A STUDY OF PROGRAM SEQUENCING IN COMPUTER-ASSISTED INSTRUCTION by TELFORD STRUTHERS B.A., University of Western Ontario, 1962 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of Mathematics Education We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1971 In p r e s e n t i n g t h i s t h e s i s in 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 at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e tha 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 tudy . I f u r t h e r ag ree t h a t 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 . It 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 P B Firinnnt.inn The U n i v e r s i t y o f B r i t i s h Co lumbia V a n c o u v e r 8, Canada Date June 2h, 1971. ABSTRACT T h i s s t u d y was u n d e r t a k e n t o i n v e s t i g a t e how program s e q u e n c i n g would e f f e c t a s i x t h - g r a d e group o f Ss. A l i n e a r program o f 111 frames t h a t t a u g h t base f i v e a r i t h m e t i c was chosen f o r t h e s t u d y . The program p r e s e n t e d i n i t s o r i g i n a l o r d e r was c a l l e d t h e l o g i c a l l y sequenced program. The program whose frame sequence was d e t e r m i n e d by a t a b l e o f random numbers was c a l l e d t h e s c r a m b l e d sequenced program. On t h e b a s i s o f IQ s c o r e s , two groups o f s t u d e n t s were formed. E q u a l numbers from each o f t h e s e two groups were t h e n a s s i g n e d a t random t o one o f the two programs o f i n s t r u c -t i o n . The two programs o f i n s t r u c t i o n were p r e s e n t e d t o t h e S_ by means o f computer t e r m i n a l s . A p o s t t e s t was t h e n a d m i n i s -t e r e d t o t e s t t h e e f f e c t o f program s e q u e n c i n g on l e a r n i n g f a c t s and s k i l l s t h a t were t a k e n d i r e c t l y from t h e program. A l s o t e s t e d was t h e e f f e c t o f program s e q u e n c i n g on t h e student's a b i l i t y t o use t h e p r i n c i p l e s d e v e l o p e d i n t h e pro-gram t o s o l v e problems t h a t a r e an e x t e n s i o n o f t h e s e p r i n -c i p l e s . There was found t o be a s i g n i f i c a n t i n c r e a s e i n t h e program e r r o r r a t e and program c o m p l e t i o n time f o r t h e s c r a m b l sequenced program when compared t o t h e l o g i c a l l y sequenced program, i m p l y i n g t h a t the program chosen f o r the s t u d y con-t a i n e d dependency among t h e frames. The r e s u l t s o f the posttest indicated that there was no s i g n i f i c a n t difference between the mean scores of the two groups although i n each case the l o g i c a l l y sequenced group did achieve a higher mean score. I t was also found that there was no s i g n i f i c a n t i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l . Many previous studies i n program sequencing have dealt with an older population i n comparison to the population chosen for t h i s study. The conclusions from these studies have generally been that sequence of i n s t r u c t i o n has been overemphasized as a variable for consideration i n program construction. While the r e s u l t s of thi s study indicate that sequence of i n s t r u c t i o n may be more important for a younger population, some doubt i s raised as to the importance of attempting to obtain a c a r e f u l l y sequenced, small error rate program. TABLE OF CONTENTS CHAPTER Page I. THE PROBLEM 1 BACKGROUND 1 Statement of the problem 5 II . REVIEW OF THE LITERATURE 6 I I I . DESIGN OF THE STUDY 13 INTRODUCTION 13 DEFINITION OF TERMS 14 FORMATION OF THE GROUPS 14 The population 14 The sample 14 DEVELOPMENT OF MATERIALS 15 Program content 15 The scrambled version 16 Posttest measures 16 PROCEDURE 18 STATISTICAL ANALYSIS 18 Statement of hypotheses 18 Data 19 S t a t i s t i c a l treatment of data 19 IV. ANALYSIS OF THE DATA 20 RESULTS OF THE STUDY 21 Means of the groups 21 CHAPTER Page ANALYSIS OF THE HYPOTHESES 21 Hypothesis I 21 Hypothesis II 23 Hypothesis III 24 Hypothesis IV 24 Hypothesis V 26 Hypothesis VI 26 EXPLICATION OF THE RESULTS 27 The program of i n s t r u c t i o n 27 The posttest scores . 28 V. CONCLUSIONS AND SUMMARY 32 THE EFFECTS OF COURSE SEQUENCE 32 LIMITATIONS OF THE STUDY 34 The program of i n s t r u c t i o n . 34 The sample 34 The Hawthorne e f f e c t s 34 IMPLICATIONS FOR FURTHER RESEARCH . . . . . . . . 35 SUMMARY 36 BIBLIOGRAPHY 38 APPENDICES 41 I. THE COMPUTER PRINT OUT OF THE TEXT MATERIAL AND A STUDENT'S RESPONSE 41 II . ORDER OF FRAME PRESENTATION FOR THE SCRAMBLED SEQUENCE 57 II I . THE POSTTEST 59 IV. THE EXPERIMENTAL DATA 66 LIST OF TABLES TABLE Page I. THE TWO FACTOR DESIGN 20 II . MEANS OF PROGRAM ERRORS 22 II I . ANALYSIS OF VARIANCE FOR HYPOTHESIS I 22 IV. MEANS OF COMPLETION TIME 23 V. ANALYSIS OF VARIANCE FOR HYPOTHESIS II . . . . 24 VI. MEANS OF THE TEST OF PROGRAM FACTS AND SKILLS . 25 VII. ANALYSIS OF VARIANCE FOR HYPOTHESIS III AND IV . . . 25 VIII. MEANS OF THE TEST OF EXTENSION PROBLEMS . . . . 26 IX. ANALYSIS OF VARIANCE FOR HYPOTHESES V AND VI 27 X. SCORES ON PROGRAM FACTS AND SKILLS FOR THE LOGICAL SEQUENCE HIGH IQ 66 XI. SCORES ON PROGRAM FACTS AND SKILLS FOR THE LOGICAL SEQUENCE LOW IQ 67 XII. SCORES ON PROGRAM FACTS AND SKILLS FOR THE SCRAMBLED SEQUENCE HIGH IQ 6 8 XIII. SCORES ON PROGRAM FACTS AND SKILLS FOR THE SCRAMBLED SEQUENCE LOW IQ 69 XIV. SCORES ON EXTENSION MATERIAL FOR THE LOGICAL SEQUENCE HIGH IQ . 70 XV. SCORES ON EXTENSION MATERIAL FOR THE LOGICAL SEQUENCE LOW IQ 71 XVI. SCORES ON EXTENSION MATERIAL FOR THE SCRAMBLED SEQUENCE HIGH IQ 72 XVII. SCORES ON EXTENSION MATERIAL FOR THE SCRAMBLED SEQUENCE LOW IQ 73 TABLE Page XVIII. PROGRAM ERRORS FOR THE LOGICAL SEQUENCE . . . . 74 XIX. PROGRAM ERRORS FOR THE SCRAMBLED SEQUENCE . . . 75 XX. TIME TAKEN TO COMPLETE THE LOGICAL SEQUENCE . . 76 XXI. TIME TAKEN TO COMPLETE THE SCRAMBLED SEQUENCE . 77 LIST OF FIGURES FIGURE Page 1. MEAN POSTTEST PERFORMANCE ON PROGRAM FACTS AND SKILLS 30 2. MEAN POSTTEST PERFORMANCE ON EXTENSION PROBLEMS 30 ACKNOWLEDGEMENT The author wishes to thank the members of his thesis committee—Dr. J. S h e r r i l l (Chairman), Dr. G. S p i t l e r , and Dr. W. S z e t e l a — f o r t h e i r cooperation and assistance. CHAPTER I THE PROBLEM BACKGROUND The c a r e f u l sequencing of i n s t r u c t i o n a l s t i m u l i has generally been considered of prime importance i n the planning of programed i n s t r u c t i o n . Skinner's (22:169) d e f i n i t i o n of programing as the "construction of c a r e f u l l y arranged se-quences of contingencies leading to the terminal performances which are the object of education" has had a tremendous e f f e c t on sequencing of programed i n s t r u c t i o n . Skinner sug-gests that i n d i v i d u a l programing makes i t possible to present small step, c a r e f u l l y sequenced items where a so l u t i o n to each problem depends upon a correct response to the preceding one and through t h i s process, an eventual complex repertoire i s made. Following an experiment dealing with a c a r e f u l l y ordered sequence of learning items, Roe, Case, and Roe (21:101) concluded: ...the importance of the ca r e f u l ordering of items became suspect when i t was discovered that a student, who f a i l e d to read the introductory i n s t r u c t i o n s of the programed testbook, read down the page instead of from page to page so that the sequence of items was numbered 1, 40, 79, 118, 157, 2, 41, 80, 119, 158, 3, 42,and so on. This student s t i l l managed to get a high score on the c r i t e r i o n t e s t . 2. Several studies have since been conducted to tes t the importance of a l o g i c a l l y sequenced i n s t r u c t i o n a l unit as opposed to a scrambled sequence of the same material content. In almost every instance, the re s u l t s of the study have indicated that there i s no s i g n i f i c a n t difference between the two types of presentation. Levin and Baker (13) , when discussing the e f f e c t s of item scrambling, concluded that program content was probably an important factor to consider when studying the e f f e c t s of program sequence on learning. Since Levin and Baker's study, the studies that have been done concerning sequencing of i n s t r u c t i o n have generally attempted to use a program i n which the mastery of some concepts were a prereq u i s i t e to the mastery of other concepts and p r i n c i p l e s i n the program. The model usually followed to describe such hierar-c h i a l learning i s Gagne's hierarchy of learning model (Nieder-meyer, 17:302-303). When the f i r s t p r i n c i p l e to be learned i s considered, i t can be analyzed into a number of subordinate concepts which must be mastered i f the f i n a l task i f to be attained. These concepts i n turn depend upon other subordinate concepts which are eventually reduced to stimulus-response type learning. What i s being developed i s a hierarchy of sub-knowledge that grows increasingly simple. Once the heir-archy i s determined, i t i s possible to organize a sequence of i n s t r u c t i o n for the f i n a l performance to be attainable. The method or analysis of the task i s begun, as Gagne (9:4) suggests, by asking the question "...what would an i n d i v i d u a l have to know how to do i n order to achieve suc-ce s s f u l performance of t h i s class of task, assuming he were given only i n s t r u c t i o n s ? " This analysis i s then repeated on each learning task u n t i l the entire hierarchy i s defined. Gagne believes that i f the hierarchy of learning model i s followed, the learning of a high order p r i n c i p l e can be made meaningful. The problem has been that Gagne's hierarchy i s a learning theory and Gagne says that some things must be learned before others (Niedermeyer, 17:314). Gagne*1 s (7:624) studies have i n f a c t shown that some of the concepts under-l y i n g a p r i n c i p l e must be known before the p r i n c i p l e i s under stood. As Niedermeyer (17:314) has concluded from his studie i n program sequencing, the sequence of learning i s d i f f e r e n t from the sequence of i n s t r u c t i o n a l frames or s t i m u l i . When students miss frames that are necessary for the understanding of a concept, they are unable to answer the question on the concept c o r r e c t l y and t h i s causes the program error rate to increase. I t i s quite possible that the concept w i l l be learned either through the correct answer being supplied i n the program or through reorganization by the student, when he eventually comes to the p r e q u i s i t e s k i l l s . 