AN EXPERIMENT USING PROGRAMED MATERIAL IN TEACHING A NONCREDIT ALGEBRA COURSE AT THE CDLLEGE LEVEL Them for fha Degree oI PII. D MICHIGAN STATE UNIVERSITY . Elaine VlVlan AIton I . x = l|||||||H|HH||||HHII||llll||Hllllllll|ll|l|1|lllH|||||||l 3 1293 00628 1194 This is to certifg that the thesis entitled AN EXPERIMENT USING PROGRAMED MATERIAL IN TEACHING A NONCRE'DIT ALGEBRA COURSE AT THE COLLEGE LEVEL presented by Elaine Vivian Alton has been accepted towards fulfillment of the requirements for _P_h.D._ degree in _Edu03tion ”iii, )”7, j/Z; va Major professor Date May 17. 1965 O-169 -1. a .1 . , t ,t .rrIYb t. . I , .f , u. o. . . t1 . . T. s ABSTRACT AN EXPERIMENT USING PROGRAMED MATERIAL IN TEACHING A NONCREDIT ALGEBRA COURSE AT THE COLLEGE LEVEL by Elaine Vivian Alton The purposes of this study were (1) to develop programed material covering the topics of the Michigan State University course Mathematics 082, and (2) to compare the effectiveness of the programed material with that of a self-help and tutor method. The students in this study were those who enrolled in Mathematics 082 at Michigan State University in the winter and spring terms of 1964. The students who enrolled during the winter term were divided into two groups by the use of random numbers. One of these groups was designated as a control group and the other as an experimental group. These groups are referred to :‘~ ‘ - ' ' - “ '— ' " ‘ ' ‘ '— tively. There were eighteen students in C and twenty-one students in E.. The students who enrolled spring term were designated as an experimental group and referred to throughout the thesis as E2. Group 32 had thirteen students. The design of the study was such that students in the experimental groups used programed materials while the students in the control group used a combination workbook—text. The number and length of class periods were the same for the control and experimental groups. These class peri- ods were work sessions, and no lectures or class discussions were held. The experimental groups used the programed materials only in class. The control group took care of their own materials and could work on them outside of class. Students in the control group could obtain tutorial cr..n.. [\- .. . SIP-$3? ....... Elaine Vivian Alton help; however)no tutorial help was available for students in the experi- mental groups. Students in El received the material in sections which contained approximately 140 frames. obtaining additional material as they needed it. Students in E2 received all the material they needed for each test in the class session immediately following each examina- tion. The programed materials used by the experimental groups consisted of 1,067 frames constructed by the writer for this study. A senior undergraduate was in charge of El and the investigator was in charge of E2. No group discussions or lectures were held for either group. Four examinations were given each term. The tests were con- structed by the writer and all students took the same examinations. Comparisons relative to student achievement on each of the four examina- tions were made for (1) groups El and C, 2) groups E2 and C, and (3) groups (E1+E2) and C. The hypothesis tested in each comparison was that students using the programed material would do no better on the examina- tion than those students who did not use the programed material. Analy- sis of variance and covariance with two independent variables was used for the analysis of the data. The two independent variables were the students’ raw scores on the College Qualification Numerical Test and the students' raw scores on the Michigan State University Reading Test. Ad- justed mean scores were computed when the hypothesis was rejected. The hypothesis was accepted for the four comparisons of groups El and C. The hypothesis was rejected for the other e'ght comparisons, four of which were for groups E2 and C and four oi which were for groups (ElTEg) and C. The adjusted means for the experimental groups in the comparisons where the hypothesis was rejected were all -igher than for the control group, ——"=:”"’* Elaine Vivian Alton Based on the statistical results of this study, a student ques- txionnaire, and the experience of the writer in handling all the work s;essions for group E2, the following conclusions appear justifiable. l. The programed materials, as used in this study, were more effective than a combination workbook— text method for teaching a noncredit algebra courSe at the college level. Effective programed materials that are designed to meet specific student needs can be constructed by the classroom teacher. Students who used the programed materials felt that some tutorial help would have been helpful. In the field of mathematics, it is desirable to show the intermediate steps of a complex problem in arriving at the solution of a problem. AN EXPERIMENT USING PROGRAMED MATERIAL IN TEACHING A NONCREDIT ALGEBRA COURSE AT THE COLLEGE LEVEL By Elaine Vivian Alton A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY College of Education AN EXPERIMENT USING PROGRAMED MATERIAL IN TEACHING A NONCREDIT ALGEBRA By Elaine Vivian Alton A THESIS Submitted to Kichigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY College of Education 1965 Copyright by ELAINE VIVIAN ALTON l {I [i '3 ACKNOWLEDGMENT The writer is deeply indebted to Dr. John M. Mason, Chairman of her Guidance Committee, who gave generously of his time. knowledge. and experience in the direction of this study. The writer also wishes to acknowledge with appreciation the as— sistance and suggestions of Dr. Carl Gross, Dr. Edward Nordhaus. and Dr. Wayne Taylor who were members of her Guidance Committee. Appreciation is also expressed to Dr. Leroy Kelly and Dr. Frederic B. Dutton for their interest and assistance in the early planning of the study. Special recognition is due Dr. Kelly for his helpful comments and suggestions re- garding the construction of the programed material. The writer is also indebted to Dr. Charles P. Wells. Chairman of the Nhthematics Department, for encouragement and administrative approval and. support of the study. Appreciation is due Mr. Frank Martin for his help in processing the (iata obtained in this study. The writer is very grateful to the students who participated in the study for their time and cooperation which made completion of the shady-possible. The writer is indebted to her parents whose sacrifices and en- °°uragement were responsible for her early educational background and cOntinuing educational experiences. TABLE OF CONTENTS ACKNOWLEDGMENT. . . . . . . . . . . . . . . . . . LIST OF TABLES. . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . LIST OF APPENDICES. . . . . . . . . . . . . . . . CHAPTERS I. INTRODUCTION . . . . . . . . . . . . . . . . II. NEVIDN or LITERATURE . III. THE DEVELOPMENT OF THE PROGRAMED MATERIALS . Iv. ORGANIZATION AND IMPLEMENTATION OF THE STUDY . v. RESULTS AND FINDINGS OF THE EXPERIMENT . . . VI. SUMMARY AND CONCLUSIONS. . . . . . . . . . . BIBLIOGRAPHY. . . . . . . . . APPENDICES. iv 101 110 Table II. III. IV. VI. VII. VIII. XI. LIST OF TABLES STUDENT AGE AND PAST EXPERIENCE IN MATHEMATICS 082.. . . . . . . . . . . . . PAST EXPERIENCE OF STUDENTS IN HIGH SCHOOL MATHEMATICS COURSES . . . . . . . . . . GRADE DISTRIBUTION FOR HIGH HOOL MATHEMATICS COURSES - GROUP - u c o o o C.) (J; O GRADE DISTRIBUTION FOR HIGH SCHOOL MATHEMATICS COURSES — GROUP E1 . . . . . . . . . GRADE DISTRIBUTION FOR HIGH SCHOOL MATHEMATICS COURSES - GROUP E2 . . . . . . . . . MEANS FOR EACH TEST FOR EACH OF THE SAMPLES USED IN THE COMPARISONS. . . . . . . . . STANDARD DEVIATIONS FOR EACH TEST FOR EACH OF THE SAMPLES USED IN THE COMPARISONS. . . STATISTICAL COMPARISONS OF GROUPS E AND C ON FOUR TESTS, WINTER TERM, 1964 . . . . . . STATISTICAL COMPARISONS OF GROUPS E AND C ON FOUR TESTS: F RATIO, DEGREES OF FREEDOM, SIGNIFICANCE, ADJUSTED MEANS, AND THE DIFFERENCE BET‘VEEN ADJUSTED MEANS . . . . . . . . . STATISTICAL COMPARISONS OF GROUPS (E1+E2) AND C ON FOUR TESTS: FRATIO, DEGREES OF FREEDOM, SIGNIFICANC ADJUSTED MEANS, AND THE DIFFERENCE BETEW EEN ADJUSTED MEANS . . . . . . . . RESULTS OF THE STATISTICAL TREATMENT OF DATA FOR THE FIRST TEST, SECOND TEST, THIRD TEST, AND FINAL EXAMINATION. . . . . . . Page . 85 . 85 Figure LIST OF FIGURES STUDENTS IN THE STUDY DURING WINTER TERM, 1964, AND THE SAMPLES USED IN MAKING COMPARISONS . . . . . . . . STUDENTS IN THE STUDY DURING SPRING TERM, 1964 AND THE S‘MPLES USED IN MAKING COM ARISONS . . . . . . . . . . . . . SAMPLES USED IN MAKING COMPARISONS . . vi Page 68 74 77 APPENDICES Appendix Page A INSTRUCTIONS GIVEN TO GROUP C . . . . . . 110 B INSTRUCTIONS GIVEN TO GROUP E1 . . . . . 112 C INSTRUCTIONS GIVEN TO GROUP EZ . . . . . . . . . . . . 115 D DATA SHEET . . . . . . . . . . . . . . . . . . . . . . 117 E TEST SCORES FOR GROUP C . . . . . . . . . . . . . . . 118 F TEST SCORES FOR GROUP 31 . . . . . . . . . . . . . . . 119 G TEST SCORES FOR GROUP 32 . . . 120 H QUESTIONNAIRE . . . . . . . . . . . . . . . . . . . . 