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The effects of an intervention using a precision teaching model on grade four students' arithmetic self-concept Tobin, Moira 1989

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THE EFFECTS OF AN INTERVENTION USING A PRECISION TEACHING MODEL ON GRADE FOUR STUDENTS' ARITHMETIC SELF-CONCEPT by MOIRA TOBIN B.A., Simon Fraser U n i v e r s i t y , 1984 M.Ed., Western Washington U n i v e r s i t y , 1984 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION i n THE FACULTY OF GRADUATE STUDIES EDUCATIONAL PSYCHOLOGY & SPECIAL EDUCATION We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 4, 1989 © MOIRA TOBIN, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT The development of a p o s i t i v e academic s e l f - c o n c e p t has been a professed o b j e c t i v e of almost a l l e d u c a t i o n a l programs from kindergarten t o high s c h o o l . However, there e x i s t few e x p e r i -mentally researched, theory-based i n t e r v e n t i o n s which address the problem of low academic s e l f - c o n c e p t . The present research sought to u t i l i z e the m u l t i f a c e t e d and h i e r a r c h i c a l theory of s e l f - c o n c e p t as proposed by Shavelson, Huber and Stanton (1976) to design an i n t e r v e n t i o n aimed at enhancing academic s e l f - c o n c e p t . S p e c i f i c a l l y , the study was designed to apply a P r e c i s i o n Teaching i n t e r v e n t i o n t o the s p e c i f i c f a c e t of m u l t i p l i c a t i o n i n a r i t h m e t i c . The e f f e c t s of t h i s i n t e r v e n t i o n were subsequently measured at the l e v e l of a r i t h m e t i c s e l f - c o n c e p t and academic s e l f - c o n c e p t . D i f f e r -ences between males and females on a r i t h m e t i c s e l f - c o n c e p t were a l s o examined before and a f t e r the i n t e r v e n t i o n . The study involved 185 grade four students of approximately nine years of age. Academic s e l f - c o n c e p t and a r i t h m e t i c s e l f -concept were measured by the Student's Perception of A b i l i t y S c ale. A 2x4, gender by groups, f a c t o r i a l a n a l y s i s of variance design was used to i n v e s t i g a t e the e f f e c t s of the i n t e r v e n t i o n . Given t h a t the study u t i l i z e d i n t a c t p r e s e l e c t e d classroom groups, the design was quasi-experimental. i i The data i n d i c a t e d t h a t the P r e c i s i o n Teaching i n t e r v e n t i o n had a s i g n i f i c a n t impact on enhancing the a r i t h m e t i c s e l f -concept of the experimental groups. A l s o , there were no s i g n i f i c a n t d i f f e r e n c e s between males and females at the grade four l e v e l i n a r i t h m e t i c s e l f - c o n c e p t . On a t h e o r e t i c a l l e v e l , the f i n d i n g s of the study seem to support the m u l t i f a c e t e d and h i e r a r c h i c a l nature of s e l f -concept. At a p r a c t i c a l l e v e l , the r e s u l t s of the study support P r e c i s i o n Teaching as an e d u c a t i o n a l p r a c t i c e t h a t p o s i t i v e l y i n f l u e n c e s student's academic s e l f - c o n c e p t . As there has only been a small amount of research done to examine techniques f o r developing p o s i t i v e a t t i t u d e s and modifying negative a t t i t u d e s toward d i f f e r e n t s u b j e c t s , i t was concluded t h a t f u r t h e r s t u d i e s were necessary to examine and r e p l i c a t e the f i n d i n g s using other f a c e t s of academic s e l f -concept. S i m i l a r l y , there e x i s t s a need f o r s t u d i e s extending over longer periods of time to examine the d u r a b i l i t y of academic se l f - c o n c e p t change. i i i TABLE OP CONTENTS A b s t r a c t i i L i s t of Tables v i L i s t of Figures . v i i Acknowledgements v i i i I . THE NATURE OF THE STUDY 1 A. I n t r o d u c t i o n 1 B. The Problem 4 C. Background to the Problem 5 D. The Purpose of the Study . 9 E. The Context of the Study 11 F. S i g n i f i c a n c e of the Study 11 I I . REVIEW OF THE LITERATURE 13 A. D e f i n i t i o n s of Self-Concept and T h e o r e t i c a l Background 14 B. Summary of Shavelson et a l ' s (1976) D e f i n i t i o n of Self-Concept 17 1. The Self-Concept as Organized 17 2. The Self-Concept as M u l t i f a c e t e d 17 3. The Self-Concept as H i e r a r c h i c a l ........ 18 4. The Self-Concept as Stable 18 5. The Self-Concept as Developmental 19 6. The Self-Concept as E v a l u a t i v e 19 7. The Self-Concept as D i f f e r e n t i a b l e 19 C. Academic Self-Concept 20 D. Self-Concept and Academic Achievement 21 E. S e l f - E f f i c a c y and Classroom Learning 28 F. P r e c i s i o n Teaching 30 1. The Beh a v i o r a l Approach t o Teaching 31 2. Data-Based I n s t r u c t i o n 31 3. Data-Based I n s t r u c t i o n and P r e c i s i o n Teaching 33 4. The Standard Behavior Chart, A P r e c i s i o n Teaching Tool 35 5. Data-Based D e c i s i o n Making 36 6. Stages of Learning 40 G. The Elementary School Student's Self-Concept 41 H. Summary of Review 46 I I I . HYPOTHESES, QUESTIONS, AND METHOD 49 A. Ra t i o n a l e f o r Hypotheses and E x p l o r a t o r y Questions 49 i v B. Hypotheses and E x p l o r a t o r y Questions 53 1. Hypotheses 53 2. E x p l o r a t o r y Questions 5 3 C. Methodology 55 1. Design 55 2. Sample 57 3. Instruments 60 4. Psychometric C h a r a c t e r i s t i c s of Measure . 62 5. Data C o l l e c t i o n Procedure 65 IV. ANALYSIS AND RESULTS 71 A. D e s c r i p t i v e S t a t i s t i c s and R e l i a b i l i t y Estimates of the SPAS 71 B. Test of the Hypotheses 76 1. G l o b a l Academic F u l l Scale R e s u l t s 77 2. A r i t h m e t i c Subscale R e s u l t s 83 C. E x p l o r a t o r y Questions and A n a l y s i s 90 1. P a r e n t a l Feedback from I n t e r v e n t i o n 90 2. Student Feedback from I n t e r v e n t i o n 93 V. DISCUSSION 97 A. A r i t h m e t i c Self-Concept Enhancement and P a r e n t a l Reinforcement 97 1. A r i t h m e t i c and Academic Self-Concept and Shavelson et a l . ' s (1976) Theory of S e l f -Concept . 98 2. Enhancing A r i t h m e t i c Self-Concept and P r e c i s i o n Teaching 101 B. Gender D i f f e r e n c e s i n A r i t h m e t i c Self-Concept at the Grade Four L e v e l 105 C. Findings from E x p l o r a t o r y A n a l y s i s 107 1. P a r e n t a l V a l i d a t i o n of the Experimental I n t e r v e n t i o n 107 2. Student V a l i d a t i o n of the Experimental I n t e r v e n t i o n 108 D. Summary of the Findings and Conclusions 109 E. L i m i t a t i o n s and Strengths of the Study I l l F. I m p l i c a t i o n s 114 G. D i r e c t i o n s f o r Further Research 121 VI. REFERENCES ' 124 V I I . APPENDIX ... 133 A. Standard Behavior Chart 133 B. SPAS Subscale f o r A r i t h m e t i c Statements 134 C. Student's Perception of A b i l t y Scale 135 D. Student Chart 139 E. Parent Information 140 F. Parent Chart 141 G. Parent S o c i a l V a l i d a t i o n Scale 142 H. Student S o c i a l V a l i d a t i o n Scale 143 I . Probes 144 v LIST OF TABLES Table 1: Summary of P r e c i s i o n Teaching Studies 39 Table 2: D i f f e r e n c e s between Groups 59 Table 3: Breakdown of Items on SPAS f o r F u l l and Subscale Scores 62 Table 4: S t a t i s t i c s and R e l i a b i l i t i e s f o r F u l l and Subscale SPAS Scores Summed over Grades 3, 4, 5 and 6 of Norming Group (N = 642) 63 Table 5: D e s c r i p t i v e S t a t i s t i c s of Norming Sample f o r F u l l and Subscale SPAS Scores as a f u n c t i o n of Sex and Grade L e v e l 64 Table 6: D e s c r i p t i v e S t a t i s t i c s f o r F u l l and Subscale SPAS Scores f o r Research Sample and Norming Sample 73 Table 7: R e l i a b i l i t y Estimates f o r Research Sample and Norming Sample 74 Table 8: Test - Retest R e l i a b i l i t y C o e f f i c i e n t s by Group 75 Table 9: F u l l Scale P r e t e s t C e l l and Marginal Means and Standard Deviations 78 Table 10: F u l l Scale P o s t t e s t C e l l and Marginal Means and Standard Deviations 8 0 Table 11: Group Comparisons on F u l l Scale Academic P o s t t e s t 82 Table 12: A r i t h m e t i c Subscale P r e t e s t C e l l and Marginal Means and Standard D e v i a t i o n s 84 Table 13: A r i t h m e t i c Subscale P o s t t e s t C e l l and Marginal Means and Standard D e v i a t i o n s 85 Table 14: Group Comparisons on Subscale A r i t h m e t i c P o s t t e s t 88 Table 15: Means, Standard D e v i a t i o n s , and t-Values of Paren-t a l Questionnaire 92 Table 16: Means, Standard D e v i a t i o n s , and t-Values f o r Stu-dent S o c i a l V a l i d a t i o n Scale 94 v i LIST OF FIGURES F i g . 1: A Representation of the Components of Self-Concept 8 F i g . 2: Representation of I n t e r v e n t i o n A p p l i c a t i o n and Areas of Measurement 51 F i g . 3: Schematic of Experimental Design 56 v i i ACKNOWLEDGEMENTS No d i s s e r t a t i o n would be completed without the e x p e r t i s e and support of many people. I thank my program ad v i s o r and committee chairman, Dr. David K e n d a l l , and the members of my d i s s e r t a t i o n committee, Dr. Ron Eeles and Dr. Perry L e s l i e , f o r the time and e x p e r t i s e they so generously contributed„ Although Dr. Barry Monroe d i d not l i v e t o see t h i s d i s s e r t a -t i o n t o i t s completion, h i s c o n t r i b u t i o n and encouragement w i l l not be f o r g o t t e n . S p e c i a l thanks must be given t o Dr. Nand Ki s h o r f o r h i s i n v a l u a b l e help and commitment t o the study. Thanks a l s o must be given t o the D e l t a School D i s t r i c t f o r t h e i r permission t o use the schools i n v o l v e d and t o the teachers, students, and parents who so k i n d l y p a r t i c i p a t e d . I g r a t e f u l l y acknowledge the S o c i a l Sciences and Humanities Research C o u n c i l of Canada f o r a Do c t o r a l F e l l o w s h i p , the Tina and Morris Wagner Foundation f o r a F e l l o w s h i p , and the Univer-s i t y of B r i t i s h Columbia f o r a Graduate F e l l o w s h i p . On a personal note, I wish t o express g r a t i t u d e t o f r i e n d s and f a m i l y f o r t h e i r patience and encouragement. I thank Sue Robinson and f a m i l y f o r t h e i r l o v i n g c h i l d c a r e ; Diana L i f t o n , my never-complaining t y p i s t ; Walter, f o r h i s continuous support; and l a s t l y but not l e a s t l y , Pat and Megan f o r t h e i r love and devotion - i t i s t o you I dedicate t h i s achievement. v i i i 1. T H E N A T U R E O P T H E S T U D Y A . I N T R O D U C T I O N Stated i n the o b j e c t i v e s of almost a l l e d u c a t i o n a l programs from kindergarten t o high s c h o o l , f o r normal, g i f t e d and men-t a l l y or p h y s i c a l l y handicapped students, i s the development of a p o s i t i v e s e l f - c o n c e p t . The B r i t i s h Columbia M i n i s t r y of Education's Curriculum Guide and Resource Book f o r kindergarten students, f o r example, s t a t e s : C o n s i d e r a t i o n f o r the emotional development of c h i l -dren i s important not only i n ensuring t h a t t h e i r s e l f -concept i s p o s i t i v e and r e a l i s t i c but a l s o i n ensuring t h a t they are able t o develop c o g n i t i v e l y . C h i l d r e n who are c o n f i d e n t of themselves and are secure i n t h e i r environment are ready f o r new l e a r n i n g . S u c c e s s f u l l e a r n i n g , i n t u r n , enhances self-esteem. C h i l d r e n w i t h self-esteem are more e n t h u s i a s t i c , more w i l l i n g t o accept c h a l l e n g e s , and more able to con-ce n t r a t e and to persevere. Supportive teachers f o s t e r the n a t u r a l development of self-esteem as c h i l d r e n attempt to explore and master t h e i r own g o a l s , (p. 7) However, a f t e r expounding on the importance of p o s i t i v e l y developing c h i l d r e n ' s s e l f - c o n c e p t , seldom i f ever are any p r a c t i c a l recommendations given on how to enhance s e l f - c o n c e p t e f f e c t i v e l y . For i n s t a n c e , the only advice o f f e r e d to the kindergarten teacher i n the Curriculum Handbook i s the quotation 1 THE NATURE OF THE STUDY / 2 from E. L. Widmer taken from The C r i t i c a l Years; E a r l y C h i l d - hood Education at the Crossroads, which s t a t e s , The fundamental step i n h e l p i n g a c h i l d f e e l worthwhile . . . i s t o b e l i e v e i n the i n t r i n s i c worth of a l l c h i l -dren, t o b e l i e v e they can grow as b a s i c human beings. B e l i e v i n g i n c h i l d r e n i s a powerful medicine t h a t can work wonders. (p. 38) However, according t o s e l f - c o n c e p t research t h i s s i m p l i s t i c approach does l i t t l e to develop p o s i t i v e s e l f - c o n c e p t i n c h i l d r e n ( H i l t o n , 1986; Crosby, 1982; L u f t i g , 1982). Within the body of research devoted t o s e l f - c o n c e p t , one of the most c o n s i s t e n t l i n e s of i n q u i r y has been d i r e c t e d towards the l i n k between performance or achievement and students' s e l f -concept. Numerous i n v e s t i g a t o r s have observed a p o s i t i v e c o r r e l a t i o n between s e l f - c o n c e p t and academic achievement. In a s i x - y e a r i n v e s t i g a t i o n , Brookover and a s s o c i a t e s (Brookover, Paterson & Thomas, 1964; Brookover, E r i c k s o n & J o i n e r , 1967) followed the progress of students from seventh grade through t w e l f t h grade i n an e f f o r t t o determine the r e l a t i o n s h i p of students' s e l f -concept t o t h e i r academic achievement. Self-concept of s c h o l a s t i c a b i l i t y or academic s e l f - c o n c e p t was reported t o be s i g n i f i c a n t l y and p o s i t i v e l y r e l a t e d to academic achievement among both males and females. " This r e l a t i o n s h i p was found t o be s u b s t a n t i a l even when I.Q. was c o n t r o l l e d . P i e r s and H a r r i s (1964) reported s i m i l a r f i n d i n g s f o r elementary school c h i l -dren. THE NATURE OF THE STUDY / 3 However, as pointed out by Hansford and H a t t i e i n t h e i r 1982 meta-analysis on the r e l a t i o n s h i p between v a r i o u s self-measures and measures of performance and achievement, i t i s p o s s i b l e t o f i n d support f o r v i r t u a l l y any viewpoint regarding the r e l a t i o n s h i p between s e l f and academic performance. Bloom (1976) s t a t e s t h a t a schedule of success and approval or f a i l u r e and d i s a p p r o v a l over a number of years w i l l lead t o a student's g e n e r a l i z i n g about him or h e r s e l f as a l e a r n e r . He concludes t h a t academic s e l f - c o n c e p t i s a c r i t i c a l v a r i a b l e t h a t i n f l u e n c e s both m o t i v a t i o n and perseverance on school r e l a t e d tasks and tha t a student's academic s e l f - c o n c e p t i s based on the feedback he or she r e c e i v e s from grades, t e s t s , teachers, parents and peers about h i s or her schoolwork. He s t a t e s : The l e a r n e r i s not born w i t h a view about reading, s c i -ence, or mathematics. Rather, the student acquires i t during h i s school experiences. I f the school can assure a h i s t o r y of s u c c e s s f u l experiences i n school l e a r n i n g , e s p e c i a l l y during the elementary school p e r i o d , the student's subsequent school h i s t o r y i s l i k e l y t o be p o s i t i v e w i t h respect to c o g n i t i v e achievement l e a r n i n g outcomes. (p.105) P a r a l l e l i n g Bloom's l i n e of thought, Brookover and G o t l e i b (1964) see academic s e l f - c o n c e p t as a " f u n c t i o n a l l y l i m i t i n g " f a c t o r i n school achievement and success. They s t a t e , F u n c t i o n a l l i m i t i s the term used to emphasize th a t we are speaking not of genetic organic l i m i t s on l e a r n i n g but r a t h e r of those perceptions of what i s a p p r o p r i a t e , d e s i r a b l e , and p o s s i b l e f o r the i n d i v i d u a l to l e a r n . We p o s t u l a t e the l a t t e r as the l i m i t s t h a t a c t u a l l y operate w i t h i n broader organic l i m i t s , i n determining THE NATURE OF THE STUDY / 4 the nature or extent of the p a r t i c u l a r behavior learned, (p. 469) Burns (1982) con c e p t u a l i z e s the s e l f - c o n c e p t as having three main f u n c t i o n s . He describes these as mai n t a i n i n g inner c o n s i s t e n c y , determining how experiences are i n t e r p r e t e d , and p r o v i d i n g a set of expectancies. He s t a t e s t h a t : What an i n d i v i d u a l t h i n k s about himself i s a v i t a l p a r t of i n t e r n a l consistency. Therefore, the i n d i v i d u a l w i l l act i n ways which he t h i n k s are c o n s i s t e n t w i t h how he sees h i m s e l f . I f he f e e l s he cannot do a task and that he i s ' t h i c k , 1 then he i s l i k e l y t o act and behave i n such a way as t o come out l o o k i n g ' t h i c k . ' (p. 9) B . T H E P R O B L E M I t appears t h a t two of the most important r o l e s played by the elementary schools are the development of b a s i c academic s k i l l s and the enhancement of students' s e l f - c o n c e p t (Burns, 1982). Witnessing the volume of l i t e r a t u r e concerned w i t h d i f f e r e n t aspects of the s e l f - c o n c e p t i n e d u c a t i o n a l s e t t i n g s , i t i s c l e a r t h a t s e l f - c o n c e p t i s considered an important v a r i a b l e i n educa t i o n a l research (e.g., Bloom, 1976; Byrne, 1984; K i f e r , 1975; Purkey, 1970). With t h i s v i s i o n , numerous researchers have attempted to design i n t e r v e n t i o n s which have focused on sel f - c o n c e p t en-hancement (e.g., Hunt and Hardt, 1969; Kenemuth, 1975; Poudrier, 1976). However, i n past i n t e r v e n t i o n s t u d i e s , measurement has THE NATURE OF THE STUDY / 5 been predominantly at the general s e l f - c o n c e p t l e v e l without regard t o the m u l t i f a c e t e d and h i e r a r c h i c a l s t r u c t u r e of the se l f - c o n c e p t . I f as Shavelson et a l . (1976) have suggested, s e l f - c o n c e p t i s a h i e r a r c h i c a l c o n s t r u c t w i t h general s e l f - c o n c e p t at the apex and s i t u a t i o n s p e c i f i c s e l f - c o n c e p t s at the base, and i f se l f - c o n c e p t changes operate from the base of the h i e r a r c h y upward, then i t would seem appropriate t o look f o r changes i n sel f - c o n c e p t a f t e r remediation or i n t e r v e n t i o n not s o l e l y at the apex of the h i e r a r c h y but at the ascending l e v e l s of the hi e r a r c h y , such as, academic s e l f - c o n c e p t , s p e c i f i c subject s e l f - c o n c e p t , and e v a l u a t i o n of behavior i n s p e c i f i c s i t u a -t i o n s . The present study was an attempt to do t h i s . The present study a l s o was an attempt t o research a p r a c t i c a l i n t e r v e n t i o n t h a t could provide classroom teachers w i t h a v i a b l e method of enhancing low s u b j e c t - s p e c i f i c s e l f - c o n c e p t . C . BACKGROUND TO THE PROBLEM I t i s i n t e r e s t i n g t o note, however, th a t although there has been an abundance of se l f - c o n c e p t research examining a l l ages of students i n a m u l t i p l i c i t y of s e t t i n g s and i n t e r v e n t i o n s , the research f i n d i n g s have been i n c o n s i s t e n t and indeterminate. Researchers have suggested t h a t weaknesses i n se l f - c o n c e p t research i n academic s e t t i n g s can be a t t r i b u t e d i n part .to THE NATURE OF THE STUDY / 6 t h e o r e t i c a l problems and/or methodological problems (Sc h e i r e r & Kraut, 1979; Wells & Marwell, 1976; Wylie, 1961, 1974). The i s s u e of d e f i n i t i o n , i n p a r t i c u l a r , has a f f e c t e d both the t h e o r e t i c a l aspect as w e l l as the measurement aspect of s e l f -concept research, although many se l f - c o n c e p t d e f i n i t i o n s overlap i n v a r i o u s ways, d e f i n i t i o n s of s e l f - c o n c e p t have been as numerous and v a r i e d as the instruments designed to measure the c o n s t r u c t . U n f o r t u n a t e l y , t h i s absence of an accepted d e f i n i t i o n of se l f - c o n c e p t has hindered a systematic i n v e s t i g a t i o n i n t o the r o l e of s e l f - c o n c e p t i n academic s e t t i n g s . However, through the research of Shavelson and h i s as s o c i a t e s (Shavelson, Huber, & Stanton, 1976; Shavelson, B u r s t e i n , & K e e s l i n g , 1977; and Shavelson & Bolus, 1982), a concise d e f i n i t i o n of se l f - c o n c e p t i s emerging. In t h e i r 1976 study, Shavelson, Huber and Stanton attempted to amalgamate the e x i s t i n g o p e r a t i o n a l d e f i n i t i o n s of sel f - c o n c e p t from the l i t e r a t u r e . From t h i s extensive study, Shavelson et a l . (1976) p o s i t e d t h a t there are seven c r u c i a l c h a r a c t e r i s t i c s t h a t can be a t t r i b u t e d t o the se l f - c o n c e p t c o n s t r u c t . These can be summarized as: (a) Self-concept i s organized or s t r u c t u r e d , i n tha t people c a t e g o r i z e the vast amount of in f o r m a t i o n they have about themselves and r e l a t e the ca t e g o r i e s to one another. THE NATURE OF THE STUDY / 7 (b) I t i s m u l t i f a c e t e d , and the p a r t i c u l a r f a c e t s r e f l e c t the category system adopted by a p a r t i c u l a r i n d i v i d u a l and/or shared group. (c) I t i s h i e r a r c h i c a l , w i t h perceptions of behavior at the base moving t o inf e r e n c e s about s e l f i n subareas (e.g., academic - E n g l i s h , h i s t o r y ) , then to in f e r e n c e s about s e l f i n academic and nonacademic areas, and then to i n f e r e n c e s about s e l f i n gener a l . (d) General s e l f - c o n c e p t i s s t a b l e , but as one descends the h i e r -archy, s e l f - c o n c e p t becomes i n c r e a s i n g l y s i t u a t i o n s p e c i f i c and as a consequence l e s s s t a b l e . (e) Self-concept becomes i n c r e a s i n g l y m u l t i f a c e t e d as the i n d i -v i d u a l develops from in f a n c y to adulthood. ( f ) I t has both a d e s c r i p t i v e and an e v a l u a t i v e dimension such t h a t i n d i v i d u a l s may descr i b e themselves (I am happy) and evaluate themselves (e.g., I do w e l l i n s c h o o l ) . (g) I t can be d i f f e r e n t i a t e d from other c o n s t r u c t s such as academic achievement. Of the e x i s t i n g t h e o r e t i c a l models of s e l f - c o n c e p t proposed to date, Shavelson e t a l . ' s (1976) model has undergone an i n t e n s i v e examination i n both c r o s s - s e c t i o n a l and l o n g i t u d i n a l designs (Byrne & Shavelson, 1986). The components of academic se l f - c o n c e p t as p o s i t e d by Shavelson et a l . (1976) are presented i n Figure 1. THE NATURE OF THE STUDY / 8 General General Self-Concept Academic Self-Concept Subareas of Academic Self-Concept Non-Academic Self-Concept Subareas of Non-Academic Self-Concept English History Math Science So c i a l S e l f -Concept Emotional S e l f -Concept Physical S e l f -Concept , 1 1 1 I I I > I I I I ' 1 I 1 ! 1 ! 1 rSrSnrS i i f t I i i i i J, Evaluation of behavior i n s p e c i f i c academic situations F i q . l ; A Representation of the Components of Self-Concept* * Shavelson et a l . (1976) THE NATURE OF THE STUDY / 9 In t e s t i n g the hypothesis t h a t s e l f - c o n c e p t i s h i e r a r c h i c -a l l y s t r u c t u r e d , Fleming and Courtney (1984), Byrne (1986) as w e l l as Shavelson and Bolus (1982) reported support f o r the h i e r a r c h i c a l s t r u c t u r e of the se l f - c o n c e p t w i t h general s e l f -concept at the apex followed by academic s e l f - c o n c e p t ; subareas of academic s e l f - c o n c e p t , such as, E n g l i s h and mathematics, and, f i n a l l y at the base, e v a l u a t i o n of behavior i n s p e c i f i c s i t u -a t i o n s . The multidimensional nature of se l f - c o n c e p t has been examined by Marsh and O ' N e i l l (1984), Marsh, Parker, and Smith (1983), as w e l l as, Shavelson and Bolus (1982) and Byrne (1986). Findings of these s t u d i e s have supported the multidimension-a l i t y of s e l f - c o n c e p t . These f i n d i n g s now make p o s s i b l e a more systematic i n v e s t i -g a t i o n i n t o the measurement of the var i o u s f a c e t s of s e l f -concept and consequently i n t o i n t e r v e n t i o n s such as the present i n t e r v e n t i o n which are s t r u c t u r e d on the m u l t i d i m e n s i o n a l i t y of se l f - c o n c e p t . D . THE PURPOSE OF THE STUDY R e a l i z i n g t h a t the two most important r o l e s played by our elementary schools are the development of b a s i c academic s k i l l s and the enhancement of students' s e l f - c o n c e p t , and f u r t h e r , t h a t many researchers have observed a p o s i t i v e c o r r e l a t i o n between THE NATURE OF THE STUDY / 10 se l f - c o n c e p t and academic achievement, i t seems p e r t i n e n t t o research p r a c t i c a l i n t e r v e n t i o n s t h a t could enhance the s e l f -concept as w e l l as enhance b a s i c academic s k i l l s . This i n v e s -t i g a t i o n proposes t o study the i n f l u e n c e of a p r a c t i c a l i n t e r -v e n t i o n t o enhance academic s e l f - c o n c e p t . S p e c i f i c a l l y , t h i s study looked at the e f f e c t s of a P r e c i s i o n Teaching i n t e r v e n t i o n on academic s e l f - c o n c e p t and a r i t h m e t i c s e l f - c o n c e p t of grade four elementary school students. Drawing on the t h e o r e t i c a l framework of a h i e r a r c h i c a l and multidimensional s e l f - c o n c e p t as proposed by Shavelson et a l . (1976), t h i s study proposed t h a t changes i n e v a l u a t i o n of behavior i n s p e c i f i c s i t u a t i o n s at the base of the h i e r a r c h y would be able t o be measured as changes i n academic s e l f - c o n c e p t i n subareas of the h i e r a r c h y . In a d d i t i o n , t h i s study served t o explore d i f f e r e n c e s , i f any, between male and female grade four students' academic s e l f - c o n c e p t when given a d a i l y feedback i n t e r v e n t i o n . A l s o , as P r e c i s i o n Teaching s t r a t e g i e s can be seen as an inn o v a t i o n i n the classroom t h a t d i f f e r s s i g n i f i c a n t l y from current p r a c t i c e , a s o c i a l v a l i d a t i o n of the i n t e r v e n t i o n was conducted. This was done by a qu e s t i o n n a i r e which was given to both students and parents who co-charted progress w i t h t h e i r c h i l d r e n . THE NATURE OF THE STUDY / 11 E. THE CONTEXT OF THE STUDY The primary g o a l of the present study was t o u t i l i z e the s e l f - c o n c e p t d e f i n i t i o n and theory of Shavelson et a l . (1976) i n designing a p r a c t i c a l i n t e r v e n t i o n t o enhance the academic s e l f -concept of grade four students. S p e c i f i c a l l y t h i s i n t e r v e n t i o n i ncluded the use of parents and P r e c i s i o n Teaching p r a c t i c e s . The b e n e f i t s of the i n v e s t i g a t i o n w i l l be mainly at a p r a c t i c a l l e v e l . To f a c i l i t a t e e x t e r n a l v a l i d i t y , the i n v e s t i g a t i o n was conducted i n a n a t u r a l i s t i c s e t t i n g . As noted by Campbell and Stanley (1963), e d u c a t i o n a l research done outside l a b o r a t o r y s e t t i n g s o f t e n has t o inc o r p o r a t e i n t o i t s design n a t u r a l l y assembled c o l l e c t i v e s such as classroom groups. These f a c t o r s u n f o r t u n a t e l y can impose c e r t a i n c o n s t r a i n t s on the design and procedure of the study. The present study i s no exception and consequently makes use of a quasi-experimental design to t e s t the hypotheses. F. SIGNIFICANCE OF THE STUDY A study using the t h e o r e t i c a l framework of the s e l f - c o n c e p t model proposed by Shavelson et a l . , 1976; Shavelson and Bolus, 1982; and Byrne and Shavelson, 1986, t o examine s e l f - c o n c e p t change would make a c o n t r i b u t i o n to compensatory education programmers. Self-enhancement t h e o r i s t s uphold t h a t the focus i n compensatory programs should be to increase the general s e l f -THE NATURE OF THE STUDY / 12 concept of c h i l d r e n . However, i f changes i n s e l f - c o n c e p t operate from base t o apex, and i f s e l f - c o n c e p t becomes i n c r e a s -i n g l y s t a b l e toward the apex, then i t would seem more productive to concentrate on c r e a t i n g changes at the lower l e v e l s of the hi e r a r c h y of s e l f - c o n c e p t , such as, s p e c i f i c areas of academic s e l f - c o n c e p t . Of f u r t h e r s i g n i f i c a n c e , the present study o f f e r s classroom teachers a theory-based, researched