4. If the objective of a program of i n s t r u c t i o n i s simply to have students learn program content, then t h i s out-come may not be affected by the method of sequencing. On the other hand, i f i t i s desired that there be an understanding of the p r i n c i p l e s taught i n the program for extension to new, though related problems, i t seems questionable that a program presented i n a scrambled version could be capable of providing the student with the necessary understanding of the p r i n c i p l e . Another dimension of consideration i n the area of program sequencing i s i n t e l l i g e n c e . Students of low i n t e l -ligence may not be as capable of organizing a scrambled program of i n s t r u c t i o n as students of high a b i l i t y . While some previous studies have considered a b i l i t y as a variable i n t e r a c t i n g with sequencing, there appear to be no clea r r e s u l t s from these studies. The problem of c a r e f u l sequencing of program material i s fundamental for Computer Assisted Instruction (CAI) where there e x i s t s many p o s s i b i l i t i e s for the organization and sequencing of course materials. While there are obvious d i f -ferences i n the many d i f f e r e n t systems for CAI, most systems have the f l e x i b i l i t y of course organization and sequencing and the a d a p t a b i l i t y of sequencing for the i n d i v i d u a l . Despite the e f f o r t s to make the sequencing of i n s t r u c t i o n f l e x i b l e , studies by Niedermeyer (17), Wodtke (26), and Payne (19) sug-gest that a c a r e f u l l y organized sequence of i n s t r u c t i o n p r o v i d e s f o r no more s i g n i f i c a n t l e a r n i n g t h a n a c o m p l e t e l y randomized sequence. Statement o f the p r o b l e m The f o l l o w i n g q u e s t i o n s w i l l be c o n s i d e r e d : 1. Does program s e q u e n c i n g have an e f f e c t on l e a r n i n g program f a c t s and s k i l l s ? 2. Does program s e q u e n c i n g have an e f f e c t on l e a r n i n g p r i n c i p l e s a p p l i c a b l e t o problems n o t i n c l u d e d i n the program? 3(a). I s t h e r e an i n t e r a c t i o n between sequence o f i n s t r u c -t i o n and a b i l i t y l e v e l on l e a r n i n g program p r i n c i p l e a p p l i c a b l e t o problems not i n c l u d e d i n the program? 3(b). I s t h e r e an i n t e r a c t i o n between sequence o f i n s t r u c -t i o n and a b i l i t y l e v e l o f l e a r n i n g program f a c t s and s k i l l s ? CHAPTER II REVIEW OF THE LITERATURE The problem of deciding when a program i s l o g i c a l l y sequenced and contains frame dependency has been tested using the c r i t e r i o n that the presentation of a l o g i c a l sequence i n a scrambled order should cause the Ss to make s i g n i f i c a n t l y more within program errors as they continue through the program when compared to the program i n i t s o r i g i n a l order (Niedermeyer, 17:302). The rationale underlying t h i s reasoning i s that i f a program contains no frame dependency, then there should be no s i g n i f i c a n t difference i n the error rate however the program i s sequenced. Using program error rate as a c r i t e r i o n measure, Holland (11:69) pointed out that the two program error rates i n the study by Roe, Case, and Roe did not d i f f e r s i g n i f i c a n t l y , suggesting that the items i n the program were not highly i n t e r -dependent. After the i n v e s t i g a t i o n by Holland, Roe revised the e a r l i e r program and th i s time the l o g i c a l version did produce s i g n i f i c a n t l y better r e s u l t s , apparently s a t i s f y i n g both Holland and Roe that c a r e f u l sequencing of i n s t r u c t i o n a l material i s an important c r i t e r i o n f o r program construction. However, several studies of the problem conducted since the one by Holland, and using the c r i t e r i o n of program error rate to determine a l o g i c a l l y sequenced program of i n s t r u c t i o n , have 7. reported "no s i g n i f i c a n t d ifference" between the means on posttest scores between the l o g i c a l and scrambled program groups. A study by Payne, Krathwohl, and Gordon (19) was conducted to examine the e f f e c t s of sequencing on the learning of three college s t a t i s t i c s programs. While scrambling of items was done by a table of random numbers, i t was found that there were no treatment e f f e c t s and also no i n t e r a c t i o n between a b i l i t y and sequencing. The f a c t that the error rate for the scrambled versions of the program were low, between four and six percent and not s i g n i f i c a n t l y d i f f e r e n t from the l o g i c a l version, indicates that e i t h e r the Ss had some p r i o r knowledge of the material or that the program chosen for the study did not have frame dependency. A second l i m i t a t i o n of the study was that the programs were presented i n booklet form and the students were allowed to complete the program at t h e i r own l e i s u r e i n an uncontrolled s i t u a t i o n . In a study conducted by Wodtke, Brown, Sands, and Fredericks (26), a program on number bases was presented to 80 education majors at Pennsylvanis State University by means of computer terminals. The program would appear to contain items that were interdependent since there was a s i g n i f i c a n t increase i n the "within program error rates" when the scrambled version of the program was compared to the l o g i c a l version. 8. Another c r i t e r i o n measure which was used to lend support to the argument that the l o g i c a l version contained frame depen-dency was that the i n s t r u c t i o n a l time increased by a s i g n i -f i c a n t amount when the program was presented i n a scrambled order. The reasoning underlying t h i s argument was that i n s t r u c t i o n a l time should increase i f Ss have to puzzle over frames i n a scrambled sequence i n comparison to a l o g i c a l sequence. The s k i l l s measured i n the program were conversion of a number i n any base, not equal to ten, to i t s base ten equivalent and conversion of a number from base ten to any other base. The study seemed to be well c o n t r o l l e d and a pre-t e s t of the Ss indicated that they had l i t t l e p r i o r knowledge i n the area of i n s t r u c t i o n . The findings of the study were no s i g n i f i c a n t difference between the two sequences of i n s t r u c -t i o n with regard to e i t h e r posttest scores on f a c t u a l material presented i n the program or transfer tasks (Wodtke et a l . , 26:62). The investigators themselves expressed surprise as to the r e s u l t s of the experiment since they f e l t the study had many controls that e a r l i e r studies had lacked. They (Wodtke et a l . , 26:67) concluded: The a b i l i t y to reorganize scrambled material i s undoubtedly a function of the cognitive development of the learner. Although i t appears l i k e l y that college students are able to accomplish such reorganization, the writers would be extremely reluctant to generalize such a conclusion to the problem of sequencing learning 9. materials for young children. I t may be that sequenc-ing i s much more c r u c i a l i n the education of young chi l d r e n who have not yet developed t h e i r own learning s t r a t e g i e s . Another i n t e r e s t i n g aspect of Wodtke's study i s that the examination of the aptitude by sequence int e r a c t i o n s provided support for the argument that a l o g i c a l l y sequenced program of i n s t r u c t i o n i s more important for students of low a b i l i t y . While the r e s u l t s were not s i g n i f i c a n t (P = .114), the obtained a tends to support the argument. In a study conducted by Stolurow (23) using a "mixed" sequence and a "consecutive" sequence to teach f r a c t i o n s to educationally handicapped high school students (mean mental age of 12.25 years) the question of i n t e r a c t i o n between sequencing and I.Q. scores was investigated. I t was found that I.Q. correlated .61 with posttest scores for students given the mixed program but did not correlate s i g n i f i c a n t l y with performance on the consecutively sequenced program. Stolurow (23:351) inte r p r e t s these r e s u l t s as suggesting "the best sequence did for the poorest a b i l i t y group what the highest a b i l i t y groups could do for themselves regardless of sequence." When con-sid e r i n g these r e s u l t s with other studies dealing with uni-v e r s i t y students of higher i n t e l l i g e n c e , t h i s study also sug-gests that sequencing may be more important for younger c h i l d -ren or Ss with low I.Q. 10. A study dealing with a younger population was con-ducted by Niedermeyer (17) when a group of grade nine students was presented with a program on number series i n a l o g i c a l , scrambled and reverse order. The program consisted of an introduction to a number series and eventually introduced the problem solving s k i l l of f i n d i n g a formula for the sum of n terms of a s e r i e s . While program error rates did d i f f e r s i g -n i f i c a n t l y (p< .05) i n favour of the l o g i c a l sequence, none of the sequenced groups d i f f e r e d s i g n i f i c a n t l y from each other on e i t h e r a t e s t of f a c t u a l material or transfer of problem solving s k i l l s . There was also no evidence of sequence by I.Q. i n t e r -a ction. There appear to be two possible explanations for the f a i l u r e of Niedermeyer's study to provide evidence of any s i g n i f -icant difference between the three programs of i n s t r u c t i o n . While the error rates of the scrambled and reversed sequenced groups d i f f e r e d s i g n i f i c a n t l y from the l o g i c a l sequence, the error rate for the l o g i c a l l y sequenced program was 35 percent. The program used for the study was obtained from Gagne* and Brown's (8) study dealing with discovery learning and the program error rate i n t h e i r experiment was much lower, i n d i -cating that perhaps the program was too d i f f i c u l t for the students used i n the study by Niedermeyer. Another factor that could have led to the large error rate was the f a c t that the o r i g i n a l program consisted of 129 frames and Niedermeyer 11. used a revised form of the program consisting of 110 frames. Perhaps some of the frames that were removed were more essen-t i a l to the understanding of the other frames i n the program than appeared to be the case when they were removed. Brown (2) , who was doing experimental work with Niedermeyer, also examined the e f f e c t s of sequencing on the learning of the number series program that Niedermeyer had used but chose as the Ss, students from the eleventh-grade. The o r i g i n a l program that had been written by Gagne and Brown, was used for this study rather than the shortened version that Niedermeyer had used. The completion time and the program error rate for the scrambled version increased s i g n i f i c a n t l y when compared to the l o g i c a l sequence again suggesting that the program contained frame dependency. There was no s i g n i f i c a n t treatment e f f e c t found on the posttest r e s u l t s of on-route tasks when the l o g i c a l and scrambled groups were compared. Nor was there any s i g n i -f i c a n t IQ by sequence i n t e r a c t i o n . However, on the posttest scores of problem-solving tasks, the group receiving the l o g i c a l sequence performed s i g n i f i c a n t l y better than the scrambled ordered group. The IQ by sequence i n t e r a c t i o n 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 . 