"LI B R^AFLY OF THE U N IVLR.SITY Of ILLINOIS 5/07 Ije64ct no M-(5 Digitized by the Internet Archive in 2013 http://archive.org/details/principlesofprog15rose s\o.y n o . 1^ ^ A^UCL. UNIVERSITY OF lUlNOIS Urbano, Illinois PRINCIPLES OF PROGRAMING: II. CHAMPAIGN COMMUNITY UNIT SCHOOL DISTRICT NUMBER k HIGH SCHOOLS ELlen F. Rosen^ Gerald L. Frincke and lavrence M. Stolurow COMPARATIVE STUDIES OF PRINCIPLES FOR PROGRAMMING MATHEMATICS IN AUTOMATED INSTRUaiON Technical Report No. I5 Septeffllaer, 1964 Co-lnvesiigalon; LowTMice M. Stolurow Professor, Deporttnont of Psychology Training Rosoorch Loborotory Max Beberman Profftssor, CoHego of Education Univorsity of Illinois Commiltoo on School MothomoHcs (UICSM) ProfecfSponsoR Educational Modia irandi U. S. Ofllco of EdvcirtiMi TIHoVII ProfMl No. 711151.01 UNtVERSin OF ILUmHS SEP 13 1966 LIBRARY U. S. Office of mucation Title VII COMPARATIVE STUDIES OF PRINCIPLES FOR PROGRAMING MATHEMATICS IN AUTOMATED INSTRUCTION Technical Report No. I5 PRINCIPLES OF PROGRAMING: II . CHAMPAIGN COMMUNITY UNIT SCHOOL DISTRICT NUMBER h HIGH SCHOOLS Ellen F. Rosen, Gerald L. Frincke and Lawrence M. Stolurow September, I96U a^w;- .V ■-; ^J^: . .:^y4r.L . ,.'p :.»5iri. >ii, A'tiS!!' -11- Ifeble of Contents Page List of Ifebles Ill Principles of Programing: II Champaign Community Unit School District Number h High Schools 1 Purpose 1 Method 1 Students 2 Subjects and Class Composition 2 Materials and Procedure 2 Formation of Experimental Groups 3 Analyses of Test Scores 3 Analysis of I^rt Times h Discussion ^ References 22 -ili. List of Tables Table p&ge 1 Composition and Treatment Conditions of Classes 6 2 Mean Score and Variance for Groups on Parts 104, 106, 107 7 3 Mean Score and Variance for Groups on Parts 110.5 and 112 8 k Summary of Analysis of Variance of Part loU 9 5 Summary of Analysis of Variance of Part 106 10 6 Summary of Analysis of Variance of Part 107 11 7 Summary of Analysis of Variance of Part 110.5 12 8 Siommary of Analysis of Variance of Part 112 13 9 Conservative F«max Tests 1^ 10 Mean Time and Variance for Groups on Parts 104 and 106 15 11 Mean Time and Variance for Groups on Parts l6 12 Summary of Analysis of Variance of Part 10^4- Times 17 13 Summary of Analysis of Variance of Part 106 Times I8 Ik Summary of Analysis of Variance of Part 110.5 Time I9 15 Summary of Analysis of Variance of Part 112 Time 20 16 Conservative F-max Tests 21 8 '■ o r -r.;. .•--f t:^ .^~~'-. ■ >•»• PRINCIPLES of PROGRAMING: II. CHAMPAIGN COMMUNITY UNIT SCHOOL DISTRICT NUMBER k HIGH SCHOOLS"'" ELlen F. Rosen, Gerald L. Frincke and Lawrence M. Stoluxow PURPOSE The studies done in the simmer session at the Urbana Junior High School (Stolurow, et. al., 1964) suggested the desirability of replicating some phases of the study with a larger sample size. The studies selected for replication were those concerned with the mode of presentation, the implementation of discovery, the sequencing of frames, and the size of step, METHOD In general, the attack on these problems was the same as that used in the summer. However, the classes in this study used only programed textbooks when they were covering the material of Parts lO^f, 106, 110.5^ and 112. The rest of the material of Unit I was taught by the teacher from the conventional UICSM Unit I. They only took the end tests for Parts lOif, 106, 107, 110.5, 112, and the Unit I review test. No pretests were administered. After com- pleting Part 112, students were asked to complete an attitude questionnaire. 1 This study would not have been possible without the cooperation and assistance of Paul W. Rainey of Jefferson Jr. High School, and Mrs. James Hill and Mrs. David Kohfeld of Champaign Senior High School. 