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The effect of the intertrial interval on the acquisition and retention of novel multiplication facts Jordan, Donald Bruce 1969

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THE EFFECT OF THE INTERTRIAL INTERVAL ON THE ACQUISITION AND RETENTION OF NOVEL MULTIPLICATION FACTS by DONALD BRUCE JORDAN B . E d . , U n i v e r s i t y o f B r i t i s h Columbia , 1967 ^ A -THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF , MASTER OF ARTS i n the Department o f E d u c a t i o n We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C o lumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada ABSTRACT The study i n v e s t i g a t e d the e f f e c t of the i n t e r t r i a l i n t e r v a l on the l e a r n i n g of n o v e l m u l t i p l i c a t i o n f a c t s by grade three s t u d e n t s . For nine c o n s e c u t i v e s c h o o l days the experimenter p l a y e d tape recorded treatments to the s t u d e n t s . A treatment c o n s i s t e d of the o r a l p r e s e n t a t i o n of a l i s t of f i f t e e n n o v e l m u l t i p l i c a t i o n problems and corresponding answers read through twice i n a random or d e r . A 3-second response i n t e r v a l was allowed between the reading of a problem and the r e a d i n g of the corresponding answer. The time i n t e r v a l between the r e a d i n g of an answer and the reading of the next problem was d e f i n e d as the i n t e r t r i a l i n t e r v a l . The sample of 210 grade three students was d i v i d e d i n t o three groups. One group had an i n t e r t r i a l i n t e r v a l of 3 seconds, the second group had an i n t e r t r i a l i n t e r v a l of 7 seconds, and the t h i r d group had an i n t e r t r i a l i n t e r v a l of 12 seconds. Fifteen n o v e l problems were determined from an item a n a l y s i s of a f o r t y - p r o b l e m p r e - t e s t a d m i n i s t e r e d before the > treatments began. A p o s t - t e s t c o n s i s t i n g of only the f ifteen n o v e l problems was a d m i n i s t e r e d immediately following the l a s t treatment. A r e t e n t i o n t e s t c o n s i s t i n g of a random order of the f i f t e e n n o v e l problems was a d m i n i s t e r e d ten days a f t e r the l a s t treatment. A c q u i s i t i o n was d e f i n e d as the d i f f e r e n c e between the p o s t - t e s t score and the p r e - t e s t n o v e l s c o r e . R e t e n t i o n was d e f i n e d as the d i f f e r e n c e between the I l l r e t e n t i o n t e s t score and the p r e - t e s t n o v e l s c o r e . A o n e - t a i l e d t t e s t was used to t e s t the s i g n i f i c a n c e o f the mean a c q u i s i t i o n score w i t h i n each group. A t w o - t a i l e d t t e s t was used to t e s t the s i g n i f i c a n c e o f the mean r e t e n t i o n score w i t h i n each group. The s i g n i f i c a n c e o f the d i f f e r e n c e i n the mean a c q u i s i -t i o n and r e t e n t i o n scores between groups was t e s t e d u s i n g a n a l y s i s o f c o v a r i a n c e and Tukey 's procedure f o r comparing ' i n d i v i d u a l means. A c q u i s i t i o n and r e t e n t i o n w i t h i n each treatment group were s i g n i f i c a n t beyond the .001 l e v e l . In both a c q u i s i t i o n and r e t e n t i o n the 7-second group and the 12-second group performed s i g n i f i c a n t l y b e t t e r (p<.001) than the 3-second group. There was no s i g n i f i c a n t d i f f e r e n c e between the 7-second group and the 12-second group i n e i t h e r a c q u i s i t i o n o r r e t e n t i o n . For the task at hand, the r e s u l t s i n d i c a t e d t h a t 7 seconds was a good a p p r o x i m a t i o n to the o p t i m a l i n t e r t r i a l i n t e r v a l . TABLE OF CONTENTS CHAPTER PAGE I THE PROBLEM 1 Background . 1 Statement o f the problem . . . . . . 2 Review o f the L i t e r a t u r e 2 S t u d i e s on l e a r n i n g motor t a s k s . . . . 3 S t u d i e s on l e a r n i n g concept i d e n t i f i c a t i o n D e f i n i t i o n s o f Terms Used . .. . .' . . 6 Statement o f the Hypotheses . . . . . . 8 I I . THE DESIGN OF THE STUDY . . . . . . . . 9 I n t r o d u c t i o n . . . . . . . . . . . . 9 F o r m a t i o n o f the Groups . . . . . . . 9 The p o p u l a t i o n . . . . . . . • ., • • 9 The sample . . . . . •> . . . ' .' 11 Assignment o f t r e a t m e n t s . . . . . . 12 Development o f M a t e r i a l s . . ; . ., . 12 The p r e - t e s t 12 The n o v e l m u l t i p l i c a t i o n f a c t s . . . . 14 The method o f s e l e c t i o n . . . . . . . 14 The d a i l y t r e a t m e n t s . . . . . . . 15 The t r e a t m e n t answer s h e e t s . . . . . 15 The p o s t - t e s t and the r e t e n t i o n t e s t . . 16 Pr o c e d u r e . . . . . . . . . 16 CHAPTER S t a t i s t i c a l A n a l y s i s . . . . D e l t l c l • • • • • • • • • S t a t i s t i c a l treatment of the dat A c q u i s i t i o n . . . . . . R e t e n t i o n I I I . ANALYSIS OF THE DATA . . . . . A n a l y s i s o f the A c q u i s i t i o n Scores A c q u i s i t i o n w i t h i n groups . A c q u i s i t i o n between groups A n a l y s i s o f the R e t e n t i o n Scores R e t e n t i o n w i t h i n groups . . R e t e n t i o n between groups I V . SUMMARY AND CONCLUSIONS . . . . Summary . . . . . . C o n c l u s i o n s . . . . . . . A c q u i s i t i o n . . . . . W i t h i n groups . . . . . . Between groups . . . . R e t e n t i o n . . . . . . . W i t h i n groups . . . Between groups . . . . C o n c l u d i n g statement . . D i s c u s s i o n . . . . . . . L i m i t a t i o n s of the Study . v i CHAPTER PAGE Problems f o r F u r t h e r Study . . . . . . 32 BIBLIOGRAPHY . . . . . . . . . . . . . 33 APPENDIX A . . . . . . . . . . . . . . 35 APPENDIX B . . . . . . . . . .. '. • • . 4 3 » ' ; ' . • . ._. . , LIST OF TABLES TABLE PAGE I . Assignment of Treatments 13 I I . The E x p e r i m e n t a l Data 44 I I I . Test of S i g n i f i c a n c e o f the Mean A c q u i s i t i o n Score f o r Each Group 22 I V . A n a l y s i s o f C o v a r i a n c e : A c q u i s i t i o n . . . 23 V . T u k e y ' s Procedure f o r Comparing the Mean A c q u i s i t i o n Scores . . . . . . . . 24 V I . Test of S i g n i f i c a n c e o f the Mean R e t e n t i o n Score f o r Each Group . . . . . . . . 25 V I I . A n a l y s i s o f C o v a r i a n c e : R e t e n t i o n . . . . 26 V I I I . T u k e y ' s Procedure f o r Comparing the Mean R e t e n t i o n Scores . . . . ... . . . . . , 27 LIST OF FIGURES FIGURE 1. The Experimental Procedure 0 9 * PAGE 10 ACKNOWLEDGEMENT The author wishes to thank the principals, teachers and students who participated in the experiment and the members of his thesis committee--Dr. E. D. MacPherson (Chairman), Dr. R. Yasui, Mr. P. Olley, and Dr. T. A. Howitz-for their cooperation and assistance. CHAPTER I THE PROBLEM I . BACKGROUND T y p i c a l experiments i n human l e a r n i n g , u s i n g a con-d i t i o n i n g method, c o n s i s t o f a s e r i e s o f t r i a l s . Each t r i a l i n c l u d e s , i n the o r d e r g i v e n , the f o l l o w i n g c r i t i c a l e v e n t s : (a) the p r e s e n t a t i o n o f a s t i m u l u s ; (b) the s u b j e c t ' s response ; and (c) the p r e s e n t a t i o n o f f e e d b a c k . * The time i n t e r v a l between the p r e s e n t a t i o n o f the s t i m u l u s and the feedback i s o f t e n c a l l e d the de lay i n t e r v a l . I n t e r v e n i n g b e f o r e the s t a r t o f the next t r i a l i s an i n t e r t r i a l i n t e r v a l , a l s o known as the post feedback i n t e r v a l . The de lay i n t e r v a l has been the most f r e q u e n t l y i n v e s t i g a t e d time v a r i a b l e i n human c o n d i t i o n i n g e x p e r i m e n t s . I t i s o n l y i n the pas t decade t h a t l e a r n i n g p s y c h o l o g i s t s have c o n s i d e r e d the p o s s i b l e s i g n i f i c a n c e o f the i n t e r t r i a l i n t e r v a l . The r e l a t i v e l y few s t u d i e s t h a t have been done suggest t h a t s u p e r i o r performance c o i n c i d e s w i t h some o p t i m a l l e n g t h i n t e r t r i a l i n t e r v a l depending on the com-p l e x i t y o f the t a s k . I f such i s the c a s e , the p o s s i b l e a p p l i c a t i o n o f the p s y c h o l o g i c a l f i n d i n g s to c lassroom ! L y l e E . Bourne J r . e t a l . , "Concept I d e n t i f i c a t i o n : The E f f e c t s o f V a r y i n g Length" and I n f o r m a t i o n a l Components o f the I n t e r t r i a l I n t e r v a l , " J o u r n a l o f E x p e r i m e n t a l  P s y c h o l o g y , 69 :624 , 1965. 