12. While the r e s u l t s of the study are i n contrast to the study by Niedermeyer, i t does indicate that scrambling the order of items may make l i t t l e difference i f the tasks being taught can be c l a s s i f i e d as learning facts and s k i l l s , but i f the tasks are complex problem-solving behaviors, then perhaps sequence may have an important e f f e c t upon learning. CHAPTER III DESIGN OF THE STUDY INTRODUCTION From the previous discussion on program sequencing, i t becomes apparent that some students have the a b i l i t y to reorganize a poorly sequenced program of i n s t r u c t i o n . Studies to date imply that at lea s t for students at a u n i v e r s i t y l e v e l , c a r e f u l sequencing of i n s t r u c t i o n may not be as important a c r i t e r i o n for program construction as was once so commonly • thought to be the case. Before these r e s u l t s can be genera l i -zed, the importance of sequencing needs to be studied more c a r e f u l l y with a pre-university group. The program chosen for t h i s study was a l i n e a r pro-gram toteach base f i v e arithmetic. The o r i g i n a l version of the program was used by Floyd (5) i n a study comparing the effectiveness of a branching program with the effectiveness of a l i n e a r program. The l i n e a r program was found to be suc-c e s s f u l i n teaching base f i v e arithmetic to sixth-grade students, for whom the program was written. A p i l o t study, conducted by the examiner, indicated that the program con-tained frame dependency since there was a s i g n i f i c a n t increase i n error rate when a scrambled version of the program was compared to the o r i g i n a l version. DEFINITION OF TERMS (a) scrambled sequence of i n s t r u c t i o n : a program of in s t r u c -t i o n that has had i t s frame sequence of presentation determined by a table of random numbers. (b) l o g i c a l sequence of i n s t r u c t i o n : a small-step program of i n s t r u c t i o n that has been found to have a s i g n i f i c a n t l y lower program error rate when compared to a scrambled version of the same frames. (c) extension questions: questions that are d i f f e r e n t from what was taught i n the program but which require the concepts and p r i n c i p l e s developed i n the program for t h e i r s o l u t i o n . FORMATION OF THE GROUPS The population The population consisted of sixth-grade students from elementary schools i n Vancouver. The students were on the regular B r i t i s h Columbia program and i t was found i n t h i s study and i n the study by Floyd (5:14) that grade six students had s u f f i c i e n t background for elementary base f i v e arithmetic, but had l i t t l e opportunity for exposure to the topic since i t s introduction i s usually encountered i n seventh-grade. The sample The sample was chosen from grade six students i n a single school due to transportation and administrative 15. d i f f i c u l t i e s . T h i r t y - s i x students were selected at random, using a table of random numbers, from the two classrooms of students i n the school. An IQ score for each of the Ss was made available to the investigator by the school and the IQ t e s t administered was the Otis-Alpha Quick-Scoring Mental A b i l i t y Test. The median IQ for the sample was 116 and ranged from 87 to 150. The students were then grouped in t o high and low IQ groups, each having eighteen members. The students from the two groups were then assigned, using a table of ran-dom numbers, to one of the two programs of i n s t r u c t i o n . DEVELOPMENT OF MATERIALS Program content The l o g i c a l sequence of i n s t r u c t i o n consisted of 111 frames and presented subsets of items i n the following order: 1. Review of the base ten number system and the concept of place value. 2. Instruction i n how to write a numeral to represent a number i n bases less than ten. 3. A discussion of the numerals required i n base f i v e arithmetic and base f i v e counting. 4. A development of base f i v e addition f a c t s , up to adding two two-digit base f i v e numerals. 5. The use of a base f i v e addition table. 6. M u l t i p l i c a t i o n of base f i v e numerals by the numeral two. 16. The program was w r i t t e n i n such a way t h a t the s t u d e n t was r e q u i r e d t o respond t o a q u e s t i o n p r e s e n t e d i n each frame. The r e s p o n s e was t h e n e v a l u a t e d and i f t h e answer was c o r r e c t , the s t u d e n t was so i n f o r m e d and then the n e x t frame was p r e s e n t e d . I f t h e answer was i n c o r r e c t , the c o r r e c t answer would be g i v e n and t h e n e x t frame p r e s e n t e d . The complete t r a c e o f the t e x t m a t e r i a l and s t u d e n t r e s p o n s e f o r s t u d e n t number one i n the l o g i c a l l y sequenced group, h i g h IQ, may be found i n Appendix I . The s c r a m b l e d v e r s i o n U s i n g a t a b l e o f random numbers, f o u r s c r a m b l e d sequences were g e n e r a t e d from the frames o f t h e l o g i c a l v e r s i o n . The Ss i n t h e s c r a m b l e d sequence group were t h e n a s s i g n e d t o one o f t h e s e f o u r s c r a m b l e d sequences a t random. Appendix I I l i s t s the o r d e r o f frame p r e s e n t a t i o n f o r each o f t h e f o u r s c r a m b l e d sequences. P o s t t e s t measures The in d e p e n d e n t v a r i a b l e s were t h e two sequence c o n -d i t i o n s and IQ. The dependent v a r i a b l e s were t i m e t o c o m p l e t e the program, e r r o r s made on the program d u r i n g i n s t r u c t i o n , and s c o r e s on the p o s t t e s t . The t e s t i n s t r u m e n t was the one d e v e l o p e d by F l o y d and was found by her (5:20) t o have a r e l i a b i l i t y c o e f f i c i e n t ( K u d e r - R i c h a r d s o n Formula 20) o f 0.92. The t e s t o f c r i t e r i o n s k i l l s c o n s i s t e d of 12 q u e s t i o n s d e a l i n g w i t h t a s k s t a k e n d i r e c t l y from the program and 30 e x t e n s i o n q u e s t i o n s . The e x t e n s i o n q u e s t i o n s were chosen from the f o l -l o w i n g a r e a s : 1. A d d i t i o n i n base f i v e o f (a) t h r e e t w o - d i g i t numerals (b) two t h r e e - d i g i t n u m e r a l s . 2. M u l t i p l i c a t i o n i n base f i v e o f (a) t h r e e - d i g i t numerals by two (b) t w o - d i g i t numerals by numbers g r e a t e r t h a n two. 3. C o u n t i n g (a) i n base f i v e beyond 30 (b) i n base f o u r . 4. U s i n g a base e i g h t a d d i t i o n t a b l e t o (a) add two t w o - d i g i t numerals. (b) m u l t i p l y t w o - d i g i t numerals by two. 5. The numerals t h a t a r e used i n base s i x . 6. D e d u c t i o n o f the base b e i n g used. 7. C o n v e r s i o n from one base t o a n o t h e r . 8. Development o f a base f o u r a d d i t i o n t a b l e . 9. S u b t r a c t i o n i n base f i v e . 10. Development o f a base f i v e m u l t i p l i c a t i o n t a b l e . The p o s t t e s t i s f o u n d i n A p p e n d i x I I I . 18. PROCEDURE The 36 grade six students i n the experiment were brought to the University of B r i t i s h Columbia to work on the programs of i n s t r u c t i o n . The course was programed for pre-sentation to the Ss v i a three teletypewriter terminals using the Coursewriter III language. The terminals were connected to the University of B r i t i s h Columbia IBM 360/67 computer. Depending on whether the student was i n the l o g i c a l l y sequenced group or the scrambled sequenced group, the program that was presented was either the l o g i c a l version or one of the four scrambled versions. Each student was given an introduction to the use of the terminal before the program of i n s t r u c t i o n began. Immediately a f t e r completing his program, each student wrote the posttest. The time for the students to complete the program and write the test-was approximately two hours. STATISTICAL ANALYSIS Statement of hypotheses In order that the program of i n s t r u c t i o n may be con-sidered to have frame dependency and be l o g i c a l l y sequenced, i t i s necessary that there be a s i g n i f i c a n t increase i n the program error rate and the program completion time when the l o g i c a l program i s compared to the scrambled program. F o l -lowing are the hypotheses tested: 19. Hi. There i s no s i g n i f i c a n t difference i n the program error rates between the l o g i c a l l y sequenced group and the scrambled sequenced group. H2. There i s no s i g n i f i c a n t difference i n the program completion time between the l o g i c a l l y sequenced group and the scrambled sequenced group. The questions presented on page 5, i n Chapter I, are stated below as n u l l hypotheses: H3. There i s no s i g n i f i c a n t difference between the means of the posttest scores of program facts and s k i l l s for the two groups dependent on a l o g i c a l or scrambled sequence of i n s t r u c t i o n . H4. There i s no s i g n i f i c a n t i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l on learning program facts and s k i l l s . H5. There i s no s i g n i f i c a n t difference between the means of the posttest scores of extension questions for the two groups dependent on a l o g i c a l or scrambled sequence of i n s t r u c t i o n . H6. There i s no s i g n i f i c a n t i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l on solving extension problems. Data For each student, two posttest scores were obtained. One score (out of 12) corresponded to the number of cor r e c t 20. responses to the test on c r i t e r i o n s k i l l s and the second score (out of 30) corresponded to the number of correct responses to the extension questions. S t a t i s t i c a l treatment of data The number of program errors, the program completion time and the two posttest scores were analyzed by means of a two factor design analysis of variance with an a l e v e l of .05. The following mean scores tabulated made for the four dependent v a r i a b l e s : TABLE I THE TWO FACTOR DESIGN High IQ Low IQ Lo g i c a l - X X Sequence 11 12 1. Scrambled ^ X X Sequence 21 22 2, X . l X.2 CHAPTER IV ANALYSIS OF THE DATA RESULTS OF THE STUDY Means o f the groups The complete t a b u l a t i o n of t h e program e r r o r s , t h e program c p m p l e t i o n time and the p o s t t e s t s c o r e s f o r each o f th e Ss may be found i n Appendix IV. As o u t l i n e d i n T a b l e I , the means o f each group f o r program e r r o r s , t h e program com-p l e t i o n t i me and the two p o s t t e s t s c o r e s a r e p r e s e n t e d i n T a b l e s I I , I V , V I , and V I I I r e s p e c t i v e l y . ANALYSIS OF THE HYPOTHESES H y p o t h e s i s I H y p o t h e s i s I s t a t e d 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 i n the program e r r o r r a t e s between t h e l o g i c a l l y sequenced group and the s c r a m b l e d sequenced group. The a n a l y s i s o f v a r i a n c e w i t h program e r r o r s as t h e dependent v a r i a b l e i s summarized i n T a b l e I I I . S i n c e the d e s i r e d a o f .05 was a t t a i n e d , the n u l l h y p o t h e s i s was r e j e c t e d and i t was c o n c l u d e d t h a t the s c r a m b l e d sequenced group p r o d u c e d s i g n i f i -c a n t l y more program e r r o r s t h a n t h e l o g i c a l l y sequenced group. 