121 CHAPTER I INTRODUCTION One task of educational research is to learn how to provide ef- fective learning conditions in the classroom. In efforts to secure tentative answers to this problem, numerous instructional techniques have been developed and employed with varying degrees of success. One of the most recent instructional techniques to be employed is programed iJistruction. Such instruction may be implemented either by machines or rion-machine techniques. While machine programing has some desirable features, the literature indicates several disadvantages of this method. Some of the disadvantages of the use of machines are the expense of equipping a classroom with machines, the limited number of programs available for any one machine, and the limited amount of material which could be presented at any one time. In an effort to avoid these dis- advantages and to try to provide more effective instruction for a par- ticular learning task and a particular kind of student, this study was concerned with the use of non—machine programed materials to teach a matllematiCS course at Michigan State University. Statement of purposes. The purposes of this study were (1) the development of programed material covering the topics of the Michigan State University course Mathematics 082, and (2) the comparison of the effectiveness of the programed material with that of a self-help and and tutor method. Need for the study. Educators have been concerned for some time 1 twith the problems of providing quality instruction for an increasing zitnnber of students. It is recognized that the increased workload of -tfieachers and the greater class sizes resulting from the expanding tpjxih rate are hindrances to adequate instruction. As Rickover states: Few classrooms are ever closed because a teacher is lost. What happens is that teaching standards are lowered or the class size is raised. Jib is also recognized that traditional practices are not sufficient to Iarpvide the quantity and quality of education needed. Stolurow writes: Attempted solutions patterned exclusively after current practice will not solve the problem; not only do they take too long, but also the resources they require _- human teachers -— are not available for the task. Furthermore, even if teachers could be made available in the needed number, the cost of providing them by today's means alone would be crushing. There have been many suggestions as to how to maintain quality iristruction without increasing personnel requirements. Some critics of lunerican education, according to AndersonB, " . . . contend that we nuist choose between educating a small segment of our population ex— cexedingly well and trying to educate the remaining mass less well." He 'ponits out that this point of view has not as yet been proved and that mau13r people are unwilling to accept it. Most of the other suggestions fOI' improving instruction have involved the use of mass-instruction tecrniiques which will allow fewer teachers to handle larger groups of lHyman G. Rickover. "Investing in Our Youth." In: Ronald Steel (Ed. ). Federal Aid to Education. New York: H. M. Wilson.. 1961. p. 31. . 2Lawrence M. Stolurow. Teaching §y Machine. washington, D. 0.: United States Government Printing Office, 19 2. p. 2. 3Kenneth E. Anderson and Allen Jack Edwards. "The Educational ProCess and Programmed Instruction." Journal of Educational Research 55: 537: August 1962. ‘77 my. — students more effectively. Foremost of these mass-instruction tech- niques is television, both commercial and closed circuit. In addition, films, team teaching, independent work, and large lecture sections are iised. Skinner criticizes current suggestions for improving instruction, including the use of mass-instruction techniques. He states: It is significant that all this [current suggestions such as more schools, better teachers, television in- struction, etczl” can be done without knowing much about teaching or learning. Those who are most actively con— cerned with improving education seldom discuss what is happening when a student reads a book, writes a paper, listens to a lecture, or solves a problem, and their proposals are only indirectly designed to make those activities more productive. In short, there is a gener— a1 neglect of education method. The need for instruction is expanding so rapidly that mass-instruction devices such as those mentioned above are not sufficient to handle this rieed. Stolurow states: In the past, many approaches have been proposed, but they have been too limited in nature. In fact, from one point of view they have been aimed at treating the symp— toms rather than the basic problem itself; for example, manipulation of the teacher/student ratio, lengthening of the school year or providing the teacher with a be- wildering array of so-called aids. Genuine instructional efficiency might be achieved, however, by a reexamination of instruction itself rather than by attempts to patch up supporting activities. This reexamination might be aided by a new point of view. Thi_s concern with education method and the demand for a reexamination 0f instruction from a new point of view resulted from a recent reemphasis ”The bracket notation is used in this thesis to denote the autlior's insertion. 5B. F. Skinner. ”Why we Need Teaching Machines." Reprint from infinilative Record, Enlarged Edition. New York: Appleton—Century-Crofts, 1. p. 1 2.0 . 6Stolurow, _p. 213.. p. 4. u, <>r1 individual instruction as opposed to mass—instruction. During the lxast decade, experimental psychologists have conducted research aimed at gazialyzing how learning takes place and at identifying the optimum con— ciiiions for learning. A further aim of this research was the develop- rnfiant of teaching techniques which would maintain high quality instruction. 131a results of this research have led to a concept of instruction as a <:<>mmunication and control process which makes use of the interaction of 1311e student's behavior with the program of instruction. The dominant ixiea, according to Lumsdaine, is: . . . the concept that the processes of teaching and learning can be made an explicit subject matter for scientific study, on the basis of which a technology of instruction can be developed. Probably the best known instructional development to come from ‘ttie laboratory is the class of systems and instruments known as the teaching machine.8 Stolurow states: It [the teaching machine} is a system providing criti- cal functions not now implemented in the familiar in— structional device or teaching aid. This new system makes it possible to accomplish in the absence of a "live" teacher some of the critical functions of instruction through auto-instruction or automated teaching. Programed instruction is one technique developed through research to lielp deal with the instructional problems of large classes, individu— aligzed instruction, and self-study. Lysaughtlo, in commenting on why 7A. A. Lumsdaine and Robert Glaser. Teaching Machines and Pro- grinned Learning: A Source Book. washington, D. C. National Education ASSOciation, Department of Audio—Visual Instruction, 1960. p. 563. _ 8All the terms teaching machine, machine teaching, automated teach- 111g, auto—instruction, programed instruction, and programed learning are fcflnid in the literature in referring to this instructional technique. 98tolurow, _p. 913., p. 3. 1 0Jerome P. Lysaught. "Industrial Training Through Programmed Learning.” Reprint from Personnel Journal: 165; September 1961. 7‘ ijadustry is concerned with learning programs, points out that industrial txraining will always require new approaches and new conditions and iden- txifies two trends in training needs which call for the examination of programed instruction. Lysaught writes: The first trend is that toward higher and more complex human skills. The mechanical engineer must keep abreast of changing developments in electronics and hydraulics be- cause our new integrated systems require inter-disciplinary handling. The second trend is related to the first. We must further individualize our training efforts because the job needs of our people will become more unique, and we will find a rising proportion of training assignments invol 'ng a single individual, or at most a very limited number. Ifliese trends affect not only industrial training but all phases of edu- cation and training . Programed instruction can be used effectively as one technique in tlie process of instruction. Studies relating to the effectiveness of pIWDgramed instruction and its use as an instructional technique are cisted in the review of literature. However, despite its use as an ef- fecrtive instructional technique, there is still a great deal to learn abcnit this technique. Lysaught writes: There is a great deal we still must learn about programed learning. The programer needs to find better and surer approaches to the construction of sequences. The psycholo- gist recognizes that we do not know the last word concern- ing reinforcement and extinction and how these factors can best be applied to a student's learning behavior. The edu- cator sees unresolved questions among which are those con- cerned with the development of conceptual skills and ab— stract relationships. He may even view this whole develOp- ment as threatening teaching positions. The administrator is aware of many problems connected with the implemegta— tion of individualized learning in today's schools. 