2 s e t t i n g s i s o f i n t e r e s t to e d u c a t o r s . Mathemat ics , i n p a r t i c u l a r , i s one area o f e d u c a t i o n where c o n d i t i o n i n g can be an e f f e c t i v e i n s t r u c t i o n a l method f o r c e r t a i n t o p i c s . I t seems u n l i k e l y , however, t h a t genera l c o n c l u s i o n s c o n c e r n i n g the e f f e c t o f the i n t e r t r i a l i n t e r v a l can be based on the present r e s e a r c h . The a v a i l a b l e p s y c h o l o g i c a l f i n d i n g s were o b t a i n e d under r i g i d l a b o r a t o r y c o n d i t i o n s and, as a r e s u l t , have q u e s t i o n a b l e re levance to c lassroom l e a r n i n g s i t u a t i o n s . The present s tudy was undertaken i n an attempt to d i s c o v e r how v a r i o u s lengths o f the i n t e r t r i a l i n t e r v a l a f f e c t the a c q u i s i t i o n and r e t e n t i o n o f u n f a m i l i a r a r i t h m e t i c m a t e r i a l i n t y p i c a l e lementary s c h o o l c l a s s r o o m s . Statement o f the problem Are there s i g n i f i c a n t d i f f e r e n c e s i n the a c q u i s i t i o n and r e t e n t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between groups o f t h i r d grade s tudents dependent on i n t e r t r i a l i n t e r v a l s o f 3 seconds , 7 seconds , and 12 seconds? I I . REVIEW OF THE LITERATURE The f o l l o w i n g rev iew o f the l i t e r a t u r e summarizes the r e s e a r c h t h a t i s p e r t i n e n t to the problem at hand. These s t u d i e s are concerned o n l y w i t h the a c q u i s i t i o n o f new i n f o r m a t i o n . No s t u d i e s were found on the e f f e c t o f the i n t e r t r i a l i n t e r v a l on the r e t e n t i o n o f knowledge. I t s h o u l d be p o i n t e d out t h a t the p s y c h o l o g i c a l s t u d i e s d e s c r i b e d i n the rev iew o f the l i t e r a t u r e used a d i f f e r e n t d e f i n i t i o n o f the d e l a y i n t e r v a l than t h a t g i v e n on page 1. In these s t u d i e s the feedback depended on the s u b j e c t ' s response. For t h i s reason the experimenters found i t more convenient to d e f i n e the delay i n t e r v a l as the time i n t e r v a l between response and feedback. In the p r e s e n t study the feedback depended on the s t i m u l u s and the delay i n t e r v a l was d e f i n e d as the time i n t e r v a l between s t i m u l u s and feedback (which i s the page 1 d e f i n i t i o n ) . The i n c o n s i s t e n c y o f t h i s d e f i n i t i o n may decrease the extent to which the r e s u l t s o f these p s y c h o l o g i c a l s t u d i e s are r e l e v a n t to the p r e s e n t study. S t u d i e s on l e a r n i n g motor tasks B i l o d e a u and B i l o d e a u ^ used a task t h a t r e q u i r e d s u b j e c t s to attempt to cause a 34° displacement of a v e r t i c a l l y suspended l e v e r . The s u b j e c t s d i d not know th a t they were supposed to e f f e c t a 34° displacement but a f t e r each response they were t o l d the a l g e b r a i c d i f f e r e n c e b e t -ween the displacement they had made and the displacement they were t r y i n g to o b t a i n . Working w i t h 300 n a t i v e males, B i l o d e a u and B i l o d e a u found no s i g n i f i c a n t d i f f e r e n c e s when they h e l d the delay i n t e r v a l constant at 5 seconds and used i n t e r t r i a l i n t e r v a l s of 15 seconds, 115 seconds and 1 hour. The r e s u l t s o f a l i n e drawing experiment conducted zEdward A. B i l o d e a u and Ina McD. B i l o d e a u , " V a r i a t i o n o f Temporal I n t e r v a l s Among C r i t i c a l Events i n F i v e S t u d i e s o f Knowledge o f R e s u l t s , " J o u r n a l o f Experimental Psychology, 55:606-07, 1958. by Denny e_t al_. showed t h a t a longer i n t e r t r i a l i n t e r v a l r e t a r d e d l e a r n i n g . The l e a r n i n g c r i t e r i o n f o r f o r t y - e i g h t c o l l e g e s tudents was drawing f i v e consecut ive l i n e s b e t -ween 2 3/4 inches and 3 1/4 inches or a maximum o f s i x t y t r i a l s . Immediate feedback was g iven to each o f two groups which had i n t e r t r i a l i n t e r v a l s of 10 seconds and 30 seconds r e s p e c t i v e l y . S i g n i f i c a n t l y b e t t e r performance was a t t a i n e d by the 10 second i n t e r t r i a l i n t e r v a l group. Weinberg , Guy and Tupper* h y p o t h e s i z e d t h a t i n c r e a s e s i n the i n t e r t r i a l i n t e r v a l would improve performance up to some optimum beyond which decremental e f f e c t s would o c c u r . The task they used r e q u i r e d f o r t y b l i n d f o l d e d psychology s tudents to p u l l a y a r d s t i c k ten inches out o f a s h e a t h . Immediately a f t e r a s u b j e c t made a response he was t o l d a number (feedback) which i n d i c a t e d the ex tent of e r r o r , above or below ten i n c h e s , i n u n i d e n t i f i e d u n i t s . Before the next t r i a l there o c c u r r e d one o f the f o l l o w i n g i n t e r t r i a l i n t e r v a l s 1 second, 5 seconds , 10 seconds , 20 seconds. The o n l y n o t a b l e r e s u l t was that the 1-second group produced s i g n i f i c a n t l y p o o r e r performance than the o t h e r three groups . Weinberg, Guy and Tupper recommended t h a t f u r t h e r s tudy s h o u l d be done 3M. Ray Denny et a l . , "Supplementary Repor t : Delay o f Knowledge o f Results,"""Knowledge o f Task , and I n t e r t r i a l I n t e r v a l , " J o u r n a l o f E x p e r i m e n t a l P s y c h o l o g y , 60 :327, 1960. 4 D o r t h e R. Weinberg , D . E . Guy, and R.W. Tupper , "Supplementary R e p o r t : V a r i a t i o n o f Ppst feedback I n t e r v a l i n Simple Motor L e a r n i n g , " J o u r n a l o f E x p e r i m e n t a l P s y c h o l o g y , 67 :98 -99 , 1964. i n the a r e a o f concept i d e n t i f i c a t i o n u s i n g a b r o a d range o f i n t e r t r i a l i n t e r v a l s . S t u d i e s on l e a r n i n g c oncept i d e n t i f i c a t i o n t a s k s Bourne and Bunderson 1* had 216 c o l l e g e s t u d e n t s c l a s s i f y g e o m e t r i c a l d e s i g n s under d e l a y i n t e r v a l s o f 0, 4, o r 8 s e c o n d s , i n t e r t r i a l i n t e r v a l s o f 1, 5, o r 9 s e c o n d s , and two l e v e l s o f t a s k c o m p l e x i t y . Each d e l a y i n t e r v a l was p a i r e d w i t h each i n t e r t r i a l i n t e r v a l and t h e s e c o m b i n a t i o n s a l o n g w i t h the two l e v e l s o f t a s k c o m p l e x i t y y i e l d e d e i g h t e e n d i f f e r e n t groups. The r e s u l t s i n d i c a t e d t h a t performance improved l i n e a r l y w i t h i n c r e a s e s i n the i n t e r t r i a l i n t e r v a l and t h a t i n c r e a s e i n the i n t e r t r i a l i n t e r v a l was more f a c i l i t a t i v e i n the t a s k o f g r e a t e r c o m p l e x i t y . Bourne e t a l . 6 e x p l o r e d a more e x t e n s i v e range o f i n t e r t r i a l i n t e r v a l s t h a n used i n p r e v i o u s s t u d i e s . They used the same two l e v e l t a s k as Bourne and Bunderson, but w i t h i n t e r t r i a l i n t e r v a l s o f 1 se c o n d , 9 s e c o n d s , 17 s e c o n d s , and 25 seconds and d e l a y i n t e r v a l s t h a t were e i t h e r s e l f - d e t e r -mined o r 5 seconds. They found t h a t a moderate i n c r e a s e i n the l e n g t h o f the i n t e r t r i a l i n t e r v a l ( t o 9 seconds f o r t h e l e s s complex t a s k and t o 17 seconds f o r the more complex t a s k ) p r o d u c e d s i g n i f i c a n t improvement i n o v e r a l l p e r f o r m a n c e . ^ L y l e E. Bourne J r . and V i c t o r C. Bunderson, " E f f e c t s o f D e l a y o f I n f o r m a t i o n Feedback and Length o f P o s t f e e d b a c k I n t e r v a l on Concept I d e n t i f i c a t i o n , " J o u r n a l o f E x p e r i m e n t a l  P s y c h o l o g y , 65:1-5, 1963. 6 L y l e E . Bourne J r . - et a l . , l o c . c i t . 6 I I I . DEFINITIONS OF TERMS USED The f o l l o w i n g d e f i n i t i o n s were used i n t h i s study: (a) m u l t i p l i c a t i o n problem or problem: a statement o f the form axb, where a and b are n a t u r a l numbers between 1 and (b) m u l t i p l i c a t i o n f a c t or f a c t : a statement of the form D axb = c, where c i s a n a t u r a l number between 1 and 100, and a and b are r e s t r i c t e d as above: (c) response: an answer to a problem (c above). A response i s e i t h e r c o r r e c t or i n c o r r e c t ; \ (d) feedback: a m u l t i p l i c a t i o n f a c t read by the experimenter; (e) response i n t e r v a l : the time i n t e r v a l between the comple-\ t i o n of a reading of a problem by the experimenter and feed-back. The response i n t e r v a l was kept constant at 3 seconds; \ ( f ) i n t e r t r i a l i n t e r v a l : the time i n t e r v a l between the completion o f feedback and the p r e s e n t a t i o n of the next problem. The i n t e r t r i a l i n t e r v a l was e i t h e r 3 seconds, 7 seconds, or 12 seconds; (g) p r e - t e s t : a t e s t c o n s i s t i n g of f o r t y s e l e c t e d m u l t i p l i c a -t i o n problems. The experimenter made t h i s s e l e c t i o n a f t e r o i n s p e c t i n g the d i f f i c u l t y i n d i c e s i n the study by Rogers . 