .0722 .0889  115. 3 . 17 4.80  .000 .072 .027  .196  CONC  MF ARF VF  .4427 -.0350 .0745  123. .756 3.43  .000 .389 ,061  ,20 2  PROB  MF ARF VF  .4153 -.0225 .0071  97.3 .286 .029  .000 .60 0 .842  ,*162  The  next h y p o t h e s i s  be no s i g n i f i c a n t predicting scores  interactions of  the achievement  were combined  were c a l c u l a t e d ;  t o be t e s t e d the  variables.  multiplicatively.  was t h a t  affective To t h i s Four  there  would  factors  in  end t h e f a c t o r  additional  MF x A £ F , MF x VF, ARF x VF, a n d MF x  scores ARF  x  118  VF*  These  additional  factor scores criterion  i n a stepwise  f o r addition  increase i n explained hypothesis included.  scores  1  not  were  used  r e g r e s s i o n procedure.  to  the equation  variance a t the  rejected;  See T a b l e 26  together  .01  was  with the  Again  the  a signficant  level,;  The  null  T h a t i s no i n t e r a c t i o n t e r m s were  f o r the  summary  of  the  analyses.  T a b l e 26 Summary o f S t e p w i s e A n a l y s e s U s i n g F a c t o r S c o r e s and Factor Score i n t e r a c t i o n s as Independent V a r i a b l e s Dependent I n d e p e n d e n t Partial Variable Variable Correlations  1  F Batio  2  F Squared M u l t i p l e Prob Correlations  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 sthe p a r t i a l prior t o entry i n the equation. 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 . 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  2  c o e f f i c i e n t s of the f i n a l Clearly was  the construct  t h e most i m p o r t a n t  equation.  underlying  p r e d i c t o r o f achievement.  did not account f o r a greater  proportion of  a c h i e v e m e n t t h a n d i d SELFCON a l o n e . that  using  the  t h e M o t i v a t i o n F a c t o r (MF)  principal  MF, h o w e v e r ,  the variance  of  I n d e e d i t c o u l d be a r g u e d  o f p a r s i m o n y SELFCON was t h e o n l y  For i n t e r e s t guadratic functions of the f a c t o r scores were calculated and also used interactively i n predictinq achievement. T h i s was o f i n t e r e s t because t h e Achievement Motivation model predicted a quadratic interaction of p r o b a b i l i t y o f success with motivation t o succeed. However, n o n e o f t h e q u a d r a t i c o r i n t e r a c t i v e t e r m s were s i q n i f i c a n t l y r e l a t e d t o achievement. 1  119  explanatory  v a r i a b l e necessary.  will  i n Chapter  appear  More d i s c u s s i o n on  this  point  5.  CROSS VALIDATION  second sample  The  cross validation  of  two  as d e s c r i b e d  composed  of 522 The  first and the  samples  cross  randomly  at t h e  students,  analyses  end 254  male and  validation  equivalence samples. factor  the  o f the  scales of t h e The  performinq  third  a n a l y s i s with a  s t e p was three  to  factor  subject  v a r i a b l e s to stepwise  were  compared  1.177  with not  male and using  degrees  female  t h e Box  of f r e e d o m  significant  f i n d i n g s o f no analysis.  of  the  second s t e p  was  affective  and  of the  overall matrices  test of  second  sample  f o u r t h step  regression  of  the  followed  The  male  the two to  by  an  was  to  analysis.  of C o r r e l a t i o n s  When t h e  was  The  solution  Procrustes transformation.  Equivalence  The  female.  s u b j e c t the  orthogonal the  in several steps.  an  variance-covariance  initial was  equivalence  intercorrelations  and  The  the  sample  268  proceded  on  from the  3.  variance-covariance matrices.  calculation  achievement  performed  selected  of Chapter  step consisted of t e s t i n g female  were  at  significant  the sex  variance-covariance  test,  the  resulting  55 and  868  095.  .10  level.  differences  The  matrices  F ratio  difference  T h i s confirmed from  was  the  the  initial  120  The variables to  correlations  of  a r e shown i n T a b l e  those  i n Tables  of equivalence  the affective  27.  and achievement  The r e s u l t s may be  18 a n d 20 f o r Sample 1*  of the variance-covariance  compared  The o v e r a l l  test  matrices resulted i n  an F r a t i o o f 0*987 w i t h d e g r e e s o f f r e e d o m 5 5 a n d  3 429 4 3 0 .  T h i s was n o t s i g n i f i c a n t a t t h e .10 l e v e l . T a b l e 27 Correlations COMP .64 CCNC PEOB .65 IAES . 12 I A E F -.01 MANX -.43 VSOC . 17 SCON .44 ENJOY .32 . 18 VSEL  Factor  o f t h e A f f e c t i v e and Achievement S c a l e s o f Sample 2  CONC  PEOB  IABS  IAEF  ,67 .06 -.01 -.40 .27 .47 .30 .23  .08 -.07 -.38 .21 . 44 .29 .20  .25 -.24 .18 .27 .22 .17  .03 .07 -.09 .03 . 11  MANX  -,38 -.72 -.72 -.37  VSOC  SCON  ENJOY  ,37 .45 .69  Analysis The  next  component  analysis  structure  appeared.  the a n a l y s e s A  step with  was  to  a three f a c t o r  The f a c t o r  solution . 1  The same  loadings of the r e s u l t s  from  o f both samples a r e i n Table 28.  t e s t of the s t a b i l i t y  an o r t h o g o n a l  s u b j e c t t h e second sample t o  Procrustean  of the factors  transformation  * The e i g e n - v a l u e s a n d s c r e e c o r r e s p o n d e d the i n i t i a l sample.  was made u s i n g  (Hackstian  & Bay,  c l o s e l y t o those  of  121 T a b l e 28 Factor  Leadings from t h e Analyses  Variable IARS IARF MANX VALSOC SELFCON ENJOY VALSEL  1973).  1  Factor 2  Factor 3  S1 *  S2  S1  S1  to  S2  .737 .745 .843 .822 - . 0 5 5 -,.032 .066 .057 .013 .016 .129 .064 .054 .085  S2  -.025 -.037 .136 .165 -. 199 - . 2 2 3 .879 .858 .110 .129 .362 .408 .866 .891  S2 = s a m p l e 2.  This transformation  procedure matrix  Factor  .321 .373 -.144 -.215 - . 8 9 3 -.883 .170 .257 .867 .870 .760 .729 .259 .195  *S1 = s a m p l e 1;  o f Sample 1 a n d Sample 2  rotate  a  uses a l e a s t squares  qiven  of factor loadings.  approximation  factor solution to a "target"  I n t h i s c a s e t h e t a r g e t m a t r i x was  the  s e t of f a c t o r loadings c a l c u l a t e d with t h e f i r s t  As  there  sample.  was no t e s t o f g o o d n e s s — o f - f i t f o r t h e a l g o r i t h m t h e  error matrix  a p p e a r s i n T a 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 Procrustean Factors t o a Target Matrix Factor IARS IARF MANX VALSOC SELFCON ENJOY VALSEL greater the  .046 -.075 .006 .102 .005 -.026 -.049  Factor  2  .011 -.021 .015 -.001 .011 -.056 .039  factor 3 -.023 .025 -.008 -.025 .004 *032 .021  t h a n .05 a n d a s t h e s o l u t i o n a c c o u n t e d  variance  solution  1  R o t a t i o n o f t h e Sample 2 o f Sample 1 L o a d i n g s  was  of  t h e seven  considered  to  affective be  f o r 76.4% o f  variables the f a c t o r  adequate.  These  results  122  indicate a stable factor Regression  space.  Analysis  Tie  fourth  step  e q u a t i o n f o r S a m p l e 2.  was t o g e n e r a t e a s t e p w i s e The r e s u l t s a r e d i s p l a y e d  regression  i n T a b l e 30.  T a b l e 30 Summary o f S t e p w i s e A n a l y s i s U s i n g Sample 2 S t a n d a r d i z e d Scores as Independent V a r i a b l e s ——— — ——  ——  Dependent Variables  —  — — — —  —  —  Independent Partial Variables Correlations  1  ——T  F Ratio  2  —  —  —  ——  —  F Squared M u l t i p l e Prob Correlations  COMP  SELFCON MANX  .436 -.177  16.74 22.82  .000 .000  .215  CONC  SELFCON VALSOC  .468 .113  107. 6.76  .000 *009  .229  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 before the variable entered the equation. Variables a r e l i s t e d i n the order they entered the equation* 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 o f t h e f i n a l equation.  2  In  comparison  with  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 c a s e  similar  e x c e p t f o r CONC w h i c h h a d a 3.9% d i f f e r e n c e .  regression could  of explained  CONC  entered.  was n o t e d b e f o r e ,  proportions  of  VALSOC  as  The  t h e r e s u l t s o f Sample 1 t h e o n l y  t h e number o f t e s t s  a n a l y s i s i s guite large.  of  variance  where were  However,  significance i n  Thus t h e n o t e d  difference  b a v e 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 with t h e seven a f f e c t i v e  variables included  i n t h e e q u a t i o n were . 2 1 9 ,  , 2 4 5 a n d .207  123  the  reduction o f explained variance  was .01  a t most 1.6%.  with the stepwise  solution  T h i s d i f f e r e n c e was n o t s i g n i f i c a n t  at t h e  level. The c r o s s v a l i d a t i o n  analysis sustained  virtually a l l  f i n d i n g s of t h e i n i t i a l a n a l y s i s . SUMMARY The rejected  equality  and t h e d a t a The a n a l y s e s  exception  of  of  correlations  were p o o l e d  b e t w e e n s e x e s was n o t  f o r a l l subsequent  analyses.  i n d i c a t e d the "block" variables, with the  IABS  and  IARF  were  inter-related.  c o r r e l a t i o n s , w i t h IARS a n d IARF e x c l u d e d ,  The  r a n q e d f r o m .296 t o  .728. The "block"  teacher  variables.  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 t h e SELFCON, ENJOY  and  MANX  were  the  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 w i t h i n d i v i d u a l Student-Behaviors  a n d .35 w i t h RANK; ENJOY, -.02 t o  -.17 a n d . 1 6 ; MANX, .04 t o *23 a n d - . 2 9 . support  the construct v a l i d i t y It  was  also  w i t h IARF e x c l u d e d ,  of theaffective variables.  shown t h a t t h e " b l o c k "  variables;  .094  significant  non-linear  correlations;  to  .518.  There  were  no  t h e maximums were MANX  (.088) a n d VALSOC w i t h COMP (.097).  The r e l a t i o n s h i p s b e t w e e n t h e the  v a r i a b l e s , again  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  w i t h PROB  These d a t a t e n d e d t o  achievement  variables  were  "block"  variables  examined u s i n g  and  m u l t i p l e and  124  stepwise  regression.  The  CONC and EBOE were .483, regression  revealed  the  explained  the  only  To interpreted analysis factors seven  of the achievement  i f t h e seven  in a  more  followed accounting  simple  by  Factor  strong  loadings  MANX;  a  Factor  (VF)  VALSEL;  Value  variables.  could  manner,  principal  component  rotation variance  from  with  from  I A E S a n d IABF.  revealed of  suggested  loadings  .36  on VF and I A E S l o a d e d  AEF  and VF f a c t o r  were  calculated  those  factor  proportion expectations  of of  showed t h a t  explained the  MF  accounted  variance.  f o r the  terms using major  to  the  model  no  s u s t a i n e d t h e f i n d i n g s above  with  Achievement  Contrary Motivation  The  cross  validation  variance-covariance  with  loaded  Stepwise r e g r e s s i o n  were i n c l u d e d i n t h e e q u a t i o n s .  the  (AEF)  Interaction  terms  There  and  VALSOC and  ENJOY  interaction  minor e x c e p t i o n s .  Motivation  were used t o c a l c u l a t e MF,  f o r each s u b j e c t .  multiplicatively.  scores  initial  .3 2 on MF.  coefficients  scores  three  ENJOY,  from  be  The f a c t o r s were i n t e r p r e t a b l e  showed a w e l l d e f i n e d s t r u c t u r e even though  score  a  Factor  and  Factor  the  SELFCON,  and an A c h i e v e m e n t E e s p o n s i b i l i t y  loadings  MANX,  variables  loadings  (MF) w i t h  Stepwise  "block"  the  Factor  COMP,  d i d so once.  orthogonal  f o r 76% o f  variables.  with  was t h e major c o n t r i b u t o r t o  variable t o enter,  see  correlations  -537 and .468 r e s p e c t i v e l y .  t h a t SELFCON  variance  other  multiple  was no s i g n i f i c a n t matrices  d i f f e r e n c e between  o f t h e sexes,  n o r was t h e r e a  125  significant  difference  between  m a t r i c e s of the two samples.  the  This  was  variance-covariance tested  at  the  10%  level. Factor  analysis  of  the  change i n the f a c t o r s t r u c t u r e . Sample  2  factors  to  the  second sample showed Procrustean r o t a t i o n  loadings  o f the r o t a t e d  of  affective  variables.  This  the  Sample 1  f a c t o r s , accounted f o r 76.4% of the o r i g i n a l v a r i a n c e seven  little  suggested a s t a b l e  of  the  factor  structure. Stepwise r e g r e s s i o n showed l i t t l e 20%.  The  variables.  differences  analysis  analysis  i n explained  showed  of  the  variance:  consistency  second  sample  approximately  i n the i n c l u s i o n of  126  Chapter  DISCUSSION AND  5  CONCLUSIONS  INTRODUCTION I n C h a p t e r s 1 and 2, i t was literature  which  mathematics  students appeared to  inhibiting  their  enjoyment,  value,  identified  A  of  an  in  self^concept  used  variable,  responsibility,  was  Chapter  s c a l e s would  following  have  to  was  a  proportion  of  "emotional  mathematics. of  in  suggest  locus  s u g g e s t e d by t h e 3  i t was  mathematics The  possible  (ENJOY),  Achievement  (VALSOC),  and  self-concept  (SELFCON).  A preliminary  or  argued t h a t f o u r  of of  motivation* academic  model.  o f mathematics  value  were  interactions  control  be t h e most a p p r o p r i a t e  v a r i a b l e s : anxiety  mathematics  of  block" Anxiety,  components when r e l a t e d t o a c h i e v e m e n t  further  (1973)  and  there  a significant  achievement  M o d e l was  the  In  that  that  a s t h e components of the " b l o c k " .  Motivation among  indicated  shown  o f t h e Sandman  measures (MANX) , 1  mathematics  for  mathematics  analysis, described  ilhe c a p i t a l i z e d terms i n the parentheses w i l l following discussion.  in  of  the  enjoyment society  achievement Chapter  3,  be used i n t h e  127  confirmed than  that  the  Test  mathematics Oneself  Anxiety  Scale  of  for  on  "emotional  the  In a d d i t i o n , a  a  Two  block"  (BANK),  Problem  Test of The  materials  C h a p t e r 3. class  homogeneity the e f f e c t s analyses, of zero;  In  were  class  the scores  analyses In  experimenter.  