50 J';.' a/^ i . ', j:>v The theoretical considerations for each problem were discussed in earlier reports (Stolurow & Beberman, I963; Stolurow et . al., 1964) and will not be reviewed here except as the data relates to them. Students There were four classes involved in this study. All four classes were composed of students who were considered to be slow learners of mathematics. Two classes were held at Champaign High School and two at Jefferson Junior High School. The teachers and class compositions are given in Table I. Also in Table I are presented the modes which the classes studied the materials under. Not all students were used in all studies. If data on a student were incomplete (student had not completed all previous parts) he was not incliided in the studies after the parts he had not finished. The number of students given in Table I is the number of students after those with incomplete data were dropped. In some cases students were not included because due to some technical error it was not known which group they belonged to. Subjects and Class Composition The subjects, as mentioned, consisted of four classes of slow mathematics learners. The classes were composed entirely of four sophmore high school students who had either previously only studied business mathematics and arith- metic or who had had first year algebra before and failed. The classes are listed in Table I. Materials and Procedure The course was based on the conventional UICSM text. Unit I was covered during the months from September until the beginning of the Christmas vacation fix o . :.'-^ X/.'- asio-e. 3 (Unit I review test administered at that time). The teachers taught their classes until they reached the topics covered by Part 104, 106, 110.5^ and 112 (Stolurow and Beberman, I963). When they reached one of these parts the teacher adopted one of the modes of presentaision using the programed text which were described before (S"Jolurow and Bebennan, I963). For the purposes of this paper, the modes will be given the following appelations: Mode E (pure) Mode E (anticipating) Mode E (following) pure (book) lead (book) follow As each booklet was finished, the appropriate end-test was administered. When Unit I was completed, the Unit I review test was given. Formation of E>cperimental Groups Students were divided by class into 2 groups for the lead-follow study. Table I indicated how the 2 groups were formed. For the rest of the studies, students were randomly assigned to treatment condition within class. One class always had the lead mode, one the follow, and two the pure. The treat- ment conditions are indicated in Table 1. Analyses of Test Scores The means and variances as well as the sample sizes are presented in Tables 2 and 3 for the parts. The means were tested for significance with a pxq analysis of variance with uneq.ual cell freq.uencies (Winer, I963). The summary tables of these analyses are presented in Tables k, 5^ 6, "J, and 8. The assumption of homogeneity of variance was tested by means of a conservative L'^'a ^ aJ: ■itiv; F maoc. test. The results of these analyses are presented in Table 9- The failure of this assumption casts some suspicion on the appropriateness of the analysis of variance model for these data. But since this analysis is reported to be robust vith respect to deviations from this assumption the results of the analysis are perhaps meaningful in spite of lack of homo- geneity of variance. The only variables which the analyses indicate had significant effects were presentation mode on P^rt 106, and sequence of frames on Part 110. 