'Wil l i a m Todd Rogers, "The E f f e c t of Delay of Knowledge of Results on the A c q u i s i t i o n and Retention o f Novel M u l t i p l i -c a t i o n F a c t s " (Unpublished Master's t h e s i s , The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver, 1967), p.11. 8 I b i d . 9 I b i d . , p.56. The n i n e t e e n most d i f f i c u l t problems used i n t h i s study were s e l e c t e d w i t h the e x p e c t a t i o n t h a t about f i f t e e n o f them would be s u i t a b l e n o v e l problems f o r use i n the present study. An a d d i t i o n a l twenty-one problems, having products l e s s than or equal to 36, were a r b i t r a r i l y s e l e c t e d to complete the p r e -t e s t and to measure the s t u d e n t s ' knowledge o f m u l t i p l i c a t i o n f a c t s ; (h) n o v e l m u l t i p l i c a t i o n f a c t or n o v e l f a c t : a m u l t i p l i c a t i o n f a c t h a v ing a d i f f i c u l t y index o f l e s s than .05 on the pre-t e s t . A n o v e l problem i s l o g i c a l l y a s s o c i a t e d w i t h each n o v e l f a c t ; ( i ) p r e - t e s t n o v e l s c o r e : f o r each stu d e n t , the number o f c o r r e c t responses, on the p r e - t e s t , to o n l y the n o v e l problems ( j ) p r e - t e s t non-novel s c o r e : f o r each s t u d e n t , the number of c o r r e c t responses, on the p r e - t e s t , to o n l y the non-novel problems; (k) p o s t - t e s t : a t e s t c o n s i s t i n g o f the f i f t e e n n o v e l m u l t i -p l i c a t i o n problems; (1) r e t e n t i o n t e s t : a t e s t c o n s i s t i n g o f the f i f t e e n n o v e l m u l t i p l i c a t i o n problems; (m) a c q u i s i t i o n : f o r each s t u d e n t , the d i f f e r e n c e between the p o s t - t e s t score and the p r e - t e s t n o v e l s c o r e ; (n) r e t e n t i o n : f o r each s t u d e n t , the d i f f e r e n c e between the r e t e n t i o n t e s t s c o r e and the p r e - t e s t n o v e l s c o r e ; (o) 3-second group: the t h i r d grade students having an i n t e r -t r i a l i n t e r v a l o f 3 seconds; 8 (p) 7-second group: the t h i r d grade s t u d e n t s h a v i n g an i n t e r -t r i a l i n t e r v a l o f 7 seconds; (q) 12-second group: the t h i r d grade s t u d e n t s h a v i n g an i n t e r -t r i a l i n t e r v a l o f 12 sec o n d s . IV. STATEMENT OF THE HYPOTHESES A. A c q u i s i t i o n HI. There i s no s i g n i f i c a n t d i f f e r e n c e i n the a c q u i s i t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between groups o f t h i r d grade s t u d e n t s dependent on i n t e r t r i a l i n t e r v a l s o f 3 s e c o n d s , 7 \ s e c o n d s , and 12 seconds. W i t h r e s p e c t t o a c q u i s i t i o n , t he e x p e r i m e n t e r ' s e x p e c t a t i o n was t h a t t h e 7-second group and t h e 12-second group w o u l d p e r f o r m s i g n i f i c a n t l y b e t t e r t h a n the 3-second group and t h a t t h e r e would be no s i g n i f i c a n t d i f f e r e n c e between the 7-second group and the 12-second group. B. R e t e n t i o n H2. There i s no s i g n i f i c a n t d i f f e r e n c e i n the r e t e n t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between groups o f t h i r d grade s t u d e n t s dependent on i n t e r t r i a l i n t e r v a l s o f 3 s e c o n d s , 7 s e c o n d s , and 12 sec o n d s . CHAPTER I I THE DESIGN OF THE STUDY I. INTRODUCTION A c o n d i t i o n i n g method was used to teach f i f t e e n novel m u l t i p l i c a t i o n f a c t s to three groups o f grade three students. The treatment method f o r each group v a r i e d only w i t h respect to the leng t h o f the i n t e r t r i a l i n t e r v a l . The three d i f f e r e n t lengths were 3 seconds, 7 seconds and 12 seconds. Twelve school days were r e q u i r e d to o b t a i n the data o f the experiment. The f i r s t two days were used to p r e - t e s t the students and to f a m i l i a r i z e them w i t h the treatment method. The treatments were given on nine consecutive school days, s t a r t i n g on the t h i r d day and ending on the eleventh day. On the eleventh day, a f t e r the l a s t treatment, a p o s t - t e s t was administered i n order to o b t a i n a measure o f a c q u i s i t i o n . On the t w e l f t h day, ten calendar days a f t e r the eleventh day, a r e t e n t i o n t e s t was administered. The experimental procedure i s summarized by Figure 1. The mean a c q u i s i t i o n and r e t e n t i o n scores f o r each group were compared using a n a l y s i s of covariance and Tukey's procedure f o r comparing i n d i v i d u a l means. I I . FORMATION OF THE GROUPS The p o p u l a t i o n Previous s t u d i e s i n d i c a t e d t h a t a p o p u l a t i o n o f t h i r d FIGURE I THE EXPERIMENTAL PROCEDURE Day 1 PRE-TEST Day 2 ORIENTATION 3 CALENDAR DAYS Day 3 STUDY SHEETS AND TREATMENT Day 4 TREATMENT Day 5 TREATMENT Day 6 TREATMENT Day 7 TREATMENT 3 CALENDAR DAYS Day 8 TREATMENT Day 9 TREATMENT Day 10 TREATMENT Day 11 TREATMENT AND POST-TEST 10 CALENDAR DAYS Day 12 RETENTION TEST grade students would be s u i t a b l e f o r the present study. Rogers*** and P r e k e g e s H both found that i t was p o s s i b l e to o b t a i n m u l t i p l i c a t i o n problems, having products l e s s than 100, that were completely u n f a m i l i a r to a great m a j o r i t y of grade three s t u d e n t s . Using c o n d i t i o n i n g methods s i m i l a r to the p r e s e n t one, they a l s o found t h a t grade three students c o u l d l e a r n a s i g n i f i c a n t number of the n o v e l problems. At the time of t h i s study the grade three c u r r i c u l u m c o n t i n u e ^ t o be r e s t r i c t e d , i n the area o f m u l t i p l i c a t i o n , t o those problems having products l e s s than or equal to 36. I t was b e l i e v e d , t h e r e f o r e , that i t would be p o s s i b l e to o b t a i n a s u i t a b l e number of n o v e l m u l t i p l i c a t i o n problems and t h a t these problems would be a p p r o p r i a t e m a t e r i a l , a t the grade three l e v e l , t o be used i n the i n v e s t i g a t i o n o f a c o n d i t i o n -i n g method o f l e a r n i n g . The sample The sample c o n s i s t e d o f n i n e c l a s s e s of heterogeneously grouped grade three s t u d e n t s . Three elementary schools i n the lower mainland of B r i t i s h Columbia each c o n t r i b u t e d three grade three c l a s s e s . The s c h o o l s were t y p i c a l o f those found i n a l a r g e m e t r o p o l i t a n area. A l l three s c h o o l s were about the same s i z e (between f i f t e e n and twenty-one classrooms; 1 0 W i l l i a m Todd Rogers, "The E f f e c t of Delay o f Knowledge of R e s u l t s on the A c q u i s i t i o n and R e t e n t i o n o f Novel M u l t i p l i -c a t i o n F a c t s " (Unpublished Master's t h e s i s , The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver, 1967). ^D.P. Prekeges, "The E f f e c t of Reinforcement on Learn-i n g of the M u l t i p l i c a t i o n F a c t s " (Unpublished study, The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver, 1968). 