and r e a d i l y implementable, p r a c t i c a l i n t e r v e n t i o n capable of enhancing the academic s e l f -concept of students. I I . REVIEW OF THE LITERATURE There are many v a r i a t i o n s i n emphasis on the nature and r o l e of the s e l f i n se l f - c o n c e p t research, however, g e n e r a l l y speaking, most schools of thought see the s e l f as a c r u c i a l f a c t o r i n the understanding and p r e d i c t i n g of human behavior. Going a step f u r t h e r , most se l f - c o n c e p t t h e o r i e s imply t h a t t o e x p l a i n and p r e d i c t human behavior without knowledge of the perceptions held by i n d i v i d u a l s w i t h respect t o themselves and t h e i r environment i s impossible (Boersma & Chapman, 1977). This chapter provides an overview and review of the s a l i e n t t h e o r e t i c a l and e m p i r i c a l l i t e r a t u r e r e l a t e d t o the two v a r i a b l e s of i n t e r e s t i n the present s t u d y — s e l f - c o n c e p t and P r e c i s i o n Teaching. In the f i r s t p a r t (A), d e f i n i t i o n s of s e l f -concept and the t h e o r e t i c a l background of the construct are discussed. Next, i n Part B, the t h e o r e t i c a l framework f o r the present study i s discussed and the model of se l f - c o n c e p t proposed by Shavelson, Huber, and Stanton (1976); Shavelson and Bolus (1982); and Shavelson and Byrne (1986) i s presented. This i s then followed (Part C) by an examination of academic s e l f - c o n c e p t , and s e l f - c o n c e p t , and academic achievement (Part D). This leads i n t o a d i s c u s s i o n of s e l f -13 REVIEW OF THE LITERATURE / 14 e f f i c a c y and classroom l e a r n i n g (Part E) and f i n a l l y to P r e c i s i o n Teaching and the b e h a v i o r a l approach to teaching (Part F ) . The chapter concludes w i t h a summary (Part G) of the preceding p a r t s . A. DEFINITIONS OF SELF-CONCEPT AND THEORETICAL BACKGROUND There have been many attempts to describe and def i n e the complex c o n s t r u c t of s e l f - c o n c e p t . Of these many attempts, perhaps the simplest was put f o r t h by Kinch (196 3 ) who saw s e l f -concept as, ". . . th a t o r g a n i z a t i o n of q u a l i t i e s t h a t the i n d i v i d u a l a t t r i b u t e s to h i m s e l f . " Samuels (1977), however, po i n t s out the problem w i t h t h i s d e f i n i t i o n i s t h a t one does not n e c e s s a r i l y get an accurate p i c t u r e of an i n d i v i d u a l ' s s e l f -f e e l i n g s from what the i n d i v i d u a l r e v e a l s s i n c e defense mechanisms can al l o w i n d i v i d u a l s to deceive themselves and others i n order t h a t s e l f - c o n c e p t enhancement can occur. Sigmund Freud (1962), w i t h h i s emphasis on unconscious m o t i v a t i o n , was a proponent of t h i s theory. Burns (1982) l i k e Kinch (1963) viewed the s e l f - c o n c e p t as the composition of a l l the b e l i e f s and e v a l u a t i o n s an i n d i v i d u a l has about him or h e r s e l f . Burns s t a t e s , "These b e l i e f s ( s e l f -images) and eva l u a t i o n s (self-esteem) a c t u a l l y determine not only who you are but what you t h i n k you are, what you t h i n k you can do, and what you t h i n k you can become." ( p . l ) REVIEW OF THE LITERATURE / 15 H i s t o r i c a l l y , W i l l i a m James i s g e n e r a l l y recognized as the e a r l i e s t " s e l f " p s y c h o l o g i s t . To date h i s w r i t i n g s are standard reference when examining self-esteem or s e l f - c o n c e p t . Wells and Marwell (1976) summarize James' d e s c r i p t i o n of the s e l f : A man' s s e l f i s the sum t o t a l of a l l he can c a l l h i s — t h e n o t i o n of a p p r o p r i a t i o n and/or i d e n t i t y — d i v i d e d i t i n t o three c o n s t i t u e n t p a r t s : the m a t e r i a l Me, the s o c i a l Me, and the s p i r i t u a l Me . . . . In order t o understand Me i n the t o t a l sense, James s a i d , we must look not only at the c o n s t i t u e n t s of the Me, but a l s o at the f e e l i n g s and emotions they arouse ( s e l f -a p p r e c i a t i o n ) and the a c t s which they prompt ( s e l f -seeking and s e l f - p r e s e r v a t i o n ) . To the extent t h a t people experience successes, they experience he i g h t -ened self-esteem, although t h i s was not described as some kind of s t a b l e s e l f - e v a l u a t i o n , but r a t h e r as a barometer which r i s e s and f a l l s from one day to another, (p. 18) An important t h e o r e t i c a l model of the s e l f - c o n c e p t , symbolic i n t e r a c t i o n theory, i s d e r i v e d from the work of G. H. Mead who saw the s e l f as "a s o c i a l phenomenon, a product of i n t e r a c t i o n s i n which the person experienced himself as r e f l e c t e d i n the behavior of the other" (Wells and Marwell, 1976, p. 17). Mead p o s i t e d t h a t the l a b e l s a p p l i e d to one's s e l f are learned during everyday i n t e r a c t i o n w i t h i n one's network of s o c i a l r e l a t i o n s h i p s and t h a t f o r c h i l d r e n f i r s t a c q u i r i n g l a b e l s the most important s o c i a l i n f l u e n c e s are those of the parents (Mead, 1934). I n i t i a l l y i d e n t i f i e d w i t h C a r l Rogers, another theory emerged during the f i f t i e s which i n f l u e n c e d s e l f and s e l f -REVIEW OF THE LITERATURE / 16 concept theory. This c l i n i c a l p e r s p e c t i v e i n p e r s o n a l i t y theory became known as c l i e n t centered. In C l i e n t Centered  Therapy (1951), Rogers defined s e l f - c o n c e p t as: An organized c o n f i g u r a t i o n of perceptions of the s e l f which are a d m i s s i b l e t o awareness. I t i s composed of such elements as the perceptions of one's c h a r a c t e r -i s t i c s and a b i l i t i e s ; the percepts and concepts of the s e l f i n r e l a t i o n t o others and to the environment; the value q u a l i t i e s which are perceived as a s s o c i a t e d w i t h experiences and o b j e c t s ; and goals and i d e a l s which are perceived as having p o s i t i v e or negative valence. (p. 136) A noteworthy aspect of Rogers' d e f i n i t i o n i s the i m p l i c a t i o n t h a t only when a f e e l i n g or a l e r t n e s s about the s e l f comes i n t o awareness w i l l i t i n f l u e n c e behavior. Another aspect of the s e l f - c o n c e p t noted by Rogers was t h a t of c o n s i s t e n c y . Rogers proposed t h a t behavior i n c o n s i s t e n t w i t h the s e l f - c o n c e p t tended to cause t e n s i o n and confusion. He l a b e l e d t h i s s t a t e one of incongruence between s e l f and experience. In order t o avoid t h i s s t a t e , Rogers t h e o r i z e d t h a t the i n d i v i d u a l ' s a n x i e t y aroused defence mechanisms t h a t e i t h e r d i s t o r t e d or denied the experience, thereby maintaining the i n d i v i d u a l ' s c o n s i s t e n t p e r c e p t i o n of s e l f (Rogers, 1979). As p r e v i o u s l y pointed out, most s e l f - c o n c e p t d e f i n i t i o n s o v e r l a y i n v a r i o u s ways and i t was through the work of Shavelson, Huber, and Stanton (1976) t h a t an amalgamation of these p r e - e x i s t i n g d e f i n i t i o n s occurred. As i d e n t i f i e d by Shavelson et a l . (1976), the seven features c r i t i c a l t o the s e l f - c o n c e p t c o n s t r u c t d e f i n i t i o n are iden-t i f i e d as: organized, m u l t i f a c e t e d , h i e r a r c h i c a l , s t a b l e , developmental, e v a l u a t i v e , and d i f f e r e n t i a b l e . REVIEW OF THE LITERATURE / 17 B. SUMMARY OF SHAVELSON ET AL'S (1976) DEFINITION OF SELF-CONCEPT G e n e r a l l y , s e l f - c o n c e p t i s perceived t o be a person's pe r c e p t i o n of him- or h e r s e l f . The formation of t h i s p e r c e p t i o n i s the r e s u l t of one's experience w i t h and i n t e r p r e t a t i o n of one's environment. The perception one has of him- or h e r s e l f i s e s p e c i a l l y i n f l u e n c e d by reinforcements, e v a l u a t i o n s by s i g n i -f i c a n t o t h e r s , and one's a t t r i b u t i o n s f o r one's own behavior (Shavelson et a l . , 1976). 1. The Self-Concept as Organized I t i s each i n d i v i d u a l ' s d i v e r s i f i e d l i f e experiences t h a t form the data on which he or she bases h i s or her perceptions of s e l f . Because of the complexity of experiences, the i n d i v i d u a l reduces experiences i n t o c a t e g o r i e s to give them meaning. Hence, the c a t e g o r i e s represent a way of o r g a n i z i n g experiences and g i v i n g them meaning. Shavelson et a l . , 1976). Examples of cate g o r i e s could i n c l u d e p h y s i c a l a t t r a c t i v e n e s s and a b i l i t y , school a b i l i t y , and s o c i a l acceptance a b i l i t y . 2. The Self-Concept as M u l t i f a c e t e d The second-feature of the s e l f - c o n c e p t i s t h a t i t i s m u l t i -f a c e t e d , and t h a t the p a r t i c u l a r f a c e t s m i r r o r the category system chosen by the i n d i v i d u a l . The category system appears t o in c l u d e the areas of sc h o o l , s o c i a l acceptance, p h y s i c a l a t t r a c t i v e n e s s , and a b i l i t y . REVIEW OF THE LITERATURE / 18 3. The Self-Concept as H i e r a r c h i c a l The m u l t i f a c e t e d s t r u c t u r e of s e l f - c o n c e p t can a l s o be seen as h i e r a r c h i c a l , meaning th a t f a c e t s of s e l f - c o n c e p t may form a h i e r a r c h y from i n d i v i d u a l experiences i n i s o l a t i o n at the base of the h i e r a r c h y to general s e l f - c o n c e p t at the apex. F u r t h e r , Shavelson et a l . (1976) d i v i d e d one's general s e l f - c o n c e p t i n t o the two components of academic s e l f - c o n c e p t and non-academic s e l f - c o n c e p t . Academic s e l f - c o n c e p t i s then f u r t h e r d i v i d e d i n t o s u bject matter areas and then i n t o s p e c i f i c areas w i t h i n a subject matter. Non-academic s e l f - c o n c e p t may be d i v i d e d i n t o s o c i a l and p h y s i c a l s e l f - c o n c e p t s and then d i v i d e d i n t o the more s p e c i f i c f a c e t s as i n academic s e l f - c o n c e p t . * 4. The Self-Concept as Stable Although Shavelson et a l . (1976 ) e n v i s i o n the s e l f - c o n c e p t as s t a b l e , they a l s o p o i n t out t h a t as one descends the s e l f -concept h i e r a r c h y , s e l f - c o n c e p t depends i n c r e a s i n g l y on s p e c i f i c s i t u a t i o n s and becomes l e s s s t a b l e . I t i s hypoth-e s i z e d t h a t at the base of the h i e r a r c h y t h a t s e l f - c o n c e p t v a r i e s g r e a t l y w i t h v a r i a t i o n s i n s i t u a t i o n s . F u r t h e r , i t i s specu-l a t e d t h a t to change general s e l f - c o n c e p t at the apex of the h i e r a r c h y , many instances i n c o n s i s t e n t w i t h general s e l f -concept would be r e q u i r e d . * See page 8 f o r diagram. REVIEW OF THE LITERATURE / 19 5. The Self-Concept as Developmental As c h i l d r e n mature and l e a r n from an ever broadening set of experiences, d i f f e r e n t i a t i o n of s e l f from environment begins. Shavelson (1976) p o i n t s out t h a t w i t h i n c r e a s i n g age and experience ( e s p e c i a l l y a c q u i s i t i o n of v e r b a l l a b e l s ) s e l f -concept becomes i n c r e a s i n g l y d i f f e r e n t i a t e d and t h a t as the c h i l d i n t e r p r e t s the v a r i o u s p a r t s of h i s or her s e l f - c o n c e p t one can speak of a m u l t i f a c e t e d , s t r u c t u r e d s e l f - c o n c e p t . 6. The Self-Concept as E v a l u a t i v e Of the e v a l u a t i v e feature of the s e l f - c o n c e p t , Shavelson et a l . (1976) s t a t e : Not only does the i n d i v i d u a l develop a d e s c r i p t i o n of himself i n a p a r t i c u l a r s i t u a t i o n or c l a s s of s i t u a t i o n s , he a l s o forms e v a l u a t i o n s of himself i n these s i t u a t i o n s . E v a l u a t i o n s can be made against absolute standards, such as the ' i d e a l , ' and they can be made against r e l a t i v e standards, such as peers or perceived e v a l u a t i o n s of ' s i g n i f i c a n t others.' (p. 414) 7. The Self-Concept as D i f f e r e n t i a b l e The seventh fe a t u r e of s e l f - c o n c e p t i n Shavelson et a l ' s (1976) d e f i n i t i o n i s t h a t i t i s d i f f e r e n t i a b l e from the other c o n s t r u c t s w i t h which i t i s t h e r o e t i c a l l y r e l a t e d . In c l a r i f y i n g t h i s / Shavelson et a l . (1976) s t a t e : Self-concept i s i n f l u e n c e d by s p e c i f i c experiences. Therefore, the more c l o s e l y s e l f - c o n c e p t i s l i n k e d w i t h s p e c i f i c s i t u a t i o n s , the c l o s e r i s the r e l a t i o n REVIEW OF THE LITERATURE / 20 ship between se l f - c o n c e p t and behavior i n the s i t u -a t i o n . I f one were t o focus on the academic s i d e of the h i e r a r c h y , one could hypothesize t h a t (a) s e l f - c o n c e p t of mental a b i l i t y should be more c l o s e l y r e l a t e d to academic achievement than t o a b i l i t y i n s o c i a l and p h y s i c a l s i t u a t i o n s , and (b) s e l f - c o n c e p t of academic a b i l i t y i n science should be more c l o s e l y r e l a t e d to achievement i n sience than t o achievement i n , say, E n g l i s h or o v e r a l l grade-point average. (p. 425) C. ACADEMIC SELF-CONCEPT Academic s e l f - c o n c e p t maybe defined as a student's concept of h i s or her a b i l i t y t o perform academic tasks i n the school s e t t i n g . As noted by Purkey (1970), a f t e r the home, the school probably i s the next strongest f o r c e i n shaping and maintaining a c h i l d ' s s e l f - c o n c e p t . Consequently, a school atmosphere o f f e r i n g success and approval or f a i l u r e and disappoval over a number of years w i l l lead to a student g e n e r a l i z i n g about him or h e r s e l f as a l e a r n e r (Bloom, 1976). F u r t h e r , a c h i l d who comes to school w i t h a low academic s e l f - c o n c e p t f o r whatever reason f r e q u e n t l y doesn't a c t i v e l y become i n v o l v e d i n new l e a r n i n g tasks (Samuels, 1976). Research done as e a r l y as 1940 (Sears) found c h i l d r e n w i t h low academic s e l f - c o n c e p t o f t e n were e i t h e r over cautious and set goals below t h e i r present achievement, or set goals e x t r a v a g a n t l y high beyond p o s s i b l e accomplishment. This study i n d i c a t e d the need f o r parents and teachers to help students set r e a l i s t i c goals thus en a b l i n g students t o more r e a d i l y succeed and gain confidence as a r e s u l t of t h e i r success. REVIEW OF THE LITERATURE / 21 Purkey and Graves (1970) r e p o r t t h a t i n d i v i d u a l i z e d teaching improved the academic s e l f - c o n c e p t s of elementary school c h i l d r e n . S i m i l a r l y , by designing i n d i v i d u a l i z e d l e a r n i n g programs i n which students charted t h e i r own success, Howard (1974) improved the academic s e l f - c o n c e p t s of second-through f i f t h - g r a d e c h i l d r e n . D. SELF-CONCEPT AND ACADEMIC ACHIEVEMENT Numerous i n v e s t i g a t o r s have observed a p o s i t i v e c o r r e l a t i o n between s e l f - c o n c e p t and achievement. Studies using c h i l d r e n a f t e r the f i r s t grade have found t h a t c h i l d r e n w i t h l e a r n i n g d i f f i c u l t i e s tend to see themselves as being l e s s adequate than those who were doing w e l l (Coopersmith, 1959; Purkey, 1970; K i f e r , 1973). F e l k e r and Thomas (1971) rep o r t i n t h e i r research t h a t c h i l d r e n w i t h high s e l f - c o n c e p t s made p o s i t i v e statements about themselves w h i l e doing schoolwork, whereas those w i t h low se l f - c o n c e p t s d i d not do so. General l y speaking, research r e p o r t s i n v e s t i g a t i n g s e l f -concept and achievement have suggested t h a t e l i m i n a t i o n of excessive f a i l u r e experiences and the c r e a t i o n of c o n d i t i o n s t h a t maximize success and i n t r i n s i c m o t i v a t i o n w i l l lead to a p o s i t i v e s e l f - c o n c e p t . In a 1962 study done by Brookover, Paterson and Thomas w i t h grade seven students, i t was found t h a t a student's s e l f - c o n c e p t REVIEW OF THE LITERATURE / 22 of a b i l i t y i s p o s i t i v e l y r e l a t e d to the image he or she perceives s i g n i f i c a n t others hold of him or her, when parents are i d e n t i f i e d as s i g n i f i c a n t others. Further t o t h i s , as p a r t of Brookover's l o n g i t u d i n a l study (Brookover & E r i c k s o n , 1969; Brookover et a l . , 1965), s e v e r a l s t u d i e s were conducted to i n v e s t i g a t e sources of i n f l u e n c e on students* s e l f - c o n c e p t s . Parents, a counselor working i n d i v i d u a l l y w i t h students, and a u n i v e r s i t y expert who provided i n f o r m a t i o n a l pep t a l k s to groups of students i n t h e i r classrooms were used as sources of i n f l u e n c e . I t was found t h a t only the experimental c o n d i t i o n w i t h parents succeeded i n i n c r e a s i n g students' s e l f - c o n c e p t of a b i l i t y and academic achievements. Brookover and A s s o c i a t e s (1976) concluded that t o be maximally e f f i c i e n t , a s t r a t e g y to change the s e l f - c o n c e p t of students' a b i l i t y should i n v o l v e i n d i v i d u a l s who are already s i g n i f i c a n t others and t h a t parents of p u b l i c school c h i l d r e n are more l i k e l y t o be academic s i g n i f i c a n t others to t h e i r c h i l d r e n than are the c h i l d r e n ' s teachers (Brookover & E r i c k s o n , 1964). To date, few s t u d i e s have i n v e s t i g a t e d elementary c h i l d r e n ' s s e l f - c o n c e p t s and the e f f e c t s of home environment on enhancing s e l f - c o n c e p t . A c o r r e l a t i o n a l study done by Brookover, Thomas and Paterson (1964) found a strong r e l a t i o n s h i p between c h i l d r e n ' s s e l f - c o n c e p t and t h e i r academic achievement. In t h i s study three major hypotheses were t e s t e d : (1) Self-concept of a b i l i t y i n school i s s i g n i f i c a n t l y and p o s i t i v e l y r e l a t e d to the REVIEW OF THE LITERATURE / 23 academic performances of students even w i t h an a b i l i t y dimension c o n t r o l l e d ; (2) Self-concept i s d i f f e r e n t i a t e d i n t o s p e c i f i c s e l f - c o n c e p t s which correspond t o s p e c i f i c subject-matter areas; and (3) Self-concept i s s i g n i f i c a n t l y and p o s i t i v e l y c o r r e l a t e d w i t h the c h i l d ' s pe r c e p t i o n of how s i g n i f i c a n t others view h i s or her a b i l i t y . These hypotheses were t e s t e d using a sample of 1,050 grade-seven students who were given the S e l f -Concept of A b i l i t y Scale t o determine h i s or her concept of a b i l i t y , both i n general and i n p a r t i c u l a r s u b j e c t s . A f t e r the e f f e c t of I.Q. was fa c t o r e d out, the students' reported concepts of t h e i r own a b i l i t y and t h e i r grade-point averages were found t o be s i g n i f i c a n t l y and p o s i t i v e l y c o r r e l a t e d . I t was a l s o found t h a t s p e c i f i c s e l f - c o n c e p t s of a b i l i t y r e l a t e d to s p e c i f i c areas of academic achievement and tha t i n some areas these were b e t t e r p r e d i c t o r s of achievement i n the subject than general s e l f - c o n c e p t of a b i l i t y . F i n a l l y , the se l f - c o n c e p t of students was found to be s i g n i f i c a n t l y and p o s i t i v e l y c o r r e l a t e d w i t h the perceived e v a l u a t i o n s of the student by other s i g n i f i c a n t people. In summarizing t h e i r research, Brookover, Paterson and Thomas (1964) concluded t h a t s e l f - c o n c e p t of academic a b i l i t y i s a s s o c i a t e d w i t h academic achievement. Purkey (1970 ) provides a review of research done s i n c e 1967 which a l s o p o i n t s to the s i g n i f i c a n t r e l a t i o n s h i p between s e l f -concept and academic achievement. In 1967, Bledsoe examined the r e l a t i o n s h i p of the s e l f - c o n c e p t of f o u r t h - and sixth-grade REVIEW OF THE LITERATURE / 24 students to t h e i r achievement, a n x i e t y , i n t e l l i g e n c e , and i n t e r e s t s . This research revealed s i g n i f i c a n t c o r r e l a t i o n s between the professed s e l f - c o n c e p t and achievement of boys but n o n - s i g n i f i c a n t c o r r e l a t i o n s f o r g i r l s . A l s o i n 1967, Campbell reported a low p o s i t i v e c o r r e l a t i o n between the Cooper- smith-Self-Esteem Inventory, a s e l f - r e p o r t q u e s t i o n n a i r e , and the achievement of f o u r t h , f i f t h , and sixth-grade c h i l d r e n . Even though the above-mentioned s t u d i e s do not provide unequivocal evidence t h a t s e l f - c o n c e p t i n f l u e n c e s academic achievement, they have, however, encouraged educators to b e l i e v e t h a t i n t e r v e n t i o n s t o enhance a student's s e l f - c o n c e p t may increase h i s or her academic achievement. One of the l a r g e s t American e d u c a t i o n a l experiments undertaken was the f e d e r a l l y sponsored Follow Through Planned V a r i a t i o n s p r o j e c t which compared d i f f e r e n t t h e o r e t i c a l models f o r compensatory e d u c a t i o n a l i n t e r v e n t i o n s i n the primary grades. S c h e i r e r and Kraut (197 9) reviewed s e v e r a l of the e v a l u a t i o n s of t h i s p r o j e c t which were of n a t i o n a l scope, i n c l u d i n g the Stanford Research I n s t i t u t e ' s o b s e r v a t i o n a l study done by S t a l l i n g s and Kaskowitz (1974). S c h e i r e r and Kraut (1979) summarize: . . . This massive research e f f o r t combining r e s u l t s from from numerous s i t e s across the n a t i o n does not support the assumption of the open education t h e o r i s t s t h a t the c h i l d ' s i n t e r n a l developmental needs, i n c l u d i n g a p o s i t i v e s e l f - c o n c e p t , must be the b a s i s f o r e d u c a t i o n a l progress. On the c o n t r a r y , the more h i g h l y s t r u c t u r a l models were a s s o c i a t e d w i t h advances i n both academic achievement and self-esteem, (p. 135) REVIEW OF THE LITERATURE / 25 G e n e r a l i z i n g from the Follow Through Planned V a r i a t i o n s p r o j e c t i t seems t h a t s e l f - c o n c e p t changes, i f they do occur, are thought to be a consequence of academic success r a t h e r than an i n t e r v e n i n g v a r i a b l e necessary f o r l e a r n i n g to occur. This g e n e r a l i z a t i o n supports the b e h a v i o r i s t s ' v i s i o n who see l e a r n i n g as the r e s u l t of the s t r u c t u r e d teaching of s p e c i f i c s k i l l s needed f o r academic success coupled w i t h the use of p o s i t i v e reinforcement t o strengthen c o r r e c t responses. A study by Hunt and Hardt (1969 ) examined changes i n s e l f -esteem and academic achievement of high school students i n the Upward Bound program. S i g n i f i c a n t p o s i t i v e increases were found i n g l o b a l s e l f - c o n c e p t over the twenty-one month period of t e s t i n g ; however, these changes were not accompanied by changes i n the students' grade-point averages 1. This research supports the p r o p o s i t i o n t h a t g l o b a l s e l f - c o n c e p t change doesn't n e c e s s a r i l y lead t o enhanced academic achievement. Since 1971 there have been many d o c t o r a l d i s s e r t a t i o n s summarized i n D i s s e r t a t i o n A b s t r a c t s which have attempted to l i n k academic achievement w i t h s e l f - c o n c e p t change. F u l l d e t a i l s on some aspects of these s t u d i e s were not always i n c l u d e d ; however, o v e r a l l r e s u l t s were reported. Poudrier (1975) i n v e s t i g a t e d the e f f e c t s of a s e l f - c o n c e p t i n t e r v e n t i o n program on the s e l f - c o n c e p t and academic achievement of f o u r t h -grade boys and g i r l s . The sample c o n s i s t e d of 74 students w i t h 38 students i n the experimental group p a r t i c i p a t i n g i n the REVIEW OF THE LITERATURE / 26 Developing Understanding of S e l f and Others Program (DUSO) f o r 13 weeks. The c o n t r o l group p a r t i c i p a t e d i n the L i p p i n c o t t S p e l l i n g Program f o r 13 weeks. The groups were pr e t e s t e d and pos t t e s t e d w i t h the Wide Range Achievement Test (WRAT) and the Self-Esteem Inventory. S i g n i f i c a n t d i f f e r e n c e s f a v o r i n g the c o n t r o l group were found on the reading and s p e l l i n g s e c t i o n s of the WRAT. The conclusions of t h i s study were th a t the DUSO Program was not an e f f e c t i v e program f o r improving the academic achievement or s e l f - c o n c e p t of the fourth-grade students i n the study. A comparison of two methods of teaching i n the elementary school as r e l a t e d t o achievement i n reading, mathematics, and sel f - c o n c e p t of students was undertaken by Bradford (1972). The major reported f i n d i n g s of t h i s study were t h a t the students' gains i n mathematics were s i g n i f i c a n t l y greater i n the experimental group which used an I n d i v i d u a l l y Guided Education Program (IGE) as compared to the gains i n mathematics i n the c o n t r o l group. A l s o , students' gains were s i g n i f i c a n t l y greater i n s e l f - c o n c e p t i n the experimental group when compared to the gains i n s e l f - c o n c e p t i n the c o n t r o l group. S i g n i f i c a n t gain scores were not found i n reading achievement. However, as Sc h e i r e r and Kraut (1979) p o i n t out i n t h e i r review, the use of only one school f o r each type of program confounds the p o t e n t i a l program e f f e c t s w i t h other p o s s i b l e d i f f e r e n c e s between the schools. REVIEW OF THE LITERATURE / 27 A study done by Lawson (1974) looked a t a comparison of the development of se l f - c o n c e p t and achievement i n reading of students i n the f i r s t , t h i r d , and f i f t h year of attendance i n graded and non-graded elementary schools. R e s u l t s found higher reading achievement f o r the non-graded schools at a l l three l e v e l s , but higher s e l f - c o n c e p t scores i n the non-graded school only f o r the f i f t h - y e a r students. I t appears t h a t s e l f - c o n c e p t change i n t h i s study was an outcome of reading success r a t h e r than an i n t e r v e n i n g v a r i a b l e . An examination of s t u d i e s by Smith (1975), Hopke (1974), and Pine (1975) revealed that none of the ed u c a t i o n a l programs used showed measurable e f f e c t s on the t a r g e t groups' s e l f -concept scores w h i l e at the same time i n c r e a s i n g academic achievement. In no cases were changes i n achievement unam-biguously a s s o c i a t e d w i t h changes i n s e l f - c o n c e p t . However, because a l l the d o c t o r a l d i s s e r t a t i o n s examined d i d produce some measurable r e s u l t s , the lack of evidence f o r a connection between improving s e l f - c o n c e p t and achievement cannot be a t t r i b u t e d t o t a l l y t o inadequate measuring instruments or a f a i l u r e t o c a r r y out the intended i n t e r v e n t i o n . The negative r e s u l t s found when reviewing the l i t e r a t u r e concerned w i t h i n t e r v e n t i o n s aimed at i n c r e a s i n g s e l f - c o n c e p t and subsequent p o s i t i v e changes i n achievement i n d i c a t e t h a t perhaps the un d e r l y i n g theory i s wrong. S c h e i r e r and Kraut (1979) suggest an a l t e r n a t i v e view t h a t m o t i v a t i o n f o r academic REVIEW OF THE LITERATURE / 28 l e a r n i n g comes from the reinforcements of one's s o c i a l e n v i r o n -ment f o r s p e c i f i c learned s k i l l s . In t h i s view, s e l f - c o n c e p t changes are l i k e l y t o be an outcome of increased achievement w i t h accompanying s o c i a l approval r a t h e r than an i n t e r v e n i n g v a r i a b l e necessary f o r achievement t o occur. From the l i t e r a -t u r e , i t seems the assumption t h a t enhancing a student's f e e l i n g s about him or h e r s e l f w i l l lead to academic achievement needs t o be met w i t h c a u t i o n . E. SELF-EFFICACY AND CLASSROOM LEARNING According to Bandura (1981) s e l f - e f f i c a c y r e f e r s t o person-a l judgments of performance c a p a b i l i t i e s i n a given domain of a c t i v i t y t h a t may con t a i n n o v e l , u n p r e d i c t a b l e , and p o s s i b l y s t r e s s f u l f e a t u r e s . Schunk (1984) hypothesized t h a t educa-t i o n a l p r a c t i c e s are an important c o n t e x t u a l i n f l u e n c e on students' s e l f - e f f i c a c y . He s t a t e s : Some educ a t i o n a l p r a c t i c e s may v a l i d a t e t h i s sense of e f f i c a c y by c l e a r l y conveying t h a t students are a c q u i r i n g s k i l l s and knowledge, which should help t o s u s t a i n m o t i v a t i o n and develop s e l f - e f f i c a c y and s k i l l s . Other p r a c t i c e s may o f f e r l e s s c l e a r i n f o r -mation about s k i l l a c q u i s i t i o n or even convey that students are not p a r t i c u l a r l y s k i l l f u l . In these l a t t e r s i t u a t i o n s , m o t i v a t i o n may s u f f e r and students may remain u n c e r t a i n of t h e i r c a p a b i l i t i e s . In sh o r t , e d u c a t i o n a l p r a c t i c e s are hypothesized t o be important c o n t e x t u a l i n f l u e n c e s on students' s e l f -e f f i c a c y , (p. 209) When a c q u i r i n g new s k i l l s , students o f t e n meet w i t h f a i l u r e s and setbacks. However, according t o Schunk (1984), the REVIEW OF THE LITERATURE / 29 pe r c e p t i o n of progress can promote students' sense of e f f i c a c y f o r f u r t h e r improvement. To develop s e l f - e f f i c a c y , students need c l e a r i n f o r m a t i o n t h a t they are a c q u i r i n g knowledge and s k i l l s . U n f o r t u n a t e l y , when progress i s slow such as during complex s k i l l l e a r n i n g where students have to master many com-ponent s k i l l s , a c q u i s i t i o n of success i n f o r m a t i o n becomes problematic. However, students can gain c a p a b i l i t y i n f o r -mation through c h a r t s of t h e i r d a i l y progress toward a g o a l . A study done by Schunk (1983) demonstrated t h a t e x p l i c i t performance feedback enhances s e l f - e f f i c a c y . Elementary school c h i l d r e n who lacked s u b t r a c t i o n s k i l l s r eceived i n s t r u c -t i o n and i n d i v i d u a l l y solved problems i n a t r a i n i n g packet over s e v e r a l s e s s i o n s . At the end of each s e s s i o n , some students recorded the number of pages of problems they completed ( s e l f -m o n i t o r i n g ) ; others had t h e i r pages recorded by an a d u l t p r o c t o r ( e x t e r n a l m o n i t o r i n g ) ; and students i n a t h i r d c o n d i t i o n worked on the packet but d i d not r e c e i v e any feedback. In t h i s study both forms of feedback were e q u a l l y e f f e c t i v e and l e d t o higher F s e l f - e f f i c a c y and s k i l l f u l performance compared w i t h the no feedback c o n d i t i o n . Schunk (1983) e x p l a i n s the r e s u l t s of t h i s study as f o l l o w s : As c h i l d r e n observe t h e i r progress during t r a i n i n g , they develop a heightened sense of e f f i c a c y . Sub-sequent monitoring d i r e c t s c h i l d r e n ' s a t t e n t i o n t o work they completed and provides an o b j e c t i v e i n d i c a n t of progress, which helps t o v a l i d a t e perceived e f f i c a c y . . . . Conversely, when c h i l d r e n ' s perform-ances are not monitored they are on t h e i r own to assess t h e i r progress. Even though s k i l l s develop, c h i l d r e n may be unsure of t h e i r c a p a b i l i t i e s , (p. 92) REVIEW OF THE LITERATURE / 30 When students are given or s e l e c t a g o a l , they are apt t o f e e l motivated and experience a sense of s e l f - e f f i c a c y f o r a t t a i n i n g i t (Schunk, 1985). S p e c i f i c goals r a i s e s e l f - e f f i c a c y more than do general goals because progress toward an e x p l i c i t goal i s e a s i e r t o gauge (Schunk, 1985). L i k e general g o a l s , progress toward a d i s t a n t goal i s more d i f f i c u l t t o gauge, thus students r e c e i v e imprecise i n f o r m a t i o n about t h e i r s k i l l s . In a s u b t r a c t i o n s k i l l - d e v e l o p m e n t program (Bandura & Schunk, 1981), students i n d i v i d u a l l y worked on a t r a i n i n g packet c o n s i s t i n g of seven sets of m a t e r i a l . Some students worked toward a proximal goal of completing one packet each s e s s i o n ; a second group was given the goal of completing a l l sets of m a t e r i a l by the end of the seventh s e s s i o n ; and a t h i r d group was given the general goal of working p r o d u c t i v e l y . The r e s u l t s showed th a t proximal goals heightened task m o t i v a t i o n , and led to the highest s e l f -e f f i c a c y and s u b t r a c t i o n s k i l l . F. PRECISION TEACHING An i n s t r u c t i o n a l s t r a t e g y which provides f o r very s p e c i f i c goals i s P r e c i s i o n Teaching. P r e c i s i o n Teaching can be defined as an e v a l u a t i o n system c h a r a c t e r i z e d by d a i l y reinforcement feedback and the v i s u a l d i s p l a y of t h i s data (Fox, 1983). I t i s a p r o p o s i t i o n of the present study t h a t through an i n t e r v e n t i o n of the use of P r e c i s i o n Teaching p r a c t i c e s , elementary students' s u b j e c t - s p e c i f i c academic s e l f - c o n c e p t s can be improved. REVIEW OF THE LITERATURE / 31 The f o l l o w i n g d i s c u s s i o n regarding the b e h a v i o r a l approach to teaching w i l l serve t o c l a r i f y some of the b a s i c tenets of t h i s method. 1. The Be h a v i o r a l Approach t o Teaching The essence of the b e h a v i o r a l approach to teaching can be located o r i g i n a l l y i n the work of Thorndike and Skinner. G e n e r a l l y , t h i s approach i s based on the premise that the environment g r e a t l y i n f l u e n c e s behavior. Many researchers have been s u c c e s s f u l i n using the b e h a v i o r a l approach i n education t o a l l e v i a t e a v a r i e t y of academic d e f i c i t s i n a v a r i e t y of po p u l a t i o n s . These i n c l u d e : the mentally retarded (Clark & Walberg, 1979); the underachieving (Hendler, 1985; Peterson, 1985), the emotionally and b e h a v i o r a l l y d i s t u r b e d (O'Leary & Becker, 1967), and the r e g u l a r school p o p u l a t i o n ( H a r r i s & Sherman, 1972). 2. Data-Based I n s t r u c t i o n Data-based i n s t r u c t i o n i s a d i r e c t s k i l l model of i n s t r u c t i o n t h a t focuses on the d i r e c t and continuous measurement of student progress toward s p e c i f i c i n s t r u c t i o n a l o b j e c t i v e s (Blankenship & L i l l y , 1981). B e n e f i t s of t h i s model of i n s t r u c t i o n have been reported by many educators i n c l u d i n g ( L o v i t t , 1984; Haring and Krug, 1975). Moreover there i s a growing body of research t h a t suggests t h a t d i r e c t and frequent measurement of school behaviors can be used t o increase student REVIEW OF THE LITERATURE / 32 m o t i v a t i o n ( M i r k i n , Deno, T i n d a l & Kuehule, 1979). Ysseldyke, Thurlow, Graden, Wesson, A l g o z z i n e , and Deno (1983) r e p o r t i n t h e i r " G e n e r a l i z a t i o n s from F i v e Years of Research on Assessment and D e c i s i o n Making" t h a t teachers found t h a t t h e i r students were more aware of t h e i r own progress because of the frequent c h a r t i n g r e q u i r e d by a data-based system and t h a t the c h a r t i n g a l s o increased the m o t i v a t i o n of both teachers and students toward reaching goals and o b j e c t i v e s . According t o T r e i b e r & Lahey (1983), the b e h a v i o r a l . approach to the remediation of academic r e l a t e d behaviors i s defined by three c h a r a c t e r i s t i c s . (1) I n d i v i d u a l i z a t i o n and mastery l e a r n i n g . The c h i l d ' s strengths and weaknesses are assessed and progression i s made at the c h i l d ' s own r a t e a f t e r the s u c c e s s f u l mastery of each task. (2) D i r e c t teaching. B a s i c p r i n c i p l e s of l e a r n i n g are used i n d i r e c t l y modifying the behaviors t h a t need to be a l t e r e d . (3) Emphasis on measurement. A v i t a l aspect of the behavior approach i s the continuous measurement of the behavior t h a t i s being t r e a t e d . This procedure r e s u l t s i n immediate feedback as to the e f f e c t i v e n e s s of the treatment program and permits changes when appr o p r i a t e . (p. 42) There are many terms c h a r a c t e r i s t i c of the b e h a v i o r a l viewpoint. Some of these being operant c o n d i t i o n i n g , d i r e c t i n s t r u c t i o n , behavior m o d i f i c a t i o n , d i r e c t measurement, and P r e c i s i o n Teaching. However, u s u a l l y a l l these terms are interwoven i n a b e h a v i o r a l approach (Mercer, 1987). REVIEW OF THE LITERATURE / 33 3. Data-Based I n s t r u c t i o n and P r e c i s i o n Teaching As data-based i n s t r u c t i o n focuses on the d i r e c t and continuous measurement of students' progress, P r e c i s i o n Teaching i s o f t e n u t i l i z e d as the e v a l u a t i v e system of data-based i n s t r u c t i o n . G e n e r a l l y speaking, data-based i n s t r u c t i o n i s comprised of f i v e components. These i n c l u d e : (1) s e l e c t i n g a t a r g e t s k i l l or behavior; (2) developing a task sheet or probe f o r measurement of p u p i l progress i n d a i l y t i m i n g s ; (3) c o l l e c t i n g and graphing data; ( 4 ) s e t t i n g i n s t r u c t i o n a l aims and designing i n s t r u c t i o n a l program; and (5) making i n s t r u c t i o n a l d e c i s i o n s and a n a l y z i n g data (Mercer, 1987). I t should be noted, however, that P r e c i s i o n Teaching per se does not d i c t a t e what should be taught or how i n s t r u c t i o n should proceed, r a t h e r i t represents an approach t o the systematic e v a l u a t i o n of whatever i n s t r u c t i o n a l t a c t i c s and c u r r i c u l a teachers u t i l i z e (White, 1986). In the data-based i n s t r u c t i o n model, when s e l e c t i n g a t a r g e t s k i l l , the student i s assessed i n terms of s k i l l mastery, and i n s t r u c t i o n begins at the lowest s k i l l not mastered (Mercer, 1987). When s e l e c t i n g t a r g e t s k i l l s , i t i s p e r t i n e n t t h a t s k i l l s or responses be described i n such a way t h a t i t w i l l be obvious t o the student and teachers of t h a t student t h a t the s k i l l was or was not d i s p l a y e d . Furthermore, i t i s compulsory t h a t the s k i l l be repeatable. As pointed out by West and Young REVIEW OF THE LITERATURE / 34 (1985), i t i s a l s o important t h a t each instance of a t a r g e t s k i l l be of s i m i l a r d u r a t i o n . For example, i t would be i n a p p r o p r i a t e t o mix simple a d d i t i o n f a c t problems w i t h long d i v i s i o n problems when the goal of a student was t o master t h i r t y problems i n a minute. I t i s commonly agreed upon among researchers of the b e h a v i o r a l approach to teaching t h a t one of the most s a l i e n t features of data-based i n s t r u c t i o n i s d i r e c t , continuous and p r e c i s e measurement of behavior (White & Haring, 1980; Van Houten, 1980). As no s i n g l e i n s t r u c t i o n a l s t r a t e g y works a l l the time and even the most c a r e f u l l y planned program can lose e f f e c t i v e n e s s , frequent e v a l u a t i o n of p u p i l progress i s paramount i n determining when and how a program should be modified (White, 1985). A l s o , s i n c e the e f f e c t i v e use of feedback hinges on p r o v i d i n g p r e c i s e feedback f o l l o w i n g small improvements, i t i s e s s e n t i a l t h a t teachers and parents be able t o measure and recognize instances of success i n t h e i r students (Van Houten, 1980). The P r e c i s i o n Teaching e v a l u a t i o n system i s an e f f e c t i v e method f o r doing t h i s . The term, continuous measurement, n e c e s s i t a t e s t h a t a behavior be counted and recorded over time; whereas the term, p r e c i s e measurement, r e q u i r e s that, r e c o r d i n g systems be r e l i a b l e (Mercer, 1987). With respect to c o l l e c t i n g and graphing data, changes i n performance can be studied more e a s i l y when scores are p l o t t e d on REVIEW OF THE LITERATURE / 35 a graph and inspected v i s u a l l y . Graphs a l s o enable the inspec-t i o n and comparison of m u l t i p l e data p o i n t s without examining vast q u a n t i t i e s of raw performance scores (West & Young, 1985). Consequently, i n data-based i n s t r u c t i o n , graphing i s the most common way of pre s e n t i n g data (Mercer, 1987). Graphs serve three purposes g e n e r a l l y : (1) they summarize data; (2) they communicate i n t e r v e n t i o n e f f e c t s ; and (3) they provide feedback and reinforcement to the l e a r n e r and teachers (Kerr & Nelson, 1983). U n f o r t u n a t e l y , however, i t i s p o s s i b l e t h a t the format of the graph can exaggerate or obscure the q u a n t i t a t i v e dimensions of the data and thus confuse i n t e r p r e -t a t i o n . One way of a v o i d i n g t h i s i s through the use of a standard behavior c h a r t . 4. The Standard Behavior Chart, A P r e c i s i o n Teaching Tool The standard behavior c h a r t * i s a s c a l e t h a t can span a wide range of performance values but r e q u i r e s l i t t l e space. This i s done by the use of a r a t i o or l o g a r i t h m i c s c a l e . West and Young (1985) s t a t e : The l o g a r i t h m i c s c a l e i s important f o r reasons other than i t s a b i l i t y t o d i s p l a y w i d e l y v a r y i n g scores. I t a l s o enables the teacher to study a p i c t u r e of l e a r n i n g t h a t i s more e a s i l y i n t e r p r e t e d . When the measures of performance are p l o t t e d on the more t y p i -c a l "equal i n t e r v a l " or " a r i t h m e t i c " s c a l e , l e a r n i n g * See Appendix A. REVIEW OF THE LITERATURE / 36 (represented by a l i n e or f u n c t i o n which "best f i t s " the data) i s found to a c c e l e r a t e . In other words, a curve w i t h an ever-steeper slope i s created. When data are p l o t t e d on the standard behavior c h a r t , l e a r n i n g i s g e n e r a l l y represented by a s t r a i g h t or n e a r l y s t r a i g h t l i n e . The value of the slope of the l i n e which best f i t s the d i s t r i b u t i o n of the values p l o t t e d on the l o g a r i t h m i c s c a l e i s thought of as an "index of l e a r n i n g . " The steeper the s l o p e , the f a s t e r the l e a r n i n g i s ; the f l a t t e r the slope, the slower the l e a r n i n g i s . (p. 6) Another u s e f u l component of the l o g a r i t h m i c s c a l e i s t h a t equal u n i t s on the s c a l e correspond t o equal r a t i o s , and equal d i s t a n c e s from one p o i n t on the l o g a r i t h m i c s c a l e t o another p o i n t c o n s i s t e n t l y r e f l e c t equal p r o p o r t i o n a l changes (West & Young, 1985). This i s of importance when c o n s i d e r i n g the d e f i n i t i o n given t o l e a r n i n g by West and Young (1985) i n which l e a r n i n g i s seen as a "change i n the r e l a t i v e values of repeated performance measures." Given t h i s d e f i n i t i o n i t would seem appropriate t o i n s p e c t r e l a t i v e changes i n a l o g a r i t h m i c s c a l e . 5 . Data-Based D e c i s i o n Making Ysseldyke et a l . (1983) i n a l o n g i t u d i n a l study of research on assessment and decision-making s t r a t e g i e s s t a t e : Student performance can be improved by a p p l y i n g data u t i l i z a t i o n s t r a t e g i e s . Students make more progress when t h e i r performance data are used s y s t e m a t i c a l l y and teachers are s a t i s f i e d w i t h the procedures. C o l l e c t i n g more frequent data on student performance leads t o more accurate d e c i s i o n s . (p. 83) S i m i l a r l y , M i r k i n , Deno, T i n d a l , .& Kuehule (1979 ) found evidence t h a t frequent e v a l u a t i o n of student performance can lead to improved student achievement. However, to d e r i v e the maximum REVIEW OF THE LITERATURE / 37 b e n e f i t of P r e c i s i o n Teaching, i t i s not s u f f i c i e n t to simply monitor performance of a l e a r n e r on a standard c h a r t . Evalua-t i o n of the data must be used to make systematic d e c i s i o n s on how i n s t r u c t i o n should continue (White, 1986). Numerous P r e c i s i o n teachers have developed g u i d e l i n e s t o a s s i s t educators i n d e c i d i n g when and how a l e a r n i n g program should be changed (Eaton, 1978; Haring, L i b e r t y , and White, 1980; White & L i b e r t y , 1976). Eaton (1978) has pointed out t h a t when a s e r i e s of data p o i n t s i s graphed, i t i s then p o s s i b l e to c a l c u l a t e the slope of the student's progress l i n e and from t h i s determine i f the program should continue or be r e d i r e c t e d . By using data on slope, i t i s now p o s s i b l e t o move i n s t r u c t i o n i n t o the area of a p p l i e d science (Deno, 1985). This o f f e r s a c o n t r a s t t o the f i n d i n g s of Fuchs, Fuchs and Warren (1982) who found t h a t the o v e r a l l discrepancy between a c t u a l student performance and teacher judgment of non- p r e c i s i o n teachers to be s t a t i s t i c a l l y s i g n i f i c a n t . The d e c i s i o n r u l e s of P r e c i s i o n Teaching have been developed to be an o b j e c t i v e set of g u i d e l i n e s t h a t can be ap p l i e d very p r e c i s e l y using only the data d i s p l a y e d on the standard behavior chart (White, 1986). However, even though numerous research s t u d i e s have supported f i n d i n g s t h a t data a n a l y s i s and decision-making g u i d e l i n e s improve academic REVIEW OF THE LITERATURE / 38 performance i n l e a r n e r s of v a r i o u s ages, educators must remain aware of the fundamental g u i d i n g p r i n c i p l e of P r e c i s i o n Teaching t h a t the " l e a r n e r knows best" or as White (1986) s t a t e s ; E x i s t i n g data d e c i s i o n r u l e s provide u s e f u l guidance, but educators must always look t o the i n d i v i d u a l l e a r n e r f o r c o n f i r m a t i o n t h a t t h e i r e f f o r t s are appro-p r i a t e , (p. 523) In summary, as p r e v i o u s l y noted, P r e c i s i o n Teaching i s not regarded as a way of teaching but r a t h e r as a way of e v a l u a t i n g the c u r r i c u l a and teaching s t r a t e g i e s being used. However, as an e v a l u a t i o n system, P r e c i s i o n Teaching has been used success-f u l l y t o f a c i l i t a t e the progress of l e a r n e r s ranging from the se v e r e l y handicapped t o u n i v e r s i t y graduate students (White, 1986). L o v i t t and Fa n t a s i a (1983 and 1985), reviewed s e v e r a l s t u d i e s they conducted t o evaluate the e f f e c t s of P r e c i s i o n Teaching i n s t r u c t i o n on the academic performance of elementary-age, mildy handicapped c h i l d r e n . The data from these s t u d i e s i n d i c a t e d t h a t P r e c i s i o n Teaching or c e r t a i n of i t s f e a t u r e s , was r e l a t e d t o p u p i l s 1 s i g n i f i c a n t achievement gains i n reading, a r i t h m e t i c , and s p e l l i n g w i t h the g r e a t e s t e f f e c t s seen i n reading. Three extensive w e l l - c o n t r o l l e d s t u d i e s done wi t h elementary school students are summarized i n Table 1. REVIEW OF THE LITERATURE / 3 9 T a b l e 1 S u m m a r y o f P r e c i s i o n T e a c h i n g S t u d i e s S t u d y D e s i g n M e a s u r e s R e s u l t s G r e a t F a l l s P r e c i s i o n T e a c h i n g P r o j e c t 1976 C h i l d r e n w i t h s k i l l d e f i c i t s i n g r a d e s 1, 2 , & 3 i n s i x s c h o o l s ; 3 s c h o o l s e m p l o y e d p r e c i s i o n t e a c h i n g T P T ) , 3 s c h o o l s d i d n o t . T o t a l e x p e r i m e n t a l n = 5 3 2 ; c o n t r o l n=kjt>. P r e t e s t / p o s t t e s t d e s i g n o v e r c i r c a 1 s c h o o l y e a r . T i m e p r o b e s i n • w r i t i n g n u m b e r s r a n d o m l y , w r i t i n g n u m b e r s d i c t a t e d , a n d s a y i n g l e t t e r s ( d i s t . s c r e e n i n g p r o c e d u r e s ) . P T g r o u p p o s t t e s t s s i g n i f i c a n t l y s u p e r i o r i n 1 5 (19%) o f t h e c o m p a r i s o n s , n o i f f e r e n c e s i n 3 16%) o f t h e c o m p a r i s o n s ; n o n -P T g r o u p s u p e r i o r i n I (5%) o f t h e c o m p a r i s o n s . G r e a t F a l l s P r e c i s i o n T e a c h i n g P r o j e c t 1979 S t u d y 1 : 1 3 4 r e g u l a r 1 s t , 2 n d , & 3 r d g r a d e r s i n a s c h o o l u s i n g P T c o m p a r e d p r e / p o s t o v e r o n e s c h o o l y e a r w i t h 1 5 5 s i m i l a r c h i l d r e n i n a c a r e f u l l y m a t c h e d s c h o o l n o t u s i n g P T . S t u d y 2 : R e g u l a r f o u r t h g r a d e r s a t , a P T s c h o o l ( n=29*0 c o m p a r e d w i t h s t u -d e n t s i n a m a t c h e d n o n - P T s c h o o l ( n - 3 1 2 ) o v e r a p e r i o d o f 4 y e a r s . I o w a T e s t o f B a s i c S k i l l s , m a t h a n d r e a d i n g s u b s e c t i o n s . S t u d y l : N o i n i t i a l d i f f e r e n c e s ; 1 s t a n d 2 n d g r a d e P T g r o u p s s i g n i f i -c a n t l y s u p e r i o r i n m a t h . I n n o c a s e d i d t h e n o n - P T g r o u p s i g n i f i c a n t -l y o u t p e r f o r m t h e P T g r o u p . S t u d y 2 : B y t h e e n d o f f o u r y e a r s , t h e P T 4 t h g r a d e r s w e r e p e r f o r m i n g a t t h e 9 5 p e r c e n t i l e i n r e a d i n g a n d t h e 8 0 t h p e r c e n t i l e i n m a t h ; t h e n o n - P T s c h o o l s t u d e n t s w e r e p e r f o r m i n g a t t h e 7 1 s t a n d 5 4 t h p e r c e n t i l e , r e s p e c t i v e l y . G r e a t F a l l s P r e c i s i o n T e a c h i n g P r o j e c t 1 9 8 1 5 3 8 2 n d , 3 r d , a n d 4 t h g r a d e r s a n d 3 0 t e a c h e r s a s s i g n e d t o 4 g r o u p s : ( l ) n o n - P T ; ( 2 ) P T ta i l y a s s e s s m e n t s 3 ) P T d a i l y a s s e s s m e n t s . + c h a r t i n g ; ( M P T d a i l y a s s e s s m e n t s + c h a r t i n g + u s e o f s p e c i a l d a t a -d e c i s i o n r u l e s . P r e - p o s t a s s e s s -m e n t s o v e r 7 m o n t h s . I o w a T e s t o f B a s i c S k i l l s , m a t h s u b s e c t i o n . 1 0 o r 1 1 c o m p a r i -s o n s s h o w e d s i g n i -f i c a n t d i f f e r e n c e s f o u n d i n t h e 1 1 t h c o m p a r i s o n . T h e u s e o f p r e s p e c i -f i e d d e c i s i o n r u l e s ( t h e t h i r d P T c o n d i t i o n ) ?r o v e d s u p e r i o r n 7 (63%) o f t h e c o m p a r i s o n s . E x e r p t e d f r o m W h i t e , 0 . R . (1986) REVIEW OF THE LITERATURE / 40 6. Stages of Learning Numerous p r a c t i t i o n e r s of the b e h a v i o r a l approach t o teaching p o s i t t h a t there are d i s t i n c t stages of student l e a r n i n g t h a t are fundamental t o designing and implementing i n s t r u c t i o n (Haring, L o v i t t , Eaton, & Hansen, 1978). Smith and L o v i t t (1976), d e f i n e these stages as a c q u i s i t i o n , p r o f i c i e n c y , and maintenance. The a c q u i s i t i o n stage occurs when the beha-v i o r t o be learned i s not i n the r e p e r t o i r e of the student and the student doesn't know how to perform the task. Once the student can a c c u r a t e l y complete the t a s k , he/she enters i n t o the p r o f i c i e n c y stage. At t h i s stage, the student i s s t i l l not sure of the process and consequently i s slow at performing the task. The t h i r d stage or maintenance i s the stage where the student has acquired the new s k i l l and i s p r o f i c i e n t i n h i s / h e r performance of the s k i l l . At the maintenance stage, the teacher must ensure t h a t the student maintains the r e q u i r e d l e v e l of p r o f i c i e n c y . Research s t u d i e s t h a t demonstrate the e f f e c t i v e n e s s of reinforcement i n improving academic performance are p l e n t i f u l . However, some researchers (Smith & L o v i t t , 1976) have reported t h a t reinforcement i s not always s u c c e s s f u l i n improving academic performance. Smith & L o v i t t (1976) found t h a t when students were l e a r n i n g how t o s o l v e a r i t h m e t i c problems (or i n the a c q u i s i t i o n of l e a r n i n g ) , reinforcement was i n e f f e c t i v e . Conversely, when students were presented w i t h a r i t h m e t i c REVIEW OF THE LITERATURE / 41 problems they knew how to solve a c c u r a t e l y ( p r o f i c i e n c y s t a g e ) , but at which they worked too s l o w l y , reinforcement contingencies proved s u c c e s s f u l . Smith & L o v i t t (1976) suggest t h a t these s t u d i e s demonstrate the importance of c a r e f u l d i a g n o s i s of c h i l d r e n ' s academic d e f i c i e n c i e s and t h a t many a r i t h m e t i c i n t e r v e n t i o n s are e f f e c t i v e w i t h only c e r t a i n types of performance. However, when students' computational p r o f i c i e n -cy needs improvement, reinforcement contingencies can i n f l u e n c e computational speed. G. THE ELEMENTARY SCHOOL STUDENT'S SELF-CONCEPT I t can be noted t h a t researchers are i n agreement t h a t when c h i l d r e n enter elementary school t h e i r s e l f - c o n c e p t s are already forming but are s t i l l very much s u s c e p t i b l e t o change (Burns, 1982). G e n e r a l l y speaking, once i n the p u b l i c school system, the most dominant value o p e r a t i n g i s t h a t of academic achievement. E v a l u a t i o n of each student's academic achievement i s pervasive and i s both v e r b a l and non-verbal. A f t e r a student encounters a s u f f i c i e n t number of f a i l i n g experiences, he or she w i l l e v e n t u a l l y succumb to a negative or inadequate s e l f - c o n c e p t i n the s p e c i f i c area of f a i l u r e . S i m i l a r l y , f o r s u c c e s s f u l encounters, a student w i l l e v e n t u a l l y come t o view him or h e r s e l f as adequate i n t h i s area (Glasser, 1964). Further, Burns (1982) p o i n t s out: REVIEW OF THE LITERATURE / 42 A few s u c c e s s f u l or unsu c c e s s f u l experiences may not have a major e f f e c t on the s e l f - c o n c e p t — i n f a c t , i t i s p o s s i b l e t h a t o c c a s i o n a l experiences which can be turned by the i n d i v i d u a l i n t o s u c c e s s f u l experiences may be of s p e c i a l s i g n i f i c a n c e i n strengthening the i n d i v i d u a l ' s self-image. However, i t i s the f r e -quency and consistency of adequacy over a p e r i o d of years which has i t s major e f f e c t s on s e l f - c o n c e p t , (p. 204) Morse (1964) has pointed out t h a t between second and seventh grade there i s a c o n s i s t e n t d e c l i n e i n c h i l d r e n ' s self-esteem. Torrance (1967) hypothesized t h a t c e r t a i n periods of s t r e s s i n c h i l d r e n ' s l i v e s c o n t r i b u t e t o behaviors t h a t cause d i s c o n -t i n u i t i e s i n c r e a t i v e growth and, i n a l o n g i t u d i n a l , c r o s s -c u l t u r a l study, found t h a t a s i g n i f i c a n t d e c l i n e i n c r e a t i v e t h i n k i n g occurred i n the f o u r t h grade. B u i l d i n g from the work of Torrance (1967), W i l l i a m s (1976) discovered t h a t fourth-grade students (at nine years of age) a l s o experienced a s i g n i f i c a n t d e c l i n e i n academic s e l f - c o n c e p t and m o t i v a t i o n but d i d not experience a d e c l i n e i n general s e l f -concept. W i l l i a m s s t a t e s , This i s not s u r p r i s i n g as one views the t y p i c a l educa-t i o n a l program i n many elementary schools; f o r at th a t time i n p u p i l s ' l i v e s they are expected t o be r a t h e r w e l l regimented i n t o a c e r t a i n academic mold imposed by teacher, peer, and parent pressures f o r school success. This i s e s p e c i a l l y t r u e i n the s k i l l areas of reading, mathematics, and language.