5 • These two parts were both ones which required the rejection of the assumption of homogeneity of variance. Analysis of Part Times The mean time and variance as well as the sample size for each part are presented in Tables 10 and 11. The means were tested for significance with the same analysis as was used for the test scores. All time scores were used from all subjects who met the following requirements: (l) they had recorded their times; (2) they had scores recorded for all preceding part tests as well as a score for the test corresponding to the part under consideration. The summary tables of these analyses (Tables 12, 13, l4, and 15) show that were significant effects in both parts 110.5 and 112. In Part 110.5 there were significant infc emotion crfi \ciriable effects and in Part 112 there were sig- nificant variable effects. > j6 ■a c f-nts- a conservative test of the assumption of homogeneity of variance for these analyses are presented in Table l6. The assumption is violated in the test on I^rt 110.5. DISCUSSION The hypotheses as formulated during the summer (Stolurow, et. al., 1964) in general -were not supported. Position of a frame in the sequence did seem to have some effect on both Part test performance and time. There is an inter- action of sequence vith mode in the time analysis; this confuses interpretation. Furtheimore the booklets which present the different sequences are of different length (logical sequence is longer). This difference in length could perhaps account for the time difference. The snail step size program is longer. Since there vas no difference on Part 112 in part test score, the Part 112 produces superior results in that immediate learning is as good as for 112 with a time saving.^ Since Part 110. 5 (random sequence) produced better learning as well as a savings in time, it is superior to the logical sequence version. 2 For a discussion of measurement of step, size, and actual rated and empirically determined step size, see Rosen and Stolurow (1964). .:jCi .iC. Ju;; j: E •;': OJ o o I O rH -P 0-i O VI o w . 0} o tj 4' v:: c: o c: d o 0) •H fi -p +3 •H oJ tJ (U d u o -p o 0) -d o a u o c« CO o c: -p d c o (U •H S -P -p •H ca TZi (U d ^1 O +3 o 0) Tj o S (in •O w CO • o d a) -d o S H O O Xi o CO M OJ x: o 05 0) EH w ra d iH o :^ CO M ft cd -P CO o H o VO ON (7\ CO CO S « 'd CO 0) CO OJ TJ CSJ (U 1^ • u • ►^ CO • • -Vh m ch 0) f^ rH H ;^ ;S >5 d • •H ^ cd s « CO OJ o •H O o rH H O MD CO o r-\ r-i O OJ OJ o rH o P>H u CO cd >s • -H m 00 a o (0 u \r\ cc; VO m (U rH 0) bO p< H ft t>0 ft ^H OJ od 0) U d) a -p H +* 05 -P rH W W U) r-i W lf\ rH nJ o •H O H CO C! u VO VD OJ CO ec ITN 1 d g M • TO •H CO x: 05 • o ft w w 0) CO en rH o OJ rH r-i a O •H O rH CO 03 03 -d Q rH • "Vh w x: 2 5 Q r J OJ o I o O O CO ■P o CO o u o u o 0) o c ca •H u o o CO d 03 Q • o 0) o d CD •H > d •P o d rH (1> I ■p o 03 H OJ u d Eh O (U o d 03 •H u > d 03 CO ltn no 00 s rH H 00 O OJ ^ oj OJ VD s O rH -d C s 05 -* O rH 03 c; ■P o ^ 03 -p CM fl ?H 05 > -r) C cS d 05 0) +3 0) o 03 0) EH -d o on 8 o ^ CM ^ CM oj m oj J- VD CM CM H ^ oo t- oo c^ f- rH \D m ^ r^ rH r^ rH ^ o 8 R OO oo CD O o i oj CM CO 00 t- IP\ 6 oJ OO CM oo oo oo oo -:* oo m c- ^ UA LTN CM VD rH rH ON en u (U u> ^H H <9 0) ^ a, s (d S -p 0) OJ ca Eh 0) o CtJ •H r-H d 0) ?H (u cd s o fciO OJ -H Ph CO S:wEH Pi -p c m :perimental studies of principles of programing. Urbana, 111.: Univer. of 111., USOE Title VII Proj. No. 711151.01, Technical Rept. No. 9, July, I96U. Stolurow, L. M. and Beberman, M. Comparative Studies of principles of programming mathematics in automated instruction. Urbana, 111.: Univor, of 111., USOE Title VII Proj. No. 7III5I.OI, Semi-Annual Report (Quarterly Reports 9 and 10), I96U. Winer, B. J. Statistical principles in experimental design. New York: McGraw-Hill, 1062. '.>,,•■■ r .: V \.iin i- ..y,;.:: ■.■^\ ^ •'■ if . '4 '« *" '\^^->