12 grades one t o seven) and a l l p r o v i d e d s i m i l a r e d u c a t i o n a l environments. A student was omitted from the study i f he was absent f o r more than one treatment or i f he was absent f o r the pr e -t e s t , the p o s t - t e s t or the r e t e n t i o n t e s t . A t o t a l o f 210 s t u d e n t s , o f mean mental age 115.3 months, were used to o b t a i n the f i n a l s e t of data. Assignment o f treatments The treatments were a s s i g n e d to the c l a s s e s such t h a t no treatment was d u p l i c a t e d i n any one s c h o o l and the treatments were d i s t r i b u t e d evenly throughout the day. A t a b l e o f random numbers 1^ was used to a s s i g n treatments t o the f i r s t s c h o o l and then the treatments were a s s i g n e d t o the second and t h i r d s c h o o l s i n a manner t h a t p r o v i d e d an even d i s t r i b u t i o n w i t h r e s p e c t to the time o f day. At the s t a r t o f the experiment there were approximately the same number o f students i n each c l a s s . Table I p r o v i d e s a summary o f the assignment o f treatments. I I I . DEVELOPMENT OF MATERIALS The p r e - t e s t The p r e - t e s t c o n s i s t e d o f f o r t y s e l e c t e d m u l t i p l i -c a t i o n problems. I t was a d m i n i s t e r e d o r a l l y to a l l nine 12A M i l l i o n Random D i g i t s With 100,000 Normal Deviates ( c o p y r i g h t 1955 by The Rand C o r p o r a t i o n . I l l i n o i s : the Free Press of G l e n c o e ) , c i t e d by F r e d e r i c k M o s t e l l e r , Robert E.K. Rourke, and George B. Thomas J r . , P r o b a b i l i t y and S t a t i s t i c s (Reading: Addison - Wesley P u b l i s h i n g Company, Inc., 1961J, p. 366. TABLE I ASSIGNMENT OF TREATMENTS School C l a s s Number o f Students Treatment (Length o f I n t e r t r i a l I n t e r v a l ) Time A 1 25 7 Seconds 9:05- 9:20 A 2 25 3 Seconds 9:25- 9:35 A 3 22 12 Seconds 9:40-10:00 B 4 26 3 Seconds 10:45-10:55 B 5 25 12 Seconds 11:00-11:20 B 6 24 7 Seconds 11:25-11:40 C 7 20 12 Seconds 1:05- 1:25 C 8 22 7 Seconds 1:30- 1:45 C 9 21 3 Seconds 1:55- 2:05 14 c l a s s e s on the f i r s t day o f the experiment. Twenty-one o f the problems had products equal to o r l e s s than 36 and n i n e t e e n problems had products g r e a t e r than 36 and l e s s than 100. A t a b l e o f random numbers was used to randomize the o r d e r o f the problems. A tape r e c o r d e r was used i n the o r a l p r e s e n t a t i o n o f the p r e - t e s t i n o r d e r to ensure the same q u a l i t y o f p r e s e n t a -t i o n to a l l c l a s s e s . The problems were read w i t h a 3-second response i n t e r v a l between problems. An a s s i s t a n t u s i n g a stop watch h e l p e d the experimenter prepare the tape. A hand s i g n a l was given to the experimenter to i n d i c a t e the c o r r e c t l e n g t h o f the i n t e r v a l . With p r a c t i c e i t was p o s s i b l e to o b t a i n a c c u r a t e 3-second i n t e r v a l s . The f o l l o w i n g i s a w r i t t e n d e s c r i p t i o n o f the p r e -t e s t : " I s everybody ready? number 1, 8x5 equals number 2, 7x8 equals number 3, 3x7 equals ... number 40, 4x6 equals t h a t ' s a l l , w i l l you p l e a s e put your p e n c i l s down." Each student was p r o v i d e d w i t h an answer sheet f o r r e c o r d i n g h i s responses to the problems on the p r e - t e s t . Copies o f the p r e - t e s t and answer sheet are c o n t a i n e d i n Appendix A. The n o v e l m u l t i p l i c a t i o n f a c t s The method o f s e l e c t i o n . A f t e r the p r e - t e s t was a d m i n i s t e r e d , i n d i c e s o f d i f f i c u l t y were found f o r each o f the f o r t y problems. I f a problem had a d i f f i c u l t y index o f l e s s than .05 i t was d e f i n e d to be a novel problem. F i f t e e n such problems were found. The n o v e l problems and d i f f i c u l t y i n d i c e s are i n c l u d e d i n Appendix A. The d a i l y treatments. Each day f o r nine c o n s e c u t i v e s c h o o l days a treatment was given to each c l a s s . A treatment s t a r t e d w i t h a r e a d i n g o f a problem, f o l l o w e d by: a 3-second response i n t e r v a l , a r e a d i n g o f the c o r r e s p o n d i n g f a c t , the a p p r o p r i a t e i n t e r t r i a l i n t e r v a l , and a r e a d i n g o f the next problem. T h i s procedure was continued u n t i l the l i s t o f f i f t e e n problems and feedback was read through t w i c e . As an example, the treatment f o r Day 3 was as f o l l o w s : " I s everybody ready? number 1, 7x8 equals 7x8 equals 56 number 2, 6x7 equals 6x7 equals 42 number 3, 9x9 equals 9x9 equals 81 number 30, 8x6 equals 8x6 equals 48 t h a t ' s a l l , w i l l you p l e a s e put your p e n c i l s down." The response i n t e r v a l was always 3 seconds and the i n t e r t r i a l i n t e r v a l was e i t h e r 3 seconds, 7 seconds, o r 12 seconds. The treatment answer sh e e t s . The students were p r o v i d e d d a i l y w i t h answer sheets to r e c o r d t h e i r responses to the treatments. Every answer sheet c o n t a i n e d t h i r t y boxes ( r e c t a n g l e s ) numbered from 1 to 30, and the boxes were 1 3 T h e d i f f i c u l t y index o f a t e s t item i s equal to the ^ t o t a l number o f c o r r e c t responses to t h a t item d i v i d e d by the t o t a l number o f students who wrote the t e s t . 16 d i v i d e d i n h a l f . Each s tudent was i n s t r u c t e d to w r i t e the answer to a problem i n the f i r s t h a l f o f the box and to then l i s t e n f o r the tape to g ive the c o r r e c t answer. I f h i s answer was c o r r e c t he was not r e q u i r e d to do a n y t h i n g but w a i t f o r the next prob lem. I f h i s answer was i n c o r r e c t , or i f he d i d not w r i t e down an answer, he was to w r i t e the c o r r e c t answer i n the second h a l f o f the box . L i s t s of the treatments and a copy o f a treatment answer sheet are i n c l u d e d i n Appendix A . The p o s t - t e s t and the r e t e n t i o n t e s t The p o s t - t e s t and the r e t e n t i o n t e s t each c o n s i s t e d o f a randomized o r a l p r e s e n t a t i o n o f the f i f t e e n n o v e l m u l t i p l i c a t i o n problems . A 3-second response i n t e r v a l was a l l o w e d between problems. The tapes f o r the p o s t - t e s t and the r e t e n t i o n t e s t were made i n the same way as the tape f o r the p r e - t e s t . The p o s t - t e s t was a d m i n i s t e r e d on Day 11 immediate ly a f t e r the l a s t t rea tment . The r e t e n t i o n t e s t was a d m i n i s t e r e d on Day 12, ten c a l e n d a r days a f t e r Day 11. Copies o f the p o s t - t e s t , the r e t e n t i o n t e s t , and the c o r r e s p o n d i n g answer sheet are p r o v i d e d i n Appendix A . I V . PROCEDURE The exper imenter met w i t h the p a r t i c i p a t i n g p r i n c i p a l s and teachers one week before the s tudy began. At t h a t time the nature o f the experiment was d i s c u s s e d and a p p r o p r i a t e 17 t imes were scheduled f o r the exper imenter to v i s i t each c l a s s r o o m . A l s o , the teachers were requested to remove from t h e i r c lassrooms a l l v i s u a l a i d s p e r t a i n i n g to m u l t i -p l i c a t i o n and t o r e f r a i n from t e a c h i n g m u l t i p l i c a t i o n f o r the d u r a t i o n o f the exper iment . On Day 1 (Wednesday), a f t e r b e i n g i n t r o d u c e d to each c l a s s , the exper imenter e x p l a i n e d t h a t he was t r y i n g to f i n d out how grade three s tudents l e a r n m u l t i p l i c a t i o n . The s tudents were then t o l d that they were going to be asked some m u l t i p l i c a t i o n q u e s t i o n s . They were t o l d to do t h e i r bes t but i t was emphasized t h a t some o f the q u e s t i o n s were / d i f f i c u l t f o r grade threes to do and they wer,e not to worry about not b e i n g able to answer a l l o f the q u e s t i o n s c o r r e c t l y . They were a l s o t o l d t h a t the exper imenter was not going to t e l l anyone, i n c l u d i n g t h e i r t e a c h e r , what scores they made on the t e s t . Answer sheets were then handed out and the tape of the p r e - t e s t was p l a y e d . The next day (Day 2 , Thursday) each c l a s s r e c e i v e d i n s t r u c t i o n s and p r a c t i c e i n the use of the treatment answer s h e e t s . Each s tudent was g iven a p r a c t i s e answer sheet to r e c o r d h i s responses to ten s i m p l e a d d i t i o n q u e s t i o n s . The s tudents were t o l d t h a t i t was c h e a t i n g to r e c o r d an answer i n the f i r s t h a l f o f the box a f t e r the tape had t o l d them what the c o r r e c t answer was. On Day 3 , the f o l l o w i n g Monday, the treatments began. Each s tudent was g i v e n f i v e minutes to s tudy a l i s t o f the f i f t e e n n o v e l m u l t i p l i c a t i o n f a c t s . The study sheets were 18 then c o l l e c t e d and the treatment answer sheets were handed o u t . The exper imenter reminded the s tudents how the answer sheets were to be u s e d . They were a l s o reminded not to worry about b e i n g unable to answer a l l the q u e s t i o n s c o r r e c t l y but o n l y to do the bes t t h a t they c o u l d . Each c l a s s then r e c e i v e d the Day 3 treatment tape w i t h the a p p r o p r i a t e i n t e r -t r i a l i n t e r v a l . For the next e i g h t c o n s e c u t i v e s c h o o l days the t r e a t -ments were c o n t i n u e d . The s tudy s h e e t s , however, were o n l y used on Day 3 and were not used on Days 4 through 11 . A three day h o l i d a y weekend o c c u r r e d between Day 7 and Day 8. On Day 11 ( F r i d a y ) , immediate ly f o l l o w i n g the l a s t t r e a t m e n t , the p o s t - t e s t was a d m i n i s t e r e d . A f t e r the t e s t was completed , the exper imenter t o l d the s tudents t h a t he would r e t u r n some time a f t e r the next week. The s tudents d i d not q u e s t i o n the purpose o f the f u t u r e v i s i t and no f u r t h e r i n f o r m a t i o n was g iven to them. The r e t e n t i o n t e s t was a d m i n i s t e r e d on Day 12 (Monday). Two weekends and f i v e s c h o o l days i n t e r v e n e d Day 11 and Day 12. Before the tape was p l a y e d the s tudents were t o l d t h a t they were b e i n g t e s t e d to see how many answers they c o u l d remember from the treatment p e r i o d . V . STATISTICAL ANALYSIS Data For each s t u d e n t , mental age i n months was determined from h i s I * Q . score and h i s c h r o n o l o g i c a l age as o f May 1, 1969. 