111mm, p. 165. 12Jerome P. Lysaught and Clarence M. Williams. ”A Community Ex. Plores Programed Learning." Reprint from New York State Education; February 1942. There is a constant need for the improvement of instruction. The Panel on wucational Research and Development which is under the auspices of the President's Science Advisory Committee states in its progress report: The effort to improve education . . . is not a one—shot affair. This activity should be carried on continuously. At the heart of the current effort lies the assumption that nobody knows the "ideal" system. Meeting immediate needs can prepare the way for longer—range reform, and new re— sults 'n fundamental research will Open up new possibili— ties. Michigan State University is faced with increasing enrollments in all fields. Since the graduation requirements in many fields include basic courses in mathematics, the Mathematics Department must offer a sufficient number of sections of these courses to accommodate both stu— dents majoring in other academic areas and students majoring in mathe- matics. Limited space, staff, and money are added problems. Another problem is that some students, according to their scores on an algebra placement test, are considered inadequately prepared to complete college algebra successfully. Although preparation in algebra is considered to be the work of the high school, many colleges offer a remedial course in this area. The Mathematics Department at Michigan State University offers a noncredit course, Mathematics 082, as such a course. Students who have had only one year of high school algebra and who fail to achieve a Satisfactory score on the mathematics placement test are required to comp1ete Mathematics 082 or its equivalent satisfactorily before they may register for any other mathematics course. Until the 1961 fall term, Mathematics 082 was scheduled to meet four days a week for the full term 13_@ovation and Experiment in Education. A Progress Report of “:18 Panel on Educational Research and Development to the U. 3. Comis- Sioner of Education, the Director of the National Science Foundation, and the Special Assistant to the President for Science and Technology. WEIShinston, o. 2.: U. 3. Printing Office, March 1964. p. 5. of ten weeks. Increased enrollments and lack of staff, time, and money n1ade it necessary either to cancel the course or devise an instructional niethod which would require less supervision. If Mathematics 082 were czanceled, the university could still require a certain proficiency in eelementary techniques in order for students to enroll in credit courses i_n mathematics, or it could abolish this requirement. The latter is not ssatisfactory as most of the students would probably fail, and course satandards over a period of time might be lowered. If a certain pro— jficiency were required and Mathematics 082 were not offered, then the aicquisition of the necessary techniques would become the student's re— sponsibility. It was decided to continue to offer Mathematics 082 but <>n a self-help and tutorial basis which would require less staff time, éLnd in this way a student could receive some help in acquiring the riecessary techniques. In conversations with Dr. Wells, Chairman of the Mathematics I)epmrtment, the writer became aware of some dissatisfaction with the ruesults obtained by using the self-help and tutor method. The tutorial seessions had been poorly attended. Only a small percentage of students ‘hsufl passed the course and approximately 60% of the total number of stu- denits enrolled had taken the examinations. For example, 132 students werwe enrolled in Mathematics 082 during the winter term of 1963. Of tinese, 100 took the midterm and 75 took the final test. Only seven stanients passed the course, and all of them received grades of D. No more than five students came to any one of the tutorial sessions, and no more than 50 different students came to these sessions in the course of the term. The number of examinations was increased to four in the fall term of 1963 to try to stimulate better student response. It seemei to the writer that if students were provided with additional help in the intermediate steps of a complex problem, a better student response might be obtained, and the students might be more suc- cessful. Many of the tasks in mathematics are of a cumulative nature in that each step mastered is used as a basis for the next. A student must retain all of the skills learned earlier and then combine or synthesize them to solve more complex problems. Many students have difficulty in retaining the earlier skills. The lack of one Specific skill will pro- duce a result which doesn't agree with the given answer. Although a student recognizes that the result is incorrect, he often has no idea as to where the error occurred. In correcting a problem, he uses a pro- cedure which produces the correct result, but this procedure may be completely wrong or may apply to special instances rather than to the general situation. Since programed instruction can be an effective in- structional tool and since some dissatisfaction with the self-help and tutor method in the Michigan State University course Mathematics 082 has been indicated, there was a need for this particular study. Design of the study. This experiment was conducted in the Depart- ment of Mathematics of Michigan State University, East Lansing, Michigan, during the winter and Spring tenns of 196A. Subjects for this study were the students who registered for Mathematics 082 during these terms through regular enrolhnent procedures. The students who enrolled for the winter term were divided into two groups by the use of random numbers. One of these groups was designated as a control group and the other as an experi- mental group. The students who enrolled Spring term were designated as a Second experimental group. The experimental groups used programed materi- als, and the control group used a workbook-textln. The programed materi- x b lLl'Fred Sparks. A Survey of Basic Mathematics -- A Text and Work- .22k for College Students. New York: McGraw-Hill, 1960. 257 p. als used were deVeloped by the writer. The experimental and control groups met one hour a day, five days a week for the ten weeks of the term. The experimental groups used the programed materials only in class and these materials were handed out at the beginning of each class session. The control group took care of their own materials and could work on them outside of class. Tutorial help was available for those in the control group. Nine hours a week of tutorial help was available and a student could attend as many sessions as he felt was necessary. All students were required to turn in the completed material in order to take the final test. The nature of programed materials. Programed instruction materials are composed of a series of items called frames. In a linear program, each frame contains a small amount of new information. Frames are ordered so that concepts are presented in a logical fashion proceeding from the simple to the complex. The number of frames needed to develop a concept depends on the concept involved and can range from only a few to several hundred or more. The frames are presented to the student one at a time through printed material. Each frame requires a response from the stu— dent as, according to psychologists. the student must be an active par- ticipant. The student can proceed at his own rate. Prompts or cues are included in most frames in order to promote correct reSponses. The stu- dent records his response in some way and receives immediate knowledge as to the correctness of his response. According to Skinner: . . . machine teaching is unusually efficient because (1) the student is frequently and immediately reinforced, (2) he is free to movo at his natural rate, and (3) he follows a coherent sequence. . . . the conditions ar- ranged by a good teaching machine make it possible to apply to education what we have learned from laboratory research and to extend our knowledge through rigorous experiments in schools and colleges. l5Skinner. 9p. c_1t_.. p. 182.12. E'.T‘-fl='£.n.§=".=:-'J£LE._' -L'=:--;.I.L-_‘ .. ',, _.._ 1 .L 10 The printed material can be presented as a programed textbook. The critical functions of a step by step presentation which requires aactive participation by the learner and keeps him informed of his pro- ggress can be served by such a book as well as by a machine. In fact, as C}reen states: . . . it must be emphasized that the machine per se does not teach. Thg machine is simply a device for pre- senting materials.1 Ace ording to Komoski: Programs, . . . , are without question the really im- portant element of this type of instruction. . . . the program, or the step by step arrangement of suerct matter, is the really essential element of this method. 