(p. 24) Drawing from h i s 1976 study, W i l l i a m s recommends s e v e r a l p r e v e n t a t i v e measures f o r educating p u p i l s i n the grade-four age REVIEW OF THE LITERATURE / 43 group to reduce t h e i r f e e l i n g s of academic inadequacy. He p o s i t s t h a t a p o s s i b l e s o l u t i o n i s f o r teachers to set a t t a i n a b l e goals f o r students and to be able to recognize movement towards these goals no matter how small the movement. P r e c i s i o n Teaching i s one way t h i s could be done i n the classroom. Using the work of Torrance (1967) and W i l l i a m s (1976) as a r a t i o n a l e , the present study used fourth-grade students as s u b j e c t s . L i k e reading and language s k i l l s , success i n a r i t h m e t i c i s an important aspect of academic s e l f - c o n c e p t . Combs and Soper (1963) have e s t a b l i s h e d t h a t f o r kindergarten and f i r s t - g r a d e c h i l d r e n academic s e l f - c o n c e p t i s already d i f f e r e n t i a t e d i n t o p a r t i c u l a r areas of competency, f o r example, reading and a r i t h m e t i c . A i t k e n (1970), i n a review of research on a t t i t u d e s toward mathematics, s t a t e s t h a t there are many methods of measuring these a t t i t u d e s . He l i s t s these as: (1) o b s e r v a t i o n a l methods; (2) i n t e r v i e w s ; and (3) s e l f - r e p o r t methods such as q u e s t i o n n a i r e s , a t t i t u d e s c a l e s , or p r o j e c t i v e techniques. F u r t h e r , Aiken (1970) s t a t e s t h a t although the m a j o r i t y of i n v e s t i g a t i o n s have d e a l t w i t h a t t i t u d e s toward mathematics i n g e n e r a l , a t t i t u d e s toward s p e c i f i c types of mathematics prob-lems can a l s o be assessed. REVIEW OF THE LITERATURE / - 4 4 G e n e r a l l y , i t i s recognized t h a t a t t i t u d e s toward mathematics i n a d u l t s can be traced t o childhood ( M o r r i s e t t & V i n s o n h a l e r , 1965). I t would seem reasonable t h a t the grades which stressed a r i t h m e t i c s t r o n g l y would be the grades th a t would be most i n f l u e n t i a l i n e a r l y a r i t h m e t i c a t t i t u d e formation. Researchers have observed t h a t c o n s i s t e n t f a i l u r e i n a r i t h m e t i c causes students to l o s e s e l f - c o n f i d e n c e and develop a negative a t t i t u d e toward the subject (Lerch, 1961). To a l l e v i -ate negative a t t i t u d e s , the teacher must provide success e x p e r i -ences f o r the student as w e l l as set reasonable goals t h a t culminate i n the reward of success (Aiken, 1970). The use of P r e c i s i o n Teaching i s one way of doing t h i s . According t o Aiken (1970), techniques f o r developing p o s i -t i v e a t t i t u d e s and modifying negative a t t i t u d e s toward a r i t h -metic have been l i t t l e studied or researched. The present study was an attempt to u t i l i z e P r e c i s i o n Teaching as a technique f o r developing p o s i t i v e a t t i t u d e s toward a r i t h m e t i c . Sex-related d i f f e r e n c e s i n mathematics performance have o f t e n been a t t r i b u t e d t o the c o g n i t i v e v a r i a b l e , s p a t i a l v i s u a l -i z a t i o n . Aiken (197 3) came to the c o n c l u s i o n t h a t s p a t i a l -p e r c eptual a b i l i t y was one of the most s a l i e n t f a c t o r s c o n t r i b u t i n g to mathematical achievement. However, Fennema and Sherman (1977) s p e c i f i c a l l y i n v e s t i g a t e d the r e l a t i o n s h i p REVIEW OF THE LITERATURE / 45 between mathematic achievement and s p a t i a l - v i s u a l i z a t i o n s k i l l s . The data from t h i s study d i d not support the idea t h a t d i f f e r e n c e s i n mathematics achievement of males and females could be explained by d i f f e r e n c e s i n s p a t i a l - v i s u a l i z a t i o n a b i l i t y . More s p e c i f i c a l l y , i n t h i s study of males and females e n r o l l e d i n grades s i x through twelve, few s e x - r e l a t e d d i f f e r -ences i n e i t h e r mathematics achievement or s p a t i a l -v i s u a l i z a t i o n s k i l l s were found. The two were r e l a t e d (r-.5) f o r both sexes and s p a t i a l - v i s u a l i z a t i o n a b i l i t y appeared t o i n f l u e n c e both females and males e q u a l l y t o continue studying mathematics. Mathematics s e l f - c o n f i d e n c e and a n x i e t y as r e l a t e d to mathematics l e a r n i n g are seen i n the l i t e r a t u r e as important a f f e c t i v e v a r i a b l e s t h a t help e x p l a i n s e x - r e l a t e d d i f f e r e n c e s i n mathematics l e a r n i n g . Bachman (1970) and Fink (1969) have recognized the importance of academic s e l f - c o n c e p t i n l e a r n i n g mathematics. In the Fennema-Sherman Study (1977), at each grade l e v e l from s i x through twelve, boys were s i g n i f i c a n t l y more co n f i d e n t i n t h e i r a b i l i t y t o d e a l w i t h mathematics than were g i r l s . Confidence i n l e a r n i n g mathematics was more h i g h l y c o r r e l a t e d w i t h mathematics achievement than was any other a f f e c t i v e v a r i a b l e . G e n e r a l l y speaking, before a student can become p r o f i c i e n t i n a r i t h m e t i c , he or she must know how t o solve s p e c i f i c types of problems. Smith and L o v i t t (1976) s t a t e : REVIEW OF THE LITERATURE / 46 The c h i l d working arithmetic problems too slowly does not complete his work as fast as his classmates. As arithmetic assignments become more complex, t h i s c h i l d often works even slower and completes fewer problems. Frequently, the reason for the d i f f i c u l t y i s a lack of proficiency i n using the basic facts that are the rudiments of larger problems (p. 22). H. SUMMARY OF REVIEW This review started with a discussion of the construct self-concept. The l i t e r a t u r e revealed that there have been many and various overlapping d e f i n i t i o n s of t h i s complex construct. However, through the t h e o r e t i c a l framework and model of self-concept proposed by Shavelson et a l . (1976); Shavelson & Bolus, 1982; and Shavelson & Byrne, 1986, a concise d e f i n i t i o n of the self-concept has emerged that now enables researchers to examine facets of the construct with greater c l a r i t y . The role of and importance of academic self-concept and self-concept of academic achievement i s discussed. The l i t e r a t u r e revealed that numerous researchers have observed a p o s i t i v e c o r r e l a t i o n between students' academic self-concept and t h e i r achievement i n academic subjects. Like-wise, the l i t e r a t u r e revealed that many self-concept researchers have attempted various strategies and interventions to enhance student achievement and global self-concept. How-ever, when reviewing the l i t e r a t u r e , i t appears that many educa-REVIEW OF THE LITERATURE / 47 t i o n a l programs were unable t o i n f l u e n c e s e l f - c o n c e p t . When an a l y z i n g the reasons f o r t h i s , i t appears t h a t a more e x p l i c i t examination of s e l f - c o n c e p t t h e o r i e s and d e f i n i t i o n s needs to be incorporated i n t o the s e l f - c o n c e p t e d u c a t i o n a l i n t e r v e n t i o n programs. Self-concept, i t seems, cannot be conceptualized as a simple phenomenon but r a t h e r needs to be viewed as a complex c o n s t r u c t . However, the l i t e r a t u r e r e v e a l s an absence of i n t e r v e n t i o n s t u d i e s based on a m u l t i d i m e n s i o n a l s e l f - c o n c e p t . Going a step f u r t h e r , data-based searches f a i l e d t o r e v e a l any i n t e r v e n t i o n s t u d i e s drawing on the m u l t i d i m e n s i o n a l and h i e r a r c h i c a l model of s e l f - c o n c e p t proposed by Shavelson et a l . (1976) or Shavelson and Bolus (1982 ). To t h i s end, the present study was conceived. Studies t h a t i n v e s t i g a t e d s e l f - e f f i c a c y were a l s o examined. From these s t u d i e s i t was learned t h a t some educa t i o n a l p r a c t i c e s b u i l d e f f i c a c y by c l e a r l y conveying t h a t students are a c q u i r i n g s k i l l s and knowledge. In sum, educational p r a c t i c e s are hypothesized t o have important c o n t e x t u a l i n f l u e n c e s on students' s e l f - e f f i c a c y . R esults of research have shown t h a t working toward proximal goals and the use of p r e c i s e feedback heightened m o t i v a t i o n and l e d to enhanced s e l f - e f f i c a c y of v a r i o u s t a s k s . The l i t e r a t u r e surveyed revealed t h a t researchers of the b e h a v i o r a l approach to teaching have been s u c c e s s f u l i n using REVIEW OF THE LITERATURE / 48 t h i s method to a l l e v i a t e a v a r i e t y of academic d e f i c i t s . S i m i l a r l y , there i s a growing body of l i t e r a t u r e t h a t i n d i c a t e s d i r e c t and frequent measurement of school tasks increases student m o t i v a t i o n and academic s k i l l s . A l s o revealed i n the l i t e r a t u r e was the concept t h a t the e f f e c t i v e use of feedback hinges on p r o v i d i n g p r e c i s e feedback f o l l o w i n g small improvements. To t h i s end, P r e c i s i o n Teaching p r a c t i c e s give e x p l i c i t performance feedback to students, teachers, and parents thus f o s t e r i n g awareness of progress i n the c u r r i c u l u m . In summary, t h i s review has examined the t h e o r e t i c a l specu-l a t i o n by Shavelson et a l . (1976 ) of the multidimensional s e l f -concept h i e r a r c h y as w e l l as an accumulation of evidence i n regards t o teaching s t r a t e g i e s t o enhance academic s e l f -concept. A l s o , upon c l o s e i n v e s t i g a t i o n of these two areas, there appears to be an absence of s t u d i e s done at the p r a c t i c a l l e v e l t h a t b u i l d on Shavelson et a l . ' s (1976) theory of a multidimensional and h i e r a r c h i c a l s t r u c t u r e of s e l f - c o n c e p t . S p e c i f i c a l l y , one i s l e f t t o wonder: Can t h i s theory be drawn upon when designing i n t e r v e n t i o n s t o enhance academic s e l f -concept and can these i n t e r v e n t i o n s be s u c c e s s f u l ? The hypotheses and methodology of the present study are presented i n the f o l l o w i n g chapter. III. HYPOTHESES, QUESTIONS, AND METHOD This chapter serves t o d e l i n e a t e the hypotheses and ex p l o r a t o r y questions of the present study as w e l l as to d e t a i l the research methodology t h a t was used. A. RATIONALE FOR HYPOTHESES AND EXPLORATORY QUESTIONS Broadly d e f i n e d , s e l f - c o n c e p t i s a person's perceptions of him or h e r s e l f . According t o Shavelson and Bolus (1982), these perceptions of s e l f are formed through one' s experience w i t h and i n t e r p r e t a t i o n s of one's environment and are "i n f l u e n c e d espe-c i a l l y by reinforcements, e v a l u a t i o n s by s i g n i f i c a n t o t h e r s , and one's a t t r i b u t i o n s f o r one's own behavior." Further, Shavelson et a l . , (1976) and Shavelson and Bolus (1982) have t h e o r i z e d t h a t the construct s e l f - c o n c e p t i s organized or s t r u c -t u r e d , m u l t i f a c e t e d , h i e r a r c h i c a l , and s t a b l e at the apex. As one descends the h i e r a r c h y , however, se l f - c o n c e p t becomes i n c r e a s i n g l y s i t u a t i o n s p e c i f i c and, consequently, l e s s s t a b l e . Self-concept a l s o becomes i n c r e a s i n g l y m u l t i f a c e t e d as the i n d i v i d u a l develops, and has both a d e s c r i p t i v e and an ev a l u a t i v e dimension, and can be d i f f e r e n t i a t e d from other c o n s t r u c t s , such as, academic achievement. 49 HYPOTHESES, QUESTIONS, AND METHOD / 50 By drawing on the t h e o r e t i c a l framework of a h i e r a r c h i c a l and multidimensional s e l f - c o n c e p t , and by i n c o r p o r a t i n g the theory t h a t one' s perceptions of s e l f are " i n f l u e n c e d e s p e c i a l l y by reinforcements and e v a l u a t i o n s by s i g n i f i c a n t others and one's a t t r i b u t i o n f o r one's own behavior" (Shavelson et a l . , 1976), the present study was conceived. The present study was designed t o i n v e s t i g a t e the e f f e c t s of an experimental i n t e r v e n t i o n t h a t incorporated reinforcement and e v a l u a t i o n by s i g n i f i c a n t others as w e l l as students* a t t r i -butions f o r t h e i r behavior on academic and a r i t h m e t i c s e l f -concept. More s p e c i f i c a l l y , the study was designed t o apply an i n t e r v e n t i o n t o a s p e c i f i c s i t u a t i o n a l l e v e l , or low l e v e l , of the h i e r a r c h y and to subsequently measure at a higher l e v e l of the h i e r a r c h y f o r e f f e c t s of the i n t e r v e n t i o n . The f o l l o w i n g Figure 2, adapted from Shavelson et a l . (1976), serves t o p i c t o r i a l l y represent t h i s i n t e n t i o n . HYPOTHESES, QUESTIONS, AND METHOD / 51 Academic S e l f - c o n c e p t A r i t h m e t i c S e l f - c o n c e p t _^ g l o b a l a r e a o f measurement s p e c i f i c a r e a o f measurement a r e a i n t e r v e n t i o n a p p l i e d t o s p e c i f i c — s i t u a t i o n / 4-m u l t i p l i c a t i o n a s c e n d i n g l e v e l s o f h i e r a r c h y base o f h i e r a r c h y F i g . 2: R e p r e s e n t a t i o n o f I n t e r v e n t i o n A p p l i c a t i o n and A reas o f Measurement* The l i t e r a t u r e r e v e a l s some c o n t r o v e r s y on t h e e f f e c t s o f feedback on performance f o r males and f e m a l e s . Two s t u d i e s done by E a g l y and Whitehead (1972) and F e a t h e r and Simon (1971) found females t o be more s e n s i t i v e t o feedback on performance. S i n c e a s a l i e n t p o r t i o n o f t h e d e s i g n e d i n t e r v e n t i o n i n v o l v e s performance feedback and s i n c e most o f t h e s t u d i e s on t h e e f f e c t of feedback have not a n a l y z e d d a t a f o r sex d i f f e r e n c e s * See page 8 f o r S h a v e l s o n e t a l . (1976) o r i g i n a l d iagram. HYPOTHESES, QUSTIONS, AND METHOD / 52 (Calsyn & Kenny, 1977 ), another goal i n the present study was t o d i s c o v e r i f the i n t e r v e n t i o n e f f e c t e d greater change w i t h one sex or the other. Many educators of mathematics have used gender as a v a r i a b l e when examining mathematic achievement. According to Fennema (1980), a l l reviews published before 1974 concerned w i t h sex-r e l a t e d d i f f e r e n c e s i n mathematic achievement were i n agreement tha t male s u p e r i o r i t y was always evident by the time l e a r n e r s were i n upper elementary school or j u n i o r high school. However, reviews published a f t e r 1974 have not shown the same consensus i n regards t o male s u p e r i o r i t y (Fennema, 1980). In her 1974 review, Fennema concluded, a f t e r reviewing t h i r t y - s i x s t u d i e s , t h a t there were no s e x - r e l a t e d d i f f e r e n c e s i n elementary school c h i l d r e n ' s mathematics achievement and sub-sequently found l i t t l e evidence t h a t d i f f e r e n c e s e x i s t between male and female students at the high school l e v e l when amount of course-taking i s c o n t r o l l e d . In c o n t r a s t t o t h i s , Marsh, Smith, and Barnes (1985) found t h a t f i f t h - g r a d e g i r l s had lower mathematic s e l f - c o n c e p t than d i d boys, even though t h e i r mathematics performance was b e t t e r on standardized t e s t s and teacher r a t i n g s . HYPOTHESES, QUESTIONS, AND METHOD / 5 3 B. HYPOTHESES AND EXPLORATORY QUESTIONS 1. Hypotheses This study was an attempt t o t e s t hypotheses concerning (a) the e f f e c t s of an experimental i n t e r v e n t i o n ( P r e c i s i o n Teach-ing) on grade four students' a r i t h m e t i c s e l f - c o n c e p t and academic s e l f - c o n c e p t as measured by the SPAS, and (b) gender d i f f e r e n c e s i n a r i t h m e t i c s e l f - c o n c e p t and academic s e l f -concept at the grade four l e v e l . Hypothesis 1: A r i t h m e t i c s e l f - c o n c e p t as measured by the SPAS w i l l be enhanced by the d a i l y experimental i n t e r v e n t i o n , P r e c i s i o n Teaching. Hypothesis l a : G l o b a l academic s e l f - c o n c e p t as measured by the SPAS w i l l be enhanced by the d a i l y experimental i n t e r v e n t i o n , P r e c i s i o n Teaching. Hypothesis 2: There w i l l be a d i f f e r e n c e between males and females i n t h e i r a r i t h m e t i c s e l f - c o n c e p t at the grade four l e v e l . Hypothesis 2a: There w i l l be a d i f f e r e n c e between males and females i n t h e i r g l o b a l academic se l f - c o n c e p t at the grade four l e v e l . 2. E x p l o r a t o r y Questions The present study a l s o sought answers f o r questions of ex p l o r a t o r y i n t e r e s t . These questions were concerned w i t h a HYPOTHESES, QUESTIONS, AND METHOD / 54 s o c i a l v a l i d a t i o n of the experimental i n t e r v e n t i o n . To t h i s end, two L i k e r t type s c a l e s were constructed t o gain feedback from both students and parents i n v o l v e d i n the i n t e r v e n t i o n . The i n f o r m a t i o n the experimenter wanted t o gain from the parents i n v o l v e d i n the study centered around the f o l l o w i n g i s s u e s : (a) Did parents l i k e knowing how t h e i r c h i l d r e n d i d i n a r i t h m e t i c each day? (b) Did parents f i n d the time t o chart w i t h and r e i n f o r c e t h e i r c h i l d r e n ' s progress each day? (c) Did parents f i n d the i n t e r v e n t i o n m o t i v a t i n g f o r t h e i r c h i l d r e n ? (d) Did parents t h i n k t h e i r c h i l d r e n ' s a r i t h m e t i c s e l f - c o n c e p t changed? S i m i l a r l y from the students i n v o l v e d i n the study, the experimenter wanted t o know: (a) Did students l i k e c h a r t i n g t h e i r a r i t h m e t i c r e s u l t s d a i l y ? (b) Did students l i k e being timed on t h e i r work sheets? (c) Did students l i k e knowing how they were doing i n a r i t h m e t i c each day? (d) Did students t h i n k they had improved i n m u l t i p l i c a t i o n d uring the program? HYPOTHESES, QUESTIONS, AND METHOD / 55 C . M E T H O D O L O G Y 1. Design As noted by Campbell and Stanley (1966), e d u c a t i o n a l r e -search done out s i d e l a b o r a t o r y s e t t i n g s o f t e n has t o in c o r p o r a t e i n t o i t s design n a t u r a l l y assembled c o l l e c t i v e s such as c l a s s -room groups. The present study, done i n the n a t u r a l school s e t t i n g i s no exception and consequently makes use of a q u a s i -experimental design. I t should be added th a t l i k e Campbell and Stanley's (1966) Non-equivalent C o n t r o l Group Design, a s s i g n -ment of the experimental treatment to one group or the other i s random and under the experimenter's c o n t r o l ; however, the experimental group and the c o n t r o l group do not have pre-experimental sampling equivalence. Campbell and Stanley (1966) s t a t e : The more s i m i l a r the experimental and the c o n t r o l groups are i n t h e i r r e c r u i t m e n t , and the more t h i s s i m i l a r i t y i s confirmed by the scores on the p r e t e s t , the more e f f e c t i v e t h i s c o n t r o l becomes. Assuming tha t these d e s i d e r a t a are approximated f o r purposes of i n t e r n a l v a l i d i t y , we can regard the design as c o n t r o l l i n g the main e f f e c t s of h i s t o r y , maturation t e s t i n g and in s t r u m e n t a t i o n , i n t h a t the d i f f e r e n c e f o r the experimental group between p r e t e s t and p o s t t e s t ( i f greater than t h a t f o r the c o n t r o l group) cannot be explained by main e f f e c t s of these v a r i a b l e s such as would be found a f f e c t i n g both the e x p e r i -mental and the c o n t r o l group. (p. 48) A 2x4 (gender by groups) f a c t o r i a l a n a l y s i s of variance design was used t o i n v e s t i g a t e the e f f e c t s of the i n t e r v e n t i o n . The schematic i s presented i n Figure 3. HYPOTHESES, QUESTIONS, AND METHOD / 56 Group 1 Group 2 Group 3 Group 4 Precision Teaching at School and Hone. Experimenter in Classroom but no Precision Teaching. Precision Teaching at School Only. Experimenter i n class for Pre and Posttest Only. Male N=89 n=26 n=26 n=22 n=15 Female N=96 n=22 n=25 n=28 n=21 N=185 N=48 N=51 N=50 N=36 Y = academic self-concept / arithmetic self-concept F i g . 3: Schematic of Experimental Design As there i s no one p r e s c r i b e d way to evaluate the hypotheses i n quasi-experimental s t u d i e s , three a n a l y s i s procedures were used ( c f : Cook & Campbell, 1979; Campbell & Stanley, 1966). These procedures were ANOVA, ANCOVA, and repeated measures ANOVA. The dependent v a r i a b l e of the present study was academic se l f - c o n c e p t as measured by the Student's Perception of A b i l i t y HYPOTHESES, QUESTIONS, AND METHOD / 57 Scale (Boersma & Chapman, 1977). The independent v a r i a b l e s were gender and experimental c o n d i t i o n s . The dependent v a r i -ables f o r the e x p l o r a t o r y questions were the a f f e c t i v e c h a r a c t e r i s t i c s toward the i n t e r v e n t i o n . 2. Sample The sample co n s i s t e d of 185 grade four students. The mean age of the subjects was approximately nine years. The subjects resided i n a m i d d l e - c l a s s , socio-economic community and were predominantly white. The sample s i z e of 185 students was considered s u f f i c i e n t l y l a r g e i n order t o detect moderate to high e f f e c t s of the independent v a r i a b l e given the design of the study. A l l p r i n c i p a l s of schools w i t h i n the lower mainland B r i t i s h Columbian suburban school d i s t r i c t which contained n o n - s p l i t grade four c l a s s e s were contacted . P r i n c i p a l s were asked by the experimenter f o r access t o grade four teachers w i l l i n g to p a r t i c i p a t e i n the study. Twenty-one classroom teachers responded p o s i t i v e l y t o being included i n the study. Subsequently, a l l w i l l i n g teachers and/or c l a s s e s were then pooled and from the pool e i g h t c l a s s e s were randomly assigned to experimental c o n d i t i o n s . This random assignment from the pool was necessary as i n Non-Equivalent C o n t r o l Group Design, assignment of c l a s s e s t o one group or the other i s assumed to be HYPOTHESES, QUESTIONS, AND METHOD / 58 random and under the experimenter's c o n t r o l . Four of the c l a s s e s formed the P r e c i s i o n Teaching groups (two i n the P r e c i s i o n Teaching at School and Home group and two i n the P r e c i s i o n Teaching at School Only group), and four formed the c o n t r o l groups (two i n the f u l l c o n t r o l group and two i n the Experimenter i n Classroom but No P r e c i s i o n Teaching group). P r i o r t o the experimenter commencing the study, p a r e n t a l permission was obtained f o r a l l students i n the study. Parents of e i g h t students d e c l i n e d involvement i n the study. Teachers of these students decided t h a t these students would work on other p r o j e c t s during the experimental time of the study. The t o t a l number of students i n v o l v e d i n the study was 18 5 w i t h 89 males and 96 females. The breakdown of boys and g i r l s i n each c o n d i t i o n was as f o l l o w s : Group 1, P r e c i s i o n Teaching at School and Home group, 26 males, 22 females, t o t a l 48; Group 2, Experimenter i n Classroom but No P r e c i s i o n Teaching group, 26 males, 25 females, t o t a l 51; Group 3, P r e c i s i o n Teaching at School Only group, 22 males, 28 females, t o t a l 50; Group 4, Experimenter i n Class f o r Pre and P o s t t e s t Only group, 15 males, 21 females, t o t a l 36. Table 2 contains an elaborated breakdown of the d i f f e r e n c e s between the four groups. HYPOTHESES, QUESTIONS, AND METHOD / 59 Table 2 DIFFERENCES BETWEEN GROUPS Group 1 Group 2 Group 3 Group 4 P r e c i s i o n Teaching at School and Home Group Students experienced d a i l y i n t e r v e n t i o n at s c h ool. Parents were a c t i v e l y i n v o l v e d d a i l y a t home as p a r t of the i n t e r v e n -t i o n . Experimenter i n Class But No P r e c i s i o n Group Experimenter v i s i t e d c l a s s d a i l y f o r 3 week period f o r 10 minutes of a r i t h m e t i c review. No i n t e r v e n t i o n was attempted. P r e c i s i o n Teaching at School Only Group Students experienced d a i l y i n t e r -v e n t i o n f o r 10 minutes. Parents were not involved i n i n t e r v e n t i o n . Experimenter i n Class Only f o r Pre and Post Test Group Experimenter v i s i t e d c l a s s only f o r pre-and p o s t t e s t . n=48 n=51 n=50 n=36 The r a t i o n a l e f o r the use of grade four students was drawn from the research of Wi l l i a m s (1976 ) who found t h a t fourth-grade students (at nine years of age) experienced a s i g n i f i c a n t d e c l i n e i n academic s e l f - c o n c e p t and mo t i v a t i o n but d i d not experience a d e c l i n e i n general s e l f - c o n c e p t . W i l l i a m s (1976) s t a t e s : HYPOTHESES, QUESTIONS, AND METHOD / 60 This i s not s u r p r i s i n g as one views the t y p i c a l educa-t i o n a l program i n many elementary schools; f o r at t h a t time i n p u p i l s ' l i v e s they are expected t o be rat h e r w e l l regimented i n t o a c e r t a i n academic mold imposed by teacher, peer, and parent pressures f o r school success. This i s e s p e c i a l l y t r u e i n the s k i l l areas of reading, mathematics, and language. (p. 24) A l l grade-four students had p r e v i o u s l y studied m u l t i p l i -c a t i o n f a c t s t o the nine-times l e v e l . I t was assumed by teachers t h a t students knew t h e i r m u l t i p l i c a t i o n f a c t s . The stage of development t h a t would c h a r a c t e r i z e student l e a r n i n g at t h i s p o i n t i n m u l t i p l i c a t i o n was t h a t of i n i t i a l p r o f i c i e n c y ( c f . L o v i t t , 1977). C h a r a c t e r i s t i c of t h i s stage, the students could respond c o r r e c t l y to almost a l l of the items; however, answers were not automatic and students had t o t h i n k before responding. The l e v e l of development of the l e a r n e r s i n t h i s p a r t i c u l a r study was of utmost importance as t h e i r developmental l e a r n i n g stage determined the appropriate i n t e r v e n t i o n t e c h -nique. According t o some res e a r c h e r s , the most appropriate technique t o use during i n i t i a l p r o f i c i e n c y i s reinforcement (e.g., L o v i t t , 1977). 3. Instruments The present study u t i l i z e d two instruments: the Student's Perception of A b i l i t y Scale (SPAS) and an experimenter designed s o c i a l v a l i d a t i o n s c a l e . The SPAS was used as the instrument f o r measuring academic s e l f - c o n c e p t and a r i t h m e t i c s e l f -concept. This s c a l e , developed by Boersma & Chapman (1977), HYPOTHESES, QUESTIONS, AND METHOD / 61 measures both general academic s e l f - c o n c e p t as w e l l as s e l f -perceptions of a b i l i t y i n s p e c i f i c academic subject areas at the elementary school l e v e l . The s c a l e , as can be seen i n Appendix C, c o n s i s t s of seventy forced-choice "yes-no" items asking c h i l d r e n about t h e i r perceptions of t h e i r general a b i l i t y , t h e i r perceptions of t h e i r a b i l i t i e s i n reading, s p e l l i n g , penman-s h i p , a r i t h m e t i c , neatness, school s a t i s f a c t i o n , and confidence i n t h e i r academic a b i l i t i e s . The authors of the SPAS d e f i n e the term " s e l f - p e r c e p t i o n of a b i l i t y " as the manner i n which i n d i v i d u a l s d e s c r i b e and d i s t i n g u i s h themselves as unique among others i n terms of i n t e r a c t i o n s and performances on school t e s t s (Boersma, Chapman & Maguire, 1979). General academic s e l f - c o n c e p t scores are c a l c u l a t e d from a subject's scores on a l l seventy items and s p e c i f i c subject areas can be c a l c u l a t e d from one of f i v e s u b t e s t s . Table 3 contains the breakdown of a l l items f o r f u l l and subscale scores. Items on the SPAS are scored i n the d i r e c t i o n of high scores being an i n d i c a t o r of high academic s e l f - c o n c e p t . The SPAS s c a l e can be scored e i t h e r by using a s c o r i n g template, or by having item responses keypunched from the booklets and fed i n t o a computer f o r s c o r i n g . In the present study, the SPAS item r e s u l t s were scored by computer. The present study a l s o u t i l i z e d two s e l f - r e p o r t s c a l e s designed t o measure s o c i a l and a f f e c t i v e i n f o r m a t i o n about the HYPOTHESES, QUESTIONS, AND METHOD / 62 i n t e r v e n t i o n . Both of these measures are included i n Appendixes G and H. Table 3 Breakdown of Items on SPAS f o r F u l l and Subscale Scores Number of Items F u l l Scale 70 General A b i l i t y 12 A r i t h m e t i c 12 School S a t i s f a c t i o n 12 Reading/Spelling 12 Penmanship/Neatness 12 Confidence 10 4. Psychometric C h a r a c t e r i s t i c s of Measure Normative data were c o l l e c t e d during April/May of 1977 on a sample of 642 c h i l d r e n i n Grades 3 t o 6 from two m i d d l e - c l a s s , p u b l i c , elementary schools w i t h i n the Edmonton, A l b e r t a , area. The sample contained seven Grade 3, seven Grade 4, s i x Grade 5 and f i v e Grade 6 c l a s s e s . From Table 4, i t can be seen t h a t the SPAS has good psychometric p r o p e r t i e s - the r e l i a b i l i t i e s are high. HYPOTHESES, QUESTIONS, AND METHOD / 63 Table 4 Statistics and R e l i a b i l i t i e s for F u l l and Subscale SPAS Scores Summed Over Grades 3, 4, 5 and 6 of Norming Group (N = 642) Number of Conbach's Test Items Mean SD SEm Alpha Retest* F u l l Scale 70 46.24 11 .71 4.77 .915 .834 General A b i l i t y 12 7.91 3 .01 1.51 .785 .750 Arithmetic 12 9.17 3 .01 1.39 .837 .787 School Satisfaction 12 7.99 2 .78 1.49 .741 .714 Reading/Spelling 12 9.07 3 .13 1.31 .855 .824 Penmanship/Neatnes 12 7.89 3 .00 1.41 .822 .780 Confidence 10 4.21 2 .25 1.14 .686 .742 *Test-retest interval 4 to 6 weeks (N = 603) A more d e t a i l e d breakdown of normative data f o r boys and g i r l s at each grade l e v e l i s presented i n Table 5. (Source: Boersma & Chapman, SPAS Manual, 1979 ). I t can be seen from the t-va l u e s t h a t sex e f f e c t s were found at Grades 3, 4, and 5, w i t h most of these o c c u r r i n g at the grade four l e v e l . HYPOTHESES, QUESTIONS, AND METHOD / 64 D e s c r i p t i v e S t a t i s t i c s of Norming Sample f o r F u l l and Table 5 Subscale SPAS Scores as a Function of Sex and Grade L e v e l Boys G i r l s L e v e l Mean SD SEm =C Mean SD SEm Grade 2 F u l l Scale General A b i l i t y A r i t h m e t i c School S a t i s f a c t i o n R e a d i n g / S p e l l i n g Penmanship/Neatness Confidence Grade 3 F u l l Scale General A b i l i t y A r i t h m e t i c School S a t i s f a c t i o n R e a d i n g / S p e l l i n g Penmanship/Neatness Confidence Grade 4 F u l l Scale General A b i l i t y A r i t h m e t i c School S a t i s f a c t i o n R e a d i n g / S p e l l i n g Penmanship/Neatness Confidence Grade 5 F u l l Scale General A b i l i t y A r i t h m e t i c School S a t i s f a c t i o n R e a d i n g / S p e l l i n g Penmanship/Neatness Confidence Grade 6 F u l l S c a l e General A b i l i t y A r i t h m e t i c School S a t i s f a c t i o n R e a d i n g / S p e l l i n g Penmanship/Neatness Confidence (n - 95) 47.69 13.33 3.35 7.63 3.11 1.44 8.92 2.94 1. 