19 Two scores were o b t a i n e d from the p r e - t e s t . One score (out o f 15) corresponded to the number o f c o r r e c t responses to the n o v e l problems and a second score (out o f 25) corresponded to the number o f c o r r e c t responses to the n o n - n o v e l problems . The p o s t - t e s t and the r e t e n t i o n t e s t each c o n t r i b u t e d a score (out o f 15) c o r r e s p o n d i n g to the t o t a l number o f c o r r e c t responses . For each s t u d e n t , a score (out o f 30) on each o f the n i n e t reatments was a l s o o b t a i n e d . T h i s score was an i n d i c a t i o n o f how many c o r r e c t responses were made to the treatment problems before feedback was g i v e n . In o ther words , t h i s score was the number o f boxes t h a t had a c o r r e c t response i n the f i r s t h a l f o f the box and a b lank space i n the second h a l f o f the box . S ince some c h e a t i n g o c c u r r e d i n a l l c l a s s e s the treatment scores c o u l d not be c o n s i d e r e d c o m p l e t e l y a c c u r a t e . Table I I i n Appendix B l i s t s the e x p e r i m e n t a l d a t a . S t a t i s t i c a l t reatment o f the da ta A c q u i s i t i o n . An a c q u i s i t i o n score f o r each s tudent j was d e f i n e d as the d i f f e r e n c e between the p o s t - t e s t score and the p r e - t e s t n o v e l s c o r e . The maximum and minimum p o s s i b l e a c q u i s i t i o n scores were 15 and -15 r e s p e c t i v e l y . A c q u i s i t i o n w i t h i n groups was t e s t e d by u s i n g a one-t a i l e d t t e s t f o r c o r r e l a t e d samples to e v a l u a t e the s i g n i f i -cance o f the mean a c q u i s i t i o n score f o r each group. The s i g n i f i c a n c e of the d i f f e r e n c e s i n mean a c q u i s i t i o n 20 scores between the groups was determined by a n a l y s i s o f c o v a r i a n c e . The c o v a r i a t e s were mental age i n months and p r e - t e s t n o n - n o v e l s c o r e . I f the F va lue showed 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 among the three means, T u k e y ' s p r o c e d u r e * 4 f o r comparing i n d i v i d u a l means was u s e d . T h i s method i n v o l v e d a r r a n g i n g the a d j u s t e d means i n o r d e r o f magnitude and check ing to see i f there was a s i g n i f i c a n t gap between ad jacent means. A t the 5 per cent l e v e l o f s i g n i f i c a n c e T u k e y ' s procedure i n v o l v e d the use o f the f o l l o w i n g f o r m u l a : S i g n i f i c a n t gap » ( t > 0 5 ) ( >/?) (s^) Where > t Q 5 » The t a b l e d va lue o f t a t the 5 per cent l e v e l f o r the degrees o f f r e e -dom a s s o c i a t e d w i t h the mean square w i t h i n groups . s% « The s t a n d a r d e r r o r o f the mean. Any d i f f e r e n c e between ad jacent means, arranged i n o r d e r o f magnitude, t h a t was equal to or g r e a t e r than the v a l u e o b t a i n e d from the f o r m u l a would be s i g n i f i c a n t at the 5 per cent l e v e l . Of c o u r s e , va lues f o r the s i g n i f i c a n t gap c o u l d be o b t a i n e d to correspond to v a r i o u s l e v e l s o f s i g n i f i c a n c e . R e t e n t i o n . A r e t e n t i o n score f o r each s tudent was d e f i n e d as the d i f f e r e n c e between h i s r e t e n t i o n t e s t score 1 4 A l l e n L . Edwards, S t a t i s t i c a l Methods f o r the B e h a v i o r a l Sc iences (New Y o r k : H o l t , R i n e h a r t and W i n s t o n , 1 9 6 4 ) , p p . 3 3 0 - 3 2 . 21 and h i s p r e - t e s t n o v e l s c o r e . R e t e n t i o n scores c o u l d p o s s i b l y range from -15 to 15. The data on r e t e n t i o n was given the same s t a t i s t i c a l treatment as the a c q u i s i t i o n data w i t h one e x c e p t i o n . A two t a i l e d t t e s t was used i n s t e a d o f a o n e - t a i l e d t t e s t i n determ i n i n g the s i g n i f i c a n c e o f the mean r e t e n t i o n s c o r e s w i t h i n groups. The a c q u i s i t i o n and r e t e n t i o n s c o r e s f o r each student are i n c l u d e d i n Appendix B, Tab l e I I . CHAPTER I I I ANALYSIS OF THE DATA I. ANALYSIS OF THE ACQUISITION SCORES A c q u i s i t i o n w i t h i n groups An a c q u i s i t i o n s c o r e f o r each student was d e f i n e d as the d i f f e r e n c e between the p o s t - t e s t score and the p r e - t e s t n o v e l s c o r e . Table I I I summarizes the o n e - t a i l e d t t e s t o f the s i g n i f i c a n c e o f the mean a c q u i s i t i o n score f o r each t r e a t -ment group. TABLE I I I TEST OF SIGNIFICANCE OF THE MEAN ACQUISITION SCORE FOR EACH GROUP Mean Treatment A c q u i s i t i o n Group Score t 3-Second Group 4.653 9.86 7-Second Group 5.944 12.71 12-Second Group 6.448 13.03 The c r i t i c a l v a lue o f t at the .0005 l e v e l was 3.45. Since the t value f o r each group exceeded 3.45, i t was con-c l u d e d t h a t the a c q u i s i t i o n w i t h i n each group was s t a t i s t i c a l l y s i g n i f i c a n t . A c q u i s i t i o n between groups A n a l y s i s of covariance was used to t e s t the s i g n i f i -cance of the d i f f e r e n c e s i n the mean a c q u i s i t i o n scores between the three treatment groups. The c o v a r i a t e s were mental age i n months and p r e - t e s t non-novel score. Table IV presents a summary of the a n a l y s i s of covariance. TABLE IV ANALYSIS OF COVARIANCE: ACQUISITION Source of Sum of Mean V a r i a t i o n df Squares Square F Group 2 333.54 166.77 14.03 E r r o r 205 2436.6 11.886 The obtained F v a l u e , 14.03, was greater than 4.71, the c r i t i c a l value at the one per cent l e v e l of s i g n i f i c a n c e . Since the F value was s i g n i f i c a n t , Tukey's procedure was used to compare the i n d i v i d u a l means. This t e s t i s summarized i n Table V. / The d i f f e r e n c e between the mean a c q u i s i t i o n score of the 7-second group and the mean a c q u i s i t i o n score of the 3-second group was greater than the value of the s i g n i f i c a n t gap c a l c u l a t e d at the .001 l e v e l of s i g n i f i c a n c e . Since the 12-second group had a mean a c q u i s i t i o n score greater than the 7-second group i t was concluded that both of these groups acquired a s i g n i f i c a n t l y greater number of novel m u l t i p l i c a t i o n 24 TABLE V TUKEY'S PROCEDURE FOR COMPARING THE MEAN ACQUISITION SCORES Ad j u s t e d Means: 3-Second Group: 3.8567 7-Second Group: 6.3473 12-Second Group: 6.8755 Comparison D i f f e r e n c e S i g n i f i c a n t Gap .05 l e v e l .01 l e v e l .001 l e v e l 7-Sec. Group -3-Sec. Group 2.4906 1.15 1.52 1.96 12-Sec. Group -7-Sec. Group 0.5282 f a c t s than the 3-second group. The d i f f e r e n c e between the mean a c q u i s i t i o n score o f the 12-second group and the mean a c q u i s i t i o n score o f the 7-second group was l e s s than the value o f the s i g n i f i c a n t gap c a l c u l a t e d at the .05 l e v e l o f s i g n i f i c a n c e . As a r e s u l t the n u l l h y p o t h e s i s concerning the d i f f e r e n c e i n a c q u i s i t i o n between these two groups was accepted. I I . ANALYSIS OF THE RETENTION SCORES Re t e n t i o n w i t h i n groups A r e t e n t i o n s c o r e f o r each student was d e f i n e d as the d i f f e r e n c e between the r e t e n t i o n t e s t score and the 25 p r e - t e s t n o v e l s c o r e . T a b l e VI summarizes the t w o - t a i l e d t t e s t o f the s i g n i f i c a n c e o f the mean r e t e n t i o n s c o r e f o r each t r e a t -ment group. TABLE VI TEST OF SIGNIFICANCE OF THE MEAN RETENTION SCORE FOR EACH GROUP Mean Treatment R e t e n t i o n Group Score t 3-Second Group 3.986 8.452 7-Second Group 5.662 13.906 12-Second Group 5.522 12.318 The c r i t i c a l v a lue o f t at the .001 l e v e l was 3.45. Sinc e the t value f o r each group exceeded 3.45, i t was con-c l u d e d t h a t the r e t e n t i o n w i t h i n each group was s t a t i s t i c a l l y s i g n i f i c a n t . R e t e n t i o n between groups A n a l y s i s o f c o v a r i a n c e was used to t e s t the s i g n i f i -cance o f the d i f f e r e n c e s i n the mean r e t e n t i o n scores between the three treatment groups. The c o v a r i a t e s were mental age i n months and p r e - t e s t non-novel s c o r e . T a b l e VII p r e s e n t s a summary o f the a n a l y s i s o f c o v a r i a n c e . 