22. It should be noted that the aste r i s k s used i n a l l the analysis of variance tables indicates that the F - r a t i o was s i g n i f i c a n t . I t w i l l also be noted that there was a s i g n i f i c a n t difference between the mean scores of the high IQ group and the low IQ group i n program er r o r s , program comple-tio n time, and the posttest scores of program facts and s k i l l s . This was expected when the variable IQ was dichotomized and was not considered as part of the hypotheses. TABLE II MEANS OF PROGRAM ERRORS High IQ Low IQ Lo g i c a l Sequence 13.67 23. 22 18.44* Scrambled Sequence 28.89 37. 22 33.06* 21.28* 30.22* 25.75** *Group means **Grand mean TABLE I I I A N A L Y S I S OF VARIANCE FOR HYPOTHESIS I Source of Variance df ss MS F Sequence 1 1921.36 1921.36 16.03* IQ 1 720.03 720.03 6.01* Sequence X IQ 1 3. 36 3. 36 0. 03 Error 32 3835.97 119.87 Hypothesis II Hypothesis II stated that there would be no s i g n i -f i c a n t difference i n the program completion time between the l o g i c a l l y sequenced group and the scrambled sequenced group. The analysis of variance with completion time as the dependent variable i s summarized i n Table V. From these r e s u l t s , the n u l l hypothesis was rejected and i t was concluded that the scrambled sequenced group took s i g n i f i c a n t l y more time to complete the program than the l o g i c a l l y sequenced group. Thus the r e j e c t i o n of hypotheses I and II indicated that the program of i n s t r u c t i o n used i n the study s a t i s f i e d the d e f i n i -tion of a l o g i c a l l y sequenced program of i n s t r u c t i o n . TABLE IV MEANS OF COMPLETION TIME (IN MINUTES) High IQ Low IQ Log i c a l Sequence 63.33 73.67 68.50* Scrambled Sequence 68.56 78.78 73.67* 65.94* 76.22* 71.08** *Group means **Grand mean 24. TABLE V ANALYSIS OF VARIANCE FOR HYPOTHESIS I I Source of Variance df ss MS F Sequence 1 240.25 240.25 4. 32* IQ 1 950.69 950.69 17.09* Sequence X IQ 1 0. 03 0.03 0.00 Error 32 1779.78 55.62 Hypothesis III Hypothesis III stated that there would be no s i g n i f -icant difference between the means on the posttest of program facts and s k i l l s for the l o g i c a l l y sequenced group and the scrambled sequenced group. The analysis of variance for t h i s posttest measure i s i n Table VII. On the basis of these r e s u l t s , the n u l l hypothesis was not rejected and i t was concluded that there was no s i g n i f i c a n t difference between the means on posttest scores of program facts and s k i l l s . Hypothesis IV Hypothesis IV stated that there would be no s i g n i f -icant i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l on a test of program facts and s k i l l s . The analysis of variance for th i s posttest measure i s i n Table VII. On the basis of these r e s u l t s , the n u l l hypothesis was not rejected and i t was concluded that there was no s i g n i f i c a n t i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l for t h i s posttest measure. TABLE VI MEANS OF THE TEST OF PROGRAM FACTS AND SKILLS High IQ Low IQ Logical Sequence 10.11 7.22 8.67* Scrambled Sequence 7.33 6.00 6.67* 8.72* 6.61* 7.67** *Group means **Grand mean TABLE VII ANALYSIS OF VARIANCE FOR HYPOTHESES III AND IV Source of Variance df ss MS F Sequence 1 36 . 00 36.00 3.89 IQ 1 40.11 40.11 4.33* Sequence X IQ 1 5.44 5.44 0.58 Error 32 296.44 9. 26 26. Hypothesis V Hypothesis V s t a t e d t h a t there would be no s i g n i f i -can d i f f e r e n c e between the mean s c o r e s f o r the two groups on a t e s t of e x t e n s i o n problems. The a n a l y s i s o f v a r i a n c e f o r t h i s p o s t t e s t measure i s i n T a b l e IX. On the b a s i s of these r e s u l t s , the n u l l h y p o t h e s i s was not r e j e c t e d and i t was concluded t h a t there was no s i g n i f i c a n t d i f f e r e n c e between the means o f the two groups f o r t h i s p o s t t e s t . Hypothesis VI Hypothesis VI s t a t e d t h a t there would be no s i g n i f i -c a n t i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l on a t e s t of e x t e n s i o n problems. The a n a l y s i s of v a r i a n c e f o r t h i s p o s t t e s t measure i s i n Tab l e IX. On the b a s i s o f these r e s u l t s , the n u l l h y p o t h e s i s was not r e j e c t e d and i t was concluded t h a t t h e r e was no s i g n i f i c a n t i n t e r a c t i o n between sequence of i n s t r u c t i o n and a b i l i t y l e v e l f o r t h i s p o s t t e s t measure. TABLE V I I I MEANS OF THE TEST OF EXTENSION PROBLEMS High IQ Low IQ L o g i c a l Sequence 17.89 12.44 15.17* Scrambled Sequence 13.56 10.78 12.17* 15.72* 11.61* 13.67** *Group means **Grand mean TABLE IX ANALYSIS OF VARIANCE FOR HYPOTHESES V AND VI Source of Variance df ss MS F Sequence 1 81.00 81.00 2.18 IQ 1 152.11 152.11 4. 09 Sequence X IQ 1 16. 00 16. 00 0.43 Error 32 1190.88 37. 22 EXPLICATION OF THE RESULTS The program of i n s t r u c t i o n The n u l l Hypotheses I and II were rejected, thus implying that the program used i n the study contained frame dependency and s a t i s f i e d the d e f i n i t i o n of a l o g i c a l sequence of i n s t r u c t i o n . I t was generally observed that the error rate started high for each of the Ss i n the scrambled sequenced group as the student encountered problems for which he s t i l l did not have the prerequisite knowledge. I t seemed that as more of the pr e r e q u i s i t e knowledge was gathered together by the student, the error rate gradually decreased to the same rate as the l o g i c a l l y sequenced group. While scrambling a program of i n s t r u c t i o n which has dependency among the frames does increase the number of errors at the beginning of the program, 28. the Ss apparently are able to organize the necessary pre-r e q u i s i t e s k i l l s so that by the end of the program, they are performing at the same l e v e l as students i n the l o g i c a l program. The same observation could be made for program comple-t i o n time. At the s t a r t of the program, the Ss i n the scrambled group were puzzled by a question for which they did not have the necessary prerequisite s k i l l s to answer, and they simply had to guess at the correct answer. As the necessary pre-r e q u i s i t e s k i l l s were eventually assimilated, the amount of response time to the question presented became approximately the same as the l o g i c a l l y sequenced group. The posttest scores While the l o g i c a l l y sequenced group did not perform s i g n i f i c a n t l y better than the scrambled sequenced group on either the t e s t of program facts and s k i l l s or the extension problems, i t was observed that i n each case, the mean score for the l o g i c a l l y sequenced group was greater than for the scrambled sequenced group. Although the obtained F value, 3.89 was not s i g n i f i c a n t , the difference between the scores of the two groups on program facts and s k i l l s tended toward si g n i f i c a n c e (.05 < p < .10). From the previous studies done in program sequencing, i t was expected that there would be very l i t t l e d ifference between the two groups on t h i s posttest measure. I t seemed possible that these facts and s k i l l s could be learned from a scrambled program, e i t h e r through the correct answer being supplied i n the program, or through the reorganiza-ti o n by the student when the prerequisite s k i l l s are eventually met. When questions concerning these facts appeared i n the posttest, he would be able to answer the questions c o r r e c t l y . The difference between the scores of the two groups i n the t e s t of extension problems did not even meet the ten percent l e v e l of s i g n i f i c a n c e and i t was the experimenter's b e l i e f that the difference between the two groups would be greater i n the posttest of extension problems than i n the post-t e s t of program facts and s k i l l s . That the students i n the scrambled sequence learned these facts and s k i l l s through t h e i r eventual appearance i n the program was not s u r p r i s i n g , but i t seemed doubtful that they would be able to assimilate the pro-gram material to solve the extension problems. Perhaps the concepts and p r i n c i p l e s that were developed i n the program were what Brown (2:44) c a l l s "low order p r i n c i p l e s . " Even though the program was presented i n a scrambled order, the Ss were s t i l l able to understand these p r i n c i p l e s and apply them to solve the extension problems. The IQ by sequence i n t e r a c t i o n for each of the two posttest measures has been plo t t e d i n Figures 1 and 2. In each case, there i s no i n d i c a t i o n that the scrambled sequence 30. FIGURE 1 MEAN POSTTEST PERFORMANCE ON PROGRAM FACTS AND SKILLS Mean Scores 12 11 10 9 8 7 6 5 High IQ Low IQ + L o g i c a l Scrambled FIGURE 2 MEAN POSTTEST PERFORMANCE ON EXTENSION PROBLEMS Mean Scores 19 18 17 16 15 14 13 12 11 10 High IQ Low IQ 1 L o g i c a l Scrambled of i n s t r u c t i o n had a more detrimental e f f e c t on the performance of the low IQ group than the high IQ group. The Ss i n the study were above average i n a b i l