S c a l e was  and  sample of  parts:  typical list  of an  specific  developed  by  were s e l e c t e d ;  Concepts  ( L e v e l 12)  of  of  were a l s o  for  a ranking  from t h e S t a n f o r d  Form  two  as  responsibility  check  Scales  The  selected  response,  Mathematics  procedure,  class  standard  a  of  Achievement (CONC)  and  (PBOB) f r o m  the  4,. test  1033  a d m i n i s t r a t i o n of subjects  were  the  described  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  means  of  the  Solving  with a  of  the  and  valid  measure  T h i s s c a l e had  "block"  Scale  a  more  o f Mathematics f o r  behaviors  and  Basic S k i l l s :  design, used  as  T h r e e a c h i e v e m e n t measures  Mathematics  some  of  a s s o c i a t e d with the  A r i t h m e t i c Computation  Canadian  by  (IABF)  description  (COMP) and  the  developed  s c a l e was  Value  forms o f t e a c h e r  T e s t : Form W  in  was  success  experimenter.  the  Children  for  L o c u s of C o n t r o l .  (IABF).  behaviors  Scale  Achievement E e s p o n s i b i l i t y  responsibility  students  Anxiety  (VALSEL)  measure  failure  Mathematics  anxiety.  Intellectual the  the  significantly variance  c o u l d be  differences in  d e v i a t i o n of one).  Chapter  4  that  To  remove  correlational  w i t h i n each c l a s s A l l scale scores  4 were s t a n d a r d i z e d the  and  accepted.  subseguent  were s t a n d a r d i z e d  of Chapter  different  hypothesis  of  (mean  used i n  i n t h i s manner,* equality  of  the  128  c o r r e l a t i o n s b e t w e e n s e x e s was n o t r e j e c t e d pooled f o r a l l subsequent analyses. the  exception  of  inter-related. scales  that  the  The c o r r e l a t i o n s  the "blcck"  Squared variables  with  explained  multiple  with  variables teacher  the stepwise Factor  t o the explained  response  of  the  structure  The  among  were  e q u a t i o n s and .213 a n d  .268  of  the  (AEF) and  the  Value  regression the  same  seven  Motivation (VF).  showed MF  I t s h o u l d be n o t e d  the of  in  The  However, t h e f a c t o r s to that  factor.  finding the  The f a c t o r s t r u c t u r e  selected  as  Regression analysis  correlations  factors  initial  were i n t e r p r e t e d  supported  stepwise  sample t y p i c a l l y  showed SELFCON  variance  was t h e m a j o r c o m p o n e n t o f t h i s  achievement v a r i a b l e s . stable.  increases  correlations  was n o t o b s e r v e d .  Cross v a l i d a t i o n differences  modest  the  m a j o r e x p l a n a t o r y component*  self-concept  affective  of  variance  three factors  were c l e a r l y i n t e r p r e t a b l e . the  tending  the  revealed three interpretable  Achievement R e s p o n s i b i l i t y  postulated  showed  The s q u a r e d m u l t i p l e  analysis  The  were  equations.  a c c o u n t i n g f o r 76% variables.  of  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  b e t w e e n .219 and .288 f o r t h e f u l l  be  the  correlations  achievement v a r i a b l e s  achievement v a r i a b l e s .  (MF),  "block"  with  variables.  t o be t h e m a j o r c o n t r i b u t o r  for  were  The a n a l y s e s showed,  were low b u t 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  to validate  of  IARP,  and t h e d a t a  of  no  sex  affective  and  was shown  the  variables  cross as  to  be  validation done  with  129  Sample  1.  The o n l y  a n a l y s i s was t h a t CONC.  d i f f e r e n c e found i n the c r o s s  VALSOC was  The p r o p o r t i o n  variables  was  included  of explained  consistently  validation  i n t h e . equation  variance  between  for  o f the achievement  19% a n d 2 3 % ; s i m i l a r t o  t h a t i n Sample 1. In t h i s chapter d i s c u s s i o n three  areas:  the  intercorrelations analysis;  and  of  the  lack the  of r e s u l t s w i l l  of  sex  "block"  multiple  and  centre  differences;  variables stepwise  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 achievement and  variables.  future research  L i m i t a t i o n s of the study,  will  a l s o be  SEX When t h e i s s u e raised  i t i s often  girls  or vice  was c o n s i d e r e d  of  here  with  the  conclusions  in  mathematics  i n terms o f average performance. the  average,  are asked.  was o f  is  That i s  perform  Although t h i s  p a r e n t h e t i c a l l y i n t h i s study  another aspect of sex d i f f e r e n c e guestion  of the  discussed.  of s e x d i f f e r e n c e s  versa?"  factor  DIFFEEENCES  q u e s t i o n s s u c h a s "Do b o y s , on than  the  and  analyses  on  better approach  (see Appendix 6 ) ,  more  interest.  The  was, " I s t h e r e l a t i o n s h i p b e t w e e n a g i v e n  pair  v a r i a b l e s t h e same f o r b o y s a s f o r g i r l s ? " A  matrices level. findings  test  of  equivalence  of  the  showed no o v e r a l l d i f f e r e n c e s This of  could sex  cast related  some  light  differences  variance-covariance  s i g n i f i c a n t a t t h e 10% on in  the  inconsistent  correlations  of  130  affective  variables  univariate  found  comparisons  i n the l i t e r a t u r e , were  made.  particularly  i f  F o r example, i t c o u l d  that items  worded  may  more i n f o r m a t i o n a s s o c i a t e d w i t h v a l u e f o r t h e b o y s  elicit  than  they  the  correlation  be  t o t a p i n f o r m a t i o n a s s o c i a t e d with  be  would f r o m  different  the  differences  reason  f o r choosing  ignored  two  alter  However, i f v a l u e  disappear.  i s n o t t o say future  sexes,  achievement  that  sex  research.  It  and  whether  differences should  in a  i n a different  block"  pedagogical  literature  as b e i n g  and  self,  out  in  that  provided  a  student  was  separate another  the  different  was  manner  for  changes, i n t u r n ,  VARIABLES  worth  situations. in  be  determined i f  in  a s s o c i a t e d with high  responsibility  could,  should  characterized  enjoyment,  achievement  anxiety  of  low  unwillingness t o accept success  items  manner,  "emotional  m a t h e m a t i c s , low v a l u e  be  o r not those  The  society  a  T h i s c o u l d be  INTERRELATIONS OF THE "BLOCK"  in  in  may  achievement.  c h a n g e s i n v a l u e change enjoyment the  find  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 o f  s c a l e s with  in  for girls.  may  may  mathematics achievement  i n c l u d e d within the s c a l e or  scale  That  Thus o t h e r s t u d i e s  o f enjoyment with  f o r boys t h a n  are s p e c i f i c a l l y  affective  the g i r l s .  enjoyment  fact,  motivated  of  the  anxiety  mathematics  to  low s e l f - c o n c e p t , and an for either Other  literature  facilitate to  failure  achieve  or  pointed  achievement or had h i g h  131  intelligence*  Therefore,  variables  would  be  different  dimensions.  i t  was  hypothesized  c o r r e l a t e d and In  that  y e t show t h a t t h e y  general  this  the tapped  hypothesis  was  accepted. It  should  Motivation, an  be  r e c a l l e d that the  o u t l i n e d i n C h a p t e r 2, h e l d  individual  was  determined  b e h a v i o r would l e a d to v a r i o u s those  outcomes,  behave i n the student class  would not  way.  might  t h a t the  Atkinson  by and  Atkinson Raynor  r e s u l t a n t tendency Tr = where the  (Ms  the  - Maf)  motivation  (Ms  an  The  inverse  equation  that  also  achievement**  - Maf)  The  Motivation and  Feather  that  a  mathematics marks  were  result  model, (1966),  part eguation  of  of  as and a  which i s x Ps x  (1 - Ps) ,  to  avoid  failure. (1 - Ps)  Ps was  a r e s u l t of the  between that  could  attend.  the r e s u l t a n t motivation  suggested  of  better  was  relation  evaluation  believe that his attention  Achievement  to act  l a t t e r was  the  reasonable  (1974), l e d t o a t h r e e  p r o b a b i l i t y o f s u c c e s s and success.  his  of  that  p r o b a b i l i t y t h a t he  (1958), A t k i n s o n  (Tr)  behavior  expectation  s t u d e n t w o u l d not  Algebraically described  and,  lead to h i s increased  m i g h t be  Achievement  paying a t t e n t i o n i n a  marks  he  his  I t would appear  better  Yet,  that the  outcomes,  his subjective  b e l i e v e that  to  important.  this  given  could led  and  by  model o f  Ps a  and factor  was  the  to succeed, l e s s the  subjective  incentive value  of  model's a s s u m p t i o n  of  Is,.  The  analysis  tripartite would  be  132  appropriate. Principal eigen-values criterion  greater than (Cattell,  eigen-values factors.  These  In  factor  particularly f a c t o r s to Factor  of  solution  increase  (MF)  with (VF)  206). p.  206)  IAES  and  the  had  of  the in  loadings  S c a l e , and ENJOY decided  I AEF..  loading  be  to c a l l the A  for  affective orthogonal  76%  from  SELFCON factor.  typically  considered  three the  variables  to  a  by  Factor the  of  the  (AEF)  as  of  SELFCON, a VALSOC,  with  loadings  should  have  in  other  Maf  measured w i t h t h e T e s t present  the  and  theory  However,  was  Motivation  MANX, ENJOY and  Anxiety  author  that  the opposite of a n x i e t y , i t  f i r s t f a c t o r the  comparison  the  of  rotation  led  a s i t h a s b e e n a r g u e d by t h e  should  a l s o suggested  w i t h h i g h l o a d i n g s f r o m VALSEL  been  of  Achievement M o t i v a t i o n model a  interpretability  a p p e a r e d as a s e p a r a t e research  Kaiser-Guttman  "scree"  accounted  an A c h i e v e m e n t E e s p o n s i b i l i l i t y  from  The  three  set of seven v a r i a b l e s .  interesting.  Value F a c t o r and  light  p.  factors  original  yielded  s a t i s f y i n g the  1966,  three  the  analysis  1.00,  1966,  (Cattell,  v a r i a n c e of the  three  component  Motivation Factor  hypothesized  and  the  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 .  was  (MF) . actual  133  Hypothesized Factor Loadings F3 F2 F1 low low high low low high low low high low low high low low high low high low low high low  Variable MANX ENJOY IAES IAEF SELFCON VALSEL VALSOC The composed  Achievement  of  IAES  correlations  and  Actual Factor Loadings F3 F2 F1 low low high low low high low low high low low high low low high low low high low high low  Eesponsibility IAEF.  The  o f a t most -.251 w i t h  individual the other  may be b e c a u s e t h e s c a l e s were t r u l y scales be  had low i n t e r n a l  suggested  may that  have the  responsibility mathematics. evidence,  validity  were  a  r a t h e r than This  latter  presented  in  i n Chapter  the  mathematics o r i e n t e d were d e v e l o p e d IARF  being  to  be  This  that  measure  associated  in  light  content  of  of  with  of  the  measures  s c a l e s were d i r e c t l y area,  achievement  other  of  r e l a t e d to Thus  i f a  responsibility  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 correlates  achievement  2, s h o w i n g b e t t e r c o r r e l a t i o n s  specified measure  1960's,  o f 1977, o r  of  specifically  the  I t might  early  and s e l f - c o n c e p t and  when t h e a f f e c t i v e  achievement  variables.  i n the  was a p o s s i b i l i t y  between m e a s u r e s o f a n x i e t y achievement  had  f o r the students  general  was  scales  c o n s i s t e n c i e s ; ,52 and .61.  reduced  scales  (AEF)  independent or  t h a t t h e s c a l e s , developed  had  Factor  affective  show I A E S and measures  in  mathematics. It Achievement  was i n d i c a t e d i n Motivation  Chapter  2  that  and L o c u s o f C o n t r o l  the theory  theory  of  correspond  134  and  that  a measure o f l o c u s  measure  of  presented to  evidence f o r  locus  related.  individual or in  achievement m o t i v a t i o n .  cf control, Locus o f  self  in  an  belief  an  suggest  external  Because,  motivation of  with t h e subjective  and  thus  success. of l e v e l  reducing  i n t h i s study, and a v o i d  t h e most l i k e l y  A belief individual  t o the task  o f achievement  the  failure,  negative  interpreted  and  VF  It  should  a r e an a r t i f a c t  (1973) f o u n d  similar correlations  degree  of  was  For  as  as the  MANX, SELFCON  MANX  analysis  also  be  noted  of the scoring  Sandman  Sandman's f a c t o r  of  c o r r e s p o n d e n c e o f AEF was  intercorrelated.  SELFCON.  correlations  overlap  would  probability  MF h a s been  a  p r o b a b i l i t y o f success.  strongly  .56 w i t h  thus  Alternatively,  and -.702 w i t h ENJOY and SELFCON r e s p e c t i v e l y  correlated  an  o f an a c t i o n  the  components o f t h e M o t i v a t i o n F a c t o r ,  ENJOY, were  -.728  of  should  which  to himself. that  was  Motivation  to  the results  suggest  cause  to succeed  success,  The  for  degree  s i t u a t i o n , attend  probability  indifference,  success*  value  i s the  could  achievement  the  in  What was n o t c l e a r  i t t c some c a u s e e x t e r n a l  increasing  the  control  a  (1973)  or achievement r e s p o n s i b i l i t y ,  responsibility  would,  with  Woulk and DuCette  o f t h e Achievement  accepts r e s p o n s i b i l i t y  attributes  would i n t e r a c t  this relation.  which o f t h e t h r e e c o n s t r u c t s  model be  of control  indicated  correlated and ENJOY that  o f MANX.  -.76 and ^.72. by  the  The  the results of  o f the scales.  e x a m p l e . Sandman's  (1973) s t u d y showed t h a t  item 4  135  on t h e ENJOY s c a l e , " I d o n ' t l i k e l o a d e d on t h e a n x i e t y f a c t o r . MANX  l o a d e d -^51  scale  i t e m s were: " 2 . feeling  of  mathematics."  of  the  on t h e e n j o y m e n t f a c t o r .  The  and  "8.  a  o r "good"  particular  I h a v e a good  feeling.  form  of  item  likely  -.46,  m a t t e r how  The  associated  intent of the  the  SELFCON  scale  The i t e m s w e r e : "4.  .32 a n a n x i e t y f a c t o r .  ' I c a n ' t do i t , » when a m a t h e m a t i c s p r o b l e m I f I don't  problem  away, I n e v e r g e t i t . "  right  see  how  to  work  relationship  with  anxiety.  