7 TFC) emphasize that the program is the essential element of this instruc- ‘tixonal technique, the writer uses the term programed instruction in this tfiieesis. A teaching machine then is a device which presents a program to a student . Programed instruction is not just one more audio—visual aid. Lysaught writes: Programmed learning, . . ., was not to be lumped with -- or confused with -- the large number of learning techniques and devices which are regularly advanced in the journals. Audio—visual aids, for instance, contribute much to the learning process, but they are inherently stimulus de- vices, and are not a complete learning system. Program- med learning is unique in theory and in practice for it offers the student a complete learning "cycle".1“ 7l_ . 1)Edward J. Green. The Learning Process and Programmed Instruc- tlon. New York: Holt, Rinehart, and Winston, 1962. p. 133. 1 u x c I a “ 7P. Kenneth Komoski. "Pregrane: Instruction and its Place in ‘ ' fl .1 ma - 4‘ uiufixation." Address presented at the ?3th Annual educational conference Spcfllsored by the Educational Records Bureau, October 78, 1960. g 1 o n . I Jerome P. Lysaught. "Programmed Learning and Teaching Aachines o? Ikniustrial Training.“ Reprint from Journal of the American Society ___12§;ining Directors, February 1961. 11 Stolurow19 points out that mass-instruction techniques such as films and television communicate effectively but do not control this communication, as they lack feedback which is essential for the modification of the learner's behavior. Fry20 has said that the main difference between pro- Egramed learning and a textbook is the requirement of a response. writers sire in general agreement that the one major difference between programed ilufiruction and other educational methods such as lecturing and the use <>f audio—visual aids concerns the assumption of the responsibility of tJhether or not a student learns. In the past, according to Skinner: . . teachers have been less given to teaching them to holding students responsible for learning. 1 131 other words, a great deal of the burden of learning was placed on the sinident. As far as programed instruction is concerned, Komoski states: If, however, he [the student} doesn't learn from a particular program, it must be assumed that there is something wrong with it _- not him! If students are willing to meet a programer half—way by answering all his questions, then the programer must fulfil his half of the bargain by asking all the right questions. Basic assumptions. thx>se cited elsewhere were: The basic assumptions of this study other than 1. The programed material constructed by the writer differs from wor1f a step by step presentation requiring the active participation of the ]_earner and which keep the learner informed of his progress. 2. Frame: a unit of the program which requires a response from the learner . 3. Linear programing: a system of programing where all students sens the same material and respond to it in a predetermined order. Each fruame presents only a small amount of new information or is a small jump irz logic and knowledge. When all students see the same material, it is scnnetimes referred to as a fixed sequence. Q. Intrinsic programing: a system of programing where a student's resgxonse determines the next item he sees. The necessary program of a1— teruiatives is built into the material so that no external programing de— vixze is required. When all students do not see the same material,it is SOmetimes referred to as a variable sequence. 5. Overt response: a response which the student must write down. 6. Covert response: a response which the student thinks but does ”3t Write down. 1h 7. Constructed response: a response which requires that the student recall the information needed in order to make the correct re- sponse. 8. thtiple choice response: a response which requires that the student recognize the correct response when other choices are also available. Limitations of the sppgy. This study was specifically limited to (1) the construction of material covering the topics of the Michigan State University course Mathematics 082 and (2) the relative effective- ness of two methods of teaching Mathematics 082 as given in the state- rnent of purposes on page 1. It was further limited by the following: 1. The programed material prepared for this study was limited ill the treatment of ideas and in the extent of coverage of topics to tJiat of the workbook. 2. The procedures and tests used in carrying the investigation t:> completion. 3. The limited amount of time that students using the programed "material had in which to complete the material. In addition to these limitations, no attempt was made in this in- vesstigation to measure or determine the following conditions or rela- tionships. 1. The relative effectiveness of the methods used in this in— Vesrtigation with any other method of teaching Mathematics 032. 2. The achievement of students in this investigation with the actuievement of students who had previously enrolled in Mathematics 082. 3. The achievement of students with respect to intelligence. Organization of the thesis. This chapter has presented the pur- FK>Ses and some pertinent facts with respect to the need for the study. 15 A brief review of the design of the study, some basic facts concerning the nature of programed materials, the basic assumptions, definitions, and limitations were also presented in this chapter. A review of the literature is presented in Chapter II. A review of the literature con- cerned with the deveIOpment of programed material and the development of the special programed materials used in this study are presented in Chapter III. Since the study was conducted in the Mathematics Depart— rnent at Michigan State University, a description of the course and the xiay it is normally conducted are presented in Chapter IV. The proce- =dures followed in administering the course and a description of the ;participating students are also set forth in Chapter IV. Chapter V is (devoted to the tests used in the study, the statistical procedures, and 'the results of the study. The summary and conclusions based upon the analyses are presented in Chapter VI. The programed materials developed for this study are of such wnalume that it was not feasible to include them with the thesis. The punogramed materials and the four tests constructed for this study to nmxasure knowledge and understanding of certain basic algebraic facts and maxiipulative techniques have been placed in a binder and designated as a sufuolement to this thesis so that interested individuals may inspect thexn. Copies of the supplement are on file in the library at Michigan State University and in the reference room of the College of Education at Michigan State University. CHAPTER II REVIEW OF LITERATURE Introdugtion and historical bagkground. Mellan1 reported that the United States Patent Office issued patents for devices aimed at ‘teaching as early as 1809. The first recognized teaching machine was cleveloped in 1926 by Sidney L. Pressey at Ohio State University. Pressey tjuilt and experimented with a mechanical device for administering and sczoring tests. He constructed a series of multiple choice questions vndich were presented to a student. The answers were immediately scored 'b3r the machine thus providing the student with quick knowledge of re— sxrlts. By moving a switch to another position, the machine could be ogxerated so that it performed a tutoring rather than a testing function. Vflien used to perform the tutoring function, a new question would not ap- pesuc until the correct response had been chosen, and the student had im— mediate knowledge of the correctness of his response. As Pressey con- tinued his experiments, he noted that: . . . the procedures in mastery of drill and informa— tional material were in many instances simple and definite enough to permit handling of much routine teaching by me— chanical means. 1I I. rellan. "Teaching and Educational Inventions." Journal of Experimental Education 4: 291-300; 1936. 2Sidney L. Pressey. "A Simple Apparatus Which Gives Tests and Scores -- and Teaches." In: A. A. Lumsdaine and Robert Glaser (Eds. ). IEéChing Machines and Programmed Learning: A Source Book. Nashington, D C Department of Audio—Visual Instruction, National Education Association, 1960. p. 35. 1? Pressey's machines were designed to be used in conjunction with lectur- ing, textbook reading and other teaching methods. They provided a sup- plement to regular classroom instruction for drill and informational rnaterial. Probably because of Pressey's concern with these machines as “testing devices, his ideas did not excite the interest of either the general public or professional educators. (In 1954, a paper by the experimental psychologist B. F. Skinner3 tvas published. The ideas Skinner proposed were based on the results of 1118 experiments, with lower animals, mostly pigeons, and were primarily c:oncerned with investigating the principles of reinforcement. This reaper further suggested that behavioristic psychology contained ideas srpplicable to the teaching process and that the implementation of these ixieas could be enhanced by the use of specially designed machines. The main idea of Skinner's work, however, was with the principle 01? reinforcement. Reinforcement, according to Skinner“, is an arranged ccnisequence of certain actions which allows one to shape behavior and to rnaiuitain it in given states of strength for long periods of time. In a ccnnplex task, an organism can be led to the desired terminal behavior thIwough a series of successive steps each of which is closer and closer to the desired behavior and each of which must be followed by appropriate corisequences which will be reinforcing. Food and water act as rein— forwzers for hungry and thirsty pigeons and other lower animals. Grades, golri stars or merely knowing that an answer is correct act as rein- forcers for human learners. Skinner writes: . 