i t y and perhaps, as Stolurow (23) found, a b i l i t y by sequence i n t e r a c t i o n i s s i g n i f i c a n t only at very low a b i l i t y l e v e l s . CHAPTER V CONCLUSION AND SUMMARY THE EFFECTS OF COURSE SEQUENCE While the present study dealt with a population that was younger than the population i n most of the previous studies, the r e s u l t s of the in v e s t i g a t i o n are i n close agreement with many of the e a r l i e r findings, which indicate that the e f f e c t s of a scrambled sequence of i n s t r u c t i o n may not be as d e t r i -mental to the learning of programed material as was o r i g i n a l l y considered to be the case. The r e s u l t s did show that scrambling a l o g i c a l l y sequenced program of i n s t r u c t i o n decreased the e f f i c i e n c y of the program as measured by the s i g n i f i c a n t increase i n error rate and completion time. Scrambling did not s i g n i f i c a n t l y e f f e c t student performance on learning program facts and s k i l l s or solving extension problems. The study attempted to control many of the l i m i t a t i o n s of previous studies. Neither the study by Krathwohl, Payne, and Gordon nor Roe, Case, and Roe discussed i n Chapter I found s i g n i f i c a n t difference i n the number of errors committed during i n s t r u c t i o n between the l o g i c a l and scrambled sequenced groups. As a conclusion to the i r studies, the impression was given that a program of i n s t r u c t i o n that f a i l e d to produce any s i g n i f i c a n t difference i n error rate when scrambled, could not be considered to have frame dependency, and could hardly be expected to have any e f f e c t on the amount learned from the scrambled program i n comparison to the o r i g i n a l version. Another c r i t i c i s m that has been offered i n the studies of program sequencing i s that scrambling the order of short programs of i n s t r u c t i o n may make l i t t l e d i fference to the desired outcomes. Evans (4:386) has stated that " . . . i t seems highly u n l i k e l y that any successful, well revised pro-gramofmore than 100 frames i n length, i n highly structured topics such as mathematics or l o g i c , could be succe s s f u l l y scrambled i n i t s e n t i r e t y and s t i l l do the job i t was designed to do." The program chosen for t h i s study s a t i s f i e d Evans' c r i t e r i a and i t was s t i l l found that scrambling of frames had no s i g n i f i c a n t e f f e c t on posttest scores. There was no i n d i c a t i o n of i n t e r a c t i o n between IQ and sequence of i n s t r u c t i o n and thi s r e s u l t i s i n agreement with many of the previous studies. I t was observed that for both posttest scores, the mean scores for the high IQ groups d i f f e r e d by a greater amount than the mean scores for the low IQ groups. Stolurow (23) found that program scrambling had a more detrimental e f f e c t on the learning of the low IQ group than the high IQ group, but the students i n his study were educationally handicapped. The Ss i n t h i s study were above average i n a b i l i t y (median IQ 116) and perhaps the low IQ group was much more able to reorganize the scrambled sequence by themselves than was the case in the study by Stolurow. LIMITATIONS OF THE STUDY The program of i n s t r u c t i o n The performance l e v e l reached by the l o g i c a l l y sequenced group on the posttest scores of program facts and s k i l l s was an average score of 72 percent. I t could be argued that the program was only p a r t i a l l y successful i n the i n s t r u c -t i o n of the program material and thus i t i s unreasonable to expect a large difference between the program and a scrambled version of the program. The sample As was discussed i n Chapter I I I , the students i n the study attended one school so that they probably were not a representative sample of the sixth-grade population. The students attending the school generally have above average a b i l i t y and t h i s might tend to lessen the i n t e r a c t i o n between a b i l i t y and sequencing. The Hawthorne ef f e c t s Since the treatment method necessitated a change from the students d a i l y routine, undoubtedly the change influenced the r e s u l t s of the study. I t was assumed that since both groups were subject to the same conditions, t h i s e f f e c t was equal for both groups. I t was not possible to assign a l l students to the teletypewriter terminals at the same time, and i t i s probable that some of the students who were l a t e r i n t h e i r assignment to the terminal could have gotten information about the study from t h e i r predecessors. I t was also necessary to t e l l several students i n the scrambled sequenced group that they should continue with t h e i r program of i n s t r u c t i o n , even though they were unable to answer some of the questions c o r r e c t l y . Some students, near the beginning of the program, were concerned about making errors and would ask f o r assistance from the examiner. This i n t e r a c t i o n d i d not e x i s t with the l o g i c a l l y sequenced group. IMPLICATIONS FOR FURTHER RESEARCH The experimenter suggests further research i n the area presented i n t h i s thesis where a more representative sample of the sixth-grade population than the sample chosen i n this study would be used. I f possible, i n further studies, the Ss should be assigned simultaneously to the teletypewriter terminals. Even though there was a lack of s i g n i f i c a n t d i f -ference between the means on the posttest scores for the two groups, i t i s important to note that i n the study by Wodtke (26) the mean scores on the posttest were greater for the scrambled sequenced group than the l o g i c a l l y sequenced group. This may indicate that perhaps sequencing of i n s t r u c t i o n should be considered more c a r e f u l l y with a younger group of Ss as was o r i g i n a l l y suggested. However, the writer would agree with the observations drawn from previous studies by Wodtke (2 6) and Niedermeyer (17) that there may be more important factors contributing to the variance i n students learning compared to the manipulation of the sequence of i n s t r u c t i o n . It i s apparent from the observation of posttest scores for students i n the scrambled sequenced group (see Appendix IV) that some students have excellent organizational s k i l l s . Studies dealing with organizational patterns employed by students might provide more information for the optimization of programed i n s t r u c t i o n than the manipulation of a sequence of i n s t r u c t i o n . SUMMARY This study was undertaken to investigate the e f f e c t s of scrambling a l o g i c a l sequence of i n s t r u c t i o n when dealing with a sixth-grade sample. While i t was expected that the scrambled sequence of i n s t r u c t i o n would not e f f e c t the learning of facts and s k i l l s developed i n the program, i t was f e l t that the scrambled sequence would be detrimental to the learning of p r i n c i p l e s developed i n the program which were needed to solve the extension problems. In each case, there was found to be no s i g n i f i c a n t difference between the l o g i c a l l y sequenced group and the scrambled sequenced group. However, there was a tendency toward s i g n i f i c a n c e (.05 < p < .10) between the mean scores on the test of the program facts and s k i l l s . The r e s u l t s of this study do not mean that course sequencing i n the writing of a program of i n s t r u c t i o n i s not important, but perhaps these r e s u l t s , together with many previous studies, r a i s e some questions on the importance of finding the ultimate sequence containing small steps and minimal error rate. I t may be that students are better able to cope with a scrambled sequence on i n s t r u c t i o n than had been considered possible, and i n s t r u c t i o n a l sequencing may be a somewhat overrated variable i n program construction. BIBLIOGRAPHY 38. Atkinson, R.C. and Wilson, H.A. (eds.). Computer-Assisted Instruction; A Book of Readings. New York: Academic Press, 1969. Brown, J.L. "Effects of L o g i c a l and Scrambled Sequences i n Mathematical Materials on Learning with Programmed Instruction Materials," Journal of Educational Psychology, LXI (1970), 41-45. Bushnell, D.D. and A l l e n , D.W. (eds.). The Computer i n American Education. New York: Wiley, 1967. Evans, J.L. "Programing i n Mathematics and Logic," Teaching Machines and Programed Learning I I , ed. Robert Glaser. Washington, D.C: National Edu-ca t i o n a l Association, 1965, pp. 371-440. Floyd, A. "An Evaluation of a Computer-Administered Challenging Teaching Strategy." Unpublished Master's t h e s i s , University of B r i t i s h Columbia, Vancouver, 1970. Gagne", R.M. The Conditions of Learning. New York: Holt, Rinehart and Winston, 1965. . "Learning and P r o f i c i e n c y i n Mathematics," Mathematics Teacher, LVI (1963), 620-626. and Brown, L.T. "Some Factors i n the Programing of Conceptual Learning," Journal of Experimental Psychology, LXII (1961), 313-321. and Paradice, N.E. " A b i l i t i e s and Learning Sets i n Knowledge A c q u i s i t i o n , " Psychological Monographs, LXXV, 14 (1961), 1-23. Heimer, R.J. (ed.). Computer-Assisted Instruction and the Teaching of Mathematics. National Council of Teachers of Mathematics, Inc., 1969. Holland, J.S. "Research on Programing Variables," Teaching Machines and Programed Learning I I , ed. Robert Glaser. Washington, D.C.: National Edu-ca t i o n a l Association, 1965, pp.66-117. . "A Quantitative Measure for Programmed Instruc-t i o n , " American Educational Research Journal, IV (1967), 87-101. 39. 13. Levin, G.R. and Baker, B.L. "Item Scrambling i n a S e l f -I n s t r u c t i o n a l Program," Journal of Educational Psychology, LIV (1963), 138-143. 14. Mager, R.F. and Clark, C. "Explorations i n Student-Controlled Instruction," Psychological Reports, XIII (1963), 71-76. 15. Maier, M.H. and Jacobs, P.I. "Eff e c t s of V a r i a t i o n i n a S e l f - I n s t r u c t i o n a l Program on I n s t r u c t i o n a l Outcomes," Psychological Reports, XVIII (1966), 539-546. 16. M i l l e r , H.R. "Sequencing and P r i o r Information i n Linear Programed Instruction," A.V. Communication Review, XVII (1969), 63-76. 17. Niedermeyer, F.C. "The Relevance of Frame Sequence i n Programed Instruction: An Addition to the Dialogue," A.V. Communication Review, XVI (1968), 301-317. 18. , Brown, J . and Sulzen, R. "Learning and Varying Sequences of Ninth-Grade Mathematics Materials," Journal of Experimental Education, XXXVII (1969), 61-66. 