In  turn,  a  No  would item  seems  underlying  explain  the  8 o f t h e ENJOY  " M a t h e m a t i c s i s more o f a game t h a n i t i s on t h e s e l f - c o n c e p t f a c t o r ,  I  mathematics  T h e r e i s an  sense o f f r u s t r a t i o n i n these i t e m s which  of  without  other than a  response  5 and 8 o f  h a r d , " and " 8 .  loaded  toward  h a r d I t r y I cannot u n d e r s t a n d mathematics," "5.  often think,  scale,  domain  a  was t o g e t 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 e x a m p l e , i t e m s 4, loaded  have  I t would appear t h a t i n the case  s t r e s s w i t h o u t u s i n g t h e word a n x i e t y .  eighth  I  feeling  feeling  i t e m number 2 t h e i n t e n t was t o g e t a  with  8  mathematics,  B o t h i t e m s t a p p e d an e m o t i o n a l  characterizing "dislike"  on  When I h e a r t h e word  dislike,"  mathematics,"  Whereas i t e m s 2 and .61  and  anything about  hard  work,"  and gave a s e n s e o f d e g r e e  difficulty. T h e s e comments a r e n o t meant a s c r i t i c i s m  of the  scale  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  of  dealing  of  the  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 t h e  subjects, t c a small  vocabulary.  age  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  more a p p r o p r i a t e complexities  t h a t the  scales, i t could  of  language  determinants of the  items could  also  be  together  affective  make  completely  independent s c a l e s i m p o s s i b l e .  to optimize  on  variance  may  followed  by  the arrangement of be  orthogonal  taken i n t h i s The Factor to  be  better  was  for the  to  was  the  that  benefits to himself  a  two  s c a l e s was  degree  of  reliabilities suggest t h a t  of the  Sandman  the  student  was  the  approach  the  The  society.  .67,  The  only  major  argument  presented  A l t h o u g h t h i s was  the  two  was  s c a l e s , VALSOC .68  "independence"  might  204)  (Nunnally,  1967,  p.  be  strong,  However, and  VALSEL  error  to the  Correlations  THE  .69,  reliabilities  the c o r r e l a t i o n  "BLOCK" VABIABLES TO  the  variance.  .98. RELATION OF  for  i n Chapter  moderately  suggested.  of  tests  VALSEL s c a l e  here t o n o t e t h a t the c o r r e l a t i o n between  independence of  the  Value  to respond i n terms of  due  THE  of  analysis  s c a l e s i n the  scale.  I n d e e d when c o r r e c t e d f o r a t t e n u a t i o n the  factor  of  trying  components  I n d e e d t h a t was  overlap  rather than  It i s sufficient  the  the  by  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 3.  the  complex  Bather than  c l e a r : the a u t h o r c o n s t r u c t e d  parallel  difference  the  in  study. reason  (VF)  rotation.  for  that  construction  the i t e m s ,  accounted  placed  argued  with  domain  be  ACHIEVEMENT  was  137  The belief  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 "  that  i t had  achievement. variables the  usually  Therefore,  were c o r r e l a t e d  affective  achievement.  been  i t with  variables  MANX c o r r e l a t e d  those  facilitating found  of  Alpert  anxiety  difference  i nsign  procedure  with  -.45,  of  -.08 and -.40.  consistent  with  Kahn  m a l e s a n d .509 f o r The  (1970)  and of  anxiety  with with  compared correlated  samples  of  .50.  Note  scoring.  data  and  that the A  similar  revealed c o r r e l a t i o n s of also  (1969) who f o u n d c o r r e l a t i o n s o f . 305  for  females.  .518,  were  between  SELFCON  a n d .462 w h i c h c o m p a r e d w i t h  mathematics self-concept In  and mathematics  and  Bachman's  were  PBOB.  W h e r e a s , VALSOC and VALSEL were more  CONC  more  strongly  related  a n d PBOB t h a n t o COMP.  similar  conjecture  achievement.  terms o f the t h r e e achievement v a r i a b l e s ,  ENJOY  and  IABF  c o r r e l a t i o n s o f .48 f o r m a l e s a n d .55 f o r f e m a l e s when  relating  to  who  the  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  strongest correlations  a c h i e v e m e n t .457,  from  and -.331  (1960)  three  artifact  debilitating  that  These c o r r e l a t i o n s  . 3 6 , .32  i s an  -.387,  Haber  a n d GPA o n  correlations  apart  poor  significantly correlated  -.410,  and  with  hypothesized  achievement.  COMP, CONC a n d PBOB r e s p e c t i v e l y . with  associated  was  were  was t h e common  f o r COMP about  and  and  t o COMP t h a n t o CONC a n d strongly  related  SELFCON was h i g h e s t f o r CONC  PBOB.  the possible  MANX  I t was  reasons.  interesting  to  M a t h e m a t i c s may be  138  t h o u g h t o f a s d e a l i n g w i t h numbers a n d a g r e a t mathematics  class  t i m e i n m i d d l e and upper e l e m e n t a r y  was s p e n t on c a l c u l a t i o n . possible  implication  begins  i n t h e early years  o f VALSOC a n d VALSEL t o of  achievement  low  achievement,  correlations  the largest  would  success, want retain  theory  of  experimental '  perceived  appeared  anxiety  reasonable  the content  of  IAES  The  was  only  in  those  expected  closely  t o that dimension.  that  successful  poor  students  to  f o r f a i l u r e as a defense t o correlation  of  a  quadratic  was t h a t o f SELFCON  The h y p o t h e s i s  stemmed  from  M o t i v a t i o n which had s u b s t a n t i a l  p r o b a b i l i t y of success.  that  with  responsibility f o r their  f o r a q u a d r a t i c term  argued  IARF  . 1 9 0 , were u n e x p e c t e d i n t h e  expected from theory  Achievement  support  and  a due r e w a r d , a n d  responsibility  self-respect* that  was  with t h e achievement v a r i a b l e s . the  of  be w i l l i n g t o a c c e p t  reject  component  mathematics  The h i g h e r c o r r e l a t i o n s  PEOB  I t was  as i f accepting  to  and  nature  of the literature.  students  of school.  CONC  the applied  that  with  areas.  The  light  was  of  school  As MANX was c o r r e l a t e d h i g h e s t  COMP a  because  proportion  the self—concept  f o r the  In t h e present of  mathematics  subjects'  study  i t was  corresponded  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  strongest guadratic  r e l a t i o n s were VALSOC w i t h COMP (.097) a n d  MANX  with  explained  PBOB  SELFCON  (.088)  variance  was  were  (p < . 0 5 ) . .9% and  not significant.  However  The  a s t h e maximum  the variables  were  not  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 Multiple Beqression The  pedagogical  variables  with  indicated  above,  associated  an  with  independence. validity  cf Standardized  other  y e t showed  of  of  v a r i a b l e s should  achievement.  independent variance  should  In  several  i n mathematics.  measuring those  I f the construct  Scores  has a s s o c i a t e d  block"  the scales  then those  prediction  Scores and F a c t o r  literature  "emotional  each  t o be o f no i m p o r t a n c e .  v a r i a b l e s were  some  degree  "emotional  of  block" has  a l lcontribute  other  As  to the  words t h a t p o r t i o n o f  e x p l a i n some  additional  variance  of t h e achievement v a r i a b l e s . When  a l l seven  regression eguation small,  i n the  compared  multiple  was  had  .01 <  an  were  present  increase,  correlation;  w i t h SELFCON by i t s e l f ;  differences for  there  variables  i n the  albeit  rather  . 4 8 3 , .537  . 4 5 7 , .518  a n d .468  and.462.  These  p < .05 f o r COMP a n d CONC a n d p > .05  PBOB. Indeed, from these  r e s u l t s one would  anticipate  that  one o r two o f t h e m e a s u r e s w o u l d e x p l a i n n e a r l y a s much a s t h e whole  set.  Stepwise  appeared i n a l l t h r e e only i n t h e equation analysis  confirmed  regression equations f o r COMP.  In  t h e f i n d i n q s were s i m i l a r .  e x p l a i n e d by SELFCON. for  regression  with  this. MANX  the cross  SELFCON appearing validation  Most o f t h e v a r i n c e was  The o t h e s i x m e a s u r e s were weak  MANX f o r COMP a n d VALSOC f o r CONC.  except  140  The variables would  to  were e x c l u d e d  add  students one  question  no  be  r a i s e d h e r e i s whether t h e  because the  significant  responding  construct.  to  The  constructs  explained  i s s u e i s one  they  measure  or  whether  variance  SELFCON were i n f l u e n c e d  other  by  more  of unidimensionality  than of  the  measures. Therefore, the to  orthogonal generate  scores  factor score  r o t a t i o n of the  factor scores.  and  coefficients  their  The  analysis included terms.  Achievement M o t i v a t i o n  theory  increase  variance.  supported. 19.5%,  Indeed,  and  16.1%  respectively.  cnly of  that  one the  This  factor  a test  interaction  terms  The  factor,  variance  the  was  variance  Most o f t h i s  from  p r i n c i p a l components were u s e d  interaction  explained  calculated  hypothesis MF,  of  would  was  explained  not  19.1%,  of COMP, CONC, and c o u l d be  the  accounted  PEOB, for  by  SELFCON. It  should  contentions low was  of  be  recalled  t h i s study  was  that  c o r r e l a t i o n s between a f f e c t i v e the  potential  multivariate  nature  interactions lends  affective  domain i n t h a t t h r e e  seven a f f e c t i v e seven  support  measures.  variables  found f o r the  in  hypothesis  to  variables  the the  one  the  and  affective  major for  multivariate  the  achievement  domain and  variables..  The  the  present of  the  f a c t o r s were needed t o span  the  However, a t l e a s t this  of  a p o s s i b l e reason  of the  among  analysis  the  that  study,  that the  little  variables  with  nature  respect  support  could  interact  in  to be the  141  prediction  of  individual most will  or  scale scores  important be  should may  achievement.  not  be  suggested  variable  noted l a t e r  of  i n the  mean t h a t  Moreover,  the  the  three  section  grouping  on  future  o t h e r v a r i a b l e s be  B e f o r e drawing  A major  l i m i t a t i o n of  was  t h i s no  useful  THE  conclusions  some l i m i t a t i o n s o f  Because of  of  the  the  single  u n d e r MF.  As  research  dismissed  achievement  this  for  they  situations  grade l e v e l s . LIMITATIONS OF  research,  analysis  SELFCON was  u s e f u l i n e i t h e r more s p e c i f i c  at e a r l i e r  it  that  the  the  t h i s study  causal  STUDY  and  suggestions for  study was  s h o u l d be  further  emphasized.  i t s c o r r e l a t i o n a l nature.  inferences  could  be  drawn.  However,  for suggesting  probable d i r e c t i o n s f o r  l i m i t a t i o n of  this  causal  research. A second measures parts, have may  used.  computation, been  be  a t the Thus  too  the  of  taught t o p i c The of  concepts  case that  while  these several may  achievement  global  introduction  material  subset  The  f o r the  the of  and  was  the  set  v a r i a b l e s , although i n problem  solving,  psychological  Achievement  new  study  material  new  three still  model c h o s e n .  Motivation or  may  quizzes  oriented  It  model o p e r a t e s  teaching  units.  t e s t s were summative i n n a t u r e s p a n n i n g years,  of  to  a  the  recently  produce d i f f e r e n t r e s u l t s .  affective  possible  variables  included  affective scales.  here  were o n l y  A t t i t u d e Toward  a  Teacher  142  and  Motivation  i n M a t h e m a t i c s were two  included  here.  is  degree  the  The  latter,  to  as  which  examples of  i n t e r p r e t e d by  the  student  choice  than  need.  i n d i v i d u a l s c a l e s t h e m s e l v e s may  l i m i t e d i n the  cases, to  or  be  too  the  from a  i t  may  constructed limited. the  general  As  well  same l e n g t h  total  as  Society  been  of  the  time  to a  made p a r a l l e l  scale*  too  On  general.  willingness  was  the  in  to the other  They  Value hand  were  than  the  author  s c a l e was  made  to  the  the  items  of  Mathematics  were,  Intellectual  constructed  i n the  keep  IARF)  to take r e s p o n s i b i l i t y f o r success  achievement s i t u a t i o n s , r a t h e r  prior  too  the  (IARS and  were  was  order  minimum, and  likely  many  that  this  some  tests  (VALSOC)  3,  been  in not  in  case  Mathematics  Achievement R e s p o n s i b i l i t y S c a l e s , been  included  Sandman s c a l e s  administration  domain,  Although t h i s  items  have  the  e i t h e r have  construct  i n d i c a t e d i n Chapter  wherever p o s s i b l e , for  of  Value  was  the  rather  Sandman s c a l e s b e c a u s e t h e  pool  scale  of  i n ethers.  case i n the  constructed scales,  sampling  by  (1973) , with  materials  too  class  Sandman  not  c h o o s e s t o work  mathematical The  outside  scales  may to  and  have measure  failure  in  more r e s t r i c t e d  set  of mathematics achievement s i t u a t i o n s . Age  level  Achievement  Motivation  introduction s t u d e n t s had the  time  was  of  new  formed  they  had  the  third  model  could  material major s e t s o f reached  limitation.  i t  be may  Although  operant a l s o be  affective  s i x t h grade.  the  at case  orientations  Therefore,  the the that by  i f more  143  global  measures  earlier  g r a d e s would be A  sample  more  drawn.  was  Insofar  elements d i f f e r ,  used  then  perhaps  appropriate.  fourth limitation  was  cultural not  o f a c h i e v e m e n t were t o be  the p o p u l a t i o n  as  from which t h e  socio-economic  level  and  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  hold. CONCLUSIONS It  would a p p e a r t h a t t h e r e  (motivation  factor),  grade s i x l e v e l . called,  in  self-concept of  this  study,  of a b i l i t y  other  validity  of these  described stepwise  as  an  included  components  in  the  analysis  component,  was  From  to  was  only  enjoyment  variables  tend  of  than  do  what  the  Sample  which  had  first  1 and 2. SELFCON  and the  of the  could  i n mathematics.  