27 8.57 2.71 1.36 9.17 2.95 1.21 8.60 3.00 1.25 4.81 2.26 1.34 (n = 84) 47.17 11.83 4.05 7.86 2.95 1.55 9.13 3.22 1.23 7.85 2.88 1.60 9.40 2.81 1.01 8.02 3.08 1.19 4.92 2.52 1.21 (n - 92) 41.91 12.75 4.87 7.07 3.20 1.65 8.34 3.43 1.48 7.72 3.09 1.47 8.32 3.42 1.27 6.54 3.10' 1.02 3.84 2.13 1.12 (n - 91) 45.29 12.75 4.70 8.12 3.20 1.52 9.36 3.43 1.51 7.31 3.09 1.30 8.84 3.42 1.35 7.30 3.10 1.50 4.36 2.13 1.18 (n .- 74) 44.85 11.90 4.12 8.36 2.83 1.17 9.76 2.58 0.91 6.84 2.52 1.39 8.42 3.51 1.38 7.46 3.09 1.32 4.00 2.17 1.01 (n .937 48.82 13.69 .785 6.87 2.96 .815 9.1-2 2.95 .747 9.34 2.75 .833 9.47 2.91 .827 9.20 3.17 .649 4.83 2.39 (n • .916 48.36 12.29 .762 7.76 3.16 .868 8.71 2.97 .762 9.09 2.65 .823 9.91 2.55 .821 8.34 3.03 .739 4.54 2.36 (n -.924 49.03 11.45 .804 7.91 • 3.09 .865 9.26 3.81 .788 9.13 2.35 .862 9.38 3.04 .812 9.40 2.38 .656 4.21 2.29 (n -.883 47.83 9.96 .738 8.11 3.02 .822 9.61 2.68 .776 8.54 2.07 .836 9.13 3.28 .811 8.37 2.42 .557 4.08 2.01 (n -.922 46.14 10.79 .779 8.36 2.71 .805 9.44 3.01 -.678 7.32 2.28 .877 9.21 2.98 .842 8.20 2.90 .662 3.61 2.17 76) 3.21 .945 .54 1.52 .735 1.63 1.99 .835 .44 1.21 .808 1.83 1.14 .847 .67 1.12 .876 1.33 1.33 .689 .06 87 4.45 .929 .64 1.29 .809 .21 0.62 .816 .88 1.44 .763 2.93 1.14 .813 1.24 1.30 .841 .71 1.09 .705 .89 77) 3.68 .922 3.82 1.56 .802 1.73 1.62 .814 1.92 1.19 .686 3.37* 0.91 .867 2.13* 0.96 .764 6.54* 1.11 .745 1.08 71) ' 2.97 .819 1.42 1.14 .800 .02 0.81 .811 .52 0.99 .549 3.03* 1.21 .880 .55 1.10 .747 2.47 0.82 .644 .86 66) 3.69 .910 .65 1.05 .757 .00 1.28 .857 .67 1.04 .602 1.06 1.12 .848 1.44 1.43 .842 1.46 1.16 .733 1.06 * p<.05 ** P<.01 Taken from Boersma & Chapman SPAS Manual 1979. HYPOTHESES, QUESTIONS, AND METHOD / 65 In terms of experimental v a l i d i t y , data r e v e a l t h a t the SPAS d i f f e r e n t i a t e s c l e a r l y between c h i l d r e n having l e a r n i n g problems and those who do not and tha t i t i s s e n s i t i v e t o change f o l l o w i n g remedial i n t e r v e n t i o n (Boersman, Chapman, and B a t t l e , 1979). A number of s t u d i e s have been conducted i n order to d e r i v e support f o r the e x t e r n a l v a l i d i t y of the SPAS. A study done by Chapman and Boersma (1979) t e s t e d 81 l e a r n i n g d i s a b l e d (LD) and 81 normally a c h i e v i n g c h i l d r e n i n Grades 3 to 6 from two larg e suburban elementary schools. Both groups of students had s i m i l a r socio-economic backgrounds and ages and a l l c h i l d r e n had normal range group-test IQ's although there was a s t a t i s t i c a l l y s i g n i f i c a n t tendency f o r the LD group t o have s l i g h t l y lower o v e r a l l IQ scores. R e s u l t s show there was a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e of 11.84 p o i n t s (p <.001) between the LD and normal group w i t h LD c h i l d r e n r e p o r t i n g c o n s i d e r a b l y lower s e l f - p e r c e p t i o n of a b i l i t y than normal a c h i e v e r s . 5. Data C o l l e c t i o n Procedure A f t e r approval from the u n i v e r s i t y e t h i c s committee and the school board o f f i c e , grade-four c l a s s e s i n the d i s t r i c t were sought t o v o l u n t a r i l y p a r t i c i p a t e i n the study. I n i t i a l l y , a f t e r meeting the c l a s s e s and o b t a i n i n g parent-a l permission, a l l c l a s s e s were given the p r e t e s t of the academic se l f - c o n c e p t measure. The same experimenter administered the HYPOTHESES, QUESTIONS, AND METHOD / 66 SPAS scale to a l l classes i n t h e i r regular arithmetic class and a l l classes were given i d e n t i c a l o r a l d i r e c t i o n s . The directions were designed to put the students at ease and to encourage them to give honest answers. The o r a l directions stated were: This questionnaire is to find out something about how kids feel about school and schoolwork. It is NOT a test. There are no right or wrong answers to the questions. The answers you give will be kept very private and it is very important to give an honest answer. The answers you give will be used to try and make schools better places to learn in. The experimenter then read aloud the statements from the scale and students marked yes/no on t h e i r forms to each item. Any d i f f i c u l t i e s or questions students had were resolved and students were urged to keep t h e i r answers c o n f i d e n t i a l . After the f i r s t reading of the statements to the cl a s s , the experimenter informed the class how she would respond to cert a i n statements. For example: Class, I would like to share with you how I would answer some of these statements. Take for example Statement 1 which states, "I always understand everything I read. " Boy! I wish that were true . . . Sometimes I have to ask someone what I've read means, so for this statement, I'd have to put NO. However, class, this doesn't mean I'm a stupid person; it simply means I don't always understand everything I read. It's not a reflection on my character. After t h i s s e l f - d i s c l o s u r e from the experimenter, the statements were reread and students were allowed to change any statements thay had made i f necessary. The SPAS measure was HYPOTHESES, QUESTIONS, AND METHOD / 67 conducted w i t h the r e g u l a r teacher absent from the classroom and c o n f i d e n t i a l i t y of responses was assured. Students were informed teachers and parents would not see t h e i r responses. Time a l o t t e d f o r p r e t e s t was approximately 20 minutes. As o u t l i n e d i n the Experimental Design s e c t i o n , the study c o n s i s t e d of randomly assigned c l a s s e s i n t o four groups each encountering d i f f e r e n t c o n d i t i o n s . Group 1 or the P r e c i s i o n Teaching at School and Home group encountered a d a i l y i n t e r v e n t i o n designed t o increase a r i t h m e t i c s e l f - c o n c e p t . The i n t e r v e n t i o n i n c l u d e d : d a i l y v i s u a l progress r e i n f o r c e -ment from charts and v e r b a l performance feedback from parents or primary c a r e g i v e r on the d a i l y a r i t h m e t i c probe; d a i l y s e l f -c h a r t i n g of a r i t h m e t i c performance w i t h the experimenter i n the classroom; p a r t i c i p a t i o n i n goal s e t t i n g of a r i t h m e t i c aims; and r e c o g n i t i o n and p o s i t i v e reinforcement by parents and teacher upon movement toward or reaching these goals. The experimental i n t e r v e n t i o n was conducted d a i l y f o r ap-proximately ten minutes i n the r e g u l a r classroom f o r a thr e e -and-a-half -week period by the experimenter. The f i r s t three days of t h i s time was used t o f a m i l i a r i z e the students w i t h the conventions of P r e c i s i o n Teaching. These conventions i n c l u -ded: how to take a probe; how to chart these r e s u l t s on a stan-dard behavior c h a r t ; how t o i n t e r p r e t chart r e s u l t s ; and how t o p r a c t i c e f o r t a k i n g a probe. During t h i s p r e l i m i n a r y time, parents were i n s t r u c t e d by l e t t e r on the P r e c i s i o n Teaching HYPOTHESES, QUESTIONS, AND METHOD / 68 Conventions.* Parents were urged t o contact the experimenter i f any questions arose as to t h e i r r e s p o n s i b l i t i e s during the i n t e r v e n t i o n . Four parents had questions and r e f e r r e d t h e i r questions t o the r e g u l a r classroom teacher who resolved the questions. During t h i s i n i t i a l time, i n d i v i d u a l aims on the m u l t i p l i -c a t i o n probes were s e t . This was done by having students w r i t e the d i g i t s zero through nine on a one-minute t i m i n g . This was c a r r i e d out twice d a i l y f o r three days and then the average number of d i g i t s w r i t t e n per minute was computed and became the student's i n i t i a l aim of d i g i t s per minute on the a r i t h m e t i c probes. Aim l i n e s were then marked on the students charts at school and at home. Before the d a i l y one-minute t i m i n g s , students were made aware of t h e i r aim l i n e s and t h e i r progress t o these goals. This was followed by two minutes of v i s u a l review using'the c o r r e c t answers at the top of the probes.** A f t e r the t i m i n g , students c i r c l e d t h e i r l a s t w r i t t e n answer and then s e l f - c o r r e c t e d t h e i r probes w i t h the answers provided on t h e i r probes. Results of c o r r e c t s and e r r o r s f o r t h a t day were then charted on student charts and noted on p o s t - i t paper t o be taken home tha t day to parents f o r home c h a r t i n g . Students who reached aim or made improvement were congratulated by the experimenter and peers. Techniques of " p a t t i n g y o u r s e l f on the back" were a l s o promoted. * See Appendix E f o r copy of parent m a t e r i a l . ** See Appendix I f o r copy of probes. HYPOTHESES, QUESTIONS, AND METHOD / 69 A l l students entered the f i r s t probe l e v e l of m u l t i p l i c a t i o n at the onset of the study which was the one-times t a b l e . When students reached t h e i r i n d i v i d u a l r a t e s per minute or aim on the probes, they immediately advanced t o the next l e v e l . Any student who f a i l e d to progress or remained at the same count f o r three days c o n s e c u t i v e l y was given a f u r t h e r i n t e r v e n t i o n . On the two occasions t h i s happened during the study, the i n t e r -v e n t i o n c o n s i s t e d of d i s t r i b u t e d p r a c t i c e w i t h c o n t i n u i n g reinforcement. The P r e c i s i o n Teaching at School Only group subjects received s i m i l a r c o n d i t i o n s as the P r e c i s i o n Teaching at School and Home group w i t h the exception of p a r e n t a l reinforcement and involvement. The c o n d i t i o n s c o n s i s t e d o f : d a i l y m u l t i p l i c a -t i o n probes, the s e t t i n g of proximal aims, c h a r t i n g of r e s u l t s , and reinforcement from teacher and peers. At the c o n c l u s i o n of the i n t e r v e n t i o n , a l l groups, P r e c i s i o n Teaching at School and Home, P r e c i s i o n Teaching at School Only, and Non P r e c i s i o n Teaching, were once again given the academic se l f - c o n c e p t s c a l e . D i r e c t i o n s f o r t h i s were i d e n t i c a l to the f i r s t a d m i n i s t r a t i o n of the measure. A l s o at t h i s time, the s o c i a l v a l i d a t i o n s c a l e was given t o both students and parents of the P r e c i s i o n Teaching at School and Home group.* * See Appendixes G and H f o r copies of s c a l e s . HYPOTHESES, QUESTIONS, AND METHOD / 70 Owing t o the l o c a t i o n s of the s e l e c t e d schools, the e x p e r i -menter conducted the i n t e r v e n t i o n w i t h four c l a s s e s i n the morning and two i n the afternoon. A l l procedures were c a r e f u l l y r e p l i c a t e d i n each group. In an attempt t o c o n t r o l the s i t u a t i o n a l v a r i a b l e of the experimenter implementing the i n t e r v e n t i o n and to guard against the Hawthorne e f f e c t , two c l a s s e s were randomly s e l e c t e d t o form an Experimenter i n Classroom but No P r e c i s i o n Teaching group. The experimenter spent ten minutes d a i l y i n these classrooms working w i t h the students o n . m u l t i p l i c a t i o n d r i l l worksheets; however, no i n t e r v e n t i o n techniques were a p p l i e d . Students d i d not work towards aims or goals and d i d not record t h e i r progress or have any p a r e n t a l involvement. The analyses of the data and the r e s u l t s are presented i n the f o l l o w i n g chapter. I V . A N A L Y S I S A N D R E S U L T S This chapter presents the r e s u l t s of the study i n three p a r t s . The f i r s t p a r t (A) presents the d e s c r i p t i v e s t a t i s t i c s and r e l i a b i l i t y estimates of the Student's Perception of A b i l i t y Scale (SPAS). The t e s t s of the research hypotheses posed i n Chapter Three are presented i n the second p a r t (B). These r e s u l t s show the e f f e c t s of the experimental i n t e r v e n t i o n on a r i t h m e t i c s e l f - c o n c e p t and academic s e l f - c o n c e p t as w e l l as gender d i f f e r e n c e s i n a r i t h m e t i c s e l f - c o n c e p t and academic s e l f - c o n c e p t at the grade four l e v e l . The t h i r d p a r t (C) i n -cludes the r e s u l t s f o r the e x p l o r a t o r y questions concerning the s o c i a l v a l i d i t y of the i n t e r v e n t i o n . The a n a l y s i s was done using SPSS:X s t a t i s t i c s software (Nie, 1983). A l l t e s t s t a t i s t i c s were i n t e r p r e t e d at the con-v e n t i o n a l alpha l e v e l of .05. A . D E S C R I P T I V E S T A T I S T I C S A N D R E L I A B I L I T Y E S T I M A T E S O F T H E S P A S Table 6 presents a d e t a i l e d breakdown of the subscale means and standard d e v i a t i o n s f o r both the present Research group and the o r i g i n a l Norming sample f o r comparison. 71 ANALYSIS AND RESULTS / 72 From the s t a t i s t i c s i n Table 6, P a r t s A and B, i t can be seen t h a t g i r l s and boys i n the research sample d i f f e r e d s i g n i f i -c a n t l y (p<.05) i n the subareas of School S a t i s f a c t i o n and Confidence on both the p r e t e s t and p o s t t e s t . A s i m i l a r r e s u l t i s reported f o r the Norming sample i n Par t C. The s i g n i f i c a n t d i f f e r e n c e s i n favor of g i r l s i n the area of School S a t i s f a c t i o n are i n agreement w i t h the l i t e r a t u r e which suggests g i r l s tend t o have more p o s i t i v e a t t i t u d e s towards school i n gene r a l . A l s o from Table 6, i t can be seen th a t the Research group d i f f e r e d i n terms of gender from the Norming group, Part C. S i g n i f i c a n t d i f f e r e n c e s (p<.01) i n favor of g i r l s were noted between g i r l s and boys i n the Norming sample i n the subscale areas of School S a t i s f a c t i o n , Penmanship/Neatness, Reading/ Sp e l l i n g , ' a n d on the F u l l Scale of the SPAS. However, t h i s wasn't the case f o r the Research sample. Instead, gender d i f f e r e n c e was s i g n i f i c a n t on the Confidence s c a l e i n the Research sample which wasn't the case f o r the Norming sample. Observed d i f f e r e n c e s between the present Research sample and the Norming sample are found i n the areas of Reading/Spell-i n g , Penmanship/Neatness, and i n F u l l Scale scores. In the Norming sample these three areas d i f f e r e d s i g n i f i c a n t l y (p<.01) between boys and g i r l s . R e l i a b i l i t y A n a l y s i s Estimates of i n t e r n a l consistency of the SPAS were de t e r -mined by Cronbach's alpha f o r the Research sample of 185 ANALYSIS AND RESULTS / 73 Table 6 Descriptive Statistics for Full and Subscale SPAS Scores for Research Sample and Nooning Sample Boys Gi r l s Mean S.D. Mean S.D. t Value (n=l Full Scale 41.63 General A b i l i t y 7.50 Research Arithmetic 7.39 A Sample School Satisfaction 6.32 Pretest Reading/Spelling 8.52 Penmanshp/Neatness 7.65 Confidence 4.24 9) (n=96) 13.40 43.07 10.98 -0.80 2.95 7.05 3.10 1.02 3.48 8.06 3.07 -1.39 3.17 7.19 2.58 -2.03* 3.35 8.91 3.16 -0.81 2.95 8.37 2.52 -1.80 2.18 3.49 1.74 2.58* B Research Sample Posttest F u l l Scale 43. 19 13. 40 44.62 11. 07 -0. 80 General A b i l i t y 7. 45 2. 86 7.00 3. 25 0. 99 Arithmetic 8. 75 3. 45 9.26 2. 96 -1. 08 School Satisfaction 6. 35 3. 22 7.33 2. 74 -2. 25* Reading/Spelling 8. 64 3. 33 8.89 3. 17 -0. 53 Perimanship/Neatness 7. 74 3. 02 8.52 2. 46 -1. 93 Confidence 4. 26 2. 13 3.61 1. 79 2. 23* (n= Full Scale 41.91 General A b i l i t y 7.07 Arithmetic 8.34 C Norming School Satisfaction 7.72 Sample Reading/Spelling 8.32 Penmanship/Neatness 6.54 Confidence 3.84 84) (n=77) 12.75 49.03 11.45 3.82** 3.20 7.91 3.09 1.73 3.43 9.26 3.81 1.92 3.09 9.13 2.35 3.37** 3.42 9.38 3.04 2.13** 3.10 9.40 2.38 6.54** 2.13 4.21 2.29 1.08 * P < .05 ** P < .01 ANALYSIS AND RESULTS / 74 s u b j e c t s . Table 7 presents the R e l i a b i l i t y Estimates f o r the p r e t e s t and p o s t t e s t of the Research sample as w e l l as the Norming sample f o r comparison. Table 7 R e l i a b i l i t y Estimates* f o r Research Sample and Norming Sample Number of Research Research Norming Items P r e t e s t P o s t t e s t Sample (n=185) (n=185) (n=642) F u l l Scale 70 .917 .920 .915 General A b i l i t y 12 .769 .777 .785 A r i t h m e t i c 12 .838 .861 .837 School S a t i s f a c t i o n 12 .733 .760 .741 Reading/Spelling 12 .850 .851 .855 Penmanship/Neatness 12 .770 .779 .822 Confidence 10 .622 .613 .686 * Cronbach's Alpha I t can be seen from Table 8 t h a t the p r e t e s t and p o s t t e s t of the Research sample compare very w e l l w i t h each other and a l s o compare very w e l l w i t h the Norming sample of 642 s u b j e c t s . I t can be observed from these comparisons th a t the SPAS has sound psychometric p r o p e r t i e s f o r each Subscale, p a r t i c u l a r l y A r i t h -metic, a dependent v a r i a b l e i n t h i s study, as w e l l as f o r the F u l l S c ale. ANALYSIS AND RESULTS / 75 T e s t - r e t e s t r e l i a b i l i t y data i n the present study were c o l l e c t e d over a 21-day i n t e r v a l . T e s t - r e t e s t c o e f f i c i e n t s f o r F u l l and Subscale scores are presented by group i n Table 8. Table 8 Test-Retest Reliability Coefficients by Group Group 1 Group 2 Group 3 Group 4 Precision Experimenter Precision Experimenter Teaching i n Classroom Teaching i n Class for at School but No Preci- at School Pre and Post-and Home. sion Teaching. Only. test Only. n=48 n=51 n=50 n=36 F u l l Scale .924 .979 .962 .982 General A b i l i t y .929 .954 .917 .961 Arithmetic .312 .968 .788 .971 School Satisfaction .975 .918 .947 .956 Reading/Spelling .965 .965 .987 .904 Penmanship/Neatness .926 .974 .936 .933 Confidence .906 .869 .887 .919 Table 8 r e v e a l s t h a t e x c l u d i n g the subscale A r i t h m e t i c f o r the P r e c i s i o n Teaching at School and Home group, a l l c o e f f i -c i e n t s are very high. Due t o the nature of the experimental i n t e r v e n t i o n i n a r i t h m e t i c w i t h t h i s group, i t i s w i t h i n expectations t h a t t h i s subscale c o e f f i c i e n t would be r e l a t i v e l y low. In summary, the d e c r i p t i v e s t a t i s t i c s and r e l i a b i l i t y a n a l y s i s of the SPAS showed t h a t the Student's Perception of A b i l i t y Scale y i e l d e d r e l i a b l e data i n t h i s study. ANALYSIS AND RESULTS / 76 B. TEST OP THE HYPOTHESES Although the research hypotheses were presented i n Chapter Three, they are repeated here f o r ease of reference. A l s o , not-w i t h s t a n d i n g the research hypotheses were d i r e c t i o n a l , they were cast i n t o the n u l l form f o r s t a t i s t i c a l t e s t i n g . The c r i t e r i o n f o r r e j e c t i o n of the two main e f f e c t s of the n u l l hypotheses on each set of data ( a r i t h m e t i c subscale and f u l l s c a l e ) was alpha .05. However, where r e q u i r e d , alpha was adjusted by Bonferroni procedure t o guard against experiment-wise e r r o r . N u l l Hypothesis 1 stated t h a t a r i t h m e t i c s e l f - c o n c e p t would not be enhanced by d a i l y feedback, c h a r t i n g of r e s u l t s , and d a i l y p a r e n t a l reinforcement. N u l l Hypothesis 2 sta t e d t h a t there would not be d i f f e r e n c e s between males and females i n a r i t h m e t i c s e l f - c o n c e p t at the grade four l e v e l . There i s no one pr e s c r i b e d way t o evaluate the hypotheses due t o the quasi-experimental nature of the study and i t i s recommended t h a t d i f f e r e n t methods be used simultaneously (Cook & Campbell, 1979). Consequently, three s t a t i s t i c a l procedures were used. These procedures were: (a) - ANOVA on p r e t e t and p o s t t e s t (b) - ANCOVA w i t h p r e t e s t as c o v a r i a t e , and (c) - Repeated measures ANOVA. ANALYSIS AND RESULTS / 77 These procedures were a p p l i e d independently so they do not have a bearing on experiment-wise e r r o r r a t e . The purpose was to see i f the f i n d i n g s matched. As p r e v i o u s l y noted i n Chapter Three, due t o the nature of the experimental s e t t i n g , i t was not p o s s i b l e to assi g n subjects randomly i n t o groups at the onset of the i n t e r v e n t i o n . As a r e s u l t , i n t a c t c l a s s groups of students were randomly assigned to experimental or c o n t r o l c o n d i t i o n s . As a consequence of t h i s d e v i a t i o n from t r u e experimental procedures i t was e s s e n t i a l t o i n v e s t i g a t e the s t a t i s t i c a l equivalence between groups on the p r e t e s t before l o o k i n g at any i n t e r v e n t i o n e f f e c t . This was done by i n v e s t i g a t i n g both the g l o b a l aspect of the measure as w e l l as the s p e c i f i c area of a r i t h m e t i c s e l f - c o n c e p t . 1. G l o b a l Academic F u l l Scale R e s u l t s To i n v e s t i g a t e s t a t i s t i c a l equivalence between groups on the p r e t e s t , a 2 x 4 (gender by groups) f a c t o r i a l f i x e d e f f e c t s ANOVA was conducted on the f u l l s c a l e of the SPAS measure. Table 9 contains the d e s c r i p t i v e s t a t i s t i c s from t h i s a n a l y s i s . The r e s u l t s of the ANOVA revealed t h a t there were no s i g n i -f i c a n t d i f f e r e n c e s , n e i t h e r between the groups F(3,177)=1.82, p=.15, nor between gender F(l,177) =.79, p=.38, on the f u l l s c a l e p r e t e s t . A l s o , the i n t e r a c t i o n e f f e c t was not s i g n i f i c a n t , F(3,177) =.20, p=.90. ANALYSIS AND RESULTS / 78 Table 9 Pull Scale Pretest Cell and Marginal Means and Standard Deviations* Total Sample Mean n=185 42.38 Group 1 (n=48) Precision Teaching at School and Home 44.85 (11.15) Group Means Group 2 (n=51) Group 3 (n=50) Experimenter i n Classroom but NO Preci-sion Teaching 41.25 (13.02) Precision Teaching at School Only 39.86 (13.16) Group 4 (n=36) Pretest and Posttest Only 44.17 (10.35) Boys Gender Means Boys (n=89) Girls (n=96) 41.63 (13.40) 43.07 (10.98) Group 1 (n=26) Group 2 (n=26) Group 3 (n=22) Group 4 (n=15) 43.50 (10.34) 41.08 (15.73) 38.27 (13.91) 44.27 (13.17) G i r l s (n=22) (n=25) (n=28) (n=21) 46.45 (12.08) 41.44 (9.76) 41.11 (12.66) 44.10 (8.14) * Standard Deviations i n parentheses ANALYSIS AND RESULTS / 79 As no s i g n i f i c a n t d i f f e r e n c e s were found between groups on the p r e t e s t , ANOVA was subsequently conducted on the p o s t t e s t . Table 10 re p o r t s the p o s t t e s t c e l l means and standard d e v i a t i o n s f o r groups and gender. The r e s u l t s of the ANOVA on the F u l l Scale P o s t t e s t revealed t h a t there were s i g n i f i c a n t d i f f e r e n c e s between groups F(3,177) = -3.52, p = 0.02, but the d i f f e r e n c e between gender was not s t a t i s t i c a l l y s i g n i f i c a n t , F(l,177) =.92, p =.34. The i n t e r -a c t i o n was not s i g n i f i c a n t as w e l l , F(3,177) =.31, p =.82. As noted p r e v i o u s l y , the second a n a l y s i s approach used w i t h the f u l l s c a l e data was a 2 x 4 (sex by groups) ANCOVA using the p r e t e s t as the c o v a r i a t e . This a n a l y s i s revealed s i m i l a r r e s u l t s t o the ANOVA i n tha t a s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e was found between groups F ( 3 ,177 ) = 13.01, p=.00, but not between gender F(l,176) =.15, p =.70. Again, the i n t e r a c t i o n F(l,176) =.65, p =.59 was not s i g n i f i c a n t . A 4 x 2 x 2 (group by sex by t e s t ) repeated measures ANOVA approach l i k e w i s e y i e l d e d p a r a l l e l f i n d i n g s . Once again there were s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e s between groups F(3,177) = 2.41, p =.05 but not between gender F(l,177) =.71, p =.40. There was a s i g n i f i c a n t d i f f e r e n c e between pre- to p o s t t e s t F(l,177) = 3.35, p =.001 and a l s o a s i g n i f i c a n t i n t e r -a c t i o n between t e s t and group F(3,177) = 11.36, p =.001. Test and gender i n t e r a c t i o n was not s i g n i f i c a n t F(l,177) = 0, p = .99 nor was the three-way i n t e r a c t i o n between group, gender, and t e s t F(3,177) = 0.61, p =.61. ANALYSIS AND RESULTS / 80 Table 10 Full Scale Posttest Cell and Marginal Means and Standard Deviations* Total Sample Mean n=185 43.94 -Group 1 (n=48) Precision Teaching at School and Home 48.42 (10.48) Total Group Mean Group 2 (n=51) Group 3 (n=50) Experimenter in Classroom but No Preci-sion Teaching 41.29 (12.92) Precision Teaching at School Only 42.08 (13.12) Group 4 (n=36) Pretest and Posttest Only 44.28 (10.81) Gender Means Boys (n-89) Girls (n=96) 43.19 (13.40) 44.63 (11.07) Group 1 Boys (n=26) 47.23 (9.13) Group 2 (n=26) 40.88 (15.48) Group 3 (n=22) 40.00 (14.22) Group 4 (n=15) 44.87 (13.76) Girls (n=22) (n=25) (n=28) (n=21) 49.82 (11.95) 41.72 (9.89) 43.71 (12.20) 43.86 (8.45) ANALYSIS AND RESULTS / 81 In summary, i t can be seen t h a t when a n a l y z i n g the f u l l s c a l e data of the SPAS measure, the three types of analyses converged on r e s u l t s r e v e a l i n g s i g n i f i c a n t s t a t i s t i c a l d i f f e r -ences between groups on the p o s t t e s t but not on the p r e t e s t . No s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e s were found between gender on p r e t e s t or p o s t t e s t using these analyses. A l s o , no i n t e r -a c t i o n between gender and groups or experimental c o n d i t i o n s was found. To determine e x a c t l y which groups d i f f e r e d on the p o s t t e s t , three c o n t r a s t s were conducted . The c o n t r a s t s were i n t e r p r e t e d at alpha .016 a f t e r B o n f e r roni adjustment to guard a g a i n s t experiment-wise e r r o r . As can be seen from Table 11, when using the f u l l s c a l e p o s t t e s t SPAS scores, the c o n t r a s t between the P r e c i s i o n Teaching at School and Home group and the P r e c i s i o n Teaching at School Only group was s i g n i f i c a n t . The mean f o r the P r e c i s i o n Teaching at School and Home group was 48.45; whereas, the mean f o r the P r e c i s i o n Teaching at School Only group was 42.08. The c o n t r a s t s between the Experimenter i n Classroom but No P r e c i s i o n Teaching group and the P r e c i s i o n Teaching at School Only group and the P r e t e s t and P o s t t e s t Only group and the P r e c i s i o n Teaching at School and Home group were not s i g -n i f i c a n t . Support f o r Hypotheses l a which stated g l o b a l academic s e l f -concept as measured by the SPAS w i l l be enhanced by the d a i l y experimental i n t e r v e n t i o n , P r e c i s i o n Teaching, was gleaned when s i g n i f i c a n t d i f f e r e n c e s were found ( i n favour of the P r e c i s i o n ANALYSIS AND RESULTS / 82 Teaching at School and Home group) on the F u l l Scale between the P r e c i s i o n Teaching at School and Home group and the P r e c i s i o n Teaching at School Only group. Table 11 Group Comparisons on Full Scale Academe Posttest Contrast Coefficient Matrix Group 1 Group 2 Group 3 Group 4 Precision Teaching at School and Home Experimenter i n Classroom but No Preci-sion Teaching Precision Teaching at School Only Experimenter in Class for Pre and Post-test Only Contrast 1 Contrast 2 Contrast 3 0.0 1.0 1.0 1.0 0.0 0.0 -1.0 -1.0 0.0 0.0 0.0 -1.0 Pooled Variance Estimate Value S. Err or T Value DF T Prob. Contrast 1 Contrast 2 Contrast 3 -0.7859 -6.3367 -4.1389 2.3870 2.4236 3.6444 -0.329 -2.615 -1.565 181 181 181 0.742 0.010* 0.119 * p < .016 ANALYSIS AND RESULTS / 83 The three foregoing analyses were now repeated on the p r e t e s t and p o s t t e s t of the subscale a r i t h m e t i c to examine d i f f e r e n c e s at t h i s l e v e l between a l l four groups. 2. A r i t h m e t i c Subscale Results Table 12 contains the marginal means and standard d e v i a -t i o n s f o r both gender and group which were used f o r the 2x4 (sex and group) f a c t o r i a l f i x e d e f f e c t s ANOVA conducted u s i n g the p r e t e s t of the subscale a r i t h m e t i c on the SPAS. L i k e the f u l l s c a l e p r e t e s t r e s u l t s , no s i g n i f i c a n t d i f f e r -ences were found between groups on the p r e t e s t subscale a r i t h -metic, F(3,177 ) =.28, p=.84, or between gender F(l,177) = 1.78, p =.18. The i n t e r a c t i o n e f f e c t was not s i g n i f i c a n t F(3,177) =.57, p =.69. A n a l y s i s of var i a n c e was now conducted on the p o s t t e s t subscale a r i t h m e t i c . ANALYSIS AND RESULTS / 84 Table 12 Arithmetic Subscale Pretest Cell and Marginal Means and Standard Deviations* Total Sample Mean n=185 7.74 Group 1 (n=48) Precision Teaching at School and Home 7.75 (3.07) Group Means Group 2 (n=51) Group 3 (n=50) Experimenter i n Classroom but No Preci-sion Teaching 7.53 (3.52) Precision Teaching at School Only 7.62 (3.32) Group 4 (n=36) Experimenter in Class for Pretest and Posttest Only 8.19 (3.23) Gender Means Boys (n=89) Girls (n=96) 7.39 (3.48) 8.06 (3.07) Group 1 Boys (n=26) 7.38 (3.20) Group 2 (n=26) 6.81 (3.85) Group 3 (n=22) 7.41 (3.46) Group 4 (n=15) 8.40 (3.40) Girls (n=22) 8.18 (2.92) (n=25) 8.28 (3.05) (n=28) 7.79 (3.26) (n=21) 8.05 (3.19) * Standard Deviations i n parentheses ANALYSIS AND RESULTS / 85 Table 13 contains the c e l l and marginal means and standard d e v i a t i o n s f o r both gender and group which were used f o r the 2x4 (sex and group) f a c t o r i a l f i x e d e f f e c t s ANOVA conducted using the p o s t t e s t of the subscale a r i t h m e t i c on the SPAS. Table 13 Arithmetic Subscale Posttest Cell and Marginal Means and Standard Deviations* Total Sample Population (n=185) 9.03 Group 1 (n=48) Precision Teaching at School and Home 10.94 (1.87) Group 2 (n=51) Experimenter i n Classroom but No Preci-sion Teaching 7.53 (3.69) Group 3 (n=50) Precision Teaching at School Only 9.30 (2.70) Group 4 (n=36) Experimenter i n Class for Pretest and Posttest Only 8.17 (3.25) Gender Means Boys (n=89) Girls (n=96) 8.75 (3.45) 9.26 (2.96) Group 1 Boys (n=26) 10.81 (1.98) Girls (n=22) 11.09 (1.77) Group 2 (n=26) 6.85 (4.10) (n=25) 8.24 (3.14) Group 3 (n=22) 8.77 (2.79) (n=28) 9.71 (2.61) Group 4 (n=15) 8.47 (3.40) (n=21) 7.95 (3.20) * Standard Deviations i n parentheses ANALYSIS AND RESULTS / 86 The r e s u l t s of the 2 x 4 (sex by groups) ANOVA on the sub-s c a l e a r i t h m e t i c p o s t t e s t revealed t h a t there was a s i g n i f i c a n t d i f f e r e n c e between the groups on the p o s t t e s t , F(3,177 ) = 12.52, p =.00, but there were no s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e s between sexes, F (1,177 ) = 2.01, p=.16. The i n t e r a c t i o n was not s i g n i f i c a n t as w e l l F(3,177) = 0.83, p =.48. Results from a 2 x 4 (sex by group) ANCOVA using the p r e t e s t subscale a r i t h m e t i c as c o v a r i a t e a l s o revealed s i m i l a r r e s u l t s . Once again a s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e was found be-tween groups on the subscale a r i t h m e t i c a n a l y s i s F(3,176) = 34.99, p = 0.00, but not between sexes F(l,176) =.33, p =.57. The i n t e r a c t i o n e f f e c t i n t h i s a n a l y s i s was not s i g n i f i c a n t F(3,176) =.82, p =.49. A 2 x 4 repeated measures ANOVA a n a l y s i s revealed s i m i l a r r e s u l t s as w e l l . S i g n i f i c a n t d i f f e r e n c e s on the a r i t h m e t i c subscale using t h i s approach w i t h the data were a l s o found between groups F(3,177) = 2.88, p =.04, but not between sexes F(l,177) = 1.53, p =.22. The pre-post t e s t e f f e c t was s i g -n i f i c a n t F(1,177) = 65.07, p =.001. A l s o the t e s t by group i n t e r a c t i o n was s i g n i f i c a n t F(3,177) = 26.32, p =.001. The sex by t e s t i n t e r a c t i o n was not s i g n i f i c a n t F(l,177) =.03, p=.88 and s i m i l a r l y , the group by sex by t e s t i n t e r a c t i o n was not s i g n i f i c a n t F(3,177) = 0.57, p =.63. ANALYSIS AND RESULTS / 87 The s p e c i f i c a r i t h m e t i c academic s e l f - c o n c e p t r e s u l t s converged r e v e a l i n g s i g n i f i c a n t s t a t i s t i c a l d i f f e r e n c e s only between groups on the subscale a r i t h m e t i c from p r e t e s t t o p o s t t e s t . N u l l Hypotheses 1 stated t h a t a r i t h m e t i c s e l f - c o n c e p t would not be enhanced by d a i l y feedback, c h a r t i n g of r e s u l t s , and d a i l y p a r e n t a l reinforcement. As d i f f e r e n t groups r e c e i v e d d i f -f e r e n t treatments and preceding a n a l y s i s revealed d i f f e r e n c e s between groups, one-way ANOVA and planned c o n t r a s t s were now c a r r i e d out on p o s t t e s t data. I t should be reported here th a t s i n c e no gender e f f e c t s were found i n the preceding analyses, these f u r t h e r analyses dropped gender as a v a r i a b l e and used only groups ( t h e r e f o r e , the one-way ANOVA). Al s o at t h i s p o i n t , n u l l Hypothesis 2, which stated there would be no d i f f e r e n c e s between males and females i n a r i t h m e t i c s e l f - c o n c e p t at the grade four l e v e l , was r e t a i n e d when no sex d i f f e r e n c e s were detected i n any of the analyses performed. The c o n t r a s t c o e f f i c i e n t matrix used i n the f o l l o w i n g group comparisons i s reported i n Table 14. ANALYSIS AND RESULTS / 88 Table 14 Group Comparisons on Subscale Arithmetic Posttest Contrast Coefficient Matrix Group 1 Group 2 Group 3 Group 4 Precision Experimenter Precision Experimenter Teaching in Classroom Teaching i n Class for at School but No Preci- at School Pre and Post-and Home sion Teaching Only test Only Contrast 1 0.0 1.0 -1.0 0.0 Contrast 2 0.0 0.0 1.0 -1.0 Contrast 3 1.0 0.0 0.0 -1.0 Pooled Variance Estimate Value S.Error T Value DF T Prob. Contrast 1 -1.7706 0.5867 -3.018 181 0.003* Contrast 2 -1.6375 0.5957 -2.749 181 0.007* Contrast 3 -2.7708 0.6500 -4.263 181 0.000* * p < .016 The c o n t r a s t s were i n t e r p r e t e d at alpha .016 a f t e r B o n f e r roni adjustment t o guard against experiment-wise e r r o r . Contrast 1 i n the preceding analyses i s the c o n t r a s t between the ANALYSIS AND RESULTS / 89 Experimenter i n Classroom but No P r e c i s i o n Teaching group and the P r e c i s i o n Teaching at School Only group. The Experimenter i n Classroom but No P r e c i s i o n Teaching group was v i s i t e d by the experimenter d a i l y f o r ten minutes of m u l t i p l i c a t i o n d r i l l ; however, no progress aims were s e t , no feedback was given, and pa r e n t a l reinforcement was not inc o r p o r a t e d . In the P r e c i s i o n Teaching at School Only group, students received the P r e c i s i o n Teaching i n t e r v e n t i o n minus p a r e n t a l involvement. Through t h i s c o n t r a s t , i t was revealed t h a t there was a s i g n i f i c a n t d i f f e r e n c e i n favour of the P r e c i s i o n Teaching group. The Experimenter i n Classroom but No P r e c i s i o n Teaching group had a mean of 7.5; whereas, the P r e c i s i o n Teaching at School Only group had a mean of 9.3. The second c o n t r a s t revealed t h a t there was a s i g n i f i c a n t d i f f e r e n c e between the two groups r e c e i v i n g P r e c i s i o n Teaching at School and Home and P r e c i s i o n Teaching at School Only. The P r e c i s i o n Teaching at School and Home group had a higher mean of 10.94; whereas, the P r e c i s i o n Teaching at School Only group had a mean of 9.30. The t h i r d c o n t r a s t i n t h i s a n a l y s i s revealed t h a t there was a s i g n i f i c a n t d i f f e r e n c e between the P r e c i s i o n Teaching at School and Home group and the P r e t e s t and P o s t t e s t Only group. The P r e c i s i o n Teaching at School and Home group had a mean of 10.94; whereas, the P r e t e s t and P o s t t e s t Only group had a mean of 8.16. ANALYSIS AND RESULTS / 90 The n u l l Hypothesis 1 which s t a t e d t h a t a r i t h m e t i c s e l f -concept would not be enhanced by d a i l y feedback, c h a r t i n g of r e s u l t s , and d a i l y p a r e n t a l reinforcement was r e j e c t e d given the r e s u l t s of the c o n t r a s t s . C. EXPLORATORY QUESTIONS AND ANALYSIS The present study was concerned w i t h two questions of ex p l o r a t o r y i n t e r e s t . Both questions r e l a t e d to a s o c i a l v a l i d a t i o n of the experimental i n t e r v e n t i o n . The f i r s t ques-t i o n was concerned w i t h the parents' response t o the i n t e r v e n -t i o n . As the i n t e r v e n t i o n r e l i e d on parents as a c t i v e p a r t i c i -pants i n the study, o b t a i n i n g feedback on t h e i r r o l e was r e l e v a n t to the study. The second question was concerned w i t h the response of the students i n v o l v e d i n the experimental i n t e r -v e n t i o n . The a n a l y s i s and r e s u l t s p e r t a i n i n g to these questions are presented below i n two separate subsections. 1. P a r e n t a l Feedback from I n t e r v e n t i o n The impact of parents as r e i n f o r c e r s and shapers of s e l f -concept has been w e l l documented (Brookover & E r i c k s o n , 1969; Brookover et a l . , 1965). However, si n c e the present study required parents t o f o l l o w a novel procedure w i t h t h e i r students which was explained t o them by way of l e t t e r s sent home, i t was of i n t e r e s t t o explore i f parents could a l l o t time d a i l y t o the c h a r t i n g task and subsequent reinforcement of t h e i r students. ANALYSIS AND RESULTS / 91 The q u e s t i o n n a i r e sent home to parents contained s i x s t a t e -ments. The parents were asked t o r a t e each of these s i x s t a t e -ments on a s c a l e of 1 to 5, 1 being the low end of the s c a l e and 5 being the top end of the s c a l e . Table 15 contains the means, standard d e v i a t i o n s , and t-values by question and c l a s s f o r the parent responses t o the q u e s t i o n n a i r e . As can be seen from Table 15, a l l means out of a s c a l e of 5 are high except f o r statement 5. This statement was d e l i b e r -a t e l y framed i n a negative manner to d i s c e r n i f a l l the s t a t e -ments were being c a r e f u l l y s c r u t i n i z e d . As can be seen from Table 15 by the low mean scores of 2.00 and 2.31 f o r t h i s s t a t e -ment, parents d i d c a r e f u l l y respond t o the statements. In C l a s s 1, 70 percent of the parents responded t o the qu e s t i o n n a i r e and i n Class 2, 73 percent of the parents responded. T-tests revealed t h a t there were no s i g n i f i c a n t d i f f e r e n c e s between parent groups on any of the ques t i o n s . ANALYSIS AND RESULTS / 92 Table 15 Means, Standard Deviations, and t-Values of Parental Questionnaire Number Standard Pooled of Cases Mean D e v i a t i o n t-Value Statement 1 I l i k e d knowing how my c h i l d d i d i n a r i t h m e t i c each day. Class 1 17 4.59 0.71 Class 2 19 4.79 0.42 -1.05 Statement 2 I l i k e d c h a r t i n g my c h i l d ' s r e s u l t s on a d a i l y b a s i s . Class 1 16 4.06 0.85 Class 2 19 4.37 0.89 -1.03 Statement 3 I l i k e d being i n v o l v e d w i t h my c h i l d ' s progress. Class 1 17 4.76 0.43 Class 2 19 4.84 0.50 0.49 Statement 4 I t h i n k t h i s program was m o t i v a t i n g f o r my c h i l d . Class 1 17 4.35 0.86 Class 2 19 4.16 0.76 0.72 Statement 5 I found i t d i f f i c u l t t o f i n d the time t o chart w i t h my c h i l d . C lass 1 17 2.00 1.32 Class 2 19 2.31 1.49 -0.67 Statement 6 I t h i n k my c h i l d f e e l s b e t t e r about a r i t h m e t i c now. Class 1 17 4.41 0.79 Class 2 18 4.11 0.90 1.04 ANALYSIS AND RESULTS / 93 2. Student Feedback from I n t e r v e n t i o n The s c a l e given to students i n the P r e c i s i o n Teaching i n t e r v e n t i o n at the end of the program was designed t o gather informa t i o n about the var i o u s components of the i n t e r v e n t i o n . This s c a l e c o n s i s t e d of 7 statements which were ra t e d on a s c a l e of 1 to 5. Table 16 contains the means, standard d e v i a t i o n s , and t-values of the s c a l e broken down by question and c l a s s . As can be seen from Table 16, the means f o r a l l statements were c o n s i s t e n t l y high; the lowest being Statement 7 which read, "I l i k e d being timed i n a r i t h m e t i c . " There were no s t a t i s t i c a l d i f f e r e n c e s between experimental c l a s s e s on any of the statements on the s c a l e . The response r a t e on the the Student S o c i a l V a l i d a t i o n Scale was 100 percent. Two e x t r a students who d i d not complete the SPAS measure but d i d partake i n the d a i l y school i n t e r v e n t i o n a l s o completed the S o c i a l V a l i d a t i o n S c a l e . This accounts f o r the two e x t r a cases. ANALYSIS AND RESULTS / 94 Table 16 Student Means, Standard Deviations, and t-Values fo r Student So c i a l V a l i d a t i o n Scale Number of Cases Mean Standard D e v i a t i o n Pooled t-Value Statement 1 I l i k e d c h a r t i n g my r e s u l t s i n a r i t h m e t i c every day. Class 1 Class 2 24 26 4.75 4.54 .61 .71 1.13 Statement 2 I l i k e d knowing how I was doing i n a r i t h m e t i c every day. Class 1 Class 2 24 26 4.67 4.58 .64 .76 0.45 Statement 3 This a r i t h m e t i c program made me t r y harder. Class 1 Class 2 24 26 4.67 4.58 .70 .50 0.52 Statement 4 I t h i n k I've gotten b e t t e r i n a r i t h m e t i c i n the l a s t 3 weeks. Class 1 Class 2 24 26 4.67 4.69 .70 .62 -0.14 Statement 5 My parents t h i n k I've gotten b e t t e r i n a r i t h -metic i n the l a s t 3 weeks. Class 1 Class 2 24 26 4.62 4.50 ,65 ,71 0.65 Statement 6 I l i k e a r i t h m e t i c more now. Class 1 Class 2 24 26 4.62 4.65 71 85 •0.13 Statement 7 I l i k e d being timed i n a r i t h m e t i c . Class 1 Class 2 24 26 3.87 3.96 1.33 1.31 -0.23 A N A L Y S I S A N D R E S U L T S / 9 5 Summary of Results I n s u m m a r y , i t w a s c o n c l u d e d t h a t t h e n u l l f o r m o f H y p o t h e s i s 1 c o u l d b e r e j e c t e d a n d t h a t t h e r e s e a r c h h y p o t h e s i s t h a t a r i t h m e t i c s e l f - c o n c e p t w o u l d b e e n h a n c e d b y d a i l y f e e d -b a c k , c h a r t i n g o f r e s u l t s , a n d d a i l y p a r e n t a l r e i n f o r c e m e n t w a s r e t a i n e d . H y p o t h e s i s 2 i n t h e n u l l f o r m s t a t e d t h a t t h e r e w o u l d n o t b e a d i f f e r e n c e i n a r i t h m e t i c s e l f - c o n c e p t a t t h e g r a d e - f o u r l e v e l b e t w e e n b o y s a n d g i r l s . T h i s h y p o t h e s e s h o w e v e r c o u l d n o t b e r e j e c t e d . T h e r e s e a r c h h y p o t h e s e s t h a t t h e r e w i l l b e a d i f f e r e n c e b e t w e e n m a l e s a n d f e m a l e s i n t h e i r a r i t h m e t i c s e l f -c o n c e p t a t t h e g r a d e f o u r l e v e l w a s n o t t e n a b l e . N u l l H y p o t h e s e s l a , w h i c h s t a t e d : G l o b a l a c a d e m i c s e l f -c o n c e p t a s m e a s u r e d b y t h e S P A S w i l l n o t b e e n h a n c e d b y t h e d a i l y e x p e r i m e n t a l i n t e r v e n t i o n , w a s r e j e c t e d w h e n d i f f e r e n c e s o n t h e f u l l s c a l e a c a d e m i c s e l f - c o n c e p t s c a l e b e t w e e n t h e P r e c i s i o n T e a c h i n g a t S c h o o l a n d H o m e a n d P r e c i s i o n T e a c h i n g a t S c h o o l O n l y g r o u p s w e r e f o u n d . N u l l H y p o t h e s e s 2a, w h i c h s t a t e d : T h e r e w i l l n o t b e d i f f e r e n c e s b e t w e e n m a l e s a n d f e m a l e s i n t h e i r g l o b a l a c a d e m i c s e l f - c o n c e p t a t t h e g r a d e f o u r l e v e l w a s r e t a i n e d w h e n a n a l y s i s r e v e a l e d n o s i g n i f i c a n t d i f f e r e n c e s b e t w e e n g e n d e r o n t h i s m e a s u r e . ANALYSIS AND RESULTS / 96 In e x p l o r a t o r y a n a l y s i s , i t was found t h a t both students and parents i n v o l v e d were capable of mastering the i n t e r v e n t i o n and l i k e d t a k i n g p a r t i n the i n t e r v e n t i o n . These f i n d i n g s are discussed i n the f o l l o w i n g chapter along w i t h t h e i r i m p l i c a -t i o n s . V. DISCUSSION The purpose of t h i s f i n a l chapter i s t o provide a review of the f i n d i n g s and t h e i r i n t e r p r e t a t i o n i n r e l a t i o n t o the th e o r i e s and research issues considered i n the foregoing chap-t e r s . The f i r s t p a r t (A) presents an i n t e r p r e t a t i o n of Hypo-t h e s i s One i n r e l a t i o n t o the work of Shavelson et a l . (1976 ) and the various c o n t r i b u t o r s t o the P r e c i s i o n Teaching body of knowledge. Part (B) gives an i n t e r p r e t a t i o n of the second hypothesis, followed by (C), a d i s c u s s i o n of the e x p l o r a t o r y r e s u l t s . A summary of the f i n d i n g s and conclusions are presented i n part (D). Part (E), presents a d i s c u s s i o n of the strengths and l i m i t a t i o n s of the study and i s followed by ( F ) , the i m p l i c a t i o n s of the study, and f i n a l l y p a r t (G) which out-l i n e s some d i r e c t i o n s f o r f u r t h e r research. A. ARITHMETIC SELF-CONCEPT ENHANCEMENT AND PARENTAL REINFORCEMENT I t was speculated i n the present study t h a t a r i t h m e t i c s e l f -concept could be enhanced by a d a i l y experimental i n t e r v e n t i o n u t i l i z i n g P r e c i s i o n Teaching w i t h p a r e n t a l e v a l u a t i o n and reinforcement. The data supported the main e f f e c t of the i n t e r v e n t i o n . The e f f e c t , however, of the i n t e r v e n t i o n was stronger when i t included the e v a l u a t i v e p a r e n t a l component of the i n t e r v e n t i o n . 97 DISCUSSION / 98 This f i n d i n g i s i n agreement w i t h the research of Brookover et a l . (1965) and Brookover and E r i c k s o n (1964), whose s t u d i e s i n v e s t i g a t i n g sources of i n f l u e n c e on students' s e l f - c o n c e p t found t h a t i t was parents who succeeded i n i n c r e a s i n g students s e l f - c o n c e p t of a b i l i t y and academic achievements. S i m i l a r l y , t h i s i s i n accord w i t h G. H. Mead who p o s i t e d t h a t the l a b e l s a p p l i e d t o one's s e l f are learned during i n t e r a c t i o n w i t h i n one's network of s o c i a l r e l a t i o n s h i p s and t h a t f o r c h i l d r e n f i r s t a c q u i r i n g l a b e l s the most important s o c i a l i n f l u e n c e s were those of parents (Mead, 19 34). However, notwithstanding t h a t the P r e c i s i o n Teaching at School and Home group e f f e c t (those r e c e i v i n g the p a r e n t a l reinforcement i n t e r v e n t i o n ) was stronger than the P r e c i s i o n Teaching at School Only group (those e x p e r i e n c i n g o n l y P r e c i s i o n Teaching i n t e r v e n t i o n ) , both groups d i d experience s i g n i f i c a n t e f f e c t s i n the study. The p r a c t i c a l i m p l i c a t i o n s of t h i s are addressed l a t e r i n S e c t i o n F; however, from the present data, i t appears t h a t the P r e c i s i o n Teaching i n t e r v e n t i o n can be success-f u l l y used w i t h or without the use of parents. 1. A r i t h m e t i c and Academic Self-Concept and Shavelson  et a l . ' s (1976) Theory of Self-Concept Returning t o Shavelson et a l . ' s (1976) d e f i n i t i o n of s e l f -concept, v a r i o u s t h e o r e t i c a l p o i n t s can be drawn from t h i s d e f i n i t i o n f o r the i n t e r p r e t a t i o n of the e f f e c t of the i n t e r v e n -t i o n on a r i t h m e t i c s e l f - c o n c e p t and academic s e l f - c o n c e p t . DISCUSSION / 99 Shavelson et a l . (1976 ) propose th a t one of the c r i t i c a l f e a t u r e s of general s e l f - c o n c e p t i s th a t i t i s s t a b l e . This i s i n c o n t r a s t , however, t o the lower l e v e l s of the h i e r a r c h y where self - c o n c e p t v a r i e s g r e a t l y w i t h v a r i a t i o n i n s p e c i f i c s i t u a t i o n s . Shavelson et a l . (1976) s t a t e : "as one descends the s e l f - c o n c e p t h i e r a r c h y , s e l f - c o n c e p t depends i n c r e a s i n g l y on s p e c i f i c s i t u a t i o n s and thus becomes l e s s s t a b l e . " (p. 414) The f i n d i n g s of the present study support the above i n t e r -p r e t a t i o n . Had the lower l e v e l s of the s e l f - c o n c e p t h i e r a r c h y been s t a b l e , i t would seem u n l i k e l y t h a t the i n t e r v e n t i o n would have been able t o e f f e c t measurable change. Since the i n t e r v e n t i o n was a p p l i e d and measured at the base of the h i e r a r c h y , change was able t o be e f f e c t e d . In c o n t r a s t , as pointed out by Shavelson et a l . (1976), the higher l e v e l s of sel f - c o n c e p t are more r e s i s t a n t to changes and changing general s e l f - c o n c e p t r e q u i r e s numerous s i t u a t i o n - s p e c i f i c instances i n c o n s i s t e n t w i t h general s e l f - c o n c e p t . The e v a l u a t i v e character of s e l f - c o n c e p t , a l s o a f e a t u r e of Shavelson et a l . ' s (1976) d e f i n i t i o n , i s of t h e o r e t i c a l impor-tance i n the present study. According t o Shavelson et a l . (1976), not only does the i n d i v i d u a l develop a d e s c r i p t i o n of himself i n p a r t i c u l a r s i t u a t i o n s but a l s o he or she forms e v a l u -a t i o n s of himself or h e r s e l f i n these s i t u a t i o n s . These s e l f -e v a l u a t i o n s can be formed against absolute " i d e a l " standards, r e l a t i v e standards, such as "peers, " or perceived e v a l u a t i o n s of " s i g n i f i c a n t o t h e r s . " DISCUSSION / 100 I f i t can be assumed t h a t " s i g n i f i c a n t o t h e r s " and the e v a l u -a t i o n system of P r e c i s i o n Teaching i n f l u e n c e d students s e l f -d e s c r i p t i o n and hence s e l f - e v a l u a t i o n i n a r i t h m e t i c , then the current f i n d i n g s are supportive of the e v a l u a t i v e c h a r a c t e r of s e l f - c o n c e p t . P a r a l l e l i n g t h i s are the r e s u l t s of a study done by Ludwig and Maehr (1967) whose r e s u l t s were i n t e r p r e t e d as supportive of the theory t h a t s e l f - c o n c e p t change i s a f u n c t i o n of the r e a c t i o n of s i g n i f i c a n t o t h e r s . S i m i l a r l y , the r e s u l t s of the present study show se l f - c o n c e p t can be i n f l u e n c e d by s p e c i f i c experiences. In the words of Shavelson et a l . (1976), "the more c l o s e l y s e l f - c o n c e p t i s l i n k e d w i t h s p e c i f i c s i t u a t i o n s , the c l o s e r i s the r e l a t i o n s h i p between s e l f - c o n c e p t and behavior i n the s i t u a t i o n " (p. 415). I t has been suggested by some c r i t i c s of education (e.g., L o v i t t , 1977) t h a t e d u c a t i o n a l p r a c t i c e s over the l a s t decades have changed but t h a t o f t e n these changes have not been brought about by e d u c a t i o n a l research and theory. One aspect of the present study was concerned w i t h the v i a b i l i t y of using Shavelson et a l . ' s (1976) theory of the s t r u c t u r e of s e l f -concept p r a c t i c a l l y t o design an i n t e r v e n t i o n t o enhance s e l f -concept. Most of the s t u d i e s t o date have not u t i l i z e d the multidimensional and h i e r a r c h i c a l s t r u c t u r e of s e l f - c o n c e p t . This d e f i c i e n c y i n the past research i s due i n p a r t , as noted by Wylie (1961), t o the d i f f i c u l t y and u n r e l i a b i l i t y a s s o c i a t e d w i t h measuring and d e f i n i n g s e l f - c o n c e p t . Consequently, the DISCUSSION / 101 present study attempted t o u t i l i z e the mu l t i d i m e n s i o n a l and h i e r a r c h i c a l i n t e r p r e t a t i o n of s e l f - c o n c e p t , to manipulate one dimension of the lowest l e v e l of the h i e r a r c h y and, subse-quently, t o measure at a higher l e v e l . I t was expected t h a t a r i t h m e t i c s e l f - c o n c e p t could be r e l i -a b l y measured by the SPAS and could be enhanced by the i n t e r v e n -t i o n . The r e s u l t s confirmed t h i s e x p e c t a t i o n . I t was a l s o confirmed that one dimension of the s e l f - c o n c e p t h i e r a r c h y could be p r e s e l e c t e d and manipulated without seemingly a l t e r i n g any of the other dimensions of the h i e r a r c h y . To t h i s end, the con-s t r u c t of s e l f - c o n c e p t as defined by Shavelson et a l . was found to be a r e l e v a n t and v i a b l e model to u t i l i z e when des i g n i n g a p r a c t i c a l i n t e r v e n t i o n t o enhance academic s e l f - c o n c e p t . 2. Enhancing A r i t h m e t i c Self-Concept and P r e c i s i o n Teaching Valued goals of education i n c l u d e enhancement of students' self-concept and s c h o l a s t i c achievement (Shavelson & Bolus, 1982). B e n e f i t s of P r e c i s i o n Teaching have been w e l l docu-mented ( L o v i t t & F a n t a s i a , 1983; L o v i t t , 1984; White, 1986). Few st u d i e s to date, i f any, have examined the e f f e c t of P r e c i s i o n Teaching on students' academic s e l f - c o n c e p t . The present study was designed to examine t h i s e f f e c t . As p r e d i c t e d , the r e s u l t s of the current study d i d confirm the e x p e c t a t i o n t h a t a r i t h m e t i c s e l f - c o n c e p t would be enhanced by the P r e c i s i o n Teaching i n t e r v e n t i o n . P r e c i s i o n Teaching DISCUSSION / 102 coupled w i t h p a r e n t a l reinforcement or without reinforcement from parents d i d s i g n i f i c a n t l y a f f e c t the a r i t h m e t i c s e l f -concept of grade four students. One p o s s i b l e e x p l a n a t i o n f o r t h i s can be found i n the s e l f -e f f i c a c y s t u d i e s by Schunk. Results of these s t u d i e s (Schunk 1981, 1982, 1983, 1985) support the idea t h a t s e l f - e f f i c a c y i s an important v a r i a b l e i n understanding students' achievement behavior. According t o Schunk (1983), there are s e v e r a l ways c h i l d r e n develop a sense of e f f i c a c y . Observation of progress on a task and goal s e t t i n g are two important sources of e f f i c a c y i n f o r m a t i o n . The a n t i c i p a t e d s a t i s f a c t i o n of a t t a i n i n g a goal helps t o s u s t a i n e f f o r t s toward improvement and, at the same time, as students observe t h e i r progress toward the g o a l , they begin to develop a sense of e f f i c a c y (Schunk, 1983). Two important aspects of the e v a l u a t i o n system of P r e c i s i o n Teaching are the s e t t i n g of a goal or aim l i n e and the d a i l y recordings of progress toward t h i s g o a l . The v i s u a l focus of P r e c i s i o n Teaching i s the informa t i o n conveyed on the standard behavior c h a r t . * With l i t t l e or no feedback on the accuracy of t h e i r work, students may be unsure of how competent they are. However, through d a i l y r e c o r d i n g of c o r r e c t s and e r r o r s and the p l o t t i n g of progress toward an a t t a i n a b l e g o a l , students u s i n g the P r e c i s i o n Teaching e v a l u a t i o n system are d a i l y given a * See Appendix A f o r copy of ch a r t . DISCUSSION / 103 wealth of i n f o r m a t i o n . C o l l e c t i v e l y , t h i s i n f o r m a t i o n can help produce changes i n m o t i v a t i o n and s e l f - p e r c e p t i o n s of com-petence and, subsequently, changes i n s e l f - c o n c e p t on the task. Further t o goal s e t t i n g and d a i l y r e c o r d i n g of progress, the present study u t i l i z e d s e l f - r e c o r d i n g , another f a c e t of P r e c i -s i o n Teaching. There i s evidence i n the l i t e r a t u r e of a growing i n t e r e s t i n the r o l e of s e l f - r e g u l a t i o n as a means of i n i t i a t i n g and m a intaining b e h a v i o r a l change (Hallahan & M a r s h a l l & L l o y d , 1981; Kazdin, 1974; Schunk, 1983). According t o Kanfer (1970), the s e l f - r e g u l a t i o n process i s composed of three i n t e g r a l p a r t s ; s e l f - m o n i t o r i n g , s e l f - e v a l u a t i o n , and s e l f - r e i n f o r c e m e n t . When employing P r e c i s i o n Teaching w i t h s e l f - c h a r t i n g as i n the current study, a l l three of these components are brought i n t o bearing. In a study done by Schunk (1983) t o i n v e s t i g a t e the e f f e c t s of progress s e l f - m o n i t o r i n g on students' s e l f - e f f i c a c y and achievement, i t was found t h a t s e l f and e x t e r n a l monitoring of progress l e d t o s i g n i f i c a n t l y higher percepts of e f f i c a c y as compared w i t h no monitoring. S e l f - r e c o r d i n g a l s o enables s t u -dents to gain c a p a b i l i t y i n f o r m a t i o n on t h e i r own and hence f o s t e r a more personal sense of r e s p o n s i b i l i t y f o r mastering l e a r n i n g . The present study's s e l f - r e c o r d i n g procedure included e l e -ments of r e c o r d i n g and of reviewing progress. I t i s b e l i e v e d that t h i s r e c o r d i n g and reviewing of progress may be more impor-ta n t f o r young c h i l d r e n who have short time frames of reference DISCUSSION / 104 and who may not always be cognizant of what they have accom-p l i s h e d (Schunk, 1983). S i m i l a r l y t o goal s e t t i n g , s e l f -r e c o r d i n g appears t o be a p r a c t i c e h i g h l y e f f e c t i v e i n promoting percepts of e f f i c a c y and achievement and, subsequently, s e l f -concept. 3. Enhancing G l o b a l Academic Self-Concept and P r e c i s i o n Teaching The r e s u l t s of the current study gleaned only p a r t i a l support f o r Hypothesis l a which stated g l o b a l academic s e l f -concept as measured by the SPAS w i l l be enhanced by the d a i l y i n t e r v e n t i o n of P r e c i s i o n Teaching. Of the three group comparisons performed using the F u l l Scale Academic P o s t t e s t , only one of the comparisons (that of the P r e c i s i o n Teaching at School and Home group wi t h the P r e c i s i o n Teaching at School Only group) was s i g n i f i c a n t . However, t h i s c o n t r a s t d i d f o l l o w the model i n so f a r as i t was s i g n i f i c a n t i n favour of the P r e c i s i o n Teaching at School and Home group. This r e s u l t can be i n t e r p r e t e d as supportive of the hypothesis of s e l f - c o n c e p t theory t h a t s e l f - c o n c e p t change i s a f u n c t i o n of the r e a c t i o n of s i g n i f i c a n t o t h e r s . One f e a s i b l e e x p l a n a t i o n f o r the i n c o n s i s t e n t p a t t e r n of r e s u l t s found at the g l o b a l l e v e l of academic s e l f - c o n c e p t i s th a t the h i e r a r c h y i s more complicated than o r i g i n a l l y a n t i c i p a t e d . Perhaps academic s e l f - c o n c e p t i s not j u s t a DISCUSSION / 105 s i n g l e higher-order f a c e t but r a t h e r made up of s p e c i f i c f a c e t s of academic s e l f - c o n c e p t . I f t h i s were the case then one i n t e r v e n t i o n at one l e v e l would not be able t o e f f e c t a change at an aggregate l e v e l of academic s e l f - c o n c e p t . B. GENDER DIFFERENCES IN ARITHMETIC SELF-CONCEPT AT THE GRADE FOUR LEVEL I t was speculated t h a t there would be d i f f e r e n c e s between males and females i n a r i t h m e t i c s e l f - c o n c e p t at the grade four l e v e l . The data d i d not support a s i g n i f i c a n t main e f f e c t of gender e i t h e r on a r i t h m e t i c s e l f - c o n c e p t or on general academic s e l f - c o n c e p t . As noted i n Chapter Three, many researchers have used gender as a v a r i a b l e when examining mathematic achievement. According t o Fennema (1980), a l l reviews published before 1974 concerned w i t h s e x - r e l a t e d d i f f e r e n c e s i n a r i t h m e t i c achieve-ment were i n agreement that males were surpassing females i n achievement by the time students were i n upper elementary school. A l s o noted by the same author (Fennema, 1980 ) was th a t published r e p o r t s a f t e r 1974 have not shown the same consensus. However, the present study d i d not examine a r i t h m e t i c achievement per se but ra t h e r a r i t h m e t i c s e l f - c o n c e p t . When reviewing the psychometric c h a r a c t e r i s t i c s and normative data of the measuring instrument used i n the present study, i t was noted t h a t there were gender e f f e c t s at grades t h r e e , f o u r , and DISCUSSION / 106 f i v e w i t h most of these o c c u r r i n g at the grade four l e v e l . * However, a d e t a i l e d a n a l y s i s of the grade four data as a f u n c t i o n of i n d i v i d u a l c l a s s e s and schools f a i l e d t o r e v e a l the source of these gender d i f f e r e n c e s on the measure (Boersma & Chapman, 1977). I t should be noted t h a t the gender d i f f e r e n c e s i n the o r i g i n a l norming sample i n a r i t h m e t i c were not s i g n i f i c a n t . Not w i t h s t a n d i n g the absence of consensus i n the l i t e r a t u r e r e l a t i n g t o gender d i f f e r e n c e s i n a r i t h m e t i c achievement and a r i t h m e t i c s e l f - c o n c e p t (Aiken, 1970; Fennema, 1980), the d i r e c t i o n a l i t y of the present hypothesis was i n f l u e n c e d by the feedback/reinforcement nature of the i n t e r v e n t i o n used i n the study. Studies done by Eagly and Whitehead (1972) and Feather and Simon (1971) both found females to be more s e n s i t i v e t o feedback on performance than males. Due t o the predominant female/male r a t i o i n the elementary schools, the hypothesis was d i r e c t e d toward d i f f e r e n c e s i n a r i t h m e t i c s e l f - c o n c e p t . However, r e s u l t s from the present study show no s i g n i f i c a n t gender d i f f e r e n c e s i n a r i t h m e t i c s e l f - c o n c e p t before or a f t e r the i n t e r v e n t i o n , and consequently do not a l l o w the researcher t o speculate on whether females are more s e n s i t i v e t o feedback on performance than males. * See page 63 f o r d e s c r i p t i v e s t a t i s t i c s f o r f u l l and sub-s c a l e SPAS scores as a f u n c t i o n of gender and grade l e v e l . DISCUSSION / 107 C. FINDINGS FROM EXPLORATORY ANALYSIS 1• P a r e n t a l V a l i d a t i o n of the Experimental I n t e r v e n t i o n As s t a t e d i n the f i r s t chapter, one purpose of the present study was t o examine the u t i l i t y of a P r e c i s i o n Teaching i n t e r v e n t i o n as a p r a c t i c a l way to enhance the academic s e l f -concept of grade four students i n a r i t h m e t i c . As noted by L o v i t t (1977), i t i s the r e s p o n s i b i l i t y of e d u c a t i o n a l researchers t o i n s u r e t h a t changes i n e d u c a t i o n a l p r a c t i c e s be supported by research and t o share and r e p o r t t h e i r f i n d i n g s i n such ways th a t can be e f f e c t i v e l y implemented. In order t o implement and examine thoroughly the present i n t e r v e n t i o n which required the support and help of parents, i t was necessary t o gain a response from the parents i n v o l v e d . Of primary i n t e r e s t were: (1) Would parents be able t o l e a r n the c h a r t i n g convention from a p r i n t e d e x p l a n a t i o n and, (2) Would parents chart w i t h t h e i r c h i l d r e n on a d a i l y b a s i s ? I t was assumed th a t before teachers w i l l be w i l l i n g to implement an i n t e r v e n t i o n u s i n g parents as partners the p r a c t i c a l i t y of conveying i n f o r m a t i o n t o parents by l e t t e r would be necessary. The feedback from parents i n the present study revealed t h a t parents d i d l i k e c h a r t i n g w i t h t h e i r c h i l d r e n on a d a i l y b a s i s . A l s o , parents were able t o l e a r n the c h a r t i n g procedure from a w r i t t e n e x p l a n a t i o n . DISCUSSION- / 108 These f i n d i n g s c o u p l e d w i t h r e s e a r c h documenting t h e impact of p a r e n t s as r e i n f o r c e r s and shapers o f s e l f - c o n c e p t (Bradshaw, 1982; Brookover & E r i c k s o n , 1969; M i l l e r , 1981) suggest t h a t e d u c a t o r s s h o u l d n ot be h e s i t a n t i n i n v o l v i n g p a r e n t s i n t h e e d u c a t i o n a l p r a c t i c e s o f t h e i r c h i l d r e n . However, i n o r d e r t o be e f f e c t i v e i n t h e i r r e i n f o r c e m e n t o f t h e i r c h i l d r e n , p a r e n t s need p r e c i s e and o n - g o i n g d a t a from t h e t e a c h e r . P r e c i s i o n T e a c h i n g p r a c t i c e s as demonstrated i n t h i s s t u d y a r e one way o f c o n v e y i n g t h i s i n f o r m a t i o n . N o t w i t h s t a n d i n g t h a t an i m p o r t a n t g o a l o f e d u c a t i o n s h o u l d be t e a c h i n g s t u d e n t s t o produce t h e i r own feedback s i n c e t h i s a b i l i t y i s a t t h e c o r e o f l e a r n i n g how t o l e a r n (Van Houten, 1980); i t i s a l s o e s s e n t i a l t h a t s t u d e n t s e x p e r i e n c i n g d i f f i c u l t i e s l e a r n t o r e c o g n i z e t h e i r s m a l l s u c -c e s s e s o r i t i s p r o b a b l e t h e y w i l l c o n t i n u e t o m a i n t a i n low s e l f -c o n cept o f a b i l i t y . P r e c i s i o n T e a c h i n g i s a way o f e n a b l i n g s t u d e n t s t o r e c o g n i z e s m a l l s u c c e s s e s . 2. Student V a l i d a t i o n o f t h e E x p e r i m e n t a l I n t e r v e n t i o n As w i t h p a r e n t a l feedback from t h e s t u d y , feedback from s t u -d e n t s on how t h e y p e r c e i v e d t h e i n t e r v e n t i o n was o f utmost con-c e r n . Means f o r a l l s t a t e m e n t s on t h e L i k e r t - t y p e s c a l e where h i g h s c o r e s i n d i c a t e d a more f a v o r a b l e a t t i t u d e were c o n s i s -t e n t l y h i g h . * F u r t h e r m o r e , t h e s e r e s u l t s r e v e a l e d t h a t s t u d e n t s l i k e d c h a r t i n g t h e i r r e s u l t s d a i l y and r e p o r t e d t h e y * See T a b l e 15. DISCUSSION / 109 thought t h e i r parents perceived improvement i n t h e i r a r i t h m e t i c a b i l i t y and th a t they l i k e d a r i t h m e t i c more s i n c e the i n t e r -v e n t i o n . Many educators tend t o assume t h a t the time i n v o l v e d t o ad-m i n i s t e r and begin an i n t e r v e n t i o n , such as used i n the present study, would be f a r too great given t h e i r d a i l y schedule. How-ever, the present study shows th a t t h i s need not be the case. With students s e l f - g r a p h i n g and s e l f - c o r r e c t i n g i n the c l a s s -room, the time r e q u i r e d d a i l y f o r the i n t e r v e n t i o n averaged s i x minutes. D. SUMMARY OF THE FINDINGS AND CONCLUSIONS The i n v e s t i g a t i o n began wi t h the primary o b j e c t i v e of examining the e f f e c t of a P r e c i s i o n Teaching i n t e r v e n t i o n t h a t incorporated reinforcement and e v a l u a t i o n on a r i t h m e t i c and academic s e l f - c o n c e p t . T h e o r e t i c a l l y and p r a c t i c a l l y the study u t i l i z e d the h i e r a r c h i c a l and m u l t i d i m e n s i o n a l model of self-c o n c e p t as proposed by Shavelson et a l . (1976). S p e c i f i c a l l y , the study was designed t o apply the i n t e r v e n t i o n t o the s i t u a t i o n a l l e v e l of m u l t i p l i c a t i o n i n a r i t h m e t i c . The e f f e c t s of t h i s i n t e r v e n t i o n were subsequently measured at the ascending l e v e l s of a r i t h m e t i c s e l f - c o n c e p t and academic s e l f -concept. D i f f e r e n c e s between males and females on a r i t h m e t i c s e l f - c o n c e p t were a l s o examined before and a f t e r the i n t e r v e n -DISCUSSION / 110 t i o n . Exploratory questions were directed toward a s o c i a l v a l i d a t i o n of the intervention by students and parents involved. The findings and conclusions that can be drawn from these findings are as follows. 1. There were no s i g n i f i c a n t differences between males and females at the grade four l e v e l i n arithmetic self-concept or global academic self-concept on either the pretest or the posttest. These findings suggest that at the grade four l e v e l g i r l s and boys have not been affected by any measurable pattern of d i f f e r i n g arithmetic self-concept or academic self-concept. S i m i l a r i l y as there were no measurable differences between males and females a f t e r the interven-t i o n i n arithmetic self-concept, these findings suggest that performance feedback likewise did not a f f e c t one sex more than another. 2 . The Precision Teaching intervention had a s i g n i f i c a n t impact on enhancing the arithmetic self-concept of both the Precision Teaching at School and Home group as well as the Precision Teaching at School Only group. These findings suggest that i t i s possible to s i g n i f i c a n t l y enhance arithmetic self-concept of grade four students with or without u t i l i z i n g reinforcement and evaluation from students' parents. 3. Precision Teaching combined with reinforcement and evalu-ation by parents produces a stronger enhancement of a r i t h -DISCUSSION / 111 metic s e l f - c o n c e p t than j u s t the u t i l i z a t i o n of P r e c i s i o n Teaching alone. This p a t t e r n of s e l f - c o n c e p t enhancement suggests t h a t , f o r the grade four student, perceptions of s e l f are i n f l u e n c e d by both a t t r i b u t i o n s f o r one's own behavior as w e l l as reinforcement and e v a l u a t i o n by s i g n i -f i c a n t o t h e r s . 4 . The e v a l u a t i o n system of P r e c i s i o n Teaching i s one t h a t both grade four students and t h e i r parents can master and enjoy t a k i n g p a r t i n . 5. The r e l i a b i l i t y of the Students' P e r c e p t i o n A b i l i t y Scale (Boersma & Chapman, 1977) as a measure of a r i t h m e t i c s e l f -concept and academic s e l f - c o n c e p t was endorsed. A l s o the present study confirms that SPAS scores are s e n s i t i v e t o increases i n academic s e l f - c o n c e p t as a f u n c t i o n of remedi-a t i o n and i n t e r v e n t i o n . In most s t u d i e s there are strengths and l i m i t a t i o n s and i t i s i n t h i s l i g h t the preceding conclusions should be e n t e r t a i n e d . The strengths and l i m i t a t i o n s of the present study are discussed i n the f o l l o w i n g s e c t i o n . E. LIMITATIONS AND STRENGTHS OP THE STUDY One of the l i m i t a t i o n s of the present study was the f a c t t h a t i t had t o be conducted using a quasi-experimental design. U n f o r t u n a t e l y , most educational research conducted i n a natur-a l i s t i c school s e t t i n g s u f f e r s from t h i s l i m i t a t i o n . When DISCUSSION / 112 d e a l i n g w i t h already assembled i n t a c t c l a s s e s , i t i s an i m p o s s i b i l i t y t o randomly ass i g n s u b j e c t s from a common population to experimental or c o n t r o l groups. Consequently, when confronted w i t h t h i s s i t u a t i o n , the experimenter i s forced to make do w i t h a quasi-experimental design r a t h e r than a t r u e experimental design and i t s accompanying s u p e r i o r i n t e r n a l v a l i d i t y . However, as pointed out by Campbell and Stanley (1966), where more e f f i c i e n t designs are u n a v a i l a b l e , u t i l i z a t i o n of quasi-experimental designs are j u s t i f i e d and w e l l worth u s i n g . One of the strengths of the Nonequivalent C o n t r o l Group Design which the present study employed i s t h a t i t s u t i l i z a t i o n of c o n t r o l groups reduces e q u i v o c a l i t y of i n t e r p r e t a t i o n of r e s u l t s . A l s o the more s i m i l a r the experimental and c o n t r o l groups are i n t h e i r recruitment and the more the s i m i l a r i t y i s confirmed by the scores on the p r e t e s t , the more e f f e c t i v e t h i s c o n t r o l becomes (Campbell & Stanley, 1966). In the present study, i t was revealed through s t a t i s t i c a l a n a l y s i s t h a t there were no s t a t i s t i c a l d i f f e r e n c e s between experimental and c o n t r o l groups on the p r e t e s t . Thus i n the present study, the design can be regarded as c o n t r o l l i n g the main e f f e c t s of h i s t o r y , maturation, t e s t i n g , and i n s t r u m e n t a t i o n . One of the strengths of the present study r e s i d e s i n the e x t e r n a l v a l i d i t y of r e s u l t s . The study was not conducted i n a c o n t r o l l e d l a b o r a t o r y s e t t i n g but r a t h e r i n preassembled c l a s s -rooms throughout an average suburban school d i s t r i c t . DISCUSSION / 113 One of the main c r i t i c i s m s of s e l f - c o n c e p t research has been the v a l i d i t y of the s e l f - r e p o r t measures. As w i t h any s e l f -r e p o r t measure of a p e r s o n a l i t y v a r i a b l e , the i n t e r p r e t a t i o n may be challenged on the grounds t h a t students w i l l s e l e c t responses they know to be s o c i a l l y d e s i r a b l e r a t h e r than responses t h a t are s e l f - d e s c r i p t i v e . As t h i s i s a l e g i t i m a t e concern, the present study attempted t o create an environment where the chance of e l i c i t i n g an honest response was maximized. Students were assured by the experimenter that teachers and parents would not see t h e i r answers and c o n f i d e n t i a l i t y of responses was assured. For some educators, the i n t e g r i t y of the P r e c i s i o n Teaching charts or the f a c t t h a t students s e l f - c o r r e c t e d t h e i r d a i l y probes may be an i s s u e . However, much of the data c o l l e c t e d t o date i n d i c a t e t h a t students are g e n e r a l l y accurate at s e l f -s c o r i n g provided there are no p u n i t i v e consequences f o r low scores (Van Houten, 1980 ). In t h i s r e s p e c t , P r e c i s i o n Teaching as an e v a l u a t i o n system serves to a s s i s t r e l i a b l e s e l f - s c o r i n g as feedback i s never pegged t o absolute l e v e l s . Student goals i n the present study were i n d i v i d u a l i z e d and the major emphasis was on improvement r a t h e r than some absolute group l e v e l of achievement. The confidence i n the r e s u l t s of any study depends i n p a r t on the r e l i a b i l i t y of the measuring instrument used t o c o l l e c t the data. The r e l i a b i l i t i e s of the measure used i n the current study as reported i n Chapter Four were high. DISCUSSION / 114 F. IMPLICATIONS According t o some educators; e.g., L o v i t t (1977), i t i s the r e s p o n s i b i l i t y of ed u c a t i o n a l researchers t o seek out educa-t i o n a l t r u t h s , t o unearth the b a s i c fundamentals of education, and t o then e x p l a i n these b a s i c s t o teachers and l e a r n e r s i n terms t h a t are understandable and implementable. Bearing t h i s i n mind, the primary goal of the present researcher has not been to s e t t l e the argument between the self-enhancement t h e o r i s t s who b e l i e v e i n i t i a l time and e f f o r t should be spent t r y i n g t o increase the general s e l f - c o n c e p t of c h i l d r e n i n an e d u c a t i o n a l program or the s k i l l development t h e o r i s t s who b e l i e v e t h a t s e l f - c o n c e p t v a r i a b l e s are p r i m a r i l y consequences of academic achievement. Instead, r e a l i z i n g t h a t the two most important r o l e s played by the elementary schools are the development of b a s i c academic s k i l l s and the enhancement of students' s e l f - c o n c e p t , the present study was conceived t o research a p r a c t i c a l i n t e r v e n t i o n t h a t could enhance academic s k i l l s and s e l f - c o n c e p t simultane-o u s l y . P r i o r t o the present research many s t u d i e s have confirmed t h a t P r e c i s i o n Teaching can be used s u c c e s s f u l l y t o f a c i l i t a t e l e a r n i n g ( L o v i t t & F a n t a s i a , 1983; White, 1986). However, even though researchers suspected and noted i n t h e i r s t u d i e s other outcomes such as increased m o t i v a t i o n as a r e s u l t of the use of DISCUSSION / 115 P r e c i s i o n Teaching, there was an absence of s t u d i e s t h a t had s p e c i f i c a l l y i n v e s t i g a t e d the e f f e c t of P r e c i s i o n Teaching on academic s e l f - c o n c e p t . The f i n d i n g s of the present study have s e v e r a l i m p l i c a t i o n s . These i m p l i c a t i o n s r e l a t e t o the t h e o r e t i c a l p o i n t s of view th a t guided the study, r e l a t e t o p r a c t i c e s t h a t are e f f e c t i v e i n enhancing the academic se l f - c o n c e p t of elementary school s t u -dents, and r e l a t e t o c e r t a i n issues regarding the r o l e of parents and schools i n developing students' academic s e l f - c o n c e p t . On a t h e o r e t i c a l l e v e l the f i n d i n g s of t h i s study support the various other researchers who p o s i t e d t h a t the s e l f - c o n c e p t i s an organized, m u l t i f a c e t e d , and h i e r a r c h i c a l c o n s t r u c t . (Byrne & Shavelson, 1986; Shavelson & Bolus, 1982). The present r e s u l t s i n d i c a t e t h a t the s i t u a t i o n s p e c i f i c s u b l e v e l s of academic s e l f - c o n c e p t i n f l u e n c e the ascending l e v e l s of the hi e r a r c h y . These f i n d i n g s have i m p l i c a t i o n s f o r e v a l u a t i n g change i n pe r c e p t i o n of a b i l i t y over time, and p a r t i c u l a r l y , f o l l o w i n g remediation. Although there are a m u l t i p l i c i t y of self- c o n c e p t measuring instruments i t seems p e r t i n e n t t o employ an instrument capable of d e t e c t i n g change at ascending l e v e l s of the se l f - c o n c e p t h i e r a r c h y r a t h e r than a t the g l o b a l l e v e l . The success of P r e c i s i o n Teaching as a s u c c e s s f u l f a c i l i t a -t o r of progress i n a wide range of l e a r n e r s has been w e l l documen-ted ( L o v i t t & F a n t a s i a , 1983; White, 1986). F u r t h e r , Schunk DISCUSSION / 116 (1985) found t h a t c e r t a i n e d u c a t i o n a l p r a c t i c e s e f f e c t judgments of performance c a p a b i l i t i e s by c l e a r l y conveying i n f o r m a t i o n t h a t students are a c q u i r i n g s k i l l s . The r e s u l t s of the present research s i m i l a r l y show t h a t e d u c a t i o n a l p r a c t i c e s are an important c o n t e x t u a l i n f l u e n c e on students' academic s e l f - c o n c e p t . Students who kept data and focused on t h i s data experienced s i g n i f i c a n t enhancement of academic s e l f - c o n c e p t whether t h e i r parents simultaneously charted w i t h them or not. The r e s u l t s of t h i s study support P r e c i s i o n Teaching as an e d u c a t i o n a l p r a c t i c e that i n f l u e n c e s students' academic s e l f -concept. There are many teaching p r a c t i c e s t h a t r e s u l t i n the d a i l y progress of students; however, unless these small improvements are r e a d i l y apparent and v i s u a l l y a v a i l a b l e t o the student, the e f f e c t s of these p r a c t i c e s may not be e f f e c t i v e i n academic s e l f - c o n c e p t enhancement. As observed i n the Experimenter i n Classroom but No P r e c i s i o n Teaching group of t h i s study, academic s e l f - c o n c e p t was not aided when students were unable to sense they were making progress. An e s s e n t i a l aspect of the e v a l u a t i o n system of P r e c i s i o n Teaching i s goal s e t t i n g and progress toward t h i s g o a l . In the present study, students working toward s p e c i f i c goals e x p e r i -enced enhancement of academic s e l f - c o n c e p t . This i s i n con-f i r m a t i o n w i t h the research of Schunk (1985) who found t h a t s p e c i f i c goals r a i s e s e l f - e f f i c a c y more than do general goals because progress toward an e x p l i c i t goal i s e a s i e r t o gauge. The info r m a t i o n conveyed to students, when u t i l i z i n g P r e c i s i o n DISCUSSION / 117 Teaching, conveys nothing about others' accomplishments and subsequently students are more able t o focus on t h e i r present performance and progress toward t h e i r p ersonal g o a l s . This b e n e f i t of P r e c i s i o n Teaching becomes s i g n i f i c a n t when working w i t h classrooms of students w i t h d i f f e r i n g l e v e l s of achievement, f o r as noted by Ruble, Boggiano, Feldman and Loebl (1980), c h i l d r e n show an i n c r e a s i n g i n t e r e s t i n s o c i a l comparison d u r i n g the e a r l y elementary school years, and, by the f o u r t h grade, use t h i s i n f o r m a t i o n t o help form s e l f - e v a l u a t i o n s of competence. As noted i n the i n t r o d u c t i o n of the study, the development of a p o s i t i v e s e l f - c o n c e p t i s an o b j e c t i v e of almost a l l educational programs from kindergarten t o high s c h o o l ; however, teachers are seldom given any p r a c t i c a l , l e t alone researched, methods f o r p r a c t i c a l l y a c h i e v i n g t h i s important g o a l . The patterns of i n f o r m a t i o n found i n the present study address t h i s problem. P r e c i s i o n Teaching o f f e r s a v i a b l e and u s e f u l e d u c a t i o n a l p r a c t i c e f o r enhancing academic s e l f - c o n c e p t . P r e c i s i o n Teaching a l s o o f f e r s a method of advantageously i n c o r p o r a t i n g parents involvement academically w i t h t h e i r c h i l d r e n . As noted i n the present study, the academic s e l f -enhancement f a c t o r was greater when students charted w i t h parents at home. This i s i n agreement w i t h the r e s u l t s of Brookover, Paterson, & Thomas (1962), who found students' s e l f -concept of a b i l i t y was p o s i t i v e l y r e l a t e d t o the image he or she DISCUSSION / 118 perceived parents held of him or her. The primary i m p l i c a t i o n to be drawn from t h i s being t h a t i n order t o be maximally e f f i -c i e n t , s t r a t e g i e s t o enhance academic s e l f - c o n c e p t w i t h elemen-t a r y school students need t o i n v o l v e parents or s i g n i f i c a n t o thers. As observed by some education c r i t i c s (e.g., L o v i t t , 1977 ), there has been a movement t o discourage parents from working w i t h t h e i r own c h i l d r e n . L o v i t t s t a t e s : In t h i s r e s p e c t , the business of education i s deserving of the same c r i t i c i s m Ivan I l l i c h l e v e l l e d at the business of medicine i n 1970 when he s a i d t h a t i t had done ever y t h i n g p o s s i b l e to hide the s i m p l i c i t y of i t s b a s i c procedures from the p u b l i c . (p. 8) I t i s perhaps t h i s s e p a r a t i o n of school and f a m i l y t h a t i s par-t i a l l y r e s p o n s i b l e f o r the recent charge voiced by Vancouver's elementary school a d m i n i s t r a t o r s (Vancouver Sun, 1988) who s t a t e t h a t s o c i e t y now expects the school t o be a "super parent" and added, "The school i s no longer j u s t supporting the f a m i l y , but i s dangerously c l o s e i n some areas of s u p p l a n t i n g i t a l t o -gether." In l i g h t of t h i s v i s i o n ; i t seems p e r t i n e n t f o r schools and teachers to in c o r p o r a t e s t r a t e g i e s t o r e - i n v o l v e parents w i t h the schools and wit h the d a i l y progress of t h e i r c h i l d r e n . P r e c i s i o n Teaching o f f e r s an o p p o r t u n i t y t o do t h i s by conveying continuous performance feedback t o parents, students, and teachers a l i k e , thus c o n s o l i d a t i n g the goals of student achievement. DISCUSSION / 119 A f u r t h e r i m p l i c a t i o n of the present research i s the neces-s i t y to acquaint classroom teachers w i t h the f i n d i n g s . As p o s i t e d by L o v i t t (1977), the m a j o r i t y of classroom teachers do not read the j o u r n a l s used by e d u c a t i o n a l researchers to docu-ment t h e i r f i n d i n g s . This would be e s p e c i a l l y t r u e f o r research theses, and, although research theses are w r i t t e n so t h a t r e p l i -c a t i o n of the research can be conducted from the methodological d e t a i l s , i t would be naive to assume t h a t classroom teachers are busy r e p l i c a t i n g these s t u d i e s . I t seems apparent from t h i s dilemma, however, t h a t there are s e v e r a l options open f o r channeling research outcomes to the