19. Payne, D.A., Krathwohl, D.R.,and Gordon, J . "The E f f e c t of Sequence on Programed Instruction," American Educational Research Journal, IV (1967), 125-132. 20. Roe, A. "A Comparison of Branching Methods for Programmed Learning," Journal of Educational Research, LV (1962), 407-416. 21. Roe, K.V., Case, H.W. and Roe, A. "Scrambled Versus Ordered Sequence i n Autoin s t r u c t i o n a l Programs," Journal of Educational Psychology, LIII (1962), 101-104. 22. Skinner, B.F. Science and Human Behavior. New York: Macmillan, 1953. 23. Stolurow, L.W. "So c i a l Impact of Programed Instruction: Aptitudes and A b i l i t i e s Revisited," Educational Technology, ed. J.P. DeCecco, New York: Holt, Rinehart and Winston, 19 64. 24. Suppes, P., Jerman, M and Brian, D. Computer-Assisted Instruction: Stanford's 1965-66 Arithmetic Program. New York: Academic Press Inc., 1968. 40. 25. Sutter, E.G. and Reid, J.B. "Learner Variables and Interpersonal Conditions i n Computer-Assisted Instruction," Journal of Educational Psychology, LX (1969), 153-157. 26. Wodtke, K.H., Brown, B.R., Sands, H.R. and Fredericks, P. Random Versus Ordered Sequencing i n Computer-Assisted Instruction. USOE Project No. 1435. Pennsylvania State University, 1967. A P P E N D I C E S APPENDIX I THE COMPUTER PRINT OUT OF THE TEXT MATERIAL AND A STUDENT'S RESPONSE Frame # A c t u a l T e x t 4 1 . 1 IN THE NUMERAL 26, WHICH OF THE FOLLOWING DOES THE 2 REPRESENT? 2 20 200 2000 20 COBRECT 2 I F THE 2 IH 26 REPRESENTS 20, WHAT DOES THE 6 REPRESENT? 6 GOOD 3 26 = 2 0 + 6 WHICH WE CAN WRITE AS 26 = 2 X 10 + 6 SO THE 2 IN 26 T E L L S YOU THERE ARE 2 ... »S 10 CORRECT 4 LOOK AT THE NUMERAL 84. 8K = 8 X ... + 1 10 COBSECT 5 8 4 = 8 X 1 0 + 4 YOU CAN SEE HOW IMPORTANT 10 IS IN 0OR COUNTING SYSTEM. ODR COUNTING SYSTEM IS BASED ON 10, AND WE SAY THAT WE COUNT IN BASE 10. HOW MANY FINGERS DO YOU HAVE (INCLUDING THUMBS ) ? 10 CORRECT 6 A LOT OF PEOPLE COUNT ON THEIR FINGERS. THAT PROBABLY EXPLAINS WHY WE COUNT IN BASE .... 10 COBRECT 7 BEFORE SOMEONE THOUGHT OF NUMBER BASES THEY HAD TO WRITE NUMERALS BY MAKING A TALLY L I K E THIS / / / / / / / / / / / / / / / / / / / / / / / / / / WOULD THIS TAKE LONGER THAN OUR USUAL WAY OF WRITING NUMERALS? ANSWER YES OR NO. YES THAT IS CORRECT 8 A CLEVER PERSON INVENTED A SHORT CODE TO SAVE ft LOT OF TIME. HE DECIDED TO COUNT IN TENS AND SEE HOW MANY GROUPS OF TEN HE COULD MAKE. / / / / / / / / / / / / / / / / / / / / / / / / / / HOW MANY GROUPS OF TEN COULD HE MAKE FROM THIS TALLY? 2 CORRECT Frame # A c t u a l T e x t 4 2 . 9 WHEN GROUPS OF TEN ARE MADE FROM THE FOLLOWING TALLY, / / / / / / / / / / / / / / / / / / / / / / / / / / HOW MANY ARE LEFT OVER? 6 GREAT 10 THE CODE FOR / / / / / / / / / / / / / / / / / / / / / / / / / / WAS 26, SINCE THERE WERE 2 GROUPS OF 10 AND 6 WERE LEFT OVER IN THE CODE,THE 2 IN 26 REPRESENTS 2 X ... 100 NO, THE 2 REPRESENTS 2 X 10 X 11 EVERYBODY WHO KNEW THE BASE 10 CODE, KNEW THAT WHEN HE WROTE 57 THE 5 REPRESENTED 5 X ... 10 THAT IS CORRECT 12 I F YOU DID NOT WANT TO COUNT BY TENS AND DECIDED TO USE A BASE EIGHT CODE, YOU WOULD THEN MAKE AS MANY GROUPS OF .... AS YOU COULD. 8 COBRECT 13 FROM THE FOLLOWING TALLY, / / / / / / / / / / / / / / / / / / / / / / / / / / HOW MANY COMPLETE GROUPS OF EIGHT CAN YOU MAKE? 3 THAT IS CORRECT 14 WHEN GROUPS OF EIGHT ARE MADE FROM THE FOLLOWING TALLY / / / / / / / / / / / / / / / / / / / / / / / / / / HOW MANY ARE LEFT OVER? 2 YES, THE ANSWER IS 2 15 SINCE YOU COULD MAKE 3 GROUPS OF 8 AND HAVE 2 LEFT OVER FROM THE TALLY / / / / / / / / / / / / / / / / / / / / / / / / / / , YOU WOULD WRITE 32 IN THIS CODE. SAY THIS TO YOURSELF AS THREE-TWO . DON'T SAY THIRTY-TWO BECAUSE IT DOES NOT MEAN THAT. WHEN WE SAY THIRTY-TWO WE MEAN THREE TENS AND TWO. IN THIS CODE THE 3 IN 32 REPRESENTS 3 ....'S 8 COBRECT 16 WHEN YOU USE BASE 8 CODE YOU MAKE AS MANY COMPLETE GROUPS OF .... AS YOU CAN. 8 CORRECT Frame # A c t u a l T e x t ^ 17 WRITE A BASE 8 NUMERAL TO REPRESENT THE FOLLOWING TALLY. / / / / / / / / / / / / / / / / / / / / / / 26 THAT IS CORRECT 18 THE BASE 8 CODE NUMERAL 26 TELLS YOU THAT THERE WERE 2 GROUPS OF . . . . . 10 NO, THERE WERE TWO GROUPS OF 8 19 I F WE WERE USING BASE FIVE CODE WE WOULD HAKE AS MANY GROUPS OF .... AS WE COULD. 5 VERY GOOD, THAT IS CORRECT 20 WRITE A NUMERAL FOR THIS TALLY IN BASE 5 CODE. / / / / / / / / / / / / / / / / / / / / / 41 YOU ARE CORRECT. 21 WRITE A NUMERAL FOR THIS TALLY IN BASE 5 CODE. / / / / / / / / / / / / / / / / / / / / / / / / 44 YOU ARE CORRECT 22 INSTEAD OF TALKING ABOUT BASE 5 CODE WE WILL JUST SAY BASE 5. I F 42 REPRESENTS 4 X 5 + 2 WE ARE USING BASS ... 5 VERY GOOD. 23 I F 42 REPRESENTS 4 X 10 + 2 WE ARE USING BASE 10 THAT IS CORRECT. 24 I F 42 REPRESENTS 4 X 8 + 2 WE ARE USING BASE 8 BASE 8 IS CORRECT 25 I F WE ARE COUNTING IN BASE 5, 43 REPRESENTS 4 X + 3 5 YOU ARE CORRECT 26 I F WE ARE COUNTING IN BASE 8, 43 REPRESENTS 4 X ... + 3 8 THAT IS CORRECT 27 DO 43 IN BASE 5 AND 43 IN BASE 8 REPRESENT THE SAME THING ANSWER YES OR NO YES NO, THE ANSWER IS NO X e #- A c t u a l T e x t kk. IN ORDER TO TELL THE DIFFERENCE BETWEEN TWO NUMERALS WE NEED TO KNOW WHAT BASES ARE BEING USED. SUPPOSE YOU WERE WATCHING SOMEONE COUNTING SOME THINGS AND TO HELP HIMSELF HE WAS ARRANGING THEM L I K E THIS. * * * * * * * * * * * * * * * * * * * * * * * WHAT NUMBER BASE WOULD YOU GUESS HE WAS USING? 10 VERY GOOD FOR THIS ARRANGEMENT, * * * * * * * * * * * * * * * * * * * * * * * HOW MANY COMPLETE GROUPS OF TEN COULD BE FORMED? 2 CORRECT HOW MANY ARE LEFT OVER WHEN GROUPS OF TEN ARE MADE FROM THIS ARRANGEMENT? * * * * * * * * * * * * * * * * * * * * * * * 3 YOU ARE CORRECT A NUMBER OF THINGS IS REPRESENTED BY 2 X 10 + 3 WHICH IS WRITTEN IN BASE 10 AS ..... 20 NO, IT IS WRITTEN AS 23 SUPPOSE THAT STARS WERE ARRANGED AS FOLLOWS, * * * * * * * * * * * * * * * * * * * * * * * WHAT BASE DO YOU THINK THIS PERSON IS USING? 6 VERY GOOD IT LOOKS L I K E BASE 6 IS BEING USED IN THIS ARRANGEMENT * * * * * * * * * * * * * * * * * * * * * * * SINCE HE HAS ARRANGED AS MANY OF THE STARS AS POSSIBLE I GROUPS OF ..... 6 CORRECT HOW MANY ARE LEFT OVER WHEN GROUPS OF 6 ARE MADE? * * * * * * * * * * * * * * * * * * * * * * * 5 GREAT Frame # A c t u a l T e x t 45. 35 HOW MANY COMPLETE GBOUPS OF 6 ARE THERE IN THIS ARRANGEMENT? * * * * * * * * * * * * * * * * * * * * * * * 3 THAT IS CORRECT 36 A NUMBER OF THINGS IS REPRESENTED BY 3 X 6 + 5. A BASE SIX PERSON WOULD WRITE - THERE ARE ..... THINGS. 23 NO, HE WOULD WRITE 35 X 37 FOR 35 IN BASE 6 THE 3 REPRESENTS 3 'S. 6 CORRECT 38 LOOK AT THE GROUP OF STARS NOT ARRANGED. * * * * * * * * * * * * * * * * * * * * * * * SUPPOSE YOU WERE ACCUSTOM TO COUNTING IN. BASE 5. THE FIRST THING YOU WOULD DO WOULD BE TO MAKE AS MANY COMPLETE GROUPS OF .... AS YOU COULD, 5 YOU ARE CORRECT 39 TO HELP YOU COUNT, MARK OFF THE STARS IN F I V E S , L I K E THIS * * * * * / * * * * * / * &ND SO ON. WITH THE FOLLOWING STARS, * * * * * * * * * * * * * * * * * * * * * * * HOW MANY COMPLETE GROUPS OF F I V E CAN YOU MAKE? 4 CORRECT 40 HOW MANY ARE LEFT OVER WHEN COMPLETE GROUPS OF FIVE ARE MADE FROM THIS COLLECTION OF STARS? * * * * * * * * * * * * * * * * * * * * * * * 4 NO, THERE ARE 3 X 41 A BASE F I V E PERSON MIGHT ARRANGE THE STARS L I K E THIS, * * * * * * * * * * * * * * * * * * * * * * * IN GROUPS OF 5 WITH 3 LEFT OVER. HE WOULD WRITE - THERE ARE .... STARS 43 VERY GOOD Frame # A c t u a l T e x t _ ^ 42 IN BASE 5 THE 4 IN 43 REPRESENTS 4 .... »S. 5 CORRECT 43 HERE IS A GROUP OF STARS. * * * * * * * * * * * * * * * A BASE 7 PERSON WOULD WRITE - THERE ARE STARS 21 VERY GOOD 44 THE 2 IN 21 IN BASE 7 TELLS YOU THAT YOU WERE ABLE TO HAKE 2 GROUPS OF 7 CORRECT 45 HERE ARE SOHE STARS. * * * * * * * * * * * * * * * WHAT IS THE BASE 8 NUMERAL FOR THE NUMBER OF STARS? 17 VERY GOOD 46 THE NUMERAL TO REPRESENT THE GROUP OF STARS, * * * * * * * * * * * * * * * IN BASE 8 I S 17 SINCE YOU CAN MAKE ONE COMPLETE GROUP OF 8 AND HAVE .... LEFT OVER. 7 CORRECT 47 17 IN BASE 8 AND 21 IN BASE 7 BOTH REPRESENT THE SAME NUMBER. DO 17 AND 21 NORMALLY REPRESENT THE SAME NUMBER? ANSWER YES OR NO. NO CORRECT 48 IT I S IMPORTANT TO KNOW WHAT BASE IS BEING USED. WE WILL WORK IN BASE 5 AND SEE HOW THIS CHANGES OUR ARITHMETIC. WHEN WE COUNT IN BASE 5 WE MAKE AS MANY GROUPS OF .... AS WE CAN. 5 CORRECT 49 HERE ARE SOME STARS. * * * * * * * * * * * * * * WHAT IS THE BASE FIVE NUMERAL FOR THE NUMBER OF STARS? 24 VERY GOOD 50 COUNTING CAN BE ILLUSTRATED THIS WAY. * ** *** **** * * * * * YOU CAN WRITE EACH OR THESE AS BASE 5 NUMERALS. WHAT IS * * * IN BASE 5 ? 3 VERY GOOD HESS® * A c t u a l Text 51 WHAT IS * * * * * IH BASE 5 ? 1 SO, THE ANSWER IS 10 52 WHAT IS * IN BASE 5 ? 1 47 5 3 54 5 5 56 57 CORRECT OOR COUNTING SO FAR IN BASE 5 I S * ** *** **** ***** 1 3 10 THERE ARE TWO SPACES HERE . WHAT GOES IN THE FIRST ONE ? 2 CORRECT WHAT GOES IN THE SECOND SPACE FOR BASE 5 COUNTING? * ** *** **** ***** 1 3 10 4 VERY GOOD WE HAVE, * 1 * * 2 * * * 3 * * * * (j * * * * * 10 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * LET'S REPRESENT THE NUMBER OF STARS IN THE MISSING SPACES BY A BASE FIVE NUMERAL. WHAT IS THE BASE FIVE NUMERAL FOR * * * * * * 1 1 VERY GOOD WHAT IS THE BASE FIVE NUMERAL FOR THIS NUMBER OF STARS * * * * * * * * 13 CORRECT WHAT IS THE BASE FIVE NUMERAL FOR THIS NUMBER OF STARS * * * * * * * * * * 20 VERY GOOD Frame # A c t u a l T e x t ^ 58 ODE COUNTING IN BASE F I V E IS 1 2 3 4 10 11 .. 13 .. 20 WHAT COMES AFTEB THE 11? 11 I S READ AS ONE-ONE, NOT ELEVEN. 12 CORRECT 59 WHAT COMES AFTER 13 IN BASE FIVE COUNTING? 14 CORRECT 60 BASE 5 COUNTING LOOKS LIKE THIS. 1 2 3 4 10 11 12 13 14 20 ... WHEN WE COUNT IN BASE 5 DO WE USE THE SYMBOL 6 ? ANSWER YES OR NO . NO THAT IS CORRECT 61 WHEN WE COUNT IN BASE 5 DO WE USE THE SYMBOL 5 ? ANSWER YES OR NO NO CORRECT 62 WHEN WE COUNT IN BASE 5 WE ONLY USE THE SYMBOLS 0,1,2,3, AND 4. IN BASE 5 WE ONLY USE THOSE SYMBOLS THAT ARE LESS THAN ..... 5 CORRECT 63 HERE IS A BASE 5 QUESTION 3 + 4 = ... WHICH WE CAN WRITE AS * * * + * * * * = * * * * * * * 3 + 4 = WHAT IS THE SUM ? REMEMBER, THIS IS BASE 5. 12 VERY GOOD 64 IN BASE 5, * * * * * * * = * * * * * / * * WHICH WE WRITE AS 12. IN BASE 5, 3 + 4 = 12 HERE IS ANOTHER QUESTION IN BASE 5. * * + * * * * = * * * * * * 2 + 4 = ... WHAT IS THE SUM IN BASE 5? 11 THAT IS CORRECT Frame # A c t u a l T e x t 49. 65 IN BASE 5, 2 + 4 = 11 TRY THIS BASE 5 QUESTION . DRAW STARS TO HELP YOU IF YOU L I K E . 1 + 1 = ... 2 CORRECT 66 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 1 + 2 = ... 3 CORRECT 67 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 1 + 3 = ... 4 THAT IS CORRECT 68 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 1 + 4 = ... 10 VERY GOOD 69 TO FIND THE SUM OF 1 + 4 WE CAN'T USE THE SYMBOL 5 IN BASE 5 CODE. OUR COUNTING WENT 1 2 3 4 10 11 ... USING STARS, THE QUESTION 1 + 4 CAN BE WRITTEN, * + * * * * - * * * * * 1 + 4 = ... WHAT IS * * * * * IN BASE 5 ? 10 CORRECT 70 WE HAVE, 1 + 1 = 2 1 + 2 = 3 1 + 3 = 4 1 + 4 = 10 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 2 + 1 = ... 3 CORRECT 71 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 2 + 2 = ... 4 CORRECT 72 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 2 + 3 = ... 10 CORRECT Frame j A c t u a l T e x t 50. 73 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 2 + 4 = ... 11 CORRECT 74 WE HAVE, 2 + 1 = 3 2 + 2 = 4 2 + 3 = 10 2 + 4 = 11 NOW TRY THIS QUESTION, USING BASE 5. 3 + 1 = ... 4 CORRECT 75 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 3 + 2 = ... 10 CORRECT 76 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 3 + 3 = ... 11 CORRECT 77 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 4 + 1 = ... 10 CORRECT 78 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 4 + 2 = 11 CORRECT 79 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5 4 + 4 = ... 13 VERY GOOD 80 WE CAN SUMMARIZE BASE 5 ADDITION FACTS IN A TABLE. IN FRONT OF YOU IS A TABLE OF BASE 5 ADDITION. TO SHOW HOW IT WORKS, LET'S FIND THE SUM OF 2 + 3. LOOK DOWN THE LEFT-HAND COLUMN TO 2, AND PUT YOUR FINGER THERE. KEEP THAT FINGER WHERE IT IS AND LOOK ACROSS THE TOP ROW TO 3 AND PUT ANOTHER FINGER THERE. MOVE THE 2 FINGER ACROSS, AND THE 3 FINGER DOWN, UNTIL THEY MEET, WHICH SHOULD BE AT 10. THIS TELLS YOU THAT 2 + 3 = 10 NOW USE THE TABLE TO FIND THE SUM, 2 + 4 = ... 1 1 VERY GOOD Frame #• A c t u a l T e x t 51 . 81 USE THE TABLE IN FRONT OF YOU TO FIND THE SOM OF THESE NUMBERS IN BASE 5 4 + 1 = ... 10 VERY GOOD 82 83 84 85 86 87 USE THE TABLE IN FRONT OF YOU TO FIND THE SUM OF THESE NUMBERS IN BASE 5 3 + 3 = ... 1 1 VERY GOOD USE THE TABLE IN FRONT OF YOU TO FIND THE SUM OF THESE NUMBERS IN BASE 5 4 + 3 = ... 12 VERY GOOD USE THE TABLE IN FRONT OF YOU TO FIND THE SUM OF THESE NUMBERS IN BASE 5 1 + 3 = ... 4 VERY GOOD THE TABLE IN FRONT OF YOU CAN HELP YOU DO HARD ADDITION PROBLEMS IN BASE 5. USE THE TABLE WHENEVER YOU L I K E . LOOK AT THIS BASE 5 ADDITION PROBLEM. 41 + 32 THE FIRST THING TO DO IS ADD 1 AND 2. WHAT IS 1 + 2 IN BASE 5 ? 3 CORRECT THE FIRST STEP IN ADDING 4 1 AND 32 IN BASE 5 I S 41 + 32 3 NEXT WE ADD 4 AND 3. WHAT IS 4+3 IN BASE 5 ? 12 VERY GOOD THE ANSWER TO THE BASE 5 ADDITION PROBLEM BELOW IS 41 + 32 123 I S THIS THE SAME ANSWER AS YOU WOULD GET IN BASE 10 ? ANSWER YES OR NO NO YOU ARE CORRECT Frame # A c t u a l T e x t 52. 88 YOU GET DIFFERENT SUMS IN BASE 5 THAN IN BASE 10 BECAUSE NUMERALS LIKE 41 MEAN.DIFFERENT THINGS IN BASE 5 THAN IN BASE 10. IN BASE 5 THE 4 IN 41 REPRESENTS 4 ... »S. 5 THAT I S CORRECT 89 IN BASE 10 THE 4 IN 41 REPRESENTS 4 'S 10 CORRECT 90 IN BASE 8 THE 4 IN 41 REPRESENTS 4 . . . » S . 8 THAT IS CORRECT 91 HERE IS A BASE 5 PROBLEM. 32 + 22 WHAT IS THE FIRST THING TO DO ? 1. 3 + 2 2. 2 + 2 ANSWER 1 OR 2 2 YOU ARE CORRECT 92 WHEN PERFORMING COLUMN ADDITION, YOU ALWAYS ADD THE RIGHT - HAND COLUMN FI R S T . 32 + 22 WHAT IS 2 + 2 IN BASE 5 ? YOU CAN USE THE BASE 5 ADDITION TABLE IN FRONT OF YOU. 4 THAT IS CORRECT 93 THE PROBLEM IN COLUMN ADDITION BEGINS AS FOLLOWS, 32 + 22 4 THE FIRST STEP IS TO ADD 2 + 2 WHICH EQUALS 4. THE NEXT STEP I S TO ADD 3 AND 2. WHAT IS THIS SUM IN BASE 5 ? 10 CORRECT Frame #•• A c t u a l T e x t 53. 94 THE ANSWER TO THE BASE 5 ADDITION PROBLEM IS 32 + 22 104 NOW TRY THIS BASE 5 PROBLEM. DSE THE TABLE IN FRONT OF YOD WHENEVER YOU L I K E . 21 + 42 113 VERY GOOD 95 96 97 98 99 FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 40 + 34 124 VERY GOOD FIND THE SUM OF THESE TWO NUMBERS IH BASE 5. 43 + 31 124 VERY GOOD FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 32 + 32 114 VERY GOOD FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 30 + 20 100 VERY GOOD THIS BASE 5 ADDITION PROBLEM NEEDS SOME CARE. 23 + 14 THE FIRST THING TO DO IS TO ADD 3 AND 4. WHAT IS 3 + 4 IN BASE 5? 12 VERY GOOD Frame J A c t u a l T e x t 100 101 102 103 104 105 TO ADD THESE TWO NUMBERS IN BASE 5 23 + 14 2 YOU HAVE TO WRITE DOWN 2 IN THE ONES COLUMN AND CARRY 1 TO THE 5«S COLUMN AS IN ADDITION FOR BASE 10. WHAT IS THE SUM OF THE SECOND COLUMN WHEN 1 IS CARRIED OVER AS PAST OF THE SUM. 4 VERY GOOD THE SUM OF 23 AND 14 IS 23 + 14 4 2 HERE IS A PROBLEM IN WHICH YOU WILL HAVE TO DO SOME CARRYING. I T IS A BASE 5 PROBLEM. 13 + 24 42 VERY GOOD FIND THE SUM OF THESE TWO NUMBERS IS BASE 5. 14 + 24 43 VERY GOOD FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 14 + 2 21 VERY GOOD FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 23 + 12 40 THAT IS CORRECT FIND THE SUM OF THESE TWO NUMBERS IN BASE 5. 13 + 23 41 THAT IS CORRECT Frame # a c t u a l Text 55. 106 WHICH OF THESE IS THE SAME AS 2 X 11 ? 1. 2 + 4 1 2. 41 X 41 3. 41 + 41 ANSWER 1 OR 2 OR 3 3 THAT IS CORRECT 107 THE MULTIPLICATION QUESTION 41 X2 AND THE ADDITION QUESTION 41 + 41 REPRESENT THE SAME THING AND SO WILL HAVE THE SAME ANSWER. YOU CAN FIND THE ANSWER TO 4 1 X 2 BY WORKING OUT 41 + 41 WHAT IS THE ANSWER TO THIS PROBLEM IN BASE 5. 132 THAT IS VERY GOOD 108 HERE IS A BASE 5 MULTIPLICATION PROBLEM. 32 X2 WRITE IT AS AN ADDITION PROBLEM ON A PIECE OF PAPER IF YOU LIKE. YOU HAVE A BASE 5 ADDITION TABLE IN FRONT OF YOU NOT A MULTIPLICATION TABLE, SO ADDITION IS PROBABLY EASIER FOR YOU. WHAT IS THE ANSWER TO THE PROBLEM? 114 THAT IS VERY GOOD 109 FIND THE PRODUCT OF THESE TWO NUMBERS IN BASE 5 23 X2 101 THAT IS CORRECT 110 FIND THE PRODUCT OF THESE TWO NUMBERS IN BASE 5 33 X2 121 THAT IS VERY GOOD Frame # A c t u a l Text 1 11 FIND THE PRODUCT OF THESE TWO NUMBERS IN BASE 5 2 4 X 2 103 THAT IS VERY GOOD 112 SO NOW YOU KNOW HOW TO COUNT IN BASE 5 AND HOW TO DO SOME ADDITION AND MULTIPLICATION . THIS IS THE END OF THE LESSON. GO AND TELL THE TEACHER YOU HAVE FINISHED. GOODBYE. APPENDIX I I ORDER OF FRAME PRESENTATION FOR THE SCRAMBLED SEQUENCE PROGRAM I 97 27 60 51 84 102 34 105 7 63 49 17 96 93 46 32 95 58 87 54 29 37 103 14 42 79 30 50 25 8 20 109 76 21 52 28 19 1 47 55 2 81 18 24 106 83 82 73 36 15 99 111 43 38 48 91 6 5 107 92 26 66 104 74 68 101 41 3 40 78 108 56 4 69 70 44 80 9 65 72 86 85 10 39 11 89 45 57 67 100 62 13 59 33 23 75 22 110 94 61 12 90 16 53 98 71 77 88 31 64 35 PROGRAM II 50 13 41 18 90 84 30 91 94 74 101 59 97 29 7 73 78 65 11 33 95 98 55 54 44 102 36 110 35 4 85 69 2 47 67 34 57 38 40 3 63 75 104 26 100 24 25 106 48 92 86 71 58 6 62 49 72 32 80 77 53 42 46 31 81 96 10 66 28 87 8 89 14 105 12 82 27 5 108 16 64 52 109 88 79 45 15 76 107 99 1 21 56 60 23 17 39 9 61 83 22 19 37 68 103 93 70 51 20 43 111 PROGRAM III 104 32 56 36 35 85 9 14 12 47 87 55 2 77 54 66 102 103 53 49 18 58 71 1 74 110 33 84 83 19 23 100 46 25 78 61 13 22 75 96 72 17 26 97 93 76 40 4 64 38 45 82 43 73 90 106 65 44 67 59 88 62 105 42 29 60 50 8 37 51 31 41 108 30 111 11 68 39 92 34 94 95 80 101 79 107 81 6 86 10 109 52 24 16 15 21 3 70 27 63 69 91 5 57 20 7 98 28 99 89 48 PROGRAM I V 68 79 100 110 80 35 34 51 28 29 6 54 108 66 52 46 32 56 37 2 77 30 58 40 42 15 83 61 89 92 7 88 3 111 12 23 41 14 71 60 21 70 39 102 17 1 20 95 16 103 72 82 99 48 98 76 73 90 96 22 25 63 84 101 81 67 97 85 13 19 47 8 24 55 50 105 31 62 107 36 87 27 38 94 74 45 86 104 11 49 44 109 78 93 106 5 10 75 65 64 26 91 53 43 4 18 9 69 33 57 APPENDIX III THE POSTTEST 59. NAME: 1. If 27 represents 2 x 9 + 7 , what number base i s being used? 2. Write a base 7 numeral to represent t h i s number of sta r s . * * * * * * * * * * * * * * * * * * 3. Write a base 6 numeral to represent t h i s number of stars. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 4. Write a base 8 numeral to represent t h i s number of squares. D D D D d D D D D Q n D D D D O D 5. Represent this sum i n base 5 arithmetic. * * * * + * * * * * * * = * * * * * * * * * * * Represent t h i s sum i n base 4 arithmetic. * * * * * + * * * * * * = * * * * * * * * * * * 7. Write the base 5 numerals from 1 to 20. (both 1 and 20 are base 5 numerals) A l l the questions on t h i s page are base 5 questions. You may use your base 5 addition table whenever you l i k e . 8. Add i n base 5. 10 42 15. Add i n base 5. 321 240 9. Add i n base 5. 13 14 16. Add i n base 5. 24 33 42 10. Add i n base 5. 32 24 17. Add i n base 5. 432 324 11. Multiply i n base 5. 32 x2 18. Multiply i n base 5. 321 x 2 12. Mul t i p l y i n base 5. 24 x2 19. Multiply i n base 5. 234 x 2 13. Add i n base 5. 21 31 40 20. Multiply i n base 5. 21 x4 14. Add i n base 5. 412 231 21. Multiply i n base 5. 34 x3 61. 22. Write the base 4 numerals from 1 to 12. (both 1 and 12 are base 4 numerals) 23. Write the base 5 numerals from 32 to 44. (both 32 and 44 are base 5 numerals) The next s i x questions (numbers 24 to 29) are base 8 questions. Use the base 8 table provided whenever you l i k e . 24. Add i n base 8. 24 27. Multiply i n base 8. 63 73 x2 25. Add i n base 8. 36 28. Mult i p l y i n base 8. 35 24 x2 26. Add in base 8. 47 29. Multiply in base 8. 57 52 x2 — — 30. I f you were counting i n base 6, what numerals would you use? 31. What base would a person be using i f he wrote: I have 14 toes? (in f a c t he has the same number of toes as everyone else) 32. What base i s thi s person counting in? 33, 34, 35, 36, 40, 41, . . 62. 33. What base i s being used here? 4 + 3 = 10 34. Here i s an addition problem: 3 4 + 6 2 Could th i s be a base f i v e sum? Why? 35. If Ann writes: "I have 18 d o l l a r s , " when she i s counting i n base ten, then i f she were using base f i v e she would write: "I have d o l l a r s . " 36. Pete and B i l l have the same number of books. Pete counts his i n base f i v e and writes that he has 43 books. B i l l counts his i n base.ten and writes that he has books. 37. What i s the smallest possible base a person could be using i f he wrote down the sum 35 + 23? 38. Here i s part of a base four addition table. F i l l i n the spaces. 39. Subtract i n base 5. 33 -4 1 2 3 40. Subtract i n base 5. 23 -14 41. Here i s part of a base f i v e m u l t i p l i c a t i o n table. F i l l i n the spaces. X 63. 1 2 3 4 42. I f I have 23 d o l l a r s i n base 6, how many do I have in base 5? BASE FIVE ADDITION TABLE + 1 2 3 4 1 2 3 4 10 2 3 4 10 11 3 4 10 11 12 4 10 11 12 13 65. BASE EIGHT ADDITION TABLE + 1 2 3 • 4 5 6 7 1 2 3 4 5 6 7 10 2 3 4 5 6 7 10 11 3 4 5 6 7 10 11 12 4 5 6 7 10 11 12 13 5 6 7 10 11 12 13 14 6 7 10 11 12 13 14 15 7 10 11 12 13 14 15 16 APPENDIX IV THE EXPERIMENTAL DATA 66. TABLE X SCORES ON PROGRAM FACTS AND SKILLS FOR THE LOGICAL SEQUENCE HIGH I.Q. SCORES FOR EACH ITEM 1 2 STUDENT NUMBER 3 4 5 6 7 8 9 1. 1 1 1 1 1 1 1 1 1 2. 1 1 1 1 1 0 1 1 1 3. 1 1 1 1 1 0 1 1 1 4. 1 1 1 1 1 0 1 1 1 5. 1 1 1 1 0 0 1 1 1 6. 1 1 1 0 0 0 1 0 1 7. 0 0 1 1 1 1 1 1 1 8. 1 1 1 1 1 1 1 1 1 9. 1 1 1 1 1 1 1 1 1 10. 1 1 1 1 1 1 0 1 0 11. 1 1 1 1 1 1 1 1 0 12. 1 1 0 1 1 0 1 1 0 TOTAL SCORE 11 11 11 11 10 6 11 11 9 67. TABLE XI SCORES ON PROGRAM FACTS AND SKILLS FOR THE LOGICAL SEQUENCE LOW I.Q. SCORES FOR EACH ITEM 1 2 STUDENT NUMBER 3 4 5 6 7 8 9 1. 0 0 1 0 1 1 0 1 1 2. 1 0 0 0 1 1 1 0 1 3. 1 0 0 0 1 1 0 1 1 4. 1 0 0 0 1 1 0 1 1 5. 1 0 1 0 0 0 0 1 1 6. 0 0 0 0 1 0 0 1 0 7. 0 1 1 0 0 1 0 0 1 8. • 1 1 1 1 1 1 1 1 1 9. 1 1 1 1 1 1 0 1 1 10. 1 1 1 1 1 1 0 1 1 11. 0 0 0 1 1 1 0 1 1 12. 1 0 1 1 0 1 0 0 1 TOTAL SCORE 8 4 7 5 9 10 2 9 11 68. TABLE XII SCORES ON PROGRAM FACTS AND SKILLS FOR THE SCRAMBLED SEQUENCE HIGH I.Q. SCORES FOR EACH ITEM 1 2 STUDENT NUMBER 3 4 5 6 7 8 9 1. 1 1 1 1 1 1 1 1 1 2. 1 0 1 0 0 1 1 0 1 3. 1 0 1 0 0 1 1 0 1 4. 1 0 1 0 0 1 1 0 1 5. 1 0 0 0 0 1 0 0 0 6. 1 0 0 0 0 1 0 0 0 7. 1 1 1 1 0 1 1 0 1 8. 1 1 1 1 0 1 1 1 1 9. 1 0 1 1 1 1 1 0 1 10. 1 1 1 1 1 1 0 0 1 11. 1 1 0 1 0 1 0 0 0 12. 1 1 0 1 0 0 1 0 1 TOTAL SCORE 12 6 8 7 3 11 8 2 9 69. TABLE XIII SCORES ON PROGRAM FACTS AND SKILLS FOR THE SCRAMBLED SEQUENCE LOW I.Q. SCORES FOR EACH ITEM 1 2 STUDENT NUMBER 3 4 5 6 7 8 9 1. 0 0 0 1 1 1 1 0 0 2. 0 0 0 0 1 1 1 0 1 3. 0 0 0 0 1 1 1 1 1 4. 0 0 0 0 1 0 1 1 1 5. 0 0 0 0 1 1 0 0 0 6. 0 0 0 0 0 0 1 0 0 7. 0 0 0 0 1 0 1 0 1 8. 0 0 1 0 1 1 1 1 1 9. 0 1 1 1 1 1 1 1 1 10. 0 1 1 1 1 1 1 1 1 11. 0 0 1 1 1 1 1 1 1 12. 0 0 0 0 0 1 1 0 0 TOTAL SCORE 0 2 4 4 1 0 9 11 6 8 70. TABLE XIV SCORES ON EXTENSION MATERIAL FOR THE LOGICAL SEQUENCE HIGH I.Q. SCORES FOR STUDENT NUMBER : ITEM 1 2 3 4 5 6 7 8 9 13. 1 1 1 1 1 1 1 1 1 14. 1 1 1 0 1 1 1 1 1 15. 1 1 1 1 1 1 1 1 1 16. 0 1 0 1 1 0 1 0 1 17. 1 1 1 1 1 1 1 1 1 18. 1 1 0 1 1 1 1 1 0 19. 1 0 1 1 1 0 1 1 0 20. 1 0 1 1 0 0 0 1 0 21. 0 0 1 1 0 0 0 0 0 22. 0 0 1 0 0 0 1 1 1 23. 1 0 0 1 1 0 1 1 1 24. 1 0 0 1 1 1 1 1 1 25. 1 1 1 1 1 1 1 1 1 26. 1 1 1 .1 1 1 1 0 1 27. 1 0 1 1 1 1 1 1 0 28. 0 1 0 1 1 1 1 1 0 29. 0 1 1 0 1 1 1 1 0 30. 1 0 0 0 0 0 0 0 1 31. 0 0 1 1 1 0 1 0 1 32. 1 0 1 1 1 0 1 0 1 33. 0 0 1 1 0 0 1 1 1 34. 0 0 0 1 0 0 1 0 1 35. 0 0 1 0 1 0 1 1 1 36. 1 0 0 1 0 0 1 0 1 37. 1 0 0 1 0 0 1 0 0 38. 1 0 0 1 0 0 1 0 0 39. 1 0 0 1 0 0 1 0 0 40. 1 0 0 1 0 0 1 0 0 41. 0 0 1 0 0 0 1 0 1 42. 1 0 1 0 0 0 1 0 1 TOTAL SCORE 20 10 18 23 17 11 27 16 19 TABLE XV SCORES ON EXTENSION MATERIAL FOR THE LOGICAL SEQUENCE LOW I.Q. SCORES FOR STUDENT NUMBER EACH ITEM 1 2 3 4 5 6 7 8 9 13. 1 0 1 1 1 1 1 0 1 14. 0 1 1 1 1 1 1 0 1 15. 1 1 1 1 1 1 1 1 1 16. 0 0 1 0 0 1 0 1 1 17. 1 0 1 0 1 1 1 1 1 18. 1 0 1 1 1 1 0 1 1 19. 1 0 0 1 0 1 0 0 1 20. 1 0 1 0 0 1 0 0 1 21. 0 0 0 0 0 0 0 0 1 22. 0 0 0 0 0 1 0 0 1 23. 1 0 0 0 0 1 0 0 1 24. 1 1 0 1 1 1 1 0 1 25. 1 1 0 1 0 1 1 1 1 26. 1 1 0 1 1 1 1 1 1 27. 1 0 0 1 1 1 0 0 1 28. 0 0 0 1 0 0 0 0 1 29. 0 0 0 1 1 0 0 0 1 30. 0 0 0 0 0 0 0 0 0 31. 0 0 0 0 0 0 0 0 1 32. 0 0 0 0 0 0 0 0 1 33. 1 0 0 1 0 0 0 1 1 34. 1 0 0 0 0 1 0 1 1 35. 1 0 0 0 1 1 0 0 1 36. 1 0 0 0 0 1 0 0 1 37. 1 0 0 0 0 0 0 0 1 38. 0 0 0 0 0 0 0 1 1 39. 0 0 1 0 0 0 0 0 0 40. 0 0 1 0 1 0 0 0 0 41. 0 0 0 0 0 0 0 0 1 42. 0 0 0 0 0 0 0 0 0 TOTAL SCORE 16 5 9 12 11 17 7 9 26 72. TABLE XVI SCORES ON EXTENSION MATERIAL FOR THE SCRAMBLED SEQUENCE HIGH I.Q. SCORES FOR STUDENT NUMBER ! ITEM 1 2 3 4 5 6 7 8 9 13. 1 1 1 1 0 1 1 1 1 14. 1 1 0 1 0 1 1 0 1 15. 1 1 1 1 1 0 1 0 1 16. 1 1 0 1 0 0 0 0 1 17. 1 1 0 1 1 1 1 0 1 18. 1 1 0 1 1 1 1 0 1 19. 1 1 0 1 0 0 0 0 1 20. 1 0 1 1 0 1 1 0 1 21. 1 0 1 0 0 0 0 0 0 22. 0 0 1 0 0 1 1 0 1 23. 1 1 1 1 0 1 1 0 1 24. 1 0 1 1 1 0 1 0 1 25. 1 0 0 1 0 0 1 0 1 26. 1 0 1 0 1 0 1 0 1 27. 1 0 0 0 1 0 1 0 1 28. 1 0 0 1 1 0 1 0 1 29. 1 0 0 0 1 0 1 0 1 30. 0 0 0 0 0 0 0 0 0 31. 0 0 0 0 1 0 1 0 1 32. 1 1 1 0 0 1 1 1 1 33. 1 0 1 0 0 0 1 0 0 34. 0 0 1 1 0 0 0 0 0 35. 1 0 0 0 0 1 1 0 0 36. 1 0 1 0 0 1 1 0 0 37. 0 0 1 0 0 0 1 0 0 38. 1 0 0 0 0 0 1 0 1 39. 1 0 0 1 0 0 1 0 0 40. 1 0 0 0 0 0 0 0 0 41. 1 0 0 0 0 0 0 0 0 42. 0 0 0 0 0 0 0 0 0 TOTAL SCORE 24 9 13 14 9 10 22 2 19 TABLE XVII SCORES ON EXTENSION MATERIAL FOR THE SCRAMBLED SEQUENCE LOW I.Q. EACH ITEM 1 2 3 4 5 6 7 8 9 13. 0 0 1 1 1 1 1 0 0 14. 0 1 1 0 1 0 1 1 0 15. 0 1 1 0 1 1 1 1 0 16. 0 0 0 1 1 1 1 0 0 17. 0 1 1 0 1 0 0 1 0 18. 1 0 0 1 1 1 1 1 1 19. 0 0 0 0 1 1 1 0 0 20. 1 0 0 0 1 0 1 0 0 21. 0 0 0 0 1 0 1 0 0 22. 0 0 0 0 0 0 1 0 1 23. 0 0 0 0 1 0 1 0 1 24. 0 1 1 0 0 1 0 1 1 25. 0 1 1 0 0 1 0 1 1 26. 0 1 1 0 0 1 1 1 1 27. 0 0 1 0 0 1 1 1 1 28. 0 0 1 1 0 1 0 1 1 29. 0 0 1 0 0 1 0 1 1 30. 0 0 0 0 0 0 1 0 0 31. 0 1 0 0 0 0 1 0 0 32. 1 1 0 0 0 0 1 0 1 33. 1 0 0 0 0 1 0 0 0 34. 0 0 1 0 0 1 1 0 0 35. 0 0 0 0 1 1 1 0 0 36. 0 0 0 0 0 1 1 0 0 37. 0 0 0 0 0 1 1 0 0 38. 0 0 0 0 0 0 0 0 1 39. 0 0 0 0 0 1 0 0 0 40. 0 0 0 0 0 1 0 0 0 41. 0 0 0 0 0 0 0 0 0 42. 0 0 0 0 0 1 0 0 0 TOTAL SCORE 4 8 11 4 11 19 19 10 11 TABLE XVIII PROGRAM ERRORS FOR THE LOGICAL SEQUENCE HIGH I.Q. LOW I.Q. STUDENT NUMBER OF STUDENT NUMBER OF NUMBER ERRORS NUMBER ERRORS 1. 7 1. 16 2. 11 2. 25 3. 15 3. 34 4. 18 4. 31 5. 23 5. 29 6. 25 6. 4 7. 2 7. 43 8. 9 8. 19 9. 13 9. 8 TABLE XIX PROGRAM ERRORS FOR THE SCRAMBLED SEQUENCE HIGH I.Q. LOW I.Q. STUDENT NUMBER OF STUDENT NUMBER OF NUMBER ERRORS NUMBER ERRORS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 46 25 20 30 33 23 47 26 1. 2. 3. 4. 5. 6. 7. 8. 9. 47 32 54 27 33 40 18 46 38 76. TABLE XX TIME TAKEN TO COMPLETE THE LOGICAL SEQUENCE HIGH I.Q. LOW I.Q. STUDENT TIME TAKEN STUDENT TIME TAKEN NUMBER (MINUTES) NUMBER (MINUTES) 1. 65 1. 70 2. 72 2. 73 3. 60 3. 75 4. 65 4. 81 5. 70 5. 75 6. 63 6. 78 7. 60 . 7. 68 8. 75 8. 75 9. 40 9. 68 77 TABLE XXI TIME TAKEN TO COMPLETE THE SCRAMBLED SEQUENCE HIGH I.Q. LOW I.Q. STUDENT TIME TAKEN STUDENT TIME TAKEN NUMBER (MINUTES) NUMBER (MINUTES) 1. 2. 3. 4. 5. 6. 7. 8. 9. 65 63 63 67 82 70 64 73 70 1. 2. 3. 4. 5. 6. 7. 8. 9. 80 78 75 70 75 75 78 80 .98 r ADDITIONS Page TITLE Page TITLE 8 AID FOR THE ASKING 5 BEHIND THE SCENE 2 BORDERS WHERE SCOTLAND & ENGLAND MEET 1 BREEDING FOR BEEF 5 CLASP SYSTEM OF BUILDING 8 CLEAR TO LAND 12 COMPUTER IN SPACE 8 CONTAINER PORT 5 COOK STRAIT STORY 4 CURIOUS HISTORY OF MONEY 8 EAST SIDE STORY - FLY PAST 3 ENCHANTED ISLE - JERSEY 11 ENDLESS WAR 10 ENVIRONMENT IN THE BALANCE 10 EXPERIMENT IN TEACHING 8 FELIXSTOWE AND THE CONTAINER 3 FOREST IS OUR FRIEND 1 FORMULA FOR PROGRESS 5 FRAMEWORK FOR THE FUTURE 8 FREIGHTLINER IN ACTION 5 GET WEAVING 10 HANDICAPPED CHILD 1 IN SEARCH OF AN ENGLISH GARDEN 6 INTERNATIONAL WOOLMARK 2 LIVINGSTONE, A TOWN FOR LOTKIANS 7 LOOKING AT LEATHER 12 MICRO-MINIATURISATION 11 NEW DIPLOMATS 9 NINTH RAIL REPORT 10 PATTERNS OF LEARNING 10 PLACE IN THE WORLD 13 PRICE OF A RECORD 12 RADIO ASTRONOMY 12 RADIO ISOTOPES 9 RESEARCH INTO CAR SAFETY 6 RETURN TO LOCHABER 13 REVIEW OF THE YEAR 13 RIDE THE WHITE HORSES 9 RIDING ON AIR 6 ROTOLOK 13 SAILS 13 SHAPE OF THE FUTURE - RESEARCH IN BRITAIN 6 THREADMAKERS 4 TOMORROW BEGINS TODAY 9 VICTORIA LINE - EQUIP AND COMPLETE 6 WATER, WATER EVERYWHERE 6 WEAVE ME A RAINBOW 7 WEST AT WORK 4 WORLD OF AUTOMATION
- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Study of program sequencing in computer- assisted instruction
Open Collections
UBC Theses and Dissertations
Featured Collection
UBC Theses and Dissertations
Study of program sequencing in computer- assisted instruction Struthers, Telford 1971
pdf
Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.
Page Metadata
Item Metadata
Title | Study of program sequencing in computer- assisted instruction |
Creator |
Struthers, Telford |
Publisher | University of British Columbia |
Date Issued | 1971 |
Description | This study was undertaken to investigate how program sequencing would effect a sixth-grade group of Ss. A linear program of 111 frames that taught base five arithmetic was chosen for the study. The program presented in its original order was called the logically sequenced program. The program whose frame sequence was determined by a table of random numbers was called the scrambled sequenced program. On the basis of IQ scores, two groups of students were formed. Equal numbers from each of these two groups were then assigned at random to one of the two programs of instruction. The two programs of instruction were presented to the Ss by means of computer terminals. A posttest was then administered to test the effect of program sequencing on learning facts and skills that were taken directly from the program. Also tested was the effect of program sequencing on the student's ability to use the principles developed in the program to solve problems that are an extension of these principles. There was found to be a significant increase in the program error rate and program completion time for the scrambled sequenced program when compared to the logically sequenced program, implying that the program chosen for the study contained dependency among the frames. The results of the posttest indicated that there was no significant difference between the mean scores of the two groups although in each case the logically sequenced group did achieve a higher mean score. It was also found that there was no significant interaction between sequence of instruction and ability level. Many previous studies in program sequencing have dealt with an older population in comparison to the population chosen for this study. The conclusions from these studies have generally been that sequence of instruction has been overemphasized as a variable for consideration in program construction. While the results of this study indicate that sequence of instruction may be more important for a younger population, some doubt is raised as to the importance of attempting to obtain a carefully sequenced, small error rate program. |
Subject |
Computer-assisted instruction Programmed instruction |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2011-05-18 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0093365 |
URI | http://hdl.handle.net/2429/34658 |
Degree |
Master of Arts - MA |
Program |
Mathematics Education |
Affiliation |
Education, Faculty of Curriculum and Pedagogy (EDCP), Department of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
Download
- Media
- 831-UBC_1971_A8 S87.pdf [ 3.52MB ]
- Metadata
- JSON: 831-1.0093365.json
- JSON-LD: 831-1.0093365-ld.json
- RDF/XML (Pretty): 831-1.0093365-rdf.xml
- RDF/JSON: 831-1.0093365-rdf.json
- Turtle: 831-1.0093365-turtle.txt
- N-Triples: 831-1.0093365-rdf-ntriples.txt
- Original Record: 831-1.0093365-source.json
- Full Text
- 831-1.0093365-fulltext.txt
- Citation
- 831-1.0093365.ris
Full Text
Cite
Citation Scheme:
Usage Statistics
Share
Embed
Customize your widget with the following options, then copy and paste the code below into the HTML
of your page to embed this item in your website.
<div id="ubcOpenCollectionsWidgetDisplay">
<script id="ubcOpenCollectionsWidget"
src="{[{embed.src}]}"
data-item="{[{embed.item}]}"
data-collection="{[{embed.collection}]}"
data-metadata="{[{embed.showMetadata}]}"
data-width="{[{embed.width}]}"
data-media="{[{embed.selectedMedia}]}"
async >
</script>
</div>
Our image viewer uses the IIIF 2.0 standard.
To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0093365/manifest