26 TABLE V I I ANALYSIS OF COVARIANCE: RETENTION Source o f V a r i a t i o n d f Squares Mean Square F Group 2 342.97 171.49 17.98 E r r o r 205 1955.4 9.5387 The o b t a i n e d F v a l u e , 17.98, was g r e a t e r than 4.71, the c r i t i c a l v a l u e a t the one p e r c e n t l e v e l o f s i g n i f i c a n c e . S i n c e the F v a l u e was s i g n i f i c a n t , Tukey's p r o c e d u r e was used t o compare the i n d i v i d u a l means. T h i s t e s t i s summarized i n T a b l e V I I I . The d i f f e r e n c e between the mean r e t e n t i o n s c o r e o f the 12-second group and the mean r e t e n t i o n s c o r e o f the 3-second group was g r e a t e r than the v a l u e o f the s i g n i f i c a n t gap c a l c u l a t e d a t the .001 l e v e l o f s i g n i f i c a n c e . S i n c e the 7-second group had a mean r e t e n t i o n s c o r e g r e a t e r than the 12-second group i t was c o n c l u d e d t h a t b o t h o f t h e s e groups r e t a i n e d a s i g n i f i c a n t l y g r e a t e r number o f n o v e l m u l t i p l i c a t i o n f a c t s t h a n the 3-second group. The d i f f e r e n c e between the mean r e t e n t i o n s c o r e o f the 7-second group and the mean r e t e n t i o n s c o r e o f the 12-second group was l e s s t h a n the v a l u e o f t h e s i g n i f i c a n t gap c a l c u l a t e d a t t h e .05 l e v e l o f s i g n i f i c a n c e . As a r e s u l t the n u l l h y p o t h e s i s c o n c e r n i n g the d i f f e r e n c e i n r e t e n t i o n between 27 TABLE V I I I TUKEY'S PROCEDURE FOR COMPARING THE MEAN RETENTION SCORES A d j u s t e d Means: 3-Second Group: 3.1807 7-Second Group: 6.0700 12-Second Group: 5.9556 Comparison D i f f e r e n c e S i g n i f i c a n t Gap .05 l e v e l .01 l e v e l .001 l e v e l 12-Sec. Group -3-Sec. Group 2.7749 1.03 1.36 1.75 7-Sec. Group -12-Sec. Group 0.1144 these two groups was accepted. CHAPTER IV SUMMARY AND CONCLUSIONS I. SUMMARY This study was designed to investigate the effect of the i n t e r t r i a l interval on the acquisition and retention of novel multiplication facts. Previous research in human conditioning, done by psychologists, indicated that an inter-t r i a l interval of the appropriate length facil i t a t e s learn-ing. Since the psychological findings were obtained under s t r i c t laboratory conditions their relevance to classroom learning situations is questionable. The present study, conducted in typical elementary school classrooms, used a conditioning method to teach novel multiplication facts to three groups of grade three students. A series of tests and treatments was given to nine classes of third grade students over a period of four weeks. In order to provide consistency, a tape recorder was used to give the oral presentations of multiplication problems and facts. A stop watch was used during the preparation of the tapes to ensure that the time intervals were accurate. The students were given a pre-test consisting of forty selected multiplication problems. Fifteen problems, having d i f f i c u l t y indices less than .05 on this test, were defined as novel problems and they were used for the treat-ments. 29 A treatment c o n s i s t e d o f an o r a l p r e s e n t a t i o n o f the l i s t o f n o v e l problems and f a c t s read through t w i c e . A 3-second response i n t e r v a l was allowed between the r e a d i n g o f a problem and feedback. A f t e r feedback, and b e f o r e the r e a d i n g o f the next problem, there o c c u r r e d an i n t e r t r i a l i n t e r v a l o f e i t h e r 3 seconds, 7 seconds, o r 12 seconds. I t was the l e n g t h o f t h i s i n t e r v a l t h a t determined the three I treatment groups. Each c l a s s r e c e i v e d a treatment on nine c o n s e c u t i v e s c h o o l days. On the l a s t treatment day a p o s t - t e s t , con-s i s t i n g o f the f i f t e e n n o v e l problems, was ad m i n i s t e r e d . Ten days l a t e r a r e t e n t i o n t e s t , c o n s i s t i n g o f a randomized o r d e r i n g o f the same problems, was ad m i n i s t e r e d . For each stu d e n t , an a c q u i s i t i o n s c o r e was d e f i n e d as the d i f f e r e n c e between h i s p o s t - t e s t score and h i s p r e - t e s t n o v e l s c o r e and a r e t e n t i o n score was d e f i n e d as the d i f f e r e n c e between h i s r e t e n t i o n t e s t score and h i s p r e - t e s t n o v e l s c o r e . A o n e - t a i l e d t t e s t was used to t e s t the s i g n i f i c a n c e o f the mean a c q u i s i t i o n score w i t h i n each group. A t w o - t a i l e d t t e s t was used t o t e s t the s i g n i f i c a n c e o f the mean r e t e n t i o n s c o r e w i t h i n each group. The s i g n i f i c a n c e o f the d i f f e r e n c e s i n the mean a c q u i s i t i o n and r e t e n t i o n scores between groups was t e s t e d u s i n g a n a l y s i s o f c o v a r i a n c e ( c o v a r i a t e s : mental age i n months and p r e - t e s t non-novel score) and Tukey's procedure f o r com-p a r i n g i n d i v i d u a l means. I I . CONCLUSIONS 30 A c q u i s i t i o n W i t h i n groups. The r e s u l t s o f the t t e s t showed t h a t the mean a c q u i s i t i o n score f o r each treatment group was s i g n i f i c a n t beyond the .0005 l e v e l . Between groups. For the hy p o t h e s i s concerning the d i f f e r e n c e s i n a c q u i s i t i o n between the three groups, the f i n d i n g s were: 1. There was a s i g n i f i c a n t d i f f e r e n c e (p<.001) i n the a c q u i s i -t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between grade three students having an i n t e r t r i a l i n t e r v a l o f 7 seconds or 12 seconds and grade three students having an i n t e r t r i a l i n t e r v a l o f 3 seconds. 2. There was no s i g n i f i c a n t d i f f e r e n c e i n the a c q u i s i t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between grade three students having an i n t e r t r i a l i n t e r v a l o f 7 seconds and grade three students h a v i n g an i n t e r t r i a l i n t e r v a l o f 12 seconds. R e t e n t i o n W i t h i n groups. The r e s u l t s o f the t t e s t showed t h a t the mean r e t e n t i o n score f o r each treatment group was s i g n i f i -cant beyond the .001 l e v e l . Between groups. For the hyp o t h e s i s concerning the d i f f e r e n c e s i n r e t e n t i o n between the three groups, the f i n d -ings were: 1. There was a s i g n i f i c a n t d i f f e r e n c e (p^.001) i n the r e t e n t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between grade three students having an i n t e r t r i a l i n t e r v a l o f 7 seconds o r 12 seconds and grade three students having an i n t e r t r i a l i n t e r v a l 31 of 3 seconds. 2. There was no s i g n i f i c a n t d i f f e r e n c e i n the r e t e n t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s between grade three students having an i n t e r t r i a l i n t e r v a l o f 7 seconds and grade three students having an i n t e r t r i a l i n t e r v a l o f 12 seconds. C o n c l u d i n g statement The r e s u l t s o f t h i s study support the c o n c l u s i o n that when a c o n d i t i o n i n g method i s used to teach n o v e l m u l t i p l i c a -t i o n f a c t s t o grade three s t u d e n t s , those students having an i n t e r t r i a l i n t e r v a l o f 7 seconds or 12 seconds w i l l perform s i g n i f i c a n t l y b e t t e r than those students having an i n t e r t r i a l i n t e r v a l o f 3 seconds. D i s c u s s i o n In view o f the p r e s e n t f i n d i n g s , i t would seem t h a t , f o r the task at hand, an i n t e r t r i a l i n t e r v a l o f 7 seconds was a good approximation to the o p t i m a l i n t e r t r i a l i n t e r v a l . S i n c e there was no s i g n i f i c a n t d i f f e r e n c e i n the performance of the 7-second group and the 12-second group, a 7 second i n t e r t r i a l i n t e r v a l would be p r e f e r r e d more o f t e n , f o r p r a c t i c a l reasons. I I I . LIMITATIONS OF THE STUDY T h i s study i n v e s t i g a t e d the e f f e c t o f i n t e r t r i a l i n t e r v a l s o f 3 seconds, 7 seconds, and 12 seconds on the a c q u i s i t i o n and r e t e n t i o n o f n o v e l m u l t i p l i c a t i o n f a c t s . S i nce the students were t o l d t h a t they were p a r t i c i -p a t i n g i n an experiment and s i n c e the treatment method 32 n e c e s s i t a t e d a departure from the s t u d e n t s ' d a i l y r o u t i n e , there can be no doubt t h a t the Hawthorne e f f e c t ^ i n f l u e n c e d the r e s u l t s o f t h i s study. I t i s assumed, however, t h a t because the Hawthorne e f f e c t was equal f o r a l l c l a s s e s , i t i n f l u e n c e d mainly the r e s u l t s p e r t a i n i n g to w i t h i n group ' l e a r n i n g and t h a t the i n f l u e n c e on the r e s u l t s p e r t a i n i n g to between group l e a r n i n g was n e g l i g i b l e . IV. PROBLEMS FOR FURTHER STUDY The r e s u l t s o f the presen t study i n d i c a t e d t h a t 7 seconds was a good approximation o f the op t i m a l i n t e r t r i a l i n t e r v a l . A study c o u l d be designed, u s i n g d i f f e r e n t l e ngths o f the i n t e r t r i a l i n t e r v a l than the pr e s e n t study, i n an attempt to f i n d a b e t t e r approximation o f the optimal i n t e r -t r i a l i n t e r v a l . A problem f o r f u r t h e r study i s the i n v e s t i g a t i o n o f the nature o f the s t u d e n t s ' c o g n i t i v e processes d u r i n g the i n t e r t r i a l i n t e r v a l . Another problem f o r f u r t h e r study i s the d i s c o v e r y o f op t i m a l i n t e r t r i a l i n t e r v a l s f o r a v a r i e t y o f l e a r n i n g t a s k s . I t would be o f i n t e r e s t to experiment w i t h o t h e r tasks i n the area o f mathematics as w e l l as w i t h tasks i n o t h e r s u b j e c t f i e l d s . 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"Supplementary Repor t : Delay of Knowledge \ o f R e s u l t s , Knowledge o f Task , and I n t e r t r i a l I n t e r v a l , " J o u r n a l o f E x p e r i m e n t a l P s y c h o l o g y , 60 :327, 1960. \ Edwards, A l l e n L . S t a t i s t i c a l Methods f o r the B e h a v i o r a l  S c i e n c e s . New Y o r k : H o l t , R i n e h a r t and W i n s t o n , 1964. M o s t e l l e r , F r e d e r i c k , Rourke , Robert E . K . , and Thomas, George B . , J r . P r o b a b i l i t y and S t a t i s t i c s . Reading : A d d i s o n - Wesley P u b l i s h i n g Company, I n c . , 1961. Prekeges , D. P . "The E f f e c t o f Reinforcement on L e a r n i n g o f the M u l t i p l i c a t i o n F a c t s , " Unpubl i shed s t u d y , The U n i v e r s i t y of B r i t i s h Columbia , Vancouver , 1968. Rogers , W i l l i a m , Todd. "The E f f e c t of Delay of Knowledge o f R e s u l t s on the A c q u i s i t i o n and R e t e n t i o n o f N o v e l M u l t i p l i c a t i o n F a c t s , " Unpubl i shed M a s t e r ' s t h e s i s , The U n i v e r s i t y of B r i t i s h C o l u m b i a , Vancouver , 1967. Weinberg , Dorthe R . , Guy, D. E . , and Tupper , R. W. "Supplementary R e p o r t : V a r i a t i o n of Postfeedback I n t e r v a l i n Simple Motor L e a r n i n g , " J o u r n a l o f  E x p e r i m e n t a l P s y c h o l o g y , 67 :98-99 , iWSTl APPENDIX A P r e - t e s t : D i f f i c u l t y I n d i c e s P r e - t e s t Answer Sheet The Treatments Treatment Answer Sheet P o s t - t e s t and R e t e n t i o n Test Answer Sheet f o r P o s t - t e s t and R e t e n t i o n Test 36 (a) PRE-TEST: DIFFICULTY INDICES Problem D i f f i c u l t y Index Problem D i f f i c u l t y Index 1) 8x5 2) 7x8* 3) 3x7 4) 6x7* 5) 9x9* 6) 4x8 7) 9x6* 8) 7x3 9) 8x6* 10) 9x7* 11) 7x4 12) 9x5 13) 8x8* 14) 7x5 15) 7x9* 16) 5x6 17) 9x4 18) 5x8 19) 3x8 20) 5x7 0.069 .000 .304 .016 .016 .069 .000 .137 .000 .000 .088 .053 .004 .099 .004 .133 .057 .053 .171 0.080 21) 3x9 22) 6x5 23) 5x9 24) 9x8* 25) 6x6 26) 6x9* 27) 8x4 28) 7x6* 29) 3x6 30) 8x9* 31) 4x9 32) 8x7* 33) 6x4 34) 4x7 35) 9x3 36) 6x8* 37) 8x3 38) 6x3 39) 7x7* 40) 4x6 0.133 .213 .065 .004 .110 .011 .053 .004 .316 .008 .080 .000 .114 .091 .065 .004 .129 .186 .000 0.140 * Novel problems (b) PRE-TEST ANSWER SHEET NAME 1) 11) 21) 31) 2) 12) 22) 32) 3) 13) 23) 33) 4) 14) 24) 34) 5) _ 15) 25) 35) 6) 16) 26) 36) 7) 17) 27) 37) 8) 18) 28) 38) 9) 19) 29) 39) 10) 20) 30) 40) 38 (c) THE TREATMENTS Day 3 Day 4 Day 5 Day 6 Day 7 1) 7x8 1) 9x9 1) 6x7 1) 6x8 1) 8x6 2) 6x7 2) 9x8 2) 9x6 2) 9x7 2) 7x7 3) 9x9 3) 6x7 3) 7x7 3) 6x9 3) 8x9 4) 9x6 4) 9x6 4) 8x8 4) 7x6 4) 8x8 5) 8x6 5) 8x6 5) 6x8 5) 9x9 5) 9x9 6) 9x7 6) 8x8 6) 9x7 6) 7x8 6) 7x8 7) 8x8 7) 7x7 7) 7x6 7) 9x6 7) 7x6 8) 7x9 8) 8x9 8) 9x8 8) 8x6 8) 6x8 9) 9x8 9) 9x7 9) 6x9 9) 6x7 9) 9x7 10) 6x9 10) 6x9 10) 8x9 10) 9x8 10) 8x7 11) 7x6 11) 6x8 U ) 8x7 11) 8x7 11) 7x9 12) 8x9 12) 7x8 12) 7x9 12) 8x9 12) 9x6 13) 8x7 13) 7x6 13) 8x6 13) 8x8 13) 6x7 14) 6x8 14) 7x9 14) 7x8 14) 7x9 14) 9x8 \ 15) 7x7 15) 8x7 15) 9x9 15) 7x7 15) 6x9 1 16) 6x7 16) 6x7 16) 9x6 16) 9x8 16) 6x7 17) 8x8 17) 9x7 17) 7x7 17) 6x8 17) 7x9 18) 9x8 18) 8x9 18) 8x6 18) 7x9 18) 7x7 19) 7x6 19) 8x7 19) 7x6 19) 8x8 19) 8x8 20) 9x9 20) 8x6 20) 9x8 20) 9x6 20) 7x8 21) 6x9 21) 6x9 21) 7x9 21) 8x7 21) 6x8 22) 9x6 22) 9x8 22) 8x7 22) 7x6 22) 8x7 2 3) 7x7 23) 8x8 2 3) 6x8 23) 9x9 23) 9x9 24) 8x9 24) 9x9 24) 8x9 24) 6x9 24) 6x9 25) 7x9 25) 7x6 25) 9x7 25) 7x7 25) 8x9 26) 6x8 26) 9x6 26) 6x9 26) 8x9 26) 9x6 27) 9x7 27) 6x8 27) 9x9 27) 7x8 27) 8x6 28) 8x7 28) 7x7 28) 8x8 28) 8x6 28) 9x8 29) 7x8 , 29) 7x9 29) 7x8 29) 6x7 29) 7x6 30) 8x6 ' 30) 7x8 30) 6x7 30) 9x7 30) 9x7 39 (c) THE TREATMENTS (Continued) Day 8 Day 9 Day 10 Day 11 1) 9x7 1) 6x7 1) 8x9 1) 7x6 2) 9x8 2) 7x9 2) 7x9 2) 9x8 3) 6x8 3) 7x7 3) 6x8 3) 7x9 4) 7x7 4) 8x9 4) 8x8 4) 8x7 5) 8x6 5) 7x8 5) 7x8 5) 7x7 6) 9x9 6) 9x6 6) 9x8 6) 6x8 7) 7x6 7) 8x6 7) 6x9 7) 9x6 8) 6x9 8) 8x7 8) 9x7 8) 8x6 9) 7x9 9) 6x9 9) 6x7 9) 6x7 10) 9x6 10) 6x8 10) 8x7 10) 9x9 11) 8x7 I D 8x8 11) 9x6 11) 9x7 12) 6x7 . 12) 9x9 12) 9x9 12) 7x8 13) 8x9 13) 9x7 13) 7x6 13) 8x9 14) 8x8 14) 7x6 14) 8x6 14) 6x9 15) 7x8 15) 9x8 15) 7x7 15) 8x8 16) 9x8 16) 7x8 16) 7x8 16) 8x7 17) 8x8 17) 6x7 17) 9x6 17) 7x6 18) 8x7 18) 8x9 18) 9x8 18) 8x6 19) 9x6 19) 9x7 19) 6x8 19) 9x9 20) 6x7 20) 8x6 20) 7x6 20) 6x8 21) 8x6 21) 9x9 21) 8x8 21) 9x7 22) 7x8 22) 9x8 22) 6x7 22) 8x9 23) 7x9 23) 6x9 2 3) 9x7 23) 7x7 24) 6x9 24) 8x7 24) 8x9 24) 7x9 25) 9x9 25) 7x9 25) 8x6 25) 6x7 26) 7x7 26) 7x7 26) 6x9 26) 9x6 27) 6x8 27) 6x8 27) 8x7 27) 7x8 28) 7x6 28) 9x6 28) 7x9 28) 8x8 29) 9x7 29) 8x8 29) 7x7 29) 6x9 30) 8x9 30) 7x6 30) 9x9 30) 9x8 NLA M E / 2 a\ 1 a\ 1 ~ s| f h\  7 |  9 1 1 ~ / o (d) TREATMENT ANSWER SHEET It /3 23 24 /5" 25 /e 26 /7 27 /8 Z8 /9 29 20 3 o (e) POST-TEST AND RETENTION TEST P o s t - T e s t R e t e n t i o n Test 1) 9x6 1) 7x9 2) 8x9 2) 9x6 3) 7x9 3) 6x8 4) 7x8 4) 7x6 5) 9x8 5) 9x8 6) 6x7 6) 8x8 7) 8x6 7) 7x8 8) 8x7 8) 7x7 9) 6x9 9) 9x7 10) 6x8 10) 8x6 11) 7x7 11) 9x9 12) 9x9 12) 6x9 13) 7x6 13) 6x7 14) 8x8 14) 8x9 15) 9x7 15) 8x7 42 (£) ANSWER SHEET FOR POST-TEST AND RETENTION TEST NAME 1) 9) 2) 10) 3) 11) 4) 12) 5) 13) 6) 14) 7) 15) 8) APPENDIX B (a) The E x p e r i m e n t a l Data / 44 TABLE II THE EXPERIMENTAL DATA STUDENT PRE-TEST TREATMENTS tn a> H c to o oo rH •M c •H c < tn o •M o > o •H •H •H t-. rH o H 4J V) o iH O a z i—t i c •H c e> *t LO r>- 00 o> »—i rH .0 1 a> +> a) 3 U e c c > tn *J er >s >> >^  3 a> o o O u a> Cd CO cd cd cd cd cd cd cd Z z z a, « < OS Q o Q a O O Q Q Q 3-SECOND GROUP 1 127 0 0 1 0 1 0 11 5 11 10 15 11 10 7 14 2 104 11 0 7 11 7 11 15 8 , 7 16 17 18 21 20 24 3 83 0 0 1 0 1 0 29 14 18 11 14 14 11 3 8 4 128 0 0 0 0 0 0 5 1 3 5 7 0 6 11 5 5 105 2 0 1 1 1 1 8 6 4 5 8 10 12 4 5 6 95 2 0 5 5 5 5 3 3 5 5 5 8 10 8 11 7 125 0 0 7 4 7 4 7 0 1 4 7 7 8 9 15 8 104 8 0 3 3 3 3 6 3 6 12 12 9 17 15 21 9 115 14 0 3 1 3 1 - 19 10 10 13 8 11 10 17 17 10 105 0 0 0 0 0 0 16 0 0 0 0 0 3 6 10 11 98 2 0 1 0 1 0 5 1 0 0 0 2 0 1 7 12 111 4 0 2 2 2 2 3 1 2 4 3 5 5 3 3 13 120 12 0 2 2 2 2 18 1 0 2 2 2 6 4 7 14 90 2 0 5 4 5 4 1 2 2 6 9 6 3 8 11 15 128 4 0 4 4 4 4 6 2 5 3 4 A* 6 5 12 16 124 0 0 1 1 1 1 10 6 1 2 1 2 0 0 8 17 112 2 0 10 6 10 6 13 6 6 12 11 11 11 12 19 18 120 2 0 0 0 0 0 30 7 10 13 11 2 11 6 6 19 86 0 '0 2 0 2 0 3 2 1 0 1 0 1 1 1 20 121 6 0 12 8 12 8 3 5 4 11 13 12 19 20 i 22 21 96 0 0 1 1 1 1 10 0 2 A 0 1 6 5 4 22 104 13 0 2 1 2 1 28 27 13 5 3 3 6 4 10 23 112 0 0 3 0 3 0 1 1 1 4 1 3 5 9 11 24 105 0 0 6 6 6 6 7 2 5 3 6 6 7 14 18 25 114 0 0 4 4 4 4 7 7 7 13 7 10 7 14 14 26 138 17 0 15 15 15 15 11 8 10 11 17 18 20 25 29 27 128 13 3 13 11 10 8 15 19 17 23 22 23 24 24 24 28 108 4 0 5 3 5 3 13 14 10 7 13 12 8 16 24 29 147 20 0 8 3 8 3 17 11 10 11 16 10 12 16 22 30 82 1 0 2 2 2 2 10 11 8 11 8 7 6 9 9 31 10 3 5 0 5 3 5 3 11 8 3 2 9 7 10 14 15 32 106 0 0 1 1 1 1 1 5 5 5 5 6 8 5 12 33 128 9 0 13 11 13 11 4 7 10 17 16 24 24 26 27 34 120 21 0 IS 15 15 15 14 11 17 14 15 21 24 28 27 35 136 15 0 6 4 6 4 17 14 19 13 17 16 17 18 18 45 TABLE I I (Continued) PRE-STUDENT TEST TREATMENTS OT O +J c •rt c < ve A C 10 1 z io rH o H +J OT 4-» o f-t CO 55 r-l i c •rt