3B. F. Skinner. "The Science of Learning and the Art of Teach— 1n8-" Harvard Educational Review 24: 86—97; Spring 1954. “Ibid” p. 86-87. Human behavior is distinguished by the fact that it is affected by small consequences. Describing something with the right word is often reinforcing. So is the clarifica- tion of a temporary puzzlement, or the solution of a com- plex problem, or simply the opportunity to move forward after completing one stage of an activity. According to Lysaught and Williams: . . . reinforcement theory provides a rationale for believing that a complex body of learning can be separated into its smallest components. Through it, the student can be taught to master all the subject matter by reinforcing or not reinforcing his responses to successive steps, ac- cording to the accuracy or inaccuracy of his replies.6 Skinner's work in human learning has been primarily with linear programing. In linear programs, the same material is presented to each student and he responds to it in a pre-determined order. The response is constructed by the student. Skinner writes: . . we want him [the student} to learn to emit the re- sponse, since this is the kind of behavior which he will later find mest useful.7 Learning is cumulative and proceeds in small steps which provide oppor- tunities for the learner to give correct responses. The number of stu— derfi;errors should be minimal, as Skinner considers the aversive effects of‘ error to be serious. Linear programing, according to Barlow, is . application of Thorndike's Modified Law of Effect, the Socratic method of answering questions, and the Cartesian method of analyzing a problem into its smallest parts and proceeding from the simple to the complex.~ 5B. F. Skinner. "Why we Need Teaching Machines." Reprint from Cunuilative Record, Enlarged Edition. New York: Appleton-Century-Crofts, 19 1. p. 1 2.03. 6Jerome P. lysaught and Clarence M. Nilliams. A Guide to Pro- grammed Instruction. New York: John Wiley and Sons, 1933. p. 8. q 7B. F. Skinner. "Nhy We Need Teaching Machines." Reprint from :Smulative Record, Enlarged Edition. New York: Appleton-Century-Crofts, "ZT“*"-—s-—~7' V o p. 1 (2.01. q - L”John Barlow. "Teaching )hchines and Educational Philosophy." :EE221_322_§221231 89: 201; April 22, 1961. 19 Intrinsic programing was developed by Norman A. Crowder, Vice- President and Technical Director of the Educational Service Division of U. S. Industries, Inc. His materials are not based on any of the theo- ries of learning. The intrinsic programer doesn't claim to know the conditions under which efficient learning will inevitably occur. In- stead, Crowder writes: . . they suspect that human learning takes place in a variety of ways and that these ways vary with the abilities and present knowledge of different students, with the nature of the subject matter, with a number of interactions between these sources of variation, and with other sources of vari- ability of which we are not even aware. Crowder sees the essential problem in programed learning as that of con- trolling a communication process by the use of feedback. The student is given a unit of material to be learned and responds to a multiple choice item on this material. The student's response determines the next item 118 sees. If he makes the wrong choice, the nature of his error is ex- plained and appropriate corrective measure are taken. For each wrong endswer that is included in the alternatives, a separate set of correction- a]. materials or branch is included. If the response is correct, then the conununication process is assumed to have been effective, and the student prcxoeeds to new information. The feature which distinguishes intrinsic programed material from that advocated by Skinner is, according to Crowder . . . the program of instructional material is completely flexible. Each piece of material the student sees is deter- mined directly by that individual student's immediately pre- ceding behavior in choosing an answer to a multiple choice question. Since the student's behavior in choosing an answer . . . is determined, presumably, by his state of knowledge at the time he makes his choice, the automatic \— ‘ _ 9Norman A. Crowder. "Automatic Tutoring by Intrinsic Program- “105-" In: A. A. Lumsdaine and Robert Glaser. Teaching Machines and :erfammed Learning: A Source Book. Nashington, D. C.: Department of udio-f1:ual Instruction, National Education Association, 1960. p. 237. 20 tutoring device adapts the program of material directly to the present state of knowledge of the individual student.10 Crowder, in contrast to Skinner, is not concerned that there be a low student error rate. He makes use of errors to build knowledge and skills. He writes: If an error has occurred, the problem is not solved by revealing the right response to the student, as the failure (of communication) occurred before the response was emitted. What is required, in the case of an error, therefore, is to repeat or revise the communication process. A great deal has been written about programed instruction and teaching machines in the last decade. An indication of the growth of the programed instructional field can be seen in the number of reports of experiments with machines and programs. According to Fine: In 1957, eight known projects were underwa ; in 1959, sixty; in 1961, over 100; and this year [1962 , over 200.12 Hanson13 lists 69 programs in the natural sciences and 123 programs in rnathematics. He states that this represents about 55% of the total xrimber of programs developed in all subject matter fields at that time. The literature might lead a person to believe that programed instruction arui teaching machines are completely new instructional devices. This impression is given by statements such as the following by Green. 1ONorman A. Crowder. "Automatic Tutoring By Means of Intrinsic Programming." In: Eugene Galanter. Automatic Teaching: The State of the Art. New York: John Wiley and Sons, 1959. p. 109f. 11Ibid., p. 114. . 12Benjamin Fine. Teaching Machines. New York: Sterling Publish- ing 00., 1962. p. 167. 13Lincoln F. Hanson (Ed.). Programs, '63: A Guide to Programed Instructional Materials. Washington, D. 0.: U. S. Printing Office, Center for Programed Instruction in cooperation with the U. S. Depart- ment of Health, Education, and Welfare, 1963. 814 p. 21 Programmed instruction is the first application of laboratory techniques utilized in the study of pfle learn- ing process to practical problems of education. Contrary to the impression given in articles in some of the popular maga— zines, writers do not view the development of programed instruction and teaching machines in a revolutionary sense. The fundamental ideas of programed instruction are basically the techniques which are involved in a tutorial situation. Lysaught writes: Programed learning stems from educational theory and will be developed and refined by educators. It promises tangible benefits to both student and teacher. William Fullagar, Dean of the College of Education, University of Rochester, has said, ”The principles of learning utilized (in programed learning) are those which the best of teachers try to apply in the classroom.” Review of studies relating to the effectiveness of programed in- struction. Much of the initial research relating to programed instruc— tion was designed to determine whether or not a program actually teaches. Pressey used his machines as a supplement to class instruction to provide the learner with immediate knowledge of results about subject matter items which he does nor doesn't know after the information is given to hiJn by a text or lecture. In 1950, Pressey16 reported the results of experiments which were aimed at showing that a teaching machine of the puxnehboard type produces better learning by providing immediate knowledge OF results. In using a punchboard, the student uses a pencil to punch a hole in the space for the response he thinks is correct. If the pencil 14Edward J. Green. The Learning Process and Programmed Instruc- 32521. New York: Holt, Rinehart and Winston, 962. vii. 15Jerome P. Lysaught. "Programed Learning and the Classroom Teacher." Reprint from New York State Edgcation: February 1961. 16- . ,. o. L. Pressey. ”Development and Appraisal of Dev1ces Providing Immediate Automatic Scoring of Objective Tests and Concomitant Self- Instruction." Journal of Psychology 29: 417—447; April 1950. 