always  to  of students  gave some e v i d e n c e  both MF,  variables  (SELFCON) and  rankings  block"  of  MF  (MANX),  a s a measure  SELFCON  the  checklist  This  "emotional  factor,  anxiety  three  teacher  variables.  a n a l y s i s of factor scores  that  These  Student-Behavior  regressions  of  mathematics  more s t r o n g l y w i t h  affective  composed  i n mathematics  (ENJOY).  a teacher-response  an a f f e c t i v e  r e l a t e d t o achievement a t the  T h i s f a c t o r was  mathematics  correlate  which was  was  be  In the to  be  In t h e as  a  included.  the Achievement  self-concept  Motivation  of a b i l i t y  s u b j e c t i v e p r o b a b i l i t y of  model  i t was  i n m a t h e m a t i c s would success.  Since  the  predicted correspond predicted  144  relations was  did  not  questioned.  ENJOY  and  factor  As  MANX  motivation  appear i n the SELFCON  In  turn  particularly  of  i n d e p e n d e n c e f r o m MF  its  i n t e r p r e t a t i o n as  control  his  Intellectual as  the  attributes control  interactions  the of  or  a  as  This opposed  belief  achievement external  possible  of  success.  with  may  have  to  be  as the  been  changing Meichenbaura  a  light  is  to that  not  Achievement  because nature  of  effort,  on  student's  (1975) s t a t e d  the the  internal  o f the  lead  the  • of  scales focus  could  of  interpretable  confirmation  research,  evidence  ability  the  luck,  the  however, d i d  experimental,  such  the  conclusion  by  with  responsibility  In  ARF,  predicted  control,  for  was  in his  achievement r e s p o n s i b i l i t y  programs  probability  together  factor).  of success.  i n t e r p r e t a t i o n , through f u t u r e specific  factor  IAES component, showed  student's  probability  correlational,  correspondence  achievement  (motivation  the  model.  As  a  A c h i e v e m e n t R e s p o n s i b i l i t y may  Motivation  study.  the  the  achievement,  subjective  display  formed  the  a more p l a u s i b l e c o r r e s p o n d e n c e  factor.  (AEF),  analyses  above  to  quite  subjective that  F o r some r e s e a r c h e r s S's s e n s e o f c o n t r o l over the threatening situation seems most critical. Presumably a person will appraise a potentially aversive situation as less threatening i f he p e r c e i v e s h i m s e l f as h a v i n g some measure o f control over the a v e r s i v e s t i m u l u s . (p. 239) Self-concept achievement However,  the  as  were variance  was  found  mathematics  to  be  anxiety  of achievement  scores  a and  correlate  of  enjoyment.  accounted  for  by  145  anxiety  and e n j o y m e n t was  virtually  self-concept  as  two  variables  i n the stepwise  an  exception  i n the case  This  was  analysis.  The  factor  the three  with  the  regression  analysis loaded  in  selected  factor.  self-concept  was a n o t h e r  on t h e same  Parsimony,  be a c c e p t e d  group.  corrected -.87  then,  and  When  .69  mathematics  with  anxiety (1965)  Sarason s f  research  piece  the  component*  should  of  the  and  self-concept  - . 9 0 with  enjoyment.  analysis  of  Meichenbaum  test  and  that  author  variables  the three to  were  correlate  e n j o y m e n t and In  anxiety  (1975)  sole  component.  present  was f o u n d  anxiety  where t h e  indicate  between  mathematics  again,  was t h e  be on t h e s e t h r e e  correlations  also  of evidence  factor  would  was  was  validation  a s t h e major e x p l a n a t o r y  f o r attenuation  cognitive  cross  the motivation factor  the focus of a t t e n t i o n a  when a n x i e t y  the  However, i t i s t h e c o n t e n t i o n  as  There  e x c e p t i o n o f t h e equation f o r computation was i n c l u d e d ,  f o r by  of the former  analysis.  of computation  confirmed  variables  value f a c t o r  that  accounted  was e v i d e n c e d b y t h e e x c l u s i o n  included.  as  that  addition  indicated  noted  that  a  some  had  demonstrated that t h e s p e c i f i c emotion e x p e r i e n c e d by a p e r s o n d e p e n d s not only upon h i s state of psychological a r o u s a l , b u t a l s o on t h e way i n w h i c h s i n t e r p r e t s or l a b e l s t h i s state. They a l s o found that this l a b e l i n g p r o c e s s i t s e l f i s i n f l u e n c e d by what t h e p e r s o n a t t r i b u t e s a s b e i n g the origin of t h i s s e l f arousal* (p. 2 3 9 ) This self-concept  researcher  holds  s h o u l d be i n t e r p r e t e d  that  the  construct  as the c o g n i t i v e  of  component  146  of  anxiety.  of  The  lower  self-concept  cognitive  and  correlation, enjoyment  component  in  correlation  may  emoticnal  an  Of of  considerable  mathematics  retrospect, associated rather the  in  it  value  effects  value  achievement  in  in  was  mathematics.  of e n j o y m e n t  to  was  of  very  minor r o l e  in  little It  o f m a t h e m a t i c s i s o f no i t should  and  suggest  of that  of teaching  be  that  and  and  the  should  increased  achievement not  t o be  in  value  of  delayed with little  predicting  n o t be  thought  that  I t may  be  case  r e s u l t s of t h i s study, be  in  incentives  the  desirable affective  The  value  Compared  importance  itself.  towards  of  e n j o y m e n t i t was  importance.  an i m p o r t a n t  anxiety  However,  of mathematics tend  mathematics.  with  achievement.  of anxiety  The  anxiety.  the  reasonable  the  wonder t h a t  that  -.88  counter note  of  attenuation,  indicate a lesser  than immediate f o r grade s i x s t u d e n t s .  immediate  value  of  predicting  was  with  (-.69) c o u l d  enjoyment  disattenuated suggest  corrected f o r  outcome  however,  e x p e c t e d as a  mathematics  as  an  do  result  affective  outcome. FUTURE BESEABCH As  indicated  correlational  in  s t u d i e s cannot  one  advantage c o r r e l a t i o n a l  is  that  and  often  suggest  they  can  the imply  with  on  limitations  causal relations.  s t u d i e s have o v e r  deal  appropriate  section  However,  causal  studies  more v a r i a b l e s or  measures  covariates  and  potential  147  interrelations research  f o r causal  will  be d i v i d e d  analysis.  The d i s c u s s i o n  i n t o two s e c t i o n s ;  of future  c o r r e l a t i o n a l and  experimental. Correlational In Abiliy the  Studies  this  study  i t was  argued  that  i n M a t h e m a t i c s was t h e e g u i v a l e n t  subjective  probabiltiy  of  Self-Concept  of  assessment  of  t o an  success.  Self-concept  found, though, t o c o r r e l a t e h i g h l y  with  which  measures.  This  f i n d i n g and  led  an  alternative  are  several  closer  other  interpretation  to  motivation  considerations o f self-concept.  answers on t h e s e l f - c o n c e p t were this  estimates may n o t  mathematics. increase  correspond a  to  "D"  It  Achievement  Motivation  model  and  h i s perception  student  s u r p a s s him.  term and  correlations  be t h a t  were t r u t h f u l  success  t o a "C" i n w h i c h c a s e a l a r g e  achievement  and  enjoyment  a student's  and t h a t  they  o f t h e mark he t h o u g h t he would r e c e i v e .  For  quadratic  to  I t could  scale  would s t i l l  the  anxiety  was  i s also  of s u b j e c t i v e yet  only  of q u a d r a t i c  success  might w e l l  proportion  in  be an  of students  interesting  predicted  that  the  c o r r e l a t i o n s between  probability two  of  Yet  of  marqinal  success  and  (.01 < p < .05)  t e r m s were f o u n d : VALSOC  with  COMP  MANX w i t h PROB. These  direction Mathematics  considerations  f o r future  research  suggest  that  one  i s t h e development  I n t e l l e c t u a l Responsibility scale.  possible of  I t could  a  then  148  be  validated  i n comparison  Responsibility tested  and  Intellectual  be  suggested  probability  i n the l i m i t a t i o n s  done w i t h a view  t o the  I t may  was  for  stages from  enough  of r e s e a r c h are i n d i c a t e d . youngsters  them* as  representive  the reasons  F o r e x a m p l e , an  "Mathematics  responses scale  is  t o such a  used  the  Value  the case t h a t  young s t u d e n t s . first  is  of  VALSOC  Thus  to  two  solicit  q u e s t i o n c o u l d be u s e d t o me  because  q u e s t i o n c o u l d form  w h i c h c o u l d be  of  mathematics i s i m p o r t a n t f o r  open ended important  be  The  why  of success.  s e c t i o n , more r e s e a r c h  expansion  Mathematics f o r O n e s e l f s c a l e . not  Achievement  t h e n have i t s c o n s t r u c t v a l i d a t i o n  as a measure o f t h e s u b j e c t i v e As  might  Scale  with the  ?"  the b a s i s of a  i n a manner s i m i l a r  such The  Likert  to that  in  this  study. It that  the  was  pointed out  Achievement  introductory present  also  t h i s out.  Motivation  s t a q e f o r new  author At t h e  first were  expected  and  places  their  typically  performed  the second  reporting  algebra then  an  course.  limitations  model  material.  The  of four reporting  students  not r e v e r t e d  the  may  a  letter were  a t a lower session  grade  taken level  i t was  by  at  sessions or  two  to that  would t a k e a c c o u n t  bears good  lower  than  who  had  However case  i n the has  the  many  students  in.algebra.  the  of  i n geometry  I f t h i s informal observation study  valid  an e x c e p t i o n a l  to a ranking s i m i l a r  appropriate  be  section  experience  t e a c h i n g a year l o n g course  algebra  had  in  by  that  previous  any  force  of the  change  149  over time  of  situation.  a  group  Such  a study  t o answer some c a u s a l technigues  of  students with  in  a  new  mathematics  periodic testing  guestions  if  c o u l d be  cross—panel  used  correlation  were u s e d .  It  may  that  were,  then  the  be  for  the  case t h a t  example,  interrelations  i f samples c o u l d  more o r  less  described  be  identified  achievement  above  oriented,  might  be  quite  different. Experimental  Studies.  The  major  motivation  finding  factor  mathematics,  which  anxiety  mathematics  was  the  achievement  and  that  Further, that  be  in  was  them  cause the  the  three.  self-concept as  noted  in  the  previous  c o g n i t i v e component enjoyment, expected  as to  of  the  self-concept  of  and  enjoyment  factor  A  on  these  should  be  measures r e l a t e d because  other  the  "emotional"  reduce  anxiety.  In  level  are  or  be  turn, of  they  two  of  underlying  causes s t r e s s then  related to anxiety  aspect The  two  another cause  s e c t i o n , may  anxiety.  groups. question  s i m i l a r c o n s t r u c t s , or  yet  of  predicting  b a s i s of t h a t f a c t o r .  as achievement  of achievement  that  sex  or i s t h e r e  Insofar  was  also consistent across  of them c a u s e s t h e  third,  of  consistent  asked i s "Are  b e c a u s e one  study  mathematics,  only  r e s p o n s e s t o them a r e b a s e d related  this  consisted  SELFCON f o r m e d t h e  should  of  and,  i n t e r p r e t e d as an  increase  anxiety,  hypothesis  the in  would  that  be  this  150  experimenter  would  hold  sustained, then anxiety a c h i e v e m e n t w i l l he It not  show  prediction  be  and  of  will  measures  specifically that  the  IABF  t h a t the as  mathematics  may  experimental  may  responses  of  to  two  It  The  the  several  first  is  that  not n e c e s s a r i l y r e l a t e d The  variables  may  third i s  that  studies  attribution is  do  may  just  second  is  be i n  the  relations show  focussing  o f s u c c e s s and this  up  in on  failure  possibility  (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  that theory  achievement. summary  experimental  each  design  one  procedures to  increase  s u c c e s s and use  of  in  However,  Thus i t i s p o s s i b l e t h a t  increase learning.  In  (b)  The  correlational  the  discusses  variables  mathematics,.  the  change  Bar-Tal and  in  studies.  techniques  self-concept  r e s u l t s of t h i s study  been suggested*  invite  importance  up  as e n j o y m e n t i s  and  achievement.  t o achievement i n  showing  long  important  introductory stage of material. not  as  he r e d u c e d  noted  p o s s i b i l i t i e s have a l r e a d y the  that  increased.  should IABS  is  enjoyment  failure* of  the  w i t h two  could  conceive  of  (a) c h a n g e s e l f - c o n c e p t and,  (c)  A potentially  alter  the  designing of  ability,  attribution  informative  study  procedures i n a three f a c t o r , f u l l y  l e v e l s i n each.  The  two  of  would crossed  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 the  procedure.  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T., 8 B i g l a n , A. Instrumentality theories: c u r r e n t uses i n p s y c h o l o g y . P s y c h o l o g i c a l B u l l e t i n , 1971, 7 6 , 432-4 54, Montanelli, D. S., & H i l l , K. T. Children's achievement expectations and performance as a function of two consecutive r e i n f o r m e m e n t e x p e r i e n c e s , s e x o f s u b j e c t , and sex o f e x p e r i m e n t e r . J o u r n a l o f P e r s p n a l i t y and S o c i a l P s y c h o l o g y . 1 9 6 9 , 13_, 115-128. Morrison, D. F. Multivariate statistical McGraw-Hill, 1967.  methods.  New  York:  Moulton, R. W. Motivational implications of individual differences i n c o m p e t e n c e . I n J . W. A t i k i n s o n and J . 0. Baynor (Eds.), Motivation and achievement. Washington: W i n s t o n & S o n s , T974, Neal, D. C. The r o l e o f a t t i t u d e s i n l e a r n i n g The A r i t h m e t i c T e a c h e r , 1 9 6 9 , .16, 631-640.  mathematics.  161  Nelson, I . fi. Dunedin, New Otago, 1974.  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S., L i g h t h a l l , F. F., & B-. B. A test anxiety scale for children. D e v e l o p m e n t , 1958, 29, 10 5-113.  