C ro LO vo 00 CT* iH rH •P • •*-> 0) s 4) e > OT 4-> cr •M >>. >> >s O O O V u 0) cd CO CO CO CO CO CO CO CO 55 55 OS < Oi Q Q Q Q Cl a o Q Q 36 133 21 1 10 9 9 8 2 4 8 11 12 15 14 12 21 37 139 11 0 11 7 11 7 2 6 7 15 18 15 18 23 27 38 127 16 0 <• 11 13 11 13 13 17 19 24 26 29 27 29 28 39 134 23 1 15 15 14 14 26 22 28 29 30 29 30 29 30 40 121 4 0 4 1 4 1 25 23 19 14 10 6 6 10 13 41 122 17 0 11 13 11 13 4 A 6 10 18 20 22 24 29 42 145 22 2 14 15 12 13 15 15 21 27 26 29 28 29 28 43 115 9 0 7 2 7 2 1 0 A 2 3 6 9 14 7 44 127 0 0 1 1 1 1 1 2 5 5 5 11 7 10 12 45 103 1 0 1 2 1 2 15 15 15 11 10 13 14 15 20 46 107 1 0 2 3 2 3 5 9 8 7 9 9 8 6 8 47 110 3 0 0 0 0 0 12 15 18 10 18 18 17 18 3 48 119 18 0 8 9 8 9 16 18 16 21 21 24 27 30 28 49 115 1 0 5 6 5 6 6 5 9 6 10 8 9 8 10 50 105 8 0 10 8 10 8 4 8 10 15 16 10 15 18 23 51 119 6 0 2 1 2 1 4 10 8 A 7 8 8 7 8 52 116 4 1 5 4 4 3 30 24 20 23 13 21 19 22 21 53 115 1 0 3 3 3 3 17 7 11 17 17 18 23 22 20 54 122 1 0 2 2 2 2 16 12 11 15 16 11 7 9 6 55 121 0 0 4 0 4 0 0 4 6 13 5 10 23 15 8 56 106 2 0 2 3 2 3 26 2 13 14 11 8 7 6 6 57 99 0 0 0 1 0 1 22 10 10 14 10 8 6 8 11 58 105 0 0 3 1 3 1 12 1 2 2 2 2 2 2 2 59 110 0 0 2 2 2 2 14 14 12 11 7 5 9 10 12 60 144 1 0 3 2 3 2 16 4 2 2 3 4 4 7 61 109 0 0 1 2 1 2 21 7 11 11 17 20 18 14 62 144 0 0 5 4 5 4 14 4 6 9 8 6 8 9 ^ i i 63 124 4 0 1 3- 1 3 25 22 20 21 23 24 21 23 23 64 118 1 0 3 1 3 1 11 9 8 7 4 11 8 •/ 9 •26 10 65 142 4 0 8 7 8 7 17 5 10 10 7 15 23 28 66 110 1 0 4 3 4 3 24 16 11 12 14 12 15 11 11 67 109 0 0 5 3 5 3 29 24 19 25 24 19 23 17 18 68 100 0 0 0 1 0 1 14 0 14 22 9 4 8 7 2 69 121 1 0 3 6 3 6 6 5 5 8 11 11 8 15 12 70 102 0 0 2 2 2 2 22 10 7 14 11 14 14 13 16 71 120 4 0 4 5 4 5 6 0 1 14 12 14 16 16 12 72 111 0 0 5 3 5 3 0 20 13 9 7 13 7 9 7 46 TABLE II (Continued) STUDENT PRE-TEST TREATMENTS tn G o 00 r-t •H c < ve es io It io rH o +J (A O rH 4) cd z rH i c «H c LO VO 00 cn rH rH .O i o •M V 3 E C c > *-> o* «J X >s >s 3 a> o o o 0) o 0) cd cd cd cd cd cd cd cd cd Z S z z Oh cc < a Q Q Q Q O O Q O O 7-SECOND GROUP 1 107 8 0 2 0 2 0 16 11 12 15 17 16 12 10 14 2 119 0 0 6 6 6 6 14 8 8 7 12 14 14 11 17 3 110 1 0 1 2 1 2 0 1 0 1 1 1 0 2 4 4 121 0 0 0 1 0 1 1 1 0 0 0 0 0 4 5 5 109 3 0 8 10 8 10 24 12 17 8 12 17 15 19 19 6 108 6 0 7 6 7 6 17 7 5 8 11 11 12 11 17 7 100 0 0 1 3 1 3 13 3 9 10 10 14 14 17 17 8 116 2 0 7 4 7 4 18 14 18 19 20 14 18 21 23 9 113 5 0 3 9 3 9 8 3 4 9 17 12 12 17 18 10 112 0 0 7 4 7 4 - 14 16 28 11 10 14 13 10 13 11 99 13 0 14 15 14 15 16 20 22 30 30 30 30 30 30 12 118 1 0 10 9 10 9 15 8 7 15 16 10 23 28 30 13 121 1 0 5 4 5 4 18 10 19 21 22 21 11 15 19 14 114 0 0 5 6 5 6 13 8 3 10 5 12 8 8 14 15 106 0 0 9 8 9 8 15 7 4 8 10 13 11 16 19 16 128 2 0 12 10 12 10 6 4 4 9 12 16 14 20 24 17 117 2 0 11 8 11 8 6 16 6 11 10 16 16 19 20 18 118 5 0 9 9 9 9 6 6 6 7 12 16 17 19 20 19 121 7 0 13 8 13 8 10 17 15 20 22 23 23 25 26 20 123 6 0 11 9 11 9 6 1 5 7 8 12 17 19 18 21 103 2 0 9 9 9 9 13 7 5 13 16 14 22 23 26 22 117 1 0 2 2 2 2 14 1 2 6 7 6 9 12 3 23 112 1 0 4 4 4 4 15 14 18 16 17 8 12 11 14 24 108 0 0 4 4 4 4 8 1 5 8 9 7 6 10 11 25 114 2 1 9 10 8 9 7 8 7 14 19 15 17 17 20 26 108 2 0 13 10 13 10 8 10 6 13 12 15 19 24 21 27 125 0 0 1 3 1 3 8 4 13 12 11 14 13 16 15 28 112 1 0 2 2 2 2 5 2 3 10 6 0 0 3 7 29 102 0 0 6 3 6 3 4 3 6 10 15 17 18 16 23 30 118 0 0 1 3 1 3 7 3 6 7 7 6 6 2 8 31 107 4 0 4 5 4 5 5 5 8 A 8 12 11 13 15 32 119 0 0 2 5 2 5 3 0 4 6 5 7 8 9 11 33 123 0 0 6 5 6 5 4 11 4 9 10 9 12 15 14 34 106 1 0 5 5 5 5 2 3 6 11 16 9 15 13 16 35 109 1 0 6 6 6 6 24 10 8 11 9 15 12 13 17 47 TABLE I I (Continued) PRE-TREATMENTS •P (A 0) i I H c 4) o OH iH •M C •H < ve es 10 it io U rH o H 4-> V) +J o rH 0) cd z iH i C •H c to m vO 00 cn r-t rH X> 4-> 1 0) •M 0) 3 0) E C e VI +J cr 4-1 >s 3 0) o o O u 0) cd cd cd cd cd cd cd cd cd 2 2 z z Cm < oi Q Q O O O O Q Q Q 36 98 0 0 1 1 1 1 15 11 10 7 A 8 10 5 9 37 120 6 0 8 5 8 5 7 9 10 11 11 14 18 19 23 38 124 1 0 10 10 10 10 26 22 27 28 25 22 23 23 25 39 132 2 0 3 4 3 4 1 A 5 7 9 5 5 14 11 40 128 1 0 2 4 2 4 7 8 5 7 8 9 10 15 14 41 135 3 0 3 6 3 6 15 1 6 8 7 7 10 12 13 42 101 0 0 3 3 3 3 16 10 4 7 6 4 7 8 4 43 109 0 0 11 11 11 11 15 4 13 19 24 25 18 21 24 44 110 0 0 6 5 6 5 2 2 7 7 7 8 12 11 11 45 125 1 0 10 6 10 6 4 9 9 13 15 14 15 19 23 46 102 1 0 3 3 3 3 13 7 3 5 10 14 13 12 11 47 127 2 0 1 3 1 3 11 2 5 4 5 6 5 4 5 48 91 0 0 8 3 8 3 22 15 23 25 16 9 9 14 14 49 130 5 0 14 15 14 15 13 10 17 18 18 16 26 26 28 50 123 1 0 9 4 9 4 24 16 14 16 12 17 13 21 23 51 122 1 0 2 0 2 0 26 22 19 19 16 23 10 12 23 52 127 0 0 3 6 3 6 7 12 7 9 11 11 13 17 24 53 109 2 0 0 2 0 2 2 0 2 12 7 3 5 2 3 54 123 6 0 11 9 11 9 24 15 16 21 9 16 15 20 26 55 117 3 1 6 4 5 3 5 8 16 23 15 15 12 20 24 56 124 0 0 10 9 10 9 3 6 8 11 9 11 16 21 21 57 117 4 0 5 3 5 3 10 8 16 9 10 8 11 10 9 58 119 0 0 3 3 3 3 15 16 18 20 19 19 18 18 18 59 113 0 0 3 2 3 2 4 5 6 5 12 8 11 12 19 60 137 14 0 9 11 9 11 24 23 21 25 19 19 21 25 25 61 113 0 0 4 3 4 3 10 7 9 13 7 5 8 13 12 62 124 4 0 6 5 6 5 A 14 13 18 20 13 16 18 14 63 127 5 0 1 5 1 5 8 4 5 10 7 11 7 15 15 64 137 3 0 9 6 9 6 11 9 7 6 A 8 15 19 22 65 100 0 0 4 6 4 6 6 9 10 10 13 13 13 13 23 66 123 1 0 2 3 2 3 5 3 2 6 10 8 15 14 20 67 131 3 0 13 15 13 15 3 7 18 24 26 30 30 30 29 68 139 4 0 4 5 4 5 0 2 3 2 3 4 7 9 11 69 125 2 0 6 4 6 4 14 8 6 8 11 6 9 17 14 70 110 0 0 14 10 14 10 17 12 9 13 13 22 22 21 26 71 130 3 0 2 3 2 3 3 5 11 5 A 5 5 9 8 48 TABLE II (Continued) / PRE-STUDENT TEST TREATMENTS 4-» </> O H o 11 <u E 3 Z t>0 r-l 4-1 •H < ve es 10 It o •H r-l o t - +-> V) 4-> o rH cd rH a •rH c ut vO 00 rH rH +J • Q> 3 V (3 c > (A 4-* O* 4-» >s >V V o o o « U 4) cd cd cd cd cd cd cd cd cd z z a, OS < CC O a Q Q Q Q a Q Q 12-SECOND GROUP 1 91 8 0 11 6 11 6 9 7 18 14 17 16 14 15 17 2 110 3 0 6 5 6 5 8 7 5 3 8 15 13 8 15 3 105 0 0 6 4 6 4 4 4 3 3 10 7 8 13 13 4 120 3 0 2 1 2 1 3 2 12 4 3 0 3 5 7 5 97 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 6 109 0 0 4 4 4 4 4 4 12 9 7 18 8 11 19 7 106 1 0 1 1 1 1 8 5 5 5 12 14 14 17 19 8 104 0 0 3 3 3 3 17 12 17 18 20 22 21 24 27 9 114 0 0 9 6 9 6 11 10 13 18 20 22 21 18 25 10 131 0 0 1 2 1 2 0 0 0 0 0 0 1 4 . . 5 11 98 0 0 4 2 4 2 0 0 2 3 5 5 6 6 7 12 115 3 0 9 7 9 7 3 7 10 8 8 9 12 20 26 13 105 4 0 8 9 8 9 9 7 . 14 20 18 18 21 20 22 14 99 2 0 8 6 8 6 4 7 9 10 11 A 12 12 16 15 112 1 0 4 3 4 3 9 0 7 5 3 8 5 6 9 16 95 3 0 3 5 3 5 12 5 14 17 18 21 13 17 20 17 113 0 0 2 0 2 0 10 0 1 0 0 0 0 3 15 18 117 4 0 7 5 7 5 13 8 7 15 13 8 14 18 25 19 105 3 0 7 7 7 7 6 3 8 11 7 9 10 12 15 20 82 0 0 9 6 9 6 3 3 7 8 11 8 10 17 18 21 102 0 0 0 1 0 1 1 4 .10 17 10 1 0 1 2 22 96 0 0 1 1 1 1 0 0 0 1 4 4 4 5 8 23 91 0 0 2 2 2 2 1 0 2 8 8 4 6 3 6 24 87 0 0 10 9 10 9 5 7 9 9 15 11 12 15 19 25 102 0 0 15 IS 15 15 4 A 6 13 15 17 21 23 25 26 96 0 0 7 3 7 3 10 3 5 10 11 17 14 13 12 27 107 0 0 8 4 8 4 0 3 6 5 7 8 11 12 ! 13 28 83 0 0 4 4 4 4 7 9 5 6 5 8 8 13 15 29 96 1 0 3 3 3 3 14 6 5 12 10 8 9 8 10 30 107 0 0 3 3' 3 3 3 4 7 4 3 6 9 9 8 31 118 . 1 0 4 5 4 5 9 9 7 6 12 9 12 15 17 32 127 4 0 13 12 13 12 17 13 15 13 22 23 25 24 29 33 132 2 0 12 11 12 11 21 7 13 15 13 20 17 22 21 34 118 12 0 6 9 6 9 8 4 3 7 13 14 18 12 15 35 125 0 0 4 4 4 4 6 6 11 8 14 13 13 16 15 / 49 TABLE I I (Continued) PRE-STUDENT TEST TREATMENTS O rH 4-* < 4) «/) > 0) O f-o CO 1 rQ P i 0) p 6 c c > V) 3 o o o 2 s 2 55 Ok p V) 0) H C o e a> p o oi o o V) P c 0) 3 cr u < a> os o rH to LO vO 00 rH rH >s >s >N CO CO CO CO CO CO CO CO CO 0 Q a o a O Q Q Q 36 106 2 0 9 7 9 7 18 9 7 13 13 12 13 20 28 37 123 1 0 6 5 6 5 5 6 6 13 14 13 18 17 21 38 125 6 0 15 12 15 12 13 8 8 12 17 17 20 21 25 39 142 2 0 8 8 8 8 17 3 4 9 11 10 10 15 22 40 122 0 0 6 2 6 2 1 4 1 1 5 7 7 9 15 41 139 5 0 11 8 11 8 6 4 5 10 13 13 13 15 15 42 125 6 0 9 9 9 9 15 12 13 19 16 13 15 21 ' 19 43 122 3 0 14 10 14 10 9 8 10 13 16 18 23 22 27 44 109 2 0 11 10 11 10 7 11 15 14 15 21 21 25 25 45 134 8 0 14 15 14 15 8 13 16 19 24 27 30 30 30 46 130 3 0 10 8 10 8 11 12 12 17 18 19 18 24 26 47 135 6 0 7 7 7 7 8 4 3 4 9 7 11 9 18 48 129 5 0 3 1 3 1 25 20 18 16 17 19 15 15 13 49 131 8 1 5 5 4 4 20 15 12 10 10 15 9 16 10 50 93 2 0 4 1 4 1 3 1 4 3 4 3 6 6 9 51 125 1 0 3 7 3 7 19 12 10 3 A 7 14 10 10 52 113 1 0 2 2 2 2 11 9 7 5 7 6 3 3 7 53 107 0 0 1 2 1 2 A 20 13 10 12 15 12 13 18 54 114 0 0 15 11 15 11 21 12 15 13 15 20 16 19 26 55 121 0 0 3 2 3 2 15 15 12 15 11 10 10 16 15 56 121 2 0 8 11 8 11 12 8 8 12 8 10" 15 21 22 57 125 2 0 4 4 4 4 1 4 7 5 12 18 8 6 8 58 98 7 0 6 4 6 4 3 5 8 6 10 5 5 10, 11 59 120 6 0 7 6 7 6 18 19 13 18 A 15 16 20, 15 60 136 7 1 9 6 8 5 17 13 10 18 14 17 - 23 21 29 61 139 2 0 10 7 10 7 1 11 24 14 15 10 12 24 13 62 110 5 0 12 11 12 11 17 20 20 20 16 13 18 23 26 63 108 1 0 2 2 2 2 17 23 10 8 7 7 9 14 20 64 122 2 0 0 2 0 2 11 5 3 7 4 7 6 11 12 65 133 4 0 10 11 10 11 1 7 3 9 14 19 A 22 26 23 66 126 3 0 8 3 8 3 15 4 7 10 6 8 8 12 12 67 117 1 0 6 5 6 5 4 9 9 11 6 A 11 11 IS * Absent 

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