22 goes all the way through, the student has chosen the correct response. If the pencil doesn't go through, then the wrong choice has been made and the student makes another choice until the correct one has been made. Thus, the student is immediately aware of his errors and the correct re- 17, three groups of students sponses. In the study reported by Pressey were used. The first group used the punchboards on practice tests. Then questions were answered but discussion was discouraged. A second group took the same tests but didn't use the punchboard. However, the tests were corrected and returned the next day, the correct answers were given and a class discussion of the points was held. The third group didn't use the practice tests but covered the same material. The point gain on midterm examinations was ten points for both of the first two groups and four points for the third group, indicating that knowledge of results produces more effective learning than study without it. Tests were used as one factor in the total instructional effort in experiments conducted by Jensen13, Angell19, and Angeli and Troyerzo. Their results substantiated Pressey's conclusions that immediate knowleige of results produces better learning. In contrast to the experiments of Press ey anl his associates, Skinner and his associates have used machines to do the complete in- structional job. When the machine is used for total instruction, most 17Ib__i_d. , p. 1117-447 188. T. Jensen. "An Independent Study Laboratory Using Self- Scoring Tests." Journal of Educational Research 43: 134-137; 1949. 19G. W. Angell. "Effect of Immediate Knowledge of Quiz Results on Final Examinati>n Scores in Freshman Chemistry." Journal of Educational Research 42: 391—39M1949. 2 . . 0G. N. Angeli and “. E. Troyer. "A New Self—Scoring Dev1ce for :‘FFQJin; Instruction." School and Society 67: 84-85; 1948. experiments have compared programed and conventional instruction. 21 . . . . Porter used a Simple mechanical deV1ce to teach spell1ng to second and sixth graders. Twenty-two weeks of the normal thirty—four weeks of in- struction were given by programing the standard lessons required by the school where the children were enrolled. The children received no oral instruction and the machine presented only one item at a time. The con- trol groups were taught by a teacher with the same words being covered in the same sentence context. In both the second and sixth grades the achievement of the experimental groups, as measured by standardized achievement tests, was significantly better than that of the control 22 23 . 24 . groups. Roe and Weltman , Hughes , and Klaus and Lumsdaine nave also reported studies showing programed instruction is superior to convention- al instruction. These studies are not conclusive, however. Silberman writes . . there is some indication that the students in many of the conventional classes which had a fixed training in— terval may not have received the same material or may not95 have used their time as efficiently as they could . . . .” In many studies, conventional instruction is not well defined, and there alwe many uncontrolled variables. Firm conclusions demand further 21D. Porter. "Some Effects of Year-Long Teaching Machine In- struction.” In: Eugene Galanter. Automatic Teaching: The State of the Art. New York: John Wiley and Sons, 1959. p. 35-90. 22J. L. Hughes. Proggammed Instruction for Schools and Indust_y. Chicago: Science Research Associates,4T962. p. 45-6. 23Hughes, 22. 333., p. L13. 2“David J. Klaus and A. A. Lumsdaine. "An Experimental Field Test Of the Value of Self—Tutoring Materials in High School Physics. An Interim Report of Progress and Findings." Pittsburgh: American Insti- tute of Research, April 1960. 18 p. 2 ), 5Harry F. Silberman. "Self—Teaching Devices and Programmed materials." Review of Educational Research 32: 179-192; April 1962. 24 eXperimentation. Some studies comparing programed and conventional in- . 26 . 27 . struction, such as Oaxes , Lew1s , and H1ckley and Anwyll2Q have re- ported no significant difference in learning. The evidence indicates that programed instruction is at least as effective as conventional instruction in many situations. Students at every level of instruction -- elementary, secondary, college, adult -- and in a variety of subject matter fields -- language arts, mathematics, foreign languages, office procedures, job training -- have learnei from it. Quackenbush29, in a survey of more than thirty research studies on programed learning, found evidence that the effectiveness of programed instruction has been shown in classroom applications. Review of studies comparing linear and branching proggams. The philos0phy and procedures of the linear and branching approaches to pro- graming differ greatly. At first, the constructed response was identi- fied only with linear programs, and the multiple choice response was identifiel only with branching prograns. As a result, some confusion resulted regarding the issue of constructed response versus multiple choice response and the linear-branching issue. Recently, there has been B . . William :. 3a an Introductory sycho October 1960. 27Earl N. Lewis. "Experimentation in the Development of More Ef- fective methods of Teaching Foreign Languages by Making Extensive Use of Electromechanical Aids." Baton Rouge: Department of Foreign Languages, Louisiana State University, July 1961. 19 p. 28Albert Hickley ani B. Jean Anwyll. "Programmei Instruction of Package Billing Clerks." Final Report to Speig e1, Inc. Lexinton, Hass.: Information Technolo: gy Laboratories, January 1961. 30 p. Z ‘ 9Jack Quackenbush. "How Effective Are the New Auto-Instructional Aaterials and Devices?" IRE Tran. on Education, No. 4, December 1961. P. 144-151, h‘ng rhehinos as a Study Aid in ' ’ r ‘0 ts 7: 297-°03; _ -~ --. . 25 an attempt to resolve this confusion, and as a result there are now some linear programs which call for multiple choice responses and some branch- . . -. 90 ing programs which use constructed responses. Coulson and oilberman’ used part of a psychology course with eighty students. They administered a posttest which required constructed responses and found no significant difference between multiple choice responses and constructed responses. They did find that the multiple choice response mode required signifi- 31 reports that cantly less time than the constructed response mode. Roe there was no significant difference in either learning time or test scores between the linear and branching programs. Roe used a program covering concepts of elementary probability with 139 students enrolled in the freshman engineering laboratory course during the fall, 1961 semester at UCLA. Campbell32 did a series of experiments using a program on set theory with students from the fourth throng h the twelfth grades. There were three forms of the program: (1) a bypass form where students only completed remedial branches when their answers to questions indicated that they needed to complete these; (2) a long form which was a linear program with all the remedial branches included; and (3) a short form which was a linear program without the remedial branches. All three forms required constructed re: punses, and were revised after each trial. I) ‘ 'fi r "N - s "\ 3\Jonn n. Coulson and harry F. oiloerman. “effects of Three Variables in a Teaching Eachine." Journal of Educational Psychology 51: 135-143; June 1960. 31Arnold Roe. "A Comparison of Branching Lethods for Programmed Learning. “ Journal of Educational Research 55: 407-409; June- July 1962. 2 U) 'Jincent N. Sampbell. Studies of Bypassing as a Nay of Adpating lfilf- -Instruction Programs to Individual Differences. Nashington, D. C.: g-y Jo1gffice of Education, Department of Health, Education, and Welfare, *319 63 p. 26 The step sizes were considerably longer than those usually used in linear programs. Campbell reported that there was no significant difference in 33 test performance between the bypass and linear programs. Coulson and others found branching su erior to a fixed sequence when a computer was used to select item sequences in terms of student answers in a program on symbolic logic. A computer was programed to select item sequences for one group of students on the basis of errors in responses and the student's preference to receive additional information about a topic. The use of the computer to select item sequences made possible greater provision for individual differences, but the gains in computer based instruction must be weighed against the cost of setting up such a system. BeaneBu used a programed unit on perpendicular and parallel lines with two tenth grade classes. There were four treatment groups. One group used a linear program only, a second group used a branching pro- gram only, the third group started with a linear program and changed to a branching program halfway through the program, and the fourth group started with the branching program and changed to the linear program at the halfway point. Immediate and seven week delayed posttests gave no significant difference among the four treatment groups. Nelson35 used three programs: (1) a constructed response, fixed sequence; (2) multiple choice response, fixed sequence; and (3) multiple 33John E. Coulson and others. "Effects of Branching in a Computer Controlled Autoinstructional Device." Journal of Applied Psychology +6: 389-392; December 1962. 