Waite, Child  Sarason, S. B., Davidson, K. S., Lighthall, F. F., W a i t e , B. fi,, S B u b u s h , B. K. Anxiety i n elementary school children. New Y o r k : J o h n W i l e y and S o n s , 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 n e e d s o f t h e s l o w l e a r n e r . In W. C. Lowry, ( E d . ) , The s l o w l e a r n e r i n m a t h e m a t i c s . Beston, Viginia: The National Council of Teachers of Mathematics, 1972. Silverblank, 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 b e t w e e n 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 talented in Mathematics, California Journal of Educational B e s e a r c h , 1973, 24, 6 1 - 6 5 .  163  S i u , P. K. 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The a p p l i c a t i o n o f s h o r t t e r m v i d e o - t a p e t h e r a p y for the treatment of test a n x i e t y o f c o l l e g e §tu dents,. Progress report. C o l o r a d o " S r a t e 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 m e a s u r e o f m a t h e m a t i c s a n x i e t y : p s y c h o m e t r i c data. J o u r n a l o f C l i n i c a l P s y c h o l o g y , 197 2, 2 8 , 3 7 3 - 3 7 5 . 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 (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 M a t h e m a t i c s E d u c a t i o n . 1 9 7 4 , 5, 283-2721 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 (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 M a t h e m a t i c s E d u c a t i o n . 1 9 7 5 , 6, 2 5 3 - 2 8 2 . Suydam, M. N., & Weaver, J . F. 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B e i n f o r c i n g math w i t h more math: c h o o s i n g s p e c i a l a c a d e m i c a c t i v i t i e s a s a r e w a r d for academic performance. Journal of Educational Psychology, 1976, 68, 579-587. T u l o c k , M. K. Emotional blocks i n T e a c h e r , 1957, 50, 572-576. W e i n e r , B. attribution ecucational process. 42, 2032 203-214.  mathematics*  Mathematics  t h e o r y , a c h i e v e m e n t m o t i v a t i o n and t h e Beview o f E d u c a t i o n a l R e s e a r c h , 1972,  Weiner, B., Heckhausen, H., Meyer, W. U* , S Cook, B. E,. C a u s a l a s c r i p t i o n and a c h i e v e m e n t behavior: a conceptual analysis of effort 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 Social Psychology, 1972, 2J, 239-248. Weiner, B., & Kukla, A. An attributional analysis of achievement m o t i v a t i o n . J o u r n a l o f P e r s o n a l i t y and Social P s y c h o l o g y , 1970, 15, 1-20. Wells, D. w . , & S h u l t e , A. P. An example o f p l a n n i n g f o r low achievers. In M, Bosskopf (Ed.), ffhe teaching of secondary school mathematics. Washington: the N a t i o n a l C o u n c i l of T e a c h e r s of Mathematics, 1970. Weston, D. 1. An e x p l o r a t i o n o f t h e i n t e r r e l a t i o n s h i p s among children's arithmetic achievement, their styles of learning, their responsibility for intellectual academic , achievement and their parents' attitudes. (Doctoral d i s s e r t a t i o n , Wayne S t a t e U n i v e r s i t y , 1968),* Dissertation Abstracts International, 196 9, 30, 1087A-1088A. (University Micrefilas~No. 69-14,690) W h i t l o c k , C., & B u s h e l l , D., J r . Some effects of "back-up" reinforcers on reading behavior. J o u r n a l of Experimental C h i l d P s y c h o l o g y , 1967, 5, 50-57. ~ Wine, J. Test anxiety Psychological Bulletin, Winer, (2nd  B. J . ed.).  and 1971,  direction 76, 92-105*  Statistical principles New Y o r k : M c G r a w - H i l l ,  of  attention.  i n experimental 1971.  design,  Wolk, S., & D u C e t t e , J. The m o d e r a t i n g effect of locus of control in relation to achievement-motivation v a r i a b l e s . J o u r n a l o f P e r s o n a l i t y , • 1 9 7 3 , 4 J , 5S-70. W y l i e , E. C. The considerations  self-concept: a review of methodological and measuring instruments (Vol* 1).  University  of  Nebraska  Press,  166  Appendix A INSTRUCTIONS FOR On each  BEHAVIORAL  CHECKLIST  t h e BACK c f t h e m a r k - s e n s e c a r d s p r o v i d e d  student)  w r i t e the i n d e n t i f i c a t i o n  (one  for  number o f e a c h 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  front  appropriate exhibiting year,.  of the item  c a r d mark t h e number  that behavior  Some  of  the  on  While  i n your  o f f one  i n c l u d e even blank  their  you  students  might h a v e o n l y c h e c k e d please  i f  o v a l with  cards  have  1 i n i t under  noticed  the  mathematics c l a s s w i l l have a blank of  the  w i t h an  the  student  during  the  card, or  you  behaviors.  However,  identification  number  back.  the  student  i s d o i n g m a t h e m t i c s have you  observed  that  he/she 1,.  tends  to  give  mathematics 2.  appears  3.  expresses  4.  tends  5.  random  answers  questions  during  class?  tense  during  mathematics  a n x i e t y or nervousness  to  to  increase  mathematics  class?  says  no  that  mathematics?  matter  disruptive  lessons? about  mathematics?  behavior  during  what he/she d o e s he/she c a n ' t  the  do  167  6.  h a s hands  7.  says  8.  sometimes  refuses  mathematics  period?  9.  When  t h a t mathematics  fidgets  you  t h a t shake  have  when d o i n g i s usless? to  answer  more d u r i n g m a t h e m a t i c s  finished  w i t h t h e YELLOW t a b .  matematics?  please  questions  during  lessons?  put the c a r d s i n t h e envelope  168  Appendix INSTRUCTIONS FOR On of  your  from  the  six  s t u d e n t s one  the d e s c r i p t i o n  name o f t h e s t u d e n t the top  RANKING OF  s e t of c a r d s p r o v i d e d ,  grade  most l i k e  B  of the  most l i k e O B the  deck,  identification  numbers  to a card.  below t o l e a s t the d e s c r i p t i o n  the  names a p p e a r on  the c a r d s : from  to  least  Beside  male o r  i t .  names o f  each  Order  the  cards  like  i t .  The  should appear  paper p r o v i d e d , l i s t  on the  s t u d e n t s i n t h e same o r d e r  the  like  w r i t e the  piece of  of  STUDENTS  most l i k e  each i d e n t i f i c a t i o n  the  as  description  number  indicate  female.  The following i s a description of observable characteristics o f s t u d e n t s who may have an " e m o t i o n a l b l o c k " i n mathematics. Try not t o c o n s i d e r achievement or ability. Very good students may exhibit the block and very poor s t u d e n t s may n o t . A student guestions  or  with  may  the b l o c k  refuse  may  give  random  t o answer them a t a l l .  answers  to  He/she  may  a p p e a r t e n s e , have hands t h a t s h a k e as  he/she w r i t e s ,  or  mathematics c l a s s .  increase disruptive  student  may  tell  b e h a v i o r i n the  you  that  he/she f e e l s  anxious  about mathematics or t h a t mathematics i s u s e l e s s . s t a t e t h a t no  matter  how  hard  he/she  or  fidgets The  nervous  He/she  works i t seems t o make  may no  difference.  When  you  have  finished  please  put the  paper i n t h e  envelope  169  with the YELLOW t a b .  170  Appendix C  ADMINISTRATION  BOOKLET  Thank y o u f o r v o l u n t e e r i n g students  to  enable  dissertation. study  will  aspects  me  to  your t i m e  gather  the  I hope t h e t e s t r e t u r n s be  o f help  to this  and i n t e r e s t  and t h a t o f  data  I need f o r my  and t h e r e s u l t s t o you.  your  of  my  There a r e three  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 m i n u t e parts. of  2. A s e t o f achievement t e s t s a l s o i n three which i s t h i r y - f i v e m i n u t e s l o n g ;  parts,  each  3. A s e t of materials f o r you t o f i l l o u t a b o u t students. T h i s c a n be done d u r i n g t h e t e s t periods so y o u r t i m e commitment i s n o t i n c r e a s e d . lo the  retain  confidentiality  students, them  I have asked  an  list. only  of  your  beginning  of the student replies  number.  number w i l l  Although NEED TO PERIODS.  DO  ALL In  The  and t o p r o t e c t  those  of  the  numbers  your  should  be  as your c l a s s  achievement  tests,  appear.  the  study  THE  TESTING  i s a b o u t m a t h e m a t i c s THESE I S NO DURING  fact, f o r at least  SCHEDULED  the f i r s t  two  THAT THE QUESTIONNAIRES  HAVE  MATHEMATICS  questionnaires  would be p r e f e r a b l e t o g i v e them i n some o t h e r  DO NOT MENTION  of  materials, t o give  a t 1 and i n t h e same o r d e r  When I r e t u r n t h e r e s u l t s the student  and  you, i n the e n c l o s e d  identification  consecutive  it  t h e anonymity  your that  period.  ANYTHING  TO  DO  171  I  WITH MATHEMATICS  AS  THE  FIRST TWO  QUESTIONNAIRE  CONCERN SCHOOL IN Please about the TESTING use  I S DONE.  results:  that  intend Are  you  t o count the  test  to  t o use  results  are  work.  Try to  f o r you If  s c h o o l or  at  you  have  my  home.  Thanks a g a i n .  will  for  u n t i l AFTER  ALL  want t o know what  The  t o be  grading? best  you  w e a k n e s s e s so t h a t you use  of  test  Are  they  answer t o g i v e i s  used by  AFTER t h e l a s t t e s t .  a class  e v a l u a t i v e comments  mathematics achievement  then  going  t o work a s h a r d  on  sudents  a d e n i a l o f the  until  the students do  avoid  ANY  of r e s u l t s  toward the r e p o r t ?  o f s t r e n g t h s and  grading  use  make o f t h e  qoing  GENERAL.  making  In p a r t i c u l a r  areas  for  from  q u e s t i o n n a i r e or the  you  going  refrain  SECTIONS  to f i n d  can  the  plan  test  I want t o  as p o s s i b l e ; j u s t  as  out  future results  encourage  they  would  test. any  questions  Jim  please  Gaskill  c o n t a c t me  at  the  172  TEACHER'S ADMINISTRATION INSTRDCTIONS STUDENT QUESTIONNAIRE  From  your  identification sheet  filled  relate  number  list  by n u m b e r i n g  to i n d i v i d u a l students  to  enables  assign your  each. list  i n by the s t u d e n t and c a r d s f i l l e d  number r e t a i n s me  class  of student  i n order*  Each  i n by y o u t h a t  information,  This allows  a l l t h e i n f o r m a t i o n a b o u t e a c h s t u d e n t , and  me t o communicate s t u d e n t  Before  an  must have t h e same number.  confidentiality  correlate  student  you  begin  r e s u l t s b a c k t o you.  administering  the  questionaires,  p l e a s e make s u r e y o u h a v e 1.  a  cassette  tape  recorder  with  speaker  (from  your  school) . 2.  a cassete  tape  labelled  SIDE ONE-  3.  an answer s h e e t f o r e a c h  4.  ten extra pencils  (Just  student* i n case  some  students  don't  have one.) 5.  an e n v e l o p e  w i t h a BLUE t a b .  6.  a q u e s t i o n n a i r e f o r each  P l e a s e attempt morning before on  on  two  to administer  consecutive  recess, separated  the second  student.  days.  by f i v e  day b e f o r e r e c e s s .  the questionnaires i n the I suggest  the f i r s t  t o t e n m i n u t e s and t h e  two  third  173  For would  be  purposes  of  preferable.  considerations  make  standardization However,  i t  But  p l e a s e have t h e  during  two  days s p e c i f i e d  above  platooning  impossible,  discretion. the  i f  the  I will  or  the  other  leave i t to  questionnaires on  seguence  envelope  your  administered with t h e  BLUE  tab. Would collected  and  because other and  you  also  be  sure  returned  to  the  classes will  be  that office  using the  a l l  materials  when you same  are  are  finished  pencils,  tapes  questionnaires.  1.  Set ONE  2.  Hand out the answer sheets. Tell the n o t t o w r i t e on them u n t i l you t e l l them.  3.  Tell the students to write the number that you w i l l g i v e them i n t h e s p a c e i n the upper left hand c o r n e r marked IDENTIFICATION NUMBER. Bead t h e numbers from your c l a s s l i s t . i  4. • I in 5.  up the tape r e c o r d e r with f a c i n g up*  the  tape  Say; am g o i n g t o hand o u t some b o o k l e t s . Do them, and do n o t open them u n t i l I t e l l  Hand o u t t h e b o o k l e t s . Say: The t e a c h e r who has sent you these a s k e d me t o r e a d t h i s l e t t e r t o you. Eoys and  c a s s e t t e SIDE  students  not w r i t e you.  booklets  has  girls:  I am interested i n h e l p i n q 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 questions—-questions that have no r i q h t or wrong a n s w e r s . They a r e questions about how you feel. You can answer h o n e s t l y b e c a u s e I w i l l n o t know y o u r name. Your t e a c h e r w i l l g i v e you a number t h a t you w i l l w r i t e on e a c h of y o u r answer sheets. Your t e a c h e r w i l l not know y o u r a n s w e r s b e c a u s e y o u r  174  answer s h e e t s w i l l he 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 t h o u g h we won't know who your are, your answers are very i m p o r t a n t s o p l e a s e answer c a r e f u l l y . On t h e answer s h e e t that has been handed out, your answers t o the f i r s t s e t of q u e s t i o n s w i l l go 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 t o chanqe any o f your answers. Make your decision before you mark your s h e e t ; I f you have t o make a chanqe e r a s e t h e o l d mark a s w e l l as ycu can. Each o f t h e f o l l o w i n q q u e s t i o n s needs a y e s or no a n s w e r . I f y o u r answer i s y e s , c i r c l e t h e YES b e s i d e t h e q u e s t i o n number. I f y o u r answer, i s no, c i r c l e t h e NO. E a c h q u e s t i o n must h a v e one answer. Please l o o k a t t h e example a t t h e bottom f i r s t page.  the  Are  as t h e y 6. 7.  Turn  9.  any  questions?  (Pause.)  Open y o u r b o o k l e t s and answer the a r e r e a d from t h e t a p e ; on  the  questions  tape.  Say: Close  8.  there  of  y o u r b o o k l e t s and  G i v e them  a 5 -  10  turn  minute  them  over.  break*  Say: Open your booklets to (Pause.) The answers t o will go i n t h e columnthe f o l l o w i n q questions two p o s s i b l e statements Remember, e a c h q u e s t i o n answer. Look a t t h e Are  there  example;  any  the second s e t of q u e s t i o n s . the next set of questions headed QUESTION SET #2. For you must s e l e c t one of the t h a t complete the sentence. must have one and only one  (Pause.)  questions?  (Pause,)  Turn o v e r y o u r answer s h e e t s . as t h e y a r e r e a d from t h e t a p e .  Answer t h e  questions  175  10.  T u r n on t h e  tape.  11. A t t h e end of t h e s e c o n d s e t o f questions STOP THE TAPE. DO NOT EEWIND. I T I S I N THE COERECT POSITION TO START THE NEXT SESSION. 12. COLLECT THE EXTRA P E N C I L S .  ANSWER  SHEETS,  THE  BOOKLETS,  AND  THE  SECOND SESSION 1. Set up t h e t a p e r e c o r d e r w i t h t h e 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 t h e t a p e 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 the tape on to see i f QUESTION SET #3 i s a n n o u n c e d . 2. Hand o u t the answer sheets. Make sure t h a t the a n s w e r s h e e t s g e t b a c k t o t h e c o r r e c t c h i l d e r n by using your c l a s s l i s t . 3.  Hand o u t e x t r a p e n c i l s i f n e e d e d ,  4.  Hand o u t  5.  the  booklets.  Say: Open y o u r b o o k l e t s t o t h e i n s t r u c t i o n s f o r t h e set of questions,.  third  In this 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 sentences* I f you a g r e e w i t h t h e s t a t e m e n t t r y to decide i f ycu feel s t r o n g l y a b o u t i t , I f so you w o u l d 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 circle the 2. Or you might disagree with the statement. 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 a b o u t i t . I f you do, c i r c l e t h e 5. I f you just disagree circle the 4. I f you c a n ' t make up y o u r mind o r d o n ' t u n d e r s t a n d t h e s e n t e n c e , then circle t h e 3. Look a t the example i n your b o o k l e t . Do  you  h a v e any  questions?  (Pause.)  (PAUSE).  Answer e a c h q u e s t i o n a s i t i s r e a d f r o m t h e 6.  T u r n on  the  tape*  tape.  176  7.  A t t h e end o f t h e t h i r d s e t o f q u e s t i o n s STOP THE TAPE. REWIND THE TAPE  8. Collect pencils.  the  booklets,  9. P l a c e t h e answer s h e e t s BLUE t a b on i t .  answer s h e e t s  i n t h e envelope  and e x t r a  with t h e  10. R e t u r n t h e c a s s e t e , b o o k l e t s , and a n s w e r sheets t o t h e o f f i c e t o b e p i c k e d up. Keep t h e 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 t h e next few d a y s . THANK YOU FOR YOUR EEFORT  AND  ASSISTANCE.  177  T E A C H E S S ADMINISTSATION INSTBUCTIONS ACHIEVEMENT TESTS 1  Before you make s u r e you h a v e :  begin administering  1.  A class  s e t of S t a n f o r d  2.  A class  s e t of Canadian T e s t s o f Basic S k i l l s  3.  An answer s h e e t  4.  Ten e x t r a  5.  An e n v e l o p e  The days.  tests  The  and  Achievement  f o r each  Tests  tests  (SAT) . (CTBS).  student*  pencils. with  should  SAT  on  a BED t a b .  be a d m i n i s t e r e d  the  CIBS-mathematics concepts day,  the achievement  morning  test  t h e CTBS-problem  of  on  two  the  first  on t h e a f t e r n o o n  solving  test  consecutive day,  of  the  the first  on t h e m o r n i n g o f t h e  s e c o n d day. For  purposes of  must be m a i n t a i n e d .  standardization  However, a l t h o u g h  preferable,  plattocning  impossible.  Therefore,  discretion.  If  the  one s h o u l d b e g i v e n  the  last  the t e s t s envelope  after  the timing  timing  will  be  during  sequence  suggested  left  t o be a d m i n i s t e r e d  b e f o r e r e c e s s , one a f t e r  lunch.  administered  above  is  o t h e r c o n s i d e r a t i o n s may make i t  t h e t e s t s HAVE  then  one  or  the  In a l l cases  to  your  on one day recess  and  though, please  have  t h e two d a y s s p e c i f i e d  on  your  w i t h t h e BED t a b . Before  you  hand  out  any  s t u d e n t s n o t t o w r i t e on t h e b o o k l e t s only as described.  m a t e r i a l s please and t o mark  ask y o u r  the  sheets  178  Would collected because  you  also  and r e t u r n e d other  classes  be  sure  that  to tbe office will  be  a l l materials  when  using  you  are  are f i n i s h e d  t h e same p e n c i l s a n d  tests.  1.  Hand o u t a n s w e r s h e e t s a n d 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 t h e number y o u a r e going to give them i n t h e s p a c e i n t h e u p p e r l e f t h a n d c o r n e r marked IDENTIFICATION NUMBEB. B e a d t h e number f r o m t h e same c l a s s l i s t t h a t y o u used t o a s s i g n numbers f o r t h e questionnaires. 3.  Say: This i s the f i r s t of a s e t of three mathematics tests t o f i n d o u t how much you h a v e 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 p e r s o n that sent the questionnaires. However, he w i l l r e t u r n t h e r e s u l t s o f t h e t e s t s t o me, s o be s u r e y o u do y o u r b e s t . I shall give y o u a^ t e s t b o o k l e t . u n t i l I t e l l y o u t o do s o .  4. 5.  Do n o t open i t  Hand o u t b o o k l e t s . Say: Now open your b o o k l e t s t o t e s t 5: Arithmetic C o m p u t a t i o n , w h i c h s t a r t s on page 16,. Look a t t h e t o p 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 says "DIBECTIONS". The d i r e c t i o n s s a y ; "Work t h e e x a m p l e i n e a c h b o x . Then l o o k a t t h e p o s s i b l e a n s w e r s a t t h e r i g h t side of t h e b o x and s e e i f y o u r a n s w e r i s g i v e n . If i t i s , c i r c l e t h e l e t t e r on y o u r a n s w e r s h e e t w h i c h i s t h e same l e t t e r a s 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 a n s w e r i s NOT g i v e n , c i r c l e t h e l e t t e r w h i c h i s t h e same a s t h e l e t t e r beside NG w h i c h 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 s a m p l e q u e s t i o n . 64 m i n u s 23 leaves what? The c o r r e c t a n s w e r , 41 , h a s 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 t h e  179  p o s s i b l e a n s w e r s a t t h e r i g h t s i d e o f t h e box i s " c " so you would c i r c l e t h e " c " on y o u r answer s h e e t . When I t e l l you t o s t a r t , b e h i n w i t h example 1 and do as many examples on pages 16 and 17 as you can. Do not spend t o o much t i m e on any one example, i f you c a n n o t do an example, go on to the next one. When you finish page 1 7 , example 3 9 , go back and c h e c k y o u r work on t h i s t e s t . Do n o t work on any o t h e r test,. Use t h e s c r a t c h p a p e r f o r f i g u r i n g . BEADY, GOJ 6. it;  B e c o r d t h e STABTING TIME. Add t h i r t y f i v e When t h i s t i m e i s r e a c h e d s a y :  STOP!  C l o s e your b o o k l e t  7. Collect pencils,.  the  booklets,  1. At t h e n e x t s e s s i o n , making sure that the sheets. 2.  3.  Hand o u t any  answer  sheets,  out  the  p e n c i l s i f needed,  booklets  down,.  and  extra  and  for  scratch  Do  not  paper.  open  the Canadian T e s t s of  Basic  Say: Now we a r e r e a d y f o r t h e second mathematics test; Open your test b o o k l e t t o page 77. (Pause.) F i n d the s e c t i o n o f your answer sheet f o r test M-1, Mathematics Concepts. (Pause.) The directions I w i l l r e a d t o you a r e a l i t t l e d i f f e r e n t , so listen carefully. This i s a t e s t system and mathematics. F o u r answers  o f how w e l l the terms  are given  to  hand out the answer sheets, students get their own answer  Say: I s h a l l g i v e you a t e s t b o o k l e t a g a i n * i t u n t i l I t e l l you t o do s o .  4. Hand Skills. 5.  and p u t y o u r p e n c i l  minutes  you and  u n d e r s t a n d t h e number operations used in  f o r each e x e r c i s e ,  but  only  180  one o f these answers i s r i g h t . You a r e t o c h o o s e t h e one a n s w e r t h a t y o u t h i n k i s b e t t e r t h a n t h e other T h e n , on t h e a n s w e r s h e e t , f i n d t h e row o f a n s w e r numbers t h a t i s numbered t h e same a s t h e exercise. Circle t h e number on t h e a n s w e r s h e e t t h a t i s t h e same a s 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. s c r a t c h paper f o r f i g u r i n g .  Use y o u r  You will have 30 m i n u t e s for this test. I f you finish early, close your test booklet and w a i t quietly. Don't look a t the other tests i n the booklet. I f y o u have a n y 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 y o u a f t e r t h e o t h e r s have b e q u n . T u r n 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 r e a c h 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*) E e a d y , go. 6. fiecord the time. reached say: STOP; 7.  Add 30 m i n u t e s .  Close your  test  When t h i s t i m e  i s  booklet.  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  session  1. Hand o u t the answer s h e e t s , making sure t h a t t h e s t u d e n t s g e t t h e i r own a n s w e r s h e e t s . 2. 3.  Hand o u t a n y p e n c i l s i f n e e d e d , and s c r a t c h p a p e r . 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,. i t u n t i l I t e l l y o u t o do s o .  4. Hand out Basic S k i l l s . 5.  Do n o t  open  t h e booklets f o r t h e Canadian Test of  Say Now we a r e r e a d y f o r t h e t h i r d mathmematics test. Open y o u r t e s t b o o k l e t t o page 8 7 . F i n d t h e s e c t i o n of your answer sheet f o r Test M-2, M a t h e m a t i c s Problem S o l v i n g . (Pause.) As t h e d i r e c t i o n s I will read a r e d i f f e r e n t from those i n t h e booklet l i s t e n carefully.  181  T h i s i s t e s t of how w e l l you c a n solve mathematics problems. The exercises i n the t e s t are l i k e the s a m p l e s 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 a n s w e r s and a "not given" meaning t h a t t h e c o r r e c t answer i s n o t g i v e n . Work e a c h e x e r c i s e and compare y o u r answer w i t h t h e t h r e e p o s s i b l e answers. I f the correct answer is given, circle the number t h a t i s t h e same as t h e number b e s i d e t h e right answer. If the correct answer i s not g i v e n , c i r c l e t h e f o u r t h number. The  sample e x e r c i s e s  show you  what t o  do.  Now read t h e f i r s t sample e x e r c i s e . (Pause.) What i s t h e r i g h t answer f o r t h i s e x e r c i s e ? (Pause for reply.) Yes, the s e c o n d a n s w e r , 3, i s t h e 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 t h e s e c o n d answer i s t h e c o r r e c t one. Sometimes t h e c o r r e c t answer i s n o t g i v e n . Now read t h e s e c o n d 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 p r o b l e m ? (Pause f o r r e p l y . ) Yes, 1, i s t h e c o r r e c t a n s w e r . S i n c e 1 i s not one o f t h e s u g g e s t e d a n s w e r s , you would c i r c l e t h e four on y o u r answer s h e e t t o show t h a t t h e 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 n o t r e w o r k an e x e r c i s e when y o u r answer is not like any of the t h r e e suggested answers. Instead, c i r c l e t h e number 4 and go on t o t h e n e x t exercise. If you c a n n o t work an e x e r c i s e , l e a v e i t and go on t o t h e n e x t one. I f you have t i m e , you may return to i t l a t e r . Do the  y o u r work on t h e test booklet.  scratch  paper.  Do  not  write  on  You w i l l h a v e 30 m i n u t e s f o r t h i s test. Now find ycur place to begin* T u r n t o page 91 and b e g i n w i t h exercise 40. Stop when you r e a c h page 93 e x e r c i s e 70. (Pause.) Does e v e r y o n e have the right place? (Pause.) Heady, go. Eecord the time. s reached say: Stop!  Time i s up.  Add  thirty  Please  minutes.  close once.  When t h i s  your t e s t  booklet  time  at  182  7. Collect answer sheets, answer s h e e t s i n t h e e n v e l o p e m a t e r i a l s t o the o f f i c e . THANK YOU  ALL  b o o k l e t s , and p e n c i l s . Put w i t h t h e RED tab. Return  FOR YOUR TIME AND  PATIENCE.  183  Appendix D QUESTIONNAIRE BOOKLET1 DC NOT OPEN THIS BOOKLET UNTIL YOUR TEACHES T E L L S YOU Beys and g i r l s : I better  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 b o y s a n d g i r l s t o do in  school.  questions—questions They a r e q u e s t i o n s  I that about  will  be  asking  have  no  riqht  how  you  feel.  h o n e s t l y b e c a u s e I w i l l n o t know y o u r name; qive  you  sheets. answer  a number t h a t you w i l l  o r wrong You  some  answers.  can  answer  Your t e a c h e r  w r i t e on e a c h o f y o u r  sheets  will  your  be  placed  i n an  are very  important  your  e n v e l o p e , s e a l e d and  H o w e v e r , e v e n t h o u g h we won't know  answers  will  answer  Y o u r t e a c h e r w i l l n o t know y o u r a n s w e r s b e c a u s e  d e l i v e r e d t o me. are,  you  so  please  who  you  answer  carefully. On t h e a n s w e r s h e e t t h a t h a s b e e n handed number t h a t t h e t e a c h e r h a s g i v e n IDENTIFICATION Your  you  out write the  i n t h e space  marked  NUMBER;. answers  to  the f i r s t  s e t o f q u e s t i o n s w i l l qo  u n d e r t h e c o l u m n s w i t h t h e h e a d i n g QUESTION SET #1.  Try not  The f i r s t s e t o f 3 0 i t e m s make up t h e T e s t A n x i e t y S c a l e f o r Children. The s e c o n d s e t o f 34 i t e m s make up t h e I n t e l l e c t u a l Achievement Responsibility Scale. The Achievement Responsibility Scale was s c o r e d a n d t h e i t e m s s p l i t i n t o t w o sub-scales as described i n C r a n d a l l , K a t k o v s y and C r a n d a l l (1965). l  184  to  c h a n g e any o f y o u r  mark y o u r s h e e t .  answers.  Make y o u r d e c i s i o n b e f o r e  I f you h a v e t o make a c h a n g e e r a s e  you  the o l d  mark as w e l l a s y o u can* Each answer.  of  number.  the q u e s t i o n for  circle  the  n e e d s a y e s o r no YES  I f y o u r answer i s no, c i r c l e  example  beside t h e NO  Do y o u l i k e  dogs? beside  4.  YES  NO  5.  YES  NO  6.  YES  NO  you have any q u e s t i o n s  number 5 c i r c l e  please  ask y o u r  the  beside  i f q u e s t i o n 5 was  answer was y e s , t h e n  If  guestions  number.  5. your  following  I f y o u r answer i s y e s ,  guestion  And  the  YES.  teacher.