classroom teacher. Educational researchers can make t h e i r f i n d i n g s a v a i l a b l e to p r a c t i t i o n e r s and d i s t r i c t s w i t h i n which they d i d t h e i r r esearch, and i n s t i t u t i o n s which t r a i n and acquaint p r o s p e c t i v e teachers w i t h pedagogy can assume r e s p o n s i b i l i t y f o r s h aring these f i n d i n g s . U l t i m a t e l y , however, the l i k e l i h o o d of researched e d u c a t i o n a l p r a c t i c e s being s u c c e s s f u l l y implemented depends i n p a r t on whether they are perceived as c o n s i s t e n t w i t h e x i s t i n g v a l u e s . F u r t h e r , i t seems l i k e l y t h a t unless educators accept and understand the importance of f o s t e r i n g a p o s i t i v e academic s e l f - c o n c e p t , classroom teachers w i l l not attempt t o conduct procedures t h a t w i l l u l t i m a t e l y enhance academic s e l f - c o n c e p t . S i m i l a r l y , unless teachers understand and are p r o f i c i e n t i n P r e c i s i o n Teaching conventions, they w i l l not attempt t o implement these DISCUSSION / 120 techniques r e g a r d l e s s of t h e i r b e n e f i t . Deno (1985) cautions t h a t teachers must be c a r e f u l l y t r a i n e d t o be maximally e f f i c i e n t i n assessment l e s t they become i n c r e a s i n g l y i n e f f i -c i e n t t o the p o i n t where the commonly held r e s e r v a t i o n t h a t d i r e c t and frequent measurement takes too much time. Although the area of i n t e r e s t f o r the researcher has been what may be c a l l e d S p e c i a l Education p r a c t i c e s , the present research was designed f o r and conducted i n the r e g u l a r classroom s e t t i n g . Given the curren t and t i m e l y trend of merging S p e c i a l Education and r e g u l a r education students, P r e c i s i o n Teaching p r a c t i c e s o f f e r a way to respond t o the wide range of i n d i v i d u a l d i f f e r e n c e s found i n the classroom. As st a t e d by Shepard (1987), teachers i n t r a i n i n g are p r e s e n t l y taught the r e f e r r a l model when d e a l i n g w i t h e x c e p t i o n a l students. However, given the current p h i l o s o p h i c a l and t h e o r e t i c a l trends i n education, i t seems expedient t o teach r e g u l a r teachers a r e p e r t o i r e of p r a c t i c a l researched technologies r a t h e r than the no t i o n t h a t classroom problems can only be solved by e x t e r n a l resources. The present study drew on s e l f - c o n c e p t t h e o r i e s , s e l f -e f f i c a c y research and e v a l u a t i o n systems res e a r c h . The r e s u l t s confirmed c e r t a i n hypothesized r e l a t i o n s h i p s . The r e s u l t s from t h i s study i n d i c a t e t h a t an attempt t o understand students' academic s e l f - c o n c e p t , p a r t i c u l a r l y the i n f l u e n c e of an e v a l u a t i o n system coupled w i t h p a r e n t a l reinforcement, i s a p o t e n t i a l l y f r u i t f u l path t o proceed upon t o understand some of the causes of s e l f - c o n c e p t problems i n the school and the f a m i l y . DISCUSSION / 121 As i n any research, the f i n d i n g s and the i m p l i c a t i o n s which have been drawn from the f i n d i n g s suggest a d d i t i o n a l i n q u i r y . Some areas stemming from the present research are discussed i n the f o l l o w i n g s e c t i o n . G. DIRECTIONS FOR FURTHER RESEARCH Given the general consensus t h a t p o s i t i v e a t t i t u d e s toward a subject i n f l u e n c e the outcome of accomplishment i n t h a t s u b j e c t , there has only been a small amount of research done to examine techniques f o r developing p o s i t i v e a t t i t u d e s and modifying negative a t t i t u d e s toward d i f f e r e n t s u b j e c t s . I t i s c l e a r t h a t there i s a need f o r more research concerned w i t h the modifying of academic s e l f - c o n c e p t i n the e a r l y school years. In regard t o both the development and the m o d i f i c a t i o n of a t t i t u d e s i s the question: How can t h i s best be achieved? New p r a c t i c e s may be i n i t i a l l y m o t i v a t i n g and c o n t r i b u t e toward enhancement of academic s e l f - c o n c e p t ; however, i t i s d o u b t f u l t h e i r e f f e c t s w i l l l a s t unless teachers are educated i n s e l f - c o n c e p t enhancement techniques, parents remain sympathetic, and the students are s u c c e s s f u l i n mastering the s u b j e c t . This i s perhaps the f i r s t study t o use P r e c i s i o n Teaching as an i n t e r v e n t i o n t o modify academic s e l f - c o n c e p t per se. As the present study only attempted to enhance a r i t h m e t i c s e l f -concept, an obvious next step would be to r e p l i c a t e the f i n d i n g s DISCUSSION / 122 using other f a c e t s of academic s e l f - c o n c e p t as described by Shavelson et a l . (1976). As noted i n Chapter Three, the present study was conducted i n an average mi d d l e - c l a s s d i s t r i c t u sing predominantly white students. As i t i s not known whether s i m i l a r r e s u l t s would be a t t a i n e d using a l e s s homogeneous group of students and parents, f u r t h e r research i n t h i s d i r e c t i o n would be of b e n e f i t . Furthermore, as school s o c i a l c l i m a t e v a r i a b l e s e x p l a i n more of the d i f f e r e n c e s i n mean se l f - c o n c e p t of academic a b i l i t y than do the student body composition (Brookover, 1979), i t would be of i n t e r e s t t o i n v e s t i g a t e variance between schools mean s e l f -concept of academic a b i l i t y and t e a c h e r / p r i n c i p a l a t t i t u d e s toward P r e c i s i o n Teaching. Although gender d i f f e r e n c e s were not observed i n the present study, d i r e c t i o n s f o r f u r t h e r research could i n c l u d e d i f f e r e n c e s i n s e n s i t i v i t y to performance feedback between males and females as noted by Eagly & Whitehead (1972). A l s o since research on the development of s e l f - c o n c e p t suggests t h a t boys s e l f - c o n c e p t i s c l o s e l y a s s ociated w i t h the r e l a t i o n s h i p w i t h the f a t h e r , but not w i t h the mother, and conversely, g i r l s ' s e l f - c o n c e p t i s c l o s e l y a s s ociated w i t h the r e l a t i o n s h i p w i t h the mother, but not w i t h the f a t h e r ( D i c k s t e i n & Posner, 1978), i t would be prudent t o continue t o explore gender d i f f e r e n c e s i n r e l a t i o n s h i p t o feedback and reinforcement from parents. DISCUSSION / 123 In c o n c l u s i o n , i f enhancement of student s e l f - c o n c e p t i n general or academic s e l f - c o n c e p t i n p a r t i c u l a r are going t o be o b j e c t i v e s of the school system, then i t seems wise t o expand our knowledge on methods of teaching t h a t f a c i l i t a t e the enhancement of s e l f - c o n c e p t . Further the f i n d i n g s of t h i s study speak t o the need of i n c o r p o r a t i n g parents and t h e i r i n d i s p e n s a b l e support back i n t o the education system. One way of accom-p l i s h i n g t h i s as confirmed by the present study i s through the sharing of s k i l l a c q u i s i t i o n i n f o r m a t i o n w i t h parents on a d a i l y b a s i s . In the f i n a l a n a l y s i s , e d u c a t i o n a l p r a c t i c e s can be seen as an important c o n t e x t u a l infuence on students' academic s e l f -concept . VI. REFERENCES Aiken, L. R. (1970). A t t i t u d e s toward mathematics. Review of  Educational Research. 4JH4), 551-596. Bandura, A. (1981). S e l f - r e f e r e n t thought: A developmental a n a l y s i s of s e l f - e f f i c a c y . In J . H. F l a v e l l & L. Ross (Eds.), S o c i a l C o g n i t i v e Development: F r o n t i e r s and  P o s s i b l e Futures. (pp. 200-239). 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WEEK i AVV\AV\AA\' 13 Y\AVV\AV\A 1/l/i/l/ l/ l/ l/ l "\/\A/\A/\A/\ 16 18 19 AAAAAA A AAAAA/ A /\A/A AA A //A/ A A A 77Z77 V A WEEKS ^ |l»" tltlt tt lit Mlt l l ip in i i , , , , , , , , , , , , , , , „ , | „ , ,p„ , [ „„ | „„ [ „ , , | , , „ [ „„ [ . . . . | . . . . [ . . . , | . . , . | . . . . | . . . . [ . . . . [ . . , , [ D A Y S ° »Q 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 IOO IIO I20 I 3 0 I 4 0 TEAM MEMBERS' BEHAVER _ MANAGER COUNTER _ AGE. .CHARTER "MOVEMENT CYCLE-CORRECT ERROR _ WWU 4 cycle paper APPENDIX / 134 B . S P A S S U B S C A L E F O R A R I T H M E T I C S T A T E M E N T S ( 5 ) 1 t h i n k my school work i s r e a l l y good. yes no o o ( 9 ) 1 u s u a l l y f i n i s h my school work. yes no o o (20) I am poor at s u b t r a c t i o n . yes no o o (27) I am good w i t h my times t a b l e s . yes no o o (34) I have d i f f i c u l t y g e t t i n g my a r i t h m e t i c f i n i s h e d on time. yes no o o (35) I have d i f f i c u l t y working w i t h numbers. yes no o o (37) I l i k e a r i t h m e t i c . yes no o o (45) My teacher t h i n k s I am dumb i n a r i t h m e t i c . yes no o o (51) I am unhappy w i t h how I do a r i t h m e t i c . yes no o o (55) I u s u a l l y get my a r i t h m e t i c r i g h t . yes no o o (66) I am good a t a r i t h m e t i c . yes no o o (69) I f i n d m u l t i p l i c a t i o n fun. yes no o o (Numbers i n parentheses correspond t o numbers i n SPAS measure.) subscale items n=12 SPAS t o t a l items n=70 APPENDIX / 135 C . STUDENT'S PERCEPTION OP ABILITY SCALE Name. Birth Date. B o y . Girl. Grade S c h o o l .S „ E r» - 5 41 cc C £ c « 'w o ^  » C CO IU (J I M P O R T A N T DIRECTIONS FOR M A R K I N G A N S W E R S Use black soft lead pencil only. Make heavy black marks that fill the circle completely. Erase clearly any answer you wish to change. Make no stray'marks on this answer sheet. Answer each item Yes or No. RIGHT YES NO 1 © O ; YES © NO 1 o : YES o NO O W R O N G j YES NO | YES NO 1 YES NO © o s ® o : o © S E X ; MoleO i PcmnleO S T U D E N T I.O. ©©©©©©©©© ©OOOO©©©© ©©©©©©©©© ©©©©©©©©© 0 © © © © © © © © ©©©©©©©©© ©©©©©©©©© © © © © © © 0 0 © ©©©©©©©©© ©©©©©©©©© G R A D E © I © : © : © © J © ! © . BIRTH D A T E MONTH ( O Jan O July O Fel) O Aug /QMur O Sept. \ O April O Oct. O Mny O Nov 0 .;»n.: O Dec YEAR Last 2 Digits © 0 © o 0 © ©© ©© ©© ©® ©© ©© ©© SPECIAL C O O E ©©©©©©©©© ©©©©©OOOO © 0 © ® ® ® ® ® ® © © © 0 ® © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © ® ® ® ® 0 ® ® ® ® © © ® ® © ® © © ® ® ® ® ® ® ® ® ® ® S T U D E N T N A M E o o o o o o o o o o o o o o o o o o o o © © 0 0 0 Q 0 © © © © © © © © © 0 © 0 ® © © © 0 © © © © ® © © © © ® © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © ' © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © o o o o o © © © © © © © © © o o © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © ©0©©©©©©.©©©©©©©©©©©"© ©@©@©©©©©'©©'® ©'©©'©'©'©©© © © © © © © © © © © © © © © © © © © © © ©©©©'©'©'©©©©©©©©©©©© @® 0 © © © © © © © © © © © © © © © © ® ® ® © © © © © © © © © © © © © © © © © © © © ® © © © © © © ® © © © © ® © ® ® ® ® © ® © © © © ® © © ® © © ® ® © © ® © © © ® © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © ® ® © ® ® © © ® ® ® ® ® ® ® ® ® ® ® © ® 0 © © © ® © © © © © © © © © © © © © © © © © © © © © © © © © © © ® © © © © © © © C 1977 Fredorie J . Boanma and J«m«i W. Chipmin AM Rights R i f « l v « d Prinlad In U.S.A. APPENDIX / 136 DIRECTIONS This booklet has a list of statements about how you (eel about school. Some of these are true and some are not. Fill in the circle t O J below the Y E S if the statement is usually true of you. Fill in the circle COl below the NO if the statement is not usually true of you. Read each question carefully and answer every item, even if it is hard to decide which answer is most like you. Do not fill in both circles. Just fill in one circle for each statement. This is not a test so there are no right or wrong answers. Please mark exactly how you really feel inside about school. YES O NO O YES o NO o YES O oi YES o NO o YES O NO O 6. 1 usually have problems understanding what 1 read YES O NO o 7. 1 am one of the smartest kids in the class YES O NO 0 YES O NO o YES O NO o YES O NO o YES O NO o 12. My printing is perfect YES O NO o YES o NO o YES O NO o YES O NO o YES O NO o YES O NO o YES O NO o YES O NO o YES O NO O APPENDIX / 137 YES NO 21, I like to answer questions O O YES NO 22. Working with my hands is hard . . .O O YES NO 23. I like doing printing .0 O YES NO 24. I have trouble drawing pictures .O O YES NO 25. I am poor at silent reading : .O O YES NO 26. I' have problems printing neatly . . . O O YES NO 27. I am good with my times tables O O YES NO 28. I am good at drawing O O YES NO 29. When school gets tough I give up Q O YES NO 30. I like to do story problems O O YES NO 31. My friends read better than I do Q O YES NO 32. I am good at printing o o YES NO 33. I always do neat work Q O YES NO 34. I have difficulty getting my arithmetic finished on time Q O YES NO 35. I have difficulty working with numbers Q O YES NO 36. I like spelling Q Q YES NO 37. I like arithmetic O O YES NO 38. I am a messy writer . Q O YES NO 39. Tests are easy for me to take O O YES NO 40. I like to sound out words O O YES NO 41 . My teacher often makes me write my work again Q O YES NO 42. I have difficulty looking up words in the dictionary , Q O YES NO 43 . I like to use big words when I talk O O YES NO 44. I like telling my friends about school work O O YES NO 45. My teacher thinks I am dumb in arithmetic" . . Q O APPENDIX / 138 YES NO 46. I like going to school O O YES NO 47. I like playing spelling games O O YES NO 48. I have difficulty thinking up good stories O O YES NO 49. My spelling is always right . O O YES NO 50. Saying new words is hard for me o o YES NO 51. I am unhappy with how I do arithmetic Q O YES NO 52. I am a smart kid O O YES NO 53. I have difficulty doing what my teacher says o o YES NO 54. I find spelling hard O O YES NO 55. I usually get my arithmetic right o o YES NO 56. I find reading hard o o YES NO 57. I am unhappy with my printing o o YES NO 58. I am n good reader o o YES NO 59. I am slow at spelling o o YES NO 60. I am a slow reader o o YES NO 61. In school I find new things difficult to learn O O YES NO 62. I usually spell words right . O O YES NO 63. My teacher thinks I am good at printing O O YES NO 64. All new words are hard for me to understand O O YES NO 65. I have trouble telling others what I mean o o YES NO 66. I am good at arithmetic . O O YES NO 6 7. I like to tell stories in class O O YES NO 68. I feel I often snv the wrong things o o YES NO 69. I find multiplication fun . O O YES NO 70. I always got everything in arithmetic right O O APPENDIX / 139 D . STUDENT CHART 200. 100. 90-80-70-60-50-AQ. 30-20-10. 9-8-7-6-5" M T W Th F M T w Th F M T w Tn F M T w Th F S *- rn T 7»TT V T ^ P i 3 r ^ T w n » r » » NAME! PROBE # APPENDIX / 140 E . PARENT INFORMATION Dear Parent or Guardian, Thank you f o r supporting me i n t h i s academic s e l f - c o n c e p t study. I f e e l o p t i m i s t i c t h a t the study w i l l be able t o c o n t r i b u t e f u r t h e r i n f o r m a t i o n toward enabling students t o f e e l b e t t e r about themselves academically. Enclosed you w i l l f i n d three charts l a b e l e d Parent Chart. One chart has s e v e r a l notes e x p l a i n i n g how to chart and the other two are f o r your use i n c h a r t i n g . Please a f f i x one chart t o your f r i d g e or some other easy-to-see spot. On the f i r s t day of the school i n t e r v e n t i o n , Wednesday, March 2, your c h i l d w i l l b r i n g home from school the r e s u l t s from h i s or her f i r s t t i m i n g . These r e s u l t s w i l l c o n s i s t of so many c o r r e c t s and so many e r r o r s on a one-minute t i m i n g on a r i t h m e t i c f a c t s . Your c h i l d w i l l a l s o t e l l you where to pla c e the aim l i n e or number to which your c h i l d i s working toward. I t i s important that you draw t h i s l i n e across the chart as i l l u s t r a t e d on your sample c h a r t . Use a crayon or b r i g h t l y coloured pen. A l s o place c o r r e c t s and e r r o r s i n the Wednesday box at the top of the chart and on the Wednesday l i n e of the graph. Use a dot f o r c o r r e c t s and an x f o r e r r o r s . Of utmost importance to t h i s study i s t h a t you p r a i s e your c h i l d f o r d a i l y improvement. P r a i s e from parents i s the most powerful r e i n f o r c e r t h a t a c h i l d can get. When your c h i l d reaches h i s or her aim f o r a c e r t a i n worksheet number, he or she w i l l s t a r t at the next l e v e l worksheet. At t h i s time the c o r r e c t s and e r r o r s w i l l change. To show on your chart t h a t a change i n worksheet has occurred, j u s t use a d i f f e r e n t coloured pen/pencil or marker and s t a r t graphing again. Your c h i l d w i l l inform you when t h i s happens as he or she i s a l s o keeping a chart at school. I f you have any questions t h a t your c h i l d cannot answer about the study, please f e e l f r e e t o c a l l me i n the evening. Once again, I appreciate your p a r t i c i p a t i o n i n t h i s study. S i n c e r e l y , APPENDIX / 141 AIM LINE •''ScudetiC i s work-in g coward t h i s many c o r r e c t 40 d i g i c s per minuce. 30 Approximate numbers i n between p r i n c e d * numbers - eg. 45 On Sacurday and Sunday, leave blank. ^ NAME: PROBE #: APPENDIX / 142 PARENT SOCIAL VALIDATION FORM Dear Parent: The purpose of t h i s q u e s t i o n n a i r e i s t o get your response t o the three-week a r i t h m e t i c program your c h i l d has j u s t completed. Your comments and response are a v a l u a b l e source of i n f o r m a t i o n i n a ssessing the b e n e f i t s of the program. Thank you f o r your help and p a r t i c i p a t i o n . Gender of parent who charted w i t h student: M/F Gender of student: M/F Please c i r c l e the number c l o s e s t t o your f e e l i n g s on the f o l l o w -i n g statements. 1. I l i k e d knowing how my c h i l d d i d i n a r i t h m e t i c each day. (not at 1 2 3 4 5 (very a l l ) much) 2. I l i k e d c h a r t i n g my c h i l d ' s r e s u l t s on a d a i l y b a s i s . 1 2 3 4 5 3. I l i k e d being i n v o l v e d w i t h my c h i l d ' s progress. 1 2 3 4 5 4. I t h i n k t h i s program was mo t i v a t i n g f o r my c h i l d . 1 2 3 4 5 5. I found i t d i f f i c u l t to f i n d the time t o ch a r t w i t h my c h i l d 1 2 3 4 5 6. I t h i n k my c h i l d f e e l s b e t t e r about a r i t h m e t i c now. 1 2 3 4 5 A P P E N D I X / 1 4 3 H . STUDENT SOCIAL VALIDATION SCALE S c h o o l : N a m e : A g e : M a l e / F e m a l e : P l e a s e p i c k t h e f a c e t h a t b e s t d e s c r i b e s y o u r f e e l i n g s a b o u t t h e f o l l o w i n g s t a t e m e n t s . 1 . I l i k e d c h a r t i n g m y r e s u l t s i n a r i t h m e t i c e v e r y d a y . 2 . I l i k e d k n o w i n g h o w I w a s d o i n g i n a r i t h m e t i c e v e r y d a y . 3 . T h i s a r i t h m e t i c p r o g r a m m a d e m e t r y h a r d e r . 4 . I t h i n k I ' v e g o t t e n b e t t e r i n a r i t h m e t i c i n t h e l a s t 3 w e e k s . 5 . M y p a r e n t s t h i n k I ' v e g o t t e n b e t t e r i n a r i t h m e t i c i n t h e l a s t 6 . I l i k e a r i t h m e t i c m o r e n o w . 7 . I l i k e d b e i n g t i m e d i n a r i t h m e t i c . APPENDIX / 144 I . PROBES Appendix I contains a copy of a l l the probes used w i t h the P r e c i s i o n Teaching I n t e r v e n t i o n . NAME DATE COUNT: CORRECT ERROR SEE TO WRITE: Mu l t ip l i ca t ion Facts - x l 0 I 2 3 4 5 6 7 8 0 xl xl xl xl xl xl xl xl xl xl 0 1 2 3 4 5 6 7 9 0 1 2 3 5 6 7 3 9 8 2 7 5 xl xl xl xl Xl Xl xl xl xl xl xl xl xl xl 2 3 6 0 9 3 7 5 1 6 8 9 2 xl xl xl xl xl xl xl xl xl xl xl xl xl xl 5 H 8 3 6 1 2 7 9 0 3 3 5 xl xl xl xl xl xi xl xl xl xl xl xl xl xl 0 2 9 7 i\ 8 i A. 3 5 6 2 0 3 7 xl xl xl xl xl xl xl xl xl xl xl xl xl Xl 9 5 8 0 6 3 2 7 1 9 i\ 5 8 xl xl xl xl xl xl xl xl xl xl xl xl xl Xl 2 6 3 1 9 7 0 8 5 3 2 6 1 xl xl xl xl xl xl xi xl xl xl xl xl xl Xi (14) (28) (42) (56) (70) (841 APPENDIX / 146 l x ro ro l x |ro o l x ro u i l x |ro ro l x |ro o l x ro cn l x |ro u i l x ro ro ix ro x r l x |ro U J O | N J O O TO I* m Nj NJ l x to U J Ifo l x |ro x r l x |ro co l x |ro to l x ro l x ro co l x ro u i x ro cn l x |ro o l x |ro ro l x |ro U J | X rr •a cu 0\ I Nj Ui — O 3 ro to lx |ro o l x ro x r IX IX ro cn |ro to 0> |rO XT <»|NI A. r» IX l x ro -vj l x |ro cn l x |ro oo Iro l x |ro u i l x |ro u i O M In l x ro x r l x ro U J |X ro ro ro x r |x |ro cn Nj Nj OA > |X ro o l x ro ro l x |ro u i l x ro VJ l x ro va l x ro vj NJ VI >—IX C\ Nj Co l x ro co |X ro vj u i l x ro to l x |ro u i |ro oo OD|NJ vo IX IX ro u i ro |fo cn |ro o |£o |ro to |X ro U J |x ro to ro ro x r lx ro cn l x ro co o o |fo ro |ro x r £o o |i lx ro u i l x ro co |x ro ro o o TO TO l X ro cn ro u i R> vj lx ro co ro to |X ro vj TO TO o TO |fo r-" |ro oo £S u i lx ro u i l x ro ro l x ro u i NJ o 03 NJ NJ APPENDIX / 147 l x M to l x M o l x M ui l x U J ro o on m l X M cn l x l x ]uj ro IS l x |uj ui l x |uj s: ^3 IX IX IX IX IX | U J U J |og xr M uo M co |V_M cn IX IX IX IX IX |UJ i-' M co |UJ -vi |UJ U J M O IS 12. Ni UJ I* cn w KJ I* VO W Ul •a o o 3 IX IX LM l£> M O l X |UJ -E-IX IX M cn |uj i£> IS »—• r s< M Ul <b. IX M -^ i l x | U J cn l x U J oo IS i x |V-M l x M K . I X Ul U Ul l X UJ Xr l x U J U J l x UJ h-i l x UJ Ni |X UJ IS cn Co W C\ l x UJ O l x U J ro l x |UJ U J l x UJ *vj l x UJ s^l IS M l * l~ Ul VI M I X ^ w oa l x UJ 00 l x |UI IS U l l x U J UD l X |uj un IS CO •sl|Ul VO |S ui |S i-* IS cn |S o |S l x l x |UJ U J l x |UJ to l x UJ Ni IS l X U J cn |X UJ CO o o l x UJ Ni IS ft lx UJ UJ l x |UJ CO l x UJ N3 O o 73 73 |X M cn |X UJ Ul ft l x UJ oo l x UJ <x> l x UJ 73 73 o 73 l X UJ l x U J 00 UJ UJ l x |UJ Ul l x UJ Ni l x |UJ Ul NAME DATE COUNT: CORRECT ERROR SEE TO WRITE: Mul t ip l ica t ion Facts - x4 0 I 2 3 4 5 6 7 8 9 x4 x4 x4 x4 x4 x4 x4 x4 x4 0 4 8 12 16 20 24 28 32 36 0 1 2 3 4 5 6 7 8 9 x4 x4 X 4 X4 x4 xii xii xii X4 2 3 6 0 9 3 4 7 5 1 6 8 9 2 5 4 8 3 6 1 2 7 9 0 4 3 8 5 0 2 9 7 4 8 1 3 5 6 2 0 7 3 9 5 4 8 0 6 3 2 7 1 9 4 5 8 2 6 3 1 9 7 4 0 8 5 3 2 6 1 X i l x A x i i x i i x i i x i i ^ x A x i i ^ x ^ ^ x / i x ^ (48) (73) (96) (121) (144) NAME DATE COUNT: CORRECT ERROR SEE TO WRITE: M u l t i p l i c a t i o n Facts - x5 0 J 2 3 4 5 6 7 9 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 0 5 10 15 20 25 30 J5 45 0 1 2 3 5 6 7 8 9 8 2 7 5 X 5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 X5. 2 3 6 0 9 3 7 5 1 6 8 9 2 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 5 8 3 6 1 2 7 9 0 3 3 5 x5 X 5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 X 5 0 2 9 7 8 1 3 5 6 2 0 7 3 x5 x5 x5 x5 x5 X 5 x5 x5 x5 X 5 X 5 x5 x5 x5 9 5 8 0 6 3 2 7 1 9 5 8 x5 x5 x5 x5 x5 xl X 5 x5 x5 x5 K5 x5 x5 x5 2 6 3 1 9 7 0 8 5 3 2 6 1 x5 X 5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 x5 " x5 (26) (52) (78) (103) (129) (154) NAME DATE o ^ SEE TO WRITE: Mul t ip l icat ion - x0-x5 \ x 0 3 1 1 2 0 5 p X 5 x i i x l x l x 2 x 4 x 2 ss w < 4 5 5 3 0 5 1 xl x3 x4 x2 xl x5 x2 2 1 4 0 5 3 2 x3 x5 x4 x2 xl x3 x5 4 2 4 0 1 2 3 x5 x4 x2 x3 x4 xl x5 3 5 0 2 1 1 3 xl x2 x4 x2 xl Xl x4 4 1 5 0 3 5 5 x3 x2 x5 xl x2 x4 x3 COUNT: CORRECT ERROR 3 2 3 5 0 4 1 xl x5 x3 xl x2 xH x5 4 3 2 1 0 4 2 Xl x5_ xl x4_ x3_ x2 xi 3 5 0 2 1 1 3 xl x2 x4 x2 xl x3 x4 4 1 5 0 3 5 5 xl x2 x5 . xl x2 x4 x3 (18) (37) (55>. (75) 0 2 1 4 0 5 3 x5 x3 x5 x4 x2 xl x3 4 4 2 4 0 1 2 xl x5 x4 x2 x3 x4 xl (90) (109) APPENDIX / 151 l x |cn ro l x Icn tX5 l x Icn o |cn u i l x Icn ro l x Icn o ix cn cn l x Icn u i l x cn ro l x Icn Xr l x |cn U J ©I CM O O 3C 73 IX m 9l CM-IX IX Icn U J |cn xr lx |cn <JO l x Icn co l x Icn cn l x Icn ro 3 c M| ON. M — l X Icn (-• |x cn co l x Icn *vj l x |cn U J l x Icn o l x Icn U J o eg MX r* Co I ON w - i . O 3 l X Icn uo ix Icn o l x Icn xr l x cn cn l x cn co l x Icn xr M i x n A, as ^ rf in IX IX Icn *vj cn cn l x cn oo Icn U J lx Icn ui X uJX cn O 01 Ul Icn xr |X cn U J |X Icn l x Icn ro l x Icn xr l x cn cn UilX C\ Ol Ol l x Icn o l x Icn ro l x Icn U J l x Icn l x Icn »vj l x |cn M Ol VI * . X Co 01 CO |X Icn co l x Icn *vj l x Icn u i l x cn uo l x cn ui l x Icn co u,ix <k 01 vo l X Icn ui IX IX Icn cn |cn o IS x Icn uo IX IX IX IX IX IX Icn U J |cn UD |cn ro |cn xr |cn cn |cn co l x Icn ro l x Icn xr |X Icn o l x cn U J l x cn co |X Icn ro |X Icn cn l x Icn ui l x Icn lx Icn Co l x Icn IX icn -vj |X Icn l x cn co |X Icn U J l x Icn ui |X Icn ro l x Icn ui Ul M VO CS Ui VI CO Ul M M 01 NAME DATE SEE TO WRITE: Mul t ip l ica t ion Facts - x7 0 I 2 4 5 6 7 a x7 x7 x7 x7 x7 x7_ x7 x7 x7 0 7 14 2 i 35 42 49 56 0 1 2 3 5 6 7 xZ xl X7 x7 xZ X7 X7 xZ 2 3 6 0 9 3 7 x7 x7 x7 X7 x7 x7 x7 x7 5 x7 4 x7 8 x7 3 x7 6 x7 1 X 7 2 x7 7 x7 0 X 7 2 x7 9 X7 7 X 7 4 x7 8 X7 1 x7 3 X 7 9 x7 5 x7 4 x7 7 x7 8 x7 0 x7 6 x7 3 x7 COUNT: CORRECT ERROR 9 63 8 9 8 x7 xZ x7 5 1 6 x7 xZ xZ 9 0 4 x7 xZ xZ 5 6 2 xZ xZ xZ 5 2 7 x7 x7 x7 8 5 3 x7 xZ xZ 2 . 7 5 xZ xZ xZ C26J 8 9 2 xZ xZ x7 (52; 3 8 5 . xZ xZ xZ C78; 0 7 3 xZ xZ xZ 1 9 4 xZ xZ xZ ri29; 2 6 1 xZ xZ x7 C154J APPENDIX / 15 3 IcS r o ice uo |oo o |co u i |co ro |oo o | X IX IX IX IX IX loo cn loo x r |co r o |co x r |co UJ CO ©|co o o COl CO K . IX IX IX IX IX IX 2 ICO KM |00 U l |00 UO |CO 00 |00 cn 00 NJ = ON I Co M IX IX IX IX IX IX |CO H |00 CO |CO *vj |CO U J |00 O |00 U J MIX •tj n A Co U i o | X IX IX IX IX IX U i l X O |co uo |OO O loo x r |oo cn |co uo |co x r M|CO X * * | X CO IX IX IX IX IX IX ^ l 0 3 w loo *v j oo cn 00 00 CO H 00 UJ CO U l IX IX IX IX IX IX 100 Xr |C0 UJ |00 r-" |O0 rv) |CO Xr 00 cn IX IX IX IX IX IX loo o |co ro |oo UJ |co *vj |oo - v i |oo ^ co I CD cn U i l X 01 CO VI O i l * £>|Co Co IX IX IX IX IX IX CO CO loo •vj |00 U l |00 (JO |00 U l |C0 CO v i |* | X |X | X | X | X | X |oo u i |co i—• |co cn ico o oo M OO UO IX IX IX IX IX IX co U J |oo uo oo U J co x r oo cn loo oo IX IX IX IX IX IX loo ro |oo x r |co o |oo U J |oo co |co ro IX IX IX IX IX IX oo cn co u i oo ro oo oo oo uo oo ^ | X |X IX IX IX IX |oo i— 1 |co oo |oo ^ |oo u i |oo r o |oo u i K i I x VI U l M K) O Co KJ Ol VO Uj V - V * V -NAME DATE SEE TO WRITE: Multiplication Facts - x9 0 I 2 3 4 5 6 7 8 x9 x9 x9 x9 x9 x9 x9 x9 0 9 18 27 36 45 54 63 72 0 1 2 3 4 5 6 7 x9 x9 x9 X9 x9 x9 X9 X9 2 3 6 0 x9 x9 X9 x9 5 4 8 3 x9 x9 x9 x9 0 2 9 7 x9 x9 x9 x9 9 4 5 8 x9 x9 x9 x9_ 2 6 3 1 *2 xS x l 9 3 4 7 x9 x9 x9_ x9 6 1 2 7 x9 x9 x9 x9 4 8 1 3 x9 x9 x9 x9 0 6 3 2 x9 x9 x9 x9 9 7 4 0 xa X9_ COUNT: CORRECT ERROR 9 x9 82 8 X 9 5 x9 9 x9 5 x9 9 x9 1 xa 0 x9 6 x9 8 x l 6 xa 4 x9 3 x9 2 x9 8 x9 3 x9 0 x9 7 xa 9 x9 8 xa 2 x9 5 xa 2 x9 5 xa (78) 7 x9 7 1 9 xa xa xa 8 5 3 xa xa xa 4 5 8 xa xa xa (129) 2 6 1 xa xa xa (154) NAME DATE ID in SEE TO WRITE: Mult ip l icat ion Facts - xlO X H o z w p* cu < iO 10 10 10 iO IO 10 xO x± £l *5 0 10 20 30 40 50 60 10 10 10 10 10 10 10 xO x l x2 x3 XA X 5 x5 10 10 10 10 10 10 10 x l Xl x2 x l X l XO x9 10 10 10 10 10 10 10 x5 xA x8 x l xfi Xl x3 10 10 10 10 10 10 10 XO x2 x9 x7 x l X 8 x l 10 X9 10 x i i 10 X l 10 X 8 10 xO 10 xfi 10 x3 10 XlO 10 x2 10 x6 10 x3 10 x lO 10 X7 10 xA COUNT: CORRECT ERROR 10 x?_ 70 JO yg 80 10 x9_ 90 10 yJO 100 10 10 10 10 10 10 10 x7 X 8 • x9 XlO X8 X l X l 10 10 10 10 10 10 10 x l XA X 7 x l Xii X6 X 8 10 10 10 10 10 10 10 x7 x9 XO x l Xl x8 X l 10 10 10 10 10 10 10 x3 x5 x6 X3 XO X l XZ 10 10 10 10 10 10 10 X l XZ X l XS XA X l X& (28) (55) (82) (108) (135) 10 10 10 10 10 10 10 xQ x8 x5 x i x2 x5 x l (164) NAME DATE ve-i n X H O 55 W PM SEE TO WRITE: Multiplication Facts - xll 11 XO 11 X l i i 11 11 11 11 11 i l xO xl x2 x3 x4 x5 Xl) 0 11 22 33 44 55 66 11 x l 11 xii 11 x2 11 x2 11 x3 11 x3 11 xii 11 x6 11 X 5 11 xO 11 x6 11 x9 11 x l l 11 x5 11 11 x8 11 x3 11 x6 11 x l 11 xii 11 X2 11 x2 11 x l 11 xii 11 x8 11 x l 11 xlO 11 XH 11 x l l 11 x8 11 x l 11 x5 11 x6 11 11 11 11 11 11 11 X9_ xii X5 x9 x l l x3 x7 COUNT: i i i i i i i i x7 xfl x9 xlO 77 88 99 110 11 11 11 11 .XZ x l xa XlO 11 11 11 11 x3 x7 XlO x l 11 11 11 11 (10 x7 xii X l 11 11 11 11 x3 x5 X5 X l 11 11 11 11 x l x2 x l X 8 11 11 11 11 x l xlO x6 x l CORRECT ERROR i i x i i i 2 i 11 11 11 X l l X 8 xZ (29) 11 11 11 x6 x8 x l l (SB) 11 11 11 x8 x l l x l „ (89) 11 11 11 XQ XlQ XZ (US.) 11 11 11 X l xO xZ (US) 11 11 11 xZ x l x l (175) NAME DATE in X H a z w ru < SEE TO WRITE: Multiplication Facts - x l 2 1 2 Xl 1 2 x i i 12 xO 0 12 Xi 12 1 2 X 2 1 2 12 x2 24-12 x3 12 x7 12 xJ 36 1 2 x l 1 2 X l 12 x4 48 12 x l 1 2 x 2 22 x5 60 1 2 X6 1 2 x l 12 x6 72 1 2 XZ 1 2 X 1 2 1 2 x5 1 2 x3 12 x3 1 2 xlO 1 2 x9 12 xl2 12 x3 12 x7 12 x8 1 2 x l 2 12 x l l 12 xlO 12 x9 12 x8 12 X5 12 X 1 2 12 X 3 12 x i n 12 x7 12 X l 12 x3 12 x !2 12 x l 12 xO 12 x3 12 x3 12 x6 12 x2 COUNT: CORRECT ERROR 12 12 12 12 i2 i2 x7 x8 x9 xlO x i i Xi2 84 96 108 120 iJ2 144 12 12 12 12 12 12 12 X 8 x9 XlO x l l X 1 2 XO X 8 12 12 12 12 12 12 12 x9 X l X l xZ xlO X l X12 12 12 12 12 12 12 12 X l x l l X l X l X l xO X l 12 12 12 12 12 12 12 XZ X l X l X l X l X l X l 12 12 12 12 12 12 12 x9 X l X l X l X l XZ X 9 12 12 12 12 12 12 12 x4 x l l X l X l Xl2 X9 XIQ (31) (75) (106) (138) (170) (202) 

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