34 .. . . , . . Donald Beane. "A Compar1son of Linear and Branching Techniques of Programed Instruction in Plane Geometry.” Dissertation Abstracts 23: 4254; No. 11, 1963. 35 7 A o \ o Charles helson. "compar1son of Three Programed Tecnniques for tPB Development of Mathematical Induction with Eighth Grade Students." -D-1_S_Sertation Abstracts 22: 142.7; No. 5, 1962. \I choi e response, variable sequence to teach mathematical induction to above average eighth graders. No significant difference was found on immediate and two week delayed posttests. 3-4 . . . . Stolurow ' discusses the fact that recognition memory is eaSier than recall memory and suggests that the purpose of instruction should determine whether to require a constructed response or a multiple choice 37 a _ response. Nelson suggests that because 3; the greater ease of con- struction and the possible advantage for recall type memory, a con- structed response, fixed sequence program is the most satisfactory form. I O Q n ‘ 33 ReView of studies comparing overt and covert regponses. Goldbecx found the overt response mode superior at intermediate difficulty levels when he studied the interaction between response mode and the difficulty of the learning material. He found the overt response less effective at the easier difficulty levels than either a reading or a covert response q9 mode. Evans, Glaser and Homme’ used a program in symbolic logic and observed no difference between overt, covert and reading modes. A read- ing mode means that the program had the responses filled in and the stu- g. b0 , . . . dent read these. Alter and silverman used a program dealing with binary 3DLawrence M. Stolurow. Teaching By Machine. washington, D. C-3 U. 3. Department of Health, Education, and welfare, 1961. p. 53. 37Nelson, gp. git. 38Robert A. Goldbeck. The Effect of Response Mode and Learning ' '“f on A tomated Instructio . Technical Report No. 1. Santa Eerbara, Cal.: American Ins itute of Research, September 1960. 39James L. Evans, Robert Glaser and Lloyd Homme. "An Investigation Of 'Teaching Machine' Variables Using Learning Programs in Symbolic Logic." igurnal of Programed Instruction 1: 55-7%; 1962. .' 4. OMillicent Alter and Robert E. Silverman. ”The Response in Pro- gramed Instruction." Journal of Proggamed Instruction 1: 55-78; 1962. 23 numbers and compared overt and reading modes. Stolurow and Walker41 used a program on descriptive statistics and Lambert, Miller and Wiley2+2 used a program on sets, relations and functions to compare overt and covert responses. All three studies report no significant differences. The covert response mode and the reading mode required less time than the overt response groups. This finding is reported by Evans, Glaser and HommeuB; Lambert, Miller and Nileyuu; and Stolurow and walkerus. In a survey of research pertaining to programed instruction in science and mathematics, Briggs and Angell state: Overt responding has not been shown to be 3 requirement for learning from autoinstructional programs. 6 However, there are other factors to be considered in determining re— 47 sponse mode. Fry discusses the important side effects of program de— velopment and revision, motivation and attention and progress records obtainable from overt responses. Fryus writes that the question of J 41L. M. Stolurow and C. C. walker. "A Comparison of Overt and Covert Response in Programmed Learning." Journal of Edggational Re- search 55: M21_#19; June-July 1962. uzPhilip Lambert, Donald M. Lfiller and [avid E. Wiley. "Experi— mental Folklore and Experimentation: The Study of Programmed Learning in the wauwatosa Public Schools.” Journal of Educational Research 55: 485—fl94; June—July 1962. L1. 3Evans, Glaser and Homme, pp. cit. 44Lambert, Miller and Wiley, 92. cit. ~53tolurow and walker, pp. git. Q6 . Leslie J. Briggs and David Angell. "Programed Instruction in Science and Dhthematics." Review of Educational Research 34: 364; June 196M. ’4. 7Edward B. Fry. Teaching Machines and Programmed Instruction: An Introduction. New York: MbGraw Hill} 19621 p. 146. ”amid. p. 1A6. 29 response mode is secondary to the question of whether the student ef- ficiently reached the learning goal. Review of studies comparing programed textbooks and machines. grams have been published in book form and no mechanical device D . 0 V 1. 1 Y._ I} n 2+9 is necessary in order for a student to use tnem. homne and elaser , Some pro working at the University of Pittsburgh, developed the programed text— book. This is a printed device which fulfils the sane functions as the 1 programs used on machines. The programed textbook developed oy Homne and Glaser presents the :aterial in a Hirizontal format. In the hori— zontal foriat, ejch page is divid:d into six or seven horizontal strips or levels. The student starts with the item in the top level of page one. After the student has given his response, he turns the page and finds, in the top level, the correct response and the next stimulus frame. The student repeats this process until he has completed the top level and then goes back to the front of the book and starts in on the second level. The student continues in this manner until the ntire text has been read. f‘ Thus, a horizontal programel text is read from the front of the book to the back at one level with succeeding frames appearing on alternative pages. All the frames on one level are allotted the same amount of space. The programer day be influenced to write frames of a uniforn length since 'wasted space resulting from short frames is an important consideration from the standpoint of printing costs. Programed textbooks may present material in a vertical format. In the vertical format, the student reads from the top of the page to the 49 g . L. a. Homme and R. Glaser. "Relationships Between the Pro— erameo Textbook and Teaching Machines.“ In: E. Galanter. Automatic Teaching: The State of the Art. New York: John Wiley and Sons, 1959, p- 103—1os. 30 bottom. The programer may vary the frame size in order to present nar- rative material of considerable length. Thus, the number of frames on any one page may vary from one to nine or ten. A slider is usually used with the vertical format. One frame together with the answers to the preceding frame are exposed one at a time as the slider is moved down the page. The answers may appear either to the right or left of the frame. Crowder has developed a scrambled book. The student starts at page one in this presentation mode but doesn't read the pages in order. The sequence a student follows depends on his choice of the alternatives given. The student must flip back and forth in the scrambled book thus spending more time finding material than with either the horizontal or vertical formats of the programed textbook. Eigen and Komoski; Silverman and Alter; Holt and Hammock; and Roe et al50 used programs in sets, re— lations and functions, binary numbers and basic electricity and ele- mentary probability respectively to compare a program on a machine with either the horizontal format or the vertical format of a programed text. Eigen, Filep, Goldstein and Angalet51 compared machine presentation with both the horizontal and vertical text formats using a program on numbers and numerals. No significant difference was reported in mastery of the material between the machine and textbook groups by any of these studies. CA \ J4 ‘ . .1 .° ' - ,.‘ .A‘ A v v A As Fry states, ". . . tnere seams to be no SUiflClent grounds for aluays SCLso 3. Joldstein and Lasser 9. Gotki-. A Review of Research: Teaching Eachines vs. Programed Textbooks as Presentation Hades. New York: The Senter for *“ gra Ci Instruction, 1W5?. O p. lewis D. Ligen, gobert T. filep, Leo 5. dolistein and Bruce X. Ansalet. "a Comparison of Three Mo‘es of Presenting a Programmed In- Structi“n jequenCe.” Journal of fiducationil ‘eSeai;h 55: 55?-QSO; 32 ‘ T“ A .‘ ._- J r‘ler’ 'V‘Lo 0.}-to , L". 70 71 / preferring one form [book or machine} to the other." Programed textbooks allow a student to look ahead before he re- sponds and so deviate from the path set down by the programer. A stu- dent using a machine cannot do this. Skinner53 thinks that it is im- portant to have the more precise control of the learner's behavior which Kn is given by the use of the machine. Homme and Glaser * think that look- ing ahead is not much of a problem since no one knows how damaging to the learning process looking ahead is and the possibility exists that it is not damaging at all. It has been argued that a student looks ahead because the tendency to emit the correct response is weak and that the deve10pment of well written programs and really adequate programing techniques would eliminate this problem. In a programed textbook the response usually is a word, number, or phrase appearing on the next page or below and opposite the next frame. Krumboltz and Bonawitz55 used a program designed to teach pro- spective teachers how to write valid classroom achievement tests in order to compare two approaches of presenting the confirming response. One group was presented the response as a single word or phrase. In the other group, the response was presented as a complete thought, usually by inserting the desired response in a repetition of the relevant part of the stimulus frame. The two groups did not differ in knowledge of 'terminology on a final test but the group where the answer was presented iJi context did excel significantly in the ability to apply principles. 