*  185  You  must answer e v e r y  q u e s t i o n YES o r NO.  1.  Do you w o r r y when t h e t e a c h e r s a y s t h a t s h e i s g o i n g ask you q u e s t i o n s t o f i n d o u t how much you know?  2.  Do you worry a b o u t b e i n g p r o m o t e d , t h a t i s , p a s s i n g from t h e s i x t h g r a d e t o t h e s e v e n t h g r a d e a t t h e end o f t h e year?  3.  When t h e t e a c h e r a s k s y o u t o g e t up i n f r o n t o f t h e 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 y c u a r e g o i n g t o make some bad mistakes?  4.  When t h e t e a c h e r s a y s s h e i s g o i n g t o c a l l upon some b o y s and g i r l s i n t h e c l a s s t o do a r i t h m e t i c p r o b l e m s , do y o u hope t h a t s h e w i l l c a l l upon someone e l s e and n o t on you?  5.  Do you sometimes dream a t n i g h t t h a t you a r e and c a n n o t answer t h e t e a c h e r * s g u e s t i o n s ?  6.  When t h e t e a c h e r s a y s t h a t she i s g o i n g t o f i n d o u t how much you h a v e l e a r n e d , does your heart begin t o beat faster?  7.  When t h e t e a c h e r i s t e a c h i n g y o u a b o u t a r i t h - m e t i c , do you feel that other children i n the c l a s s understand her b e t t e r t h a n you?  8.  When y o u a r e i n bed a t a b o u t how you a r e g o i n g  9.  When t h e t e a c h e r a s k s you t o w r i t e on t h e b l a c k b o a r d i n frpnt of the c l a s s , does t h e hand you w r i t e with sometimes shake a l i t t l e ?  10.  When the teacher i s t e a c h i n g you a b o u t 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 better t h a n you?  11.  Do you t h i n k children?  12.  When y o u a r e a t home and you a r e t h i n k i n g about your arithmetic l e s s o n f o r t h e n e x t d a y , do you become a f r a i d t h a t you w i l l g e t the answers wronq when the teacher c a l l s upon you?  13.  I f y o u a r e s i c k and m i s s s c h o o l , do you worry t h a t you will do more poorly i n your schoolwork than other c h i l d r e n when y c u r e t u r n .  you  in  to  school  night, do y o u sometimes worry t o do i n c l a s s t h e n e x t day?  worry  more  about s c h o o l than  other  186  14.  Do you s o m e t i m e s dream a t n i g h t t h a t o t h e r b o y s and g i r l s i n y o u r c l a s s c a n do t h i n g s y o u c a n n o t d o ?  15.  When y o u a r e home a n d y o u a r e t h i n k i n g a b o u t y o u r r e a d i n g lesson f o r t h e n e x t d a y , do you w o r r y t h a t y o u w i l l do p o o r l y on t h e l e s s o n ?  16.  When t h e t e a c h e r s a y s t h a t s h e i s g o i n g t o f i n d o u t how much y o u h a v e l e a r n e d , do y o u g e t a f u n n y f e e l i n g i n y o u r stomach?  17.  I f you d i d v e r y p o o r l y when t h e t e a c h e r c a l l e d on y o u , w o u l d y o u p r o b a b l y f e e l l i k e c r y i n g even t h o u g h y o u w o u l d try not t o cry?  18.  Do you s o m e t i m e s dream a t n i g h t t h a t t h e t e a c h e r i s a n g r y b e c a u s e y o u do n o t know y o u r l e s s o n s ?  In What  I  the following  q u e s t i o n s t h e word  "test"  i s  used.  mean b y " t e s t " i s a n y t i m e t h e t e a c h e r a s k s y o u t o do  s o m e t h i n g t o f i n d o u t how much y o u know o r how much learned.  It  could  be  by y o u r w r i t i n g  s p e a k i n g a l o u d , o r by y o u r w r i t i n g understand  what  I  mean  by  to  - find  have  on p a p e r , o r by y o u r  on t h e b l a c k b o a r d .  "test"  t e a c h e r a s k s y o u t o do s o m e t h i n g  you  Do  you  i t i s any t i m e t h e out  how  much  you  well  know.  19.  Are you a f r a i d o f s c h o o l  tests?  20.  Do y o u w o r r y a l o t b e f o r e y o u t a k e a t e s t ?  21.  Do y o u w o r r y a l o t w h i l e y o u a r e t a k i n g  22;  After you h a v e t a k e n a t e s t d o y o u w o r r y a b o u t how you d i d on t h e t e s t ?  23.  Do y o u s o m e t i m e s dream a t n i g h t t h a t y o u d i d p o o r l y o n t e s t y o u had i n s c h o o l t h a t d a y ?  24.  When y o u a r e t a k i n g a t e s t ,  a test?  a  d o e s t h e hand y o u a r e w r i t i n g  with  shake a  \11  little?  25.  When t h e t e a c h e r s a y s t h a t s h e i s g o i n g t o g i v e t h e c l a s s a t e s t , do y o u become a f r a i d t h a t you w i l l do p o o r l y ?  26.  When you a r e t a k i n g a hard t h i n g s y o u knew v e r y w e l l b e f o r e test?  t e s t , do y o u f o r g e t you s t a r t e d taking  27.  Do y o u wish a l o t o f t i m e s t h a t about t e s t s ?  you d i d n ' t  28.  When t h e t e a c h e r s a y s t h a t s h e i s g o i n g t o g i v e t h e c l a s s a t e s t , do you g e t a n e r v o u s o r f u n n y f e e l i n g ?  29*.  While you a r e t a k i n g doing poorly?  30*  While y o u a r e on y o u r way t o s c h o o l , do you s o m e t i m e s w o r r y t h a t t h e t e a c h e r may g i v e t h e c l a s s a t e s t ?  a t e s t do you u s u a l l y  DO NOT TORN THE PAGE UNTIL THE TEACHER TELLS YOU  some the  w o r r y s o much  think  you  are  188  The the  answers to the n e x t  column  headed  q u e s t i o n s you that  must s e l e c t  complete the 6.  If the  you  QUESTION one  sentence.  If you choose 1. 2.  were  s e t of q u e s t i o n s #2.  SET  o f t h e two For  For  will the  possible  qo  in  followinq statements  example  given  a  choice of  p i e would  you  apple, or cherry?  p r e f e r cherry then  beside  number 6 .  You  would  circle  2.  If  you  have any  questions  p l e a s e ask  I f a t e a c h e r p a s s e s you to the next p r o b a b l y be 1. because she l i k e d you, o r 2. b e c a u s e o f the work you d i d ?  your  teacher.  grade,  would  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 t o be 1. b e c a u s e you s t u d i e d f o r i t , or 2. b e c a u s e t h e t e s t was e s p e c i a l l y e a s y ?  i t  likely  When you have t r o u b l e u n d e r s t a n d i n g s o m e t h i n g i n school, i s i t usually 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. b e c a u s e you d i d n ' t l i s t e n c a r e f u l l y ? When you r e a d a s t o r y and c a n ' t remember much o f i t , i s i t usually 1. b e c a u s e t h e s t o r y wasn't w e l l w r i t t e n , o r 2. b e c a u s e you w e r e n ' t i n t e r e s t e d i n t h e s t o r y ? Suppose Is t h i s 1. 2. Suppose Would i 1. 2.  your p a r e n t s s a y you a r e d o i n g well l i k e l y t o happen b e c a u s e y o u r s c h o o l work i s g o o d , o r b e c a u s e t h e y a r e i n a good mood?  in  school.  you d i d b e t t e r t h a n u s u a l i n a s u b j e c t a t s c h o o l . t p r o b a b l y happen b e c a u s e you t r i e d h a r d e r , o r b e c a u s e someone h e l p e d you?  189  7.  When • y o u 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 , d o e s i t u s u a l l y happen 1. b e c a u s e t h e o t h e r p l a y e r i s good a t t h e game, o r 2. because you don't p l a y w e l l ?  8.  Suppose a p e r s o n d o e s n ' t t h i n k y o u a r e v e r y bright or clever. 1. c a n y o u make h i m c h a n g e h i s mind i f y o u t r y t o , or 2. a r e t h e r e some p e o p l e who w i l l t h i n k y o u r ' r e n o t v e r y b r i g h t no m a t t e r what y o u d o ?  9.  I f you s o l v e a puzzle g u i c k l y , i s i t fl. b e c a u s e i t w a s n ' t a v e r y h a r d p u z z l e , o r 2. b e c a u s e y o u worked on i t c a r e f u l l y ?  10.  I f a b o y o r g i r l t e l l s y o u t h a t y o u a r e dumb, i s i t more l i k e l y t h a t they say t h a t 1. b e c a u s e t h e y a r e mad a t y o u , o r 2. b e c a u s e what y o u d i d r e a l l y wasn't v e r y b r i g h t ?  11.  Suppose and you 1. 2.  12;  When y o u l e a r n s o m e t h i n g 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,. b e c a u s e y o u 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 ?  13.  I f a t e a c h e r s a y s t o y o u , " Y o u r work i s f i n e , " i s i t 1. s o m e t h i n g t e a c h e r s u s u a l l y s a y t o e n c o u r a g e pupils, or 2. b e c a u s e y o u d i d a good j o b ?  14;  When y o u f i n d i t h a r d t o work a r i t h m e t i c o r math p r o b l e m s at s c h o o l , i s i t 1. b e c a u s e y o u d i d n ' t s t u d y w e l l enough b e f o r e y o u t r i e d them, o r 2. b e c a u s e t h e t e a c h e r gave p r o b l e m s t h a t w e r e t o o hard?  15.  When y o u f o r g e t s o m e t h i n g y o u h e a r d i n c l a s s , i s i t 1. because t h e teacher d i d n ' t e x p l a i n i t very w e l l , or 2. b e c a u s e y o u d i d n ' t t r y v e r y h a r d t o remember?  16.  Suppose you w e r e n ' t s u r e a b o u t t h e a n s w e r t o a q u e s t i o n y o u r t e a c h e r a s k e d y o u , b u t y o u r answer t u r n e d o u t t o be right. I s i t l i k e l y t o happen  y o u 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 , or doctor fail; Do y o u t h i n k t h i s w o u l d happen b e c a u s e y o u d i d n ' t work h a r d e n o u g h , o r b e c a u s e y o u needed some h e l p , a n d 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?  190  1. 2.  b e c a u s e s h e w a s n ' t a s p a r t i c u l a r as u s u a l , o r b e c a u s e y o u gave t h e b e s t a n s w e r y o u c o u l d t h i n k of?  17.  When y o u r e a d a story a n d remember most o f i t , i s i t usually 1. b e c a u s e y o u were i n t e r e s t e d i n t h e s t o r y , o r 2. b e c a u s e t h e s t o r y was w e l l w r i t t e n ?  18.  I f your parents t e l l you you're a c t i n g silly and n o t 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. b e c a u s e o f s o m e t h i n g you d i d , o r 2. b e c a u s e t h e y h a p p e n t o be f e e l i n g c r a n k y ?  19.  When y o u d o n ' t d o w e l l on a t e s t a t s c h o o l , i s i t 1. b e c a u s e 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 y o u w i n a t a game o f c a r d s o r c h e c k e r s , does i t happen 1. b e c a u s e y o u p l a y r e a l l y w e l l , o r 2. because t h e other person doesn't play 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. b e c a u s e t h e y happen t o l i k e y o u , o r 2. b e c a u s e y o u 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 n e x t g r a d e , would i t p r o b a b l y be 1. b e c a u s e s h e "had i t i n f o r y o u , " o r 2. b e c a u s e y o u r s c h o o l work wasn't good enough?  23.  Suppose y o u d o n ' t do a s w e l l a s u s u a l i n a s u b j e c t a t school; Would t h i s p r o b a b l y h a p p e n 1. because you weren't as c a r e f u l a s u s u a l , o r 2. b e c a u s e somebody b o t h e r e d y o u a n d k e p t y o u f r o m 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 , usually 1. b e c a u s e y o u t h o u g h t up a good i d e a , o r 2. b e c a u s e t h e y l i k e y o u ?  25.  S u p p o s e 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 y o u t h i n k t h i s would happen 1. b e c a u s e o t h e r p e o p l e h e l p e d you when y o u n e e d e d i t , or 2. because you worked v e r y hard?  26.  Suppose your parents s a y you a r e n ' t d o i n g w e l l i n y o u r s c h o o l work. I s t h i s l i k e l y t o happen more  i si t  191  1. 2.  b e c a u s e y o u r work i s n ' t v e r y g o o d , o r because they a r e f e e l i n g cranky?  27.  Suppose y o u a r e s h o w i n g a f r i e n d how t o p l a y a game and he h a s t r o u b l e w i t h i t . Would t h a t h a p p e n 1. b e c a u s e he w a s n ' 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 y o u f i n d i t e a s y t o work a r i t h m e t i c o r math p r o b l e m s at s c h o o l , i s i t u s u a l l y 1. b e c a u s e t h e t e a c h e r gave y o u e s p e c i a l l y e a s y problems, or 2. b e c a u s e y o u s t u d i e d y o u r book w e l l b e f o r e y o u t r i e d them?  29.  When y o u remember s o m e t h i n g y o u h e a r d i n c l a s s , usually 1. b e c a u s e y o u t r i e d h a r d t o remember, o r 2. b e c a u s e t h e 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 y o u c a n ' t work a p u z z l e , i s i t more l i k e l y t o happen 1. b e c a u s e y o u a r e n o t e s p e c i a l l y good a t w o r k i n g puzzles, or 2. because t h e 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 y o u r p a r e n t s t e l l you t h a t you a r e b r i g h t i s i t more l i k e l y 1. b e c a u s e t h e y a r e f e e l i n g g o o d , o r 2. because o f something you did?  32.  Suppose y o u 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. b e c a u s e y o u e x p l a i n e d i t w e l l , o r 2. b e c a u s e he was a b l e t o u n d e r s t a n d i t ?  33.  Suppose you're n o t s u r e a b o u t t h e 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 y o u g i v e turns out t o be wrong. I s i t l i k e l y t o happen 1. b e c a u s e s h e 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 t o o q u i c k l y ?  34.  I f a t e a c h e r s a y s t o y o u , " T r y t o do b e t t e r , " w o u l d i t be 1. because t h i s i s somethinq she miqht say t o g e t pupils t c t r y harder, or 2. b e c a u s e y o u r work w a s n ' t a s good a s u s u a l ?  or  DO NOT TOBN THE PAGE UNTIL YOUB TEACHEB TELLS YOU  i s i t  clever,  192  In sentences;  this  next  section  I f you a g r e e w i t h t h e s t a t e m e n t t r y t o  you f e e l s t r o n g l y about i t . you j u s t  you w i l l be g i v e n a number o f  agree, c i r c l e  statement.  If  so,  it.  I f y o u do c i r c l e  4.  If  you  can't  I f so you would  t h e 2.  c i r c l e t h e 1„  If  O r , you might d i s a g r e e w i t h t h e  t r y t o d e c i d e i f you f e e l t h e 5.  decide i f  strongly  about  I f you j u s t d i s a g r e e c i r c l e  make up y o u r mind o r d o n ' t  the  understand 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. For  e x a m p l e , i f t h e s t a t e m e n t was 8.  I l i k e i c e cream.  I f y o u l o v e i t y o u w c u l d c i r c l e t h e 1. If  you j u s t  If  y o u c a n ' t make up y o u r m i n d o r d o n ' t c a r e y o u would the  like  i t you would c i r c l e  t h e 2. circle  3.  If  you d o n ' t  like  i t y o u would c i r c l e  If  you h a t e i t y o u w o u l d c i r c l e t h e 5.  t h e 4.  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 p a g e when y o u r t e a c h e r t e l l s y o u . The column  answers  f o r these  h e a d e d QUESTION SET #3.  questions  will  go u n d e r t h e  193  1.  I enjoy t a l k i n g  2.  Mathematics  3.  I t makes me mathematics.  4.  Mathematics i s something which I enjoy very  much.  5.  D o i n g w e l l i n m a t h e m a t i c s h e l p s me  subjects.  6.  When I dislike.  people about  mathematics.  7.  I am  8.  I f I d o n ' t s e e how t o work a away, I n e v e r g e t i t ;  9.  Mathematics  i s more o f a game t h a n i t i s h a r d work. nervous  hear  good  to other  the  to  even  think  about  i n other  doing  word m a t h e m a t i c s , I have a f e e l i n g  a t working mathematics  i s u s e f u l f o r my  problems.  mathematics  problem  right  p r o b l e m s i n e v e r y day  life.  10.  Most p e o p l e s h o u l d s t u d y some  11.  I feel  mathematics.  12.  I d o n ' t do v e r y w e l l i n m a t h e m a t i c s .  13.  I h a v e a good  14.  You can get along without mathematics.  ,15.  Mathematics  16.  I would like mathematics.  17.  M a t h e m a t i c s i s u s e f u l f o r t h e p r o b l e m s o f e v e r y day  18.  I can get along mathematics.  perfectly  w e l l i n e v e r y day l i f e  19.  No matter how mathematics.  hard  try,  20.  Working  21.  If I got better m a t h e m a t i c s more.  22.  Mathematics h e l p s  t e n s e when someone t a l k s  feeling  mathematics.  mathematics,; well  in  e v e r y day  life  i n understanding today's world.  spend  mathematics  t o me a b o u t  perfectly  i s helpful to  toward  of  I  less  time  I  in  school  cannot  doing life.  without  understand  i s fun. marks  in  mathematics  I would e n j o y  me u n d e r s t a n d t o d a y ' s w o r l d .  1 94  23.  Mathematics i s easy f o r  24.  I like  25.  There i s l i t t l e  27-  I feel  28.  There i s l i t t l e would want.  2S.  I t scares  30.  I would  31.  Mathematics developaent.  32.  Most o f t h e i d e a s i n m a t h e m a t i c s a r e n ' t me*  33.  It get  34.  I don't l i k e  35.  I remember most o f t h e t h i n g s I l e a r n i n m a t h e m a t i c s .  36.  I t doesn't d i s t u r b  t o play  me.  games t h a t  use  numbers.  n e e d f o r m a t h e m a t i c s i n most  a t ease i n a mathematics  me  like  class.  need f o r m a t h e m a t i c s i n t h e j o b s  t o have  to take  that  I  mathematics.  a j o b w h i c h d o e s n ' t use any m a t h e m a t i c s . is  i s important a gccd j o b .  of  great  importance  to  a  very  country's  useful  for  f o r me t o know m a t h e m a t i c s i n o r d e r t o  a n y t h i n g about mathematics.  me  t o work m a t h e m a t i c s p r o b l e m s .  37. I t i s i m p o r t a n t t o know m a t h e m a t i c s i n good job. 38.  Working  w i t h numbers u p s e t s  39.  I often think, "I p r o b l e m seems h a r d ,  40.  Most o f t h e i d e a s THANK YOU  jobs.  FOE  can't  order  to  get  a  me. do  i t , " when a  i n mathematics a r e n ' t  very  mathematics useful.  ANSWERING ALL THESE QUESTIONS  195  Appendix IAY  E  OUT OF THE STUDENT ANSWEE FORMS  Eeproduced below a r e t h e f i r s t sheets f o r t h e achievement tests. Identification  Number - — — — " ' •"• - • — — T  Card  K e y p u n c h C a r d #1 I n f o Only  a f a  response  b g b  c h c  d i d  — ~  Card  #2  52. 53. 54.  e j e  1 1 1  2 2 2  3 3 3  Number  Keypunch Card I n f o Only  #4  Question Set 1  Card  yes yes yes  no no no  1 1 1  1 1 1  2 2 2  3 3 3  lines  4 4 4  of the  C a r d #6  Question Set 2  1. 2. 3.  few  #5  Question Set 3 Strongly Agree  1. 2. 3.  40. 41. 42.  4 4 4  R e p r o d u c e d below are the f i r s t sheets f o r the a f f e c t i v e s c a l e s .  Identification  #3  T e s t M-2 Math Problem S o l v i n g  T e s t M-1 Math C o n c e p t s  Computation Test 1. 2. 3.  few l i n e s o f t h e a n s w e r  2 2 2  1. 2. 3.  1 1 1  Don«t Strongly Know Disagree Agree Disagree  2 2 2  3 3 3  4 4 4  5 5 5  196  Appendix F CLASS MEANS AND  STANDARD DEVIATIONS  VARIABLES AND  OF THE  ACHIEVEMENT  AFFECTIVE VARIABLES  C l a s s COMP CONC PROB TASC IABS IARF MANX VSOC SCON ENJOY VSELF  1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21  16.9 6.66 20.0 6.36 20.4 7.53 18.7 8. 14 25.1 5. 04 26.2 4.24 19.4 5. 76 14.2 3.85 20.2 7.06 22.5 2.88 18.3 7.54 23.9 6. 92 17.4 6.05 18.2 7.77 24.8 5. 34 14.4 5.62 15.2 6.03 23.7 6.63 18.0 7.47 19.4 7- 21  20.5 8.63 25.7 7. 94 29.5 8.35 22.6 9.38 32.8 5.70 33. 1 5.62 26.5 6.28 20.6 7.02 29.2 6.58 35.3 3.50 24.4 8.S5 28. 1 8.04 23.6 6.79 23.6 7.52 27.5 6.78 23.0 9.29 20.2 6.70 26.4 7.65 27.5 6.76 26.6 6.31  12.6 7.01 16.3 5,49 21.1 6.03 15.0 6.21 22.8 3.83 21.7 5.04 17.3 5.41 13. 4 4.43 20. 1 5.78 25.0 2.61 15.9 6.00 20. 1 6.35 14.7 5.50 15.0 5.72 20.2 5.35 14.0 6.64 12.8 5. 11 18.7 3.35 20.3 4.59 19.2 5.61  14.6 30.0 27.4 5.06 2.10 3.01 14.5 28.0 26.9 5.01 3.01 2.49 9.9 29.9 29.3 6,06 2.4 7 2.02 11.7 30.0 28.1 6.29 2.17 2.81 13.9 29.8 29.7 8,49 1.72 1.32 9.63 29.5 27.2 4. 19 2.42 3.47 11.3 30.7 27.7 5.16 1.74 2.69 15.2 30.0 27.3 5,21 2.37 2.69 13.8 29.8*26.8 3.37 2.79 3.1 1 8.5 31.8 29,3 1,97 0.98 2.25 11.3 30.1 26.4 4.11 1.78 2.70 13.0 29.8 28.7 6.82 2.19 2.70 12.0 28.2 26.8 5,93 2.94 2.66 11.9 29.9 29.1 5.88 2.37 2.59 11.0 29.7 27.4 5.96 2.31 3. 16 11.2 28.8 27.7 7. 17 2.66 2.39 12.2 29.7 28.0 5.78 1.95 2.55 12.3 29.9 29.2 4.30 2.26 2.68 11.4 29.8 26.6 5,25 2.66 2.93 13.1 29.8 27.2 4,94 1,86 3.67  19.6 31.0 5.55 5.28 17.4 34.1 6.26 3. 97 20.8 31.9 8. 56 3. 98 21.8 30.4 6.41 5:. 40 18.3 34.2 5. 22 3.80 17.2 32.4 6.89 4.88 18.4 32.3 5.04 4,94 18.2 32.9 5.00 4.67 17.2 32.7 5.30 5. 45 21.7 33.2 2.73 2.32 16.8 30.9 5.06 4.58 17.9 32,9 6.00 4.48 19.3 31.3 5.22 5.27 19.4 33.6 7.34 4.56 20.0 33.5 4.23 4. 19 19.6 32.6 7. 10 4.67 18,3 30.8 7. 10 4.36 18.3 33.6 3.81 5.61 21.3 30.2 5. 46 5.26 27.7 26.9 5.29 5.21  26.6 25.2 6,49 6. 18 29.4 25.7 5.84 8, 20 27.9 24.5 7.30 8. 22 27.7 20.7 6. 12 5.68 28.3 26.4 5. 43 6. 29 29.5 26,0 5.51 6. 57 28.7 24.1 5.78 6.68 29.0 24.0 6. 27 5.83 30.2 25,1 5.66 7.99 30.8 18.3 3.92 2.42 29.3 24.1 4. 92 6.67 27.6 26,0 6. 24 5.81 27.5 26.2 3. 86 5. 12 27.4 25.8 7. 25 6.51 28.6 24.4 3. 22 6.09 29.6 26.3 6. 76 6.09 28,7 24.8 5. 95 7.59 28.3 25.2 4.36 5.70 26.4 22,6 6.25 6.51 23.4 13,8 5.85 4.41  30.0 6.01 31.1 4.48 29.8 3.57 27.2 5. 45 31.3 2.87 30.7 4.61 30,8 5.46 29.8 4.35 29.4 4.27 28.8 3. 49 27.0 5.63 31.9 4.44 30.0 5.83 31.0 5,39 30.4 5.02 29.5 5.71 27.9 5.15 33,4 4.36 28.6 4,54 22.1 6.66  197  22 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 42 43 44 45 46 47 51  18 . 1 16. 8 14. 1 14.9 28,0 26.1 21.7 31.8 25.7 5.64 3.77 3.79 4.65 1.32 3.66 7.16 5.31 4.27 23.0 25-3 17.5 12.8 29.0 26.4 19.1 31.7 28. 4 7.71 9.52 6.87 6.98 2.37 3.19 6.62 4.86 6.22 20.9 27.1 17.0 13.5 29.7 28.0 20.9 29.7 28. 1 7.56 7. 86 6.97 5.58 2.30 2.50 6. 93 5.34 4.59 15. 1 22.0 15.4 16.0 29,9 28.5 18.9 34.3 27.9 6. 50 8. 22 5. 36 5.26 2.32 2.70 5.84 3.60 6.75 19.8 22.8 18.3 11.7 30.2 27.6 16.4 31.2 30.6 7.52 8,03 6.17 6.81 2.50 3.02 5.90 4.90 6.62 16. 1 20.7 13.6 15.2 30.3 27.7 19.0 34.5 28.6 5.00 5.68 3.92 5.01 1.49 3.15 5.42 3.72 6.64 15.3 21.5 16.9 11.1 28.4 26.7 17.0 30.3 3 1 . 3 9.78 7.72 5.61 5* 93 2.63 1. 16 6.53 4. 85 5.68 12.3 17. 9 13.7 14.3 29.7 27.3 18.3 31.6 27.3 6. 38 5. 34 5.21 6.05 2.67 2.58 3.51 5.27 5.75 17.7 25.8 17.0 12.5 30,7 28.8 17.4 31.4 29. 2 5.40 7.23 5.07 5.93 1.90 2.27 6. 13 4.75 5.16 15.0 18.0 12.0 14.1 31.3 30.5 17.8 35.6 29.0 4.47 10. 5 4.50 4.39 1.04 1.93 8.28 4.14 5. 15 23.9 25.3 17.6 12.2 29.4 28.4 17.3 33.3 31.3 7. 95 9-05 6.72 6.77 1,54 2.36 5.49 3.82 4.89 12.7 19.9 11.1 12,3 30.6 28.8 19.2 30. 1 28.0 4.76 7.53 5.05 5.55 1.69 1.78 4.17 3.67 6.87 19.9 20.1 15.4 11.3 29.3 26.8 17.2 32.2 31.6 7. 58 7.36 6.24 5.78 3.34 2.55 5.68 7.13 5.33 25.6 22.4 18.8 10,4 31.5 27.9 13. 9 35.1 31.6 3. 20 5.76 5.04 2.72 1.513 3.52 3.56 4.85 4.63 18.1 25.0 19.5 11.6 30.0 28.4 16.5 31.2 32. 6 5. 61 5.71 3.93 3. 14 2.45 2.06 3.96 4.77 4.01 17. 1 19.8 14.6 13.4 29.4 26.5 18.2 30.6 27.4 7.09 8.98 7.09 5.94 2.36 3.42 5.95 4.85 6.91 21.4 23.8 17.5 13.3 29.0 27.8 18.5 32.5 26.6 7. 92 7,58 6.06 5.62 2.27 2.43 6.00 3.52 6.15 27.0 35.0 24.2 16.8 30.2 25.8 18.2 34.6 29. 8 5. 24 3. 54 3.90 6.06 0.45 3.35 8.35 4.04 8. 11 26.3 27.9 18.1 14.6 29.1 27.6 20.0 30.0 25,0 5. 82 5.74 7.08 5.50 2.30 2.33 4.78 4.34 5.45 15.5 23.0 16.3 13.1 29.0 26.5 17.7 31.8 29. 4 5. 99 8. 31 6. 84 5.63 1.97 3.78 5.36 4.51 5.66 17.7 20.1 14.4 13.7 29.0 28. 1 19.7 29.9 28.3 4. 15 5. 05 3.87 3.73 1.63 3.24 4. 35 6,99 5.47 14.7 17.7 11.2 11.8 28.8 25.2 21.0 29.0 25.4 7. 17 6. 28 4. 24 5.07 2.95 3.19 5.73 4,71 6.48 16.8 23.3 14.7 12.9 2 9.4 28.6 19.3 33.5 29. 3 5.73 5.32 4.76 5.69 2.17 2.21 5.60 3.81 4.02 20.6 24.9 16.8 16,0 28.7 28.4 20.3 32.4 25. 9 7. 02 10. 3 6. 24 5.68 2-87 2.19 6.87 4.19 5.82 19.6 24.1 16.4 6.3 28.3 26.5 19.8 25.4 29.4 4. 22 8.29 5.39 4.23 2.11 3.24 5.S8 6.63 7.57 12.8 19.3 15.3 11.9 29.2 26.3 18.4 31.0 26.3  22,3 7.30 26.5 7.37 24. 1 7.05 27.3 6.76 27.9 6.52 26.9 8.20 26.8 5.01 24.4 6.40 26,9 6.62 27.8 5.70 26.8 6.35 23.8 5.53 25.2 7.64 28.3 9.68 26.4 6.99 24.1 8.12 26. 1 6.92 29.2 6.22 23.9 6.08 24.8 5.14 25. 1 6.31 24.4 6.47 28.4 6.07 26.8 7.28 20.6 6.35 26.9  32.4 5.25 29.7 5.12 27. 9 5.97 33.4 3.85 29.8 5.53 32.7 4.30 29.7 3.56 30.6 4.47 28.1 4.76 31.0 6.07 29.4 3.84 27.0 4.15 30.1 7.04 33.5 6.95 28.9 5.36 28.3 5.61 31.0 4.89 33.6 4.88 27.9 4.64 28.7 4.26 28.5 5.99 29.5 5.38 33.9 4.24 29.4 5.08 24.4 6.05 27.9  198  52 53 54 55 56 57 58 59 62 63  4.90 28.9 5.34 16.8 6. 03 17.3 6. 16 14.6 6.47 17.3 5.79 17.0 7.52 17.3 6.00 16.0 5.57 21.9 5. 93 22.4 8. 33  8.37 38. 5 3.26 20.9 7.97 25. 2 4.84 20.3 7.93 20.0 9.49 24.7 8,05 17. 6 6.23 20.2 6.02 26.8 8.17 28.8 10. 1  4.73 24.3 3. 97 14.4 5.25 15.2 4.82 13.3 5.59 15.3 5.68 15.4 6.27 12.4 5.98 16.3 4.79 15.5 5.68 20.5 5.29  7. 68 30.3 3. 98 27.2 4.66 29.3 3. 50 26.3 5.63 30.5 3.78 27.3 5. 61 26.8 8. 48 27.0 5. 76 27.6 5. 95 29.6 4. 44  6.54 21.5 7. 67 22.1 6.87 25.8 3.70 26.0 5. 51 26.3 5. 13 24.3 6.43 22.4 8.00 26.6 7.69 24.7 5. 25 25.9 5.33  4.79 29.9 4.58 28.8 4.44 30.6 5.66 31.4 5. 10 31.3 5.67 28.9 3.73 29.7 5.87 31.3 3.99 3,1.0 2.60 29.1 5.26  18.7 23.9 16.3 12.5 29.5 27.6 18.9 32.0 28,3  25.0  29,8  OVERALL MEANS FOR  7,45 9.7 5,08 12.8 4.94 13.3 4.80 12-6 3.84 12. 8 4.17 8.7 4.98 14.0 7.98 14.4 5.10 15.9 4.63 12.8 5.57  3.00 3.28 30.4 27.4 2.22 1.97 28.6 27.1 2.30 2.48 30.0 28.4 1.73 1.81 30.0 28.7 2.44 2.03 28.8 27.8 2.93 3.37 28.8 27.2 2.35 2.57 28. 1 26.3 2.50 2.05 28.3 28.8 2.66 2.33 29.6 27.4 2.37 2.32 30.1 26.8 1.73 3.33  6.81 19, 9 5.87 19.6 4. 54 18.6 3.81 18.1 5.49 17.7 3.27 19.9 4.58 19.5 7.90 18.9 6. 19 18.8 4.52 16.8 5. 18  4, 17 32.6 4.45 32.7 3.86 33.8 3.49 33.7 4. 17 32.3 5.32 30.3 4.63 32.9 5. 13 34.2 3.89 32.4 3.58 32.4 5. 18  EACH TEST  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 S e x a s a Dependent V a r i a b l e a n d t h e T h r e e A c h i e v e m e n t a n d Seven A f f e c t i v e Scales as independent V a r i a b l e s Variable  Mean  S.D.  N = 1033 MSW  F  MSB  Ratio  F  Prob  .0000  1728.3  33. 1  64,3  .9  .348  38.4  287.4  7.5  .006  2.51 2.26  5.7  24.0  4. 2  .041  27.3 27.8  2-89 2.76  8.0  46.9  5.9  .016  M F  18.9 18.8  6. 21 5.65  35.3  1.6  .04  . 834  VALSOC  M F  32.0 31. 8  5.05 4. 76  24.1  5.7  . 24  .627  SELFCON  M F  28.8 27.9  6.08 5.81  35.4  203.3  ENJOY  M F  24.9 25.1  7.05 6.57  46.5  13.0  VALSEL  M F  29.8 29.8  5.40 5.08  27.5  .3  COMP  M F  17.5 20.1  7.24 7.21  52.2  CONC  M F  23.7 24, 2  8.51 8.58  73. 1  PROB  M F  15.8 116.9  6.32 6. 06  IARS  M F  29.4 29.7  I ARF  M F  MANX  Analysis  of  variance  .017  5. 7 . 28  .597  .01  .922  showed a s i g n i f i c a n t  (p < -01) f a v o r i n g t h e f e m a l e s i n b o t h COMP  and  difference  PROB.  Only  200..  three o f t h e seven showed accept  affective variables,  significant  males  than  d i d the females.  analysis  had  on  each  two COMP  pairs at  i n mathematics  above summarizes t h e  and o v e r  t h e complete  males  one-way f r o m raw  1033 c a s e s ;  529  females. differences  significant  2.6,  differences  between  males  on some o f t h e s c a l e s ,  into  and  PBOB  a t 1.1-  proportions  become  less  accounts  2,1% o f t h e v a r i a n c e  of  f o r only o f PBOB,  female  there are only  one s c a l e  explained  point:  variance  the  When s e x i s c o r r e l a t e d  the squared 3.8%  and  When t h e s e d i f f e r e n c e s a r e  important.  with t h e achievement v a r i a b l e s sex  self-concept  o f means which d i f f e r by more t h a n  translated  that  Females tended t o  f o r males and f e m a l e s c a l c u l a t e d  scale  Although the are  The t a b l e  .05).  and s u c c e s s more t h a n  a somewhat h i g h e r  of v a r i a n c e  m a l e s a n d 50 4  means  (p <  responsibility forfailure  and  scores  differences  IABS, IABF and SELFCON  correlations  of the variance  show  o f COMP and  201  Appendix H INTEE—CORRELATIONS OF  1 2 3 4 5 6 7 8 9  1  2  3  1.00 .19 .23 .30 .33 .12 .30 .33 .09  1.00 .51 .06 .19 .26 .02 .11 .16  STUDENT-BEHAVIORS  4  1,00 .01 .27 .23 .12 ,04 .23  5  1.00 .12 -.02 .36 .35 .37  6  1.00 .06 .31 .16 .28  1.00 .00 .01 .07  1.00 .22 .31  Tends t o g i v e random mathematics c l a s s .  2.  Appears tense during  3.  Expresses a n x i e t y o r nervousness about mathematics.  4.  Tends to mathematics  5.  S a y s t h a t no m a t t e r mathematics.  6.  Has h a n d s t h a t s h a k e when d o i n g m a t h e m a t i c s .  7.  Says t h a t mathematics i s u s e l e s s .  8.  Sometimes period.  9.  F i d g e t s more d u r i n g  mathematics  increase class..  to  8  1.  refuses  answers  7  he/she  t o answer  behavior does  questions  mathematics.  durinq  lessons.  disruptive what  questions  he/she  during  durng can't  the do  mathematics  

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