53 Skinner, ”why We Need Teaching Lhchines." 3p. cit. Homme and Glaser, 22. cit. 55John D. Krumboltz and Barbara Bonawitz. ”The Effect of Receiving 'Ehe Chonfirming Response in Context in Programmed flaterial." Journal of Lxhlcational Research 55: 472-475; June-July 1962. 32 Studies in programing relating to ability and individual differ- gnggg. Linear programs do not make much provision for individual dif- ferences. It is assumed that if programs are well prepared, there is essentially one sequence which will serve for all students. Slow students will require more time to complete a sequence and it is assumed that ad- ditional instruction will do the bright student no harm. Little56, using an educational psychology program on college students with teaching ma- chines of the Pressey type, reported that slower students profited most. Klausmeier and Check57 investigated retention and transfer on low, aver— age and high intelligence children whose mean age was 131 months. The programs dealt with socially useful arithmetic learnings, and the learn- ing tasks were graded to each child's present achievement level. They found that when children of all three levels of intelligence receive learning tasks which are graded appropriately to their levels of achieve- ment, they retain and transfer equally well to new situations of appropri- ate difficulty. Evans, Glaser and Hommes8 found that intelligence was one of the major factors producing significant differences in their study. Lambert, Miller and Wiley59 observed that intelligence was the most Sig- nificant factor associated with immediate acquisition of the factors 1 ' -1 60 . . u I studied. ooulson and others found no Significant correlation between 56J. K. Little. “Results of the Use of Machines for Testing and for Drill Upon Learning in Educational Psychology." Journal of Experi- mental Education 3: 45-N9; 193%. 7 . 5'Herbert J. Klausmeier and John Check. "Retention and Transfer in Children of Low, Average, and High Intelligence.” Journal of Educa- tional Research 55: 319-322; April 1962. 8 5 Evans, Glaser and Homme, 2p. cit. 59Lambert, Miller and Jiley, op. cit. \On 1 - soulson and others, 3p, Cit. 33 ability and performance for either branching or linear programs. Nit- trock61 used a molecular theory program to compare an overt oral response with a reading mode. He found no significant difference in response mode but did find an interaction between response node and mental age. Chil— dren with above average mental ages performed better with the reading re— sponse mode, while children with average mental ages performed more ade- quately when they used the overt response mode. Campbell62 reports that when method comparisons were made separately for high and low ability groups, bypassing seemed to be better for high ability students in grades four and nine, better for low ability students in grade eight and not much good for either ability group in grade twelve. The relative learn— ing efficiency of the three methods which were bypass, long and short did not depend appreciably on ability level, but for all methods substan— tial differences were found between ability levels and amount learned. Henderson63 used a traditional treatment of second year high school alge— bra for remedial work that began three-fourths of the way through the course. Areas needing further study were identified for each student, and small groups of students needing work in a given area shared one copy of the program sequence. One student completed one page of the program and passed it on to the next student and then started in on the next page. The students did this three periods a week with instruction on new topics the other two periods a week. Henderson noted values for the slow 61%. C. Wittrock. ”Response Mode in the Programing of Kinetic Molecular Theory Concepts." Journal of Educational ngcholg y 5h: 89-93; April 1963. 62Campbell, pp, git. / _OBGeorge L. Henderson. ”An Independent Classroom dxperiment Using Teaching lbchine Programmed Materials." The Mathematics Teacher. 56: 248-251; April 1963. 34 learner and that programed materials seemed to be the answer for remedial work, self-study by students absent from school for health reasons, tutor- ing and self-education. Randolphéu used a program on sets, relations and functions on better eighth grade students. Students were selected on the basis of intelligence, achievement test scores and previous grades. Every student but one improved, and there was real gain in mathematical ability as measured on pre-posttest gains on the mathematics part of the Purdue Entrance and Placement Test which is given to all entering fresh- men at Purdue. Randolph thinks the gain can be attributed to both the programed learning materials and the relatively modern mathematics found in the program. Randolph found that the programed material was better for the faster students and that the slower students had to be prodded to complete the material. He noted that these results were opposed to those of Henderson and attributes this to the different types of subject ma— terial used in the two programs. dandolph suggested that "a reasonable conclusion would be that programed instruction can be a valuable aid for both extremes of a class, with different material for each extremity.”bj The concept of general ability or intelligence and its relation- ship to the rate of learning is not very clear. 3tolurow writes: Until new information is forthcoming, there seems to be no need to prepare special programs for learners who differ in general intelligence test scores, provided they are all above the minimum level required “or learning the task 'nd that adequate provision for review is made, if the program is a long one. One important research problem seems to be that of defining minimum ability for particular tasksy3 04 . n f . . . . . Paul H. mandolph. An experiment in Programmed Instruction in Junior High School." The Mathematics Teacher 57: 160-162; march 1964. 65f ' Randolph, Op. c1t., p. 152. 64 ’Stolurow. Teaching By Machine. p. 54. v.) \Fi Studies on student attitude towards programed materials. Hughes67 and E‘el-‘ihusen68 report that students are generally receptive to programed learning. However, it is recognized that there is a point at which the student loses interest in the subject, becomes bored or (9 7O tired and stops learninc. BeaneD , Henderson and Randolph71 reported that students found programed learning fun at first but soon became bored, and agreed that students, especially the bright ones, needed class discussion. Randolph reports that his students began a contest to find typographical errors and became rather adept at it which indicated that they were understanding the subject matter. None of the studies offered any suggestions as to how to avoid student boredom with programed material and still permit the student to maintain his own pace. Use of programed material. The literature does not indicate that advocates of programed instruction expect it to be a panacea for the problems of education. writers do not advocate using this technique as the sole means of instruction. It is another tool and its potentiali- ties must be investigated further. Henderson72 suggests that programed instruction can be an effective teaching aid to supplement conventional classroom teaching, provided students receive a variety of eXperiences 6?. o. L. Hughes. Prowrammed Instruction for Schools and Industry. Chicago: Science Research Lssociates, 1937- Po 55« /a "John A. Feldhusen. ”Reactions of College Students to a Self- Instructional Teaching Device and Programed Instruction." Auto— Instructional devices 1: 37—33; August 1961. 9 _ LvaILG, nf'v ‘ 11. 7o 1.“ . nandolph, on. Cit. 7 2 , . Henderson, 0:. Cit. 36 734 i of a motivational nature. Goldbeck, Shearer, Campeau and Willis n- vestigated integrating programed instruction with conventional classroom a teaching using a social studies unit on the U. a. Government. They re- ported a substantial increase in the amount of learning for the integrated programed classes over the nonprogramed classes for both general level ability students and college preparatory students. Dessart writes: Even to entertain a notion the a t e placed by a programed textbook or machine reflects an extremely narrow view of the stud t t e e tion- ship. . . . Advocates of programe? instruction certainly had no intention of fostering a methol that might be in- terpreted as a teacher replacement: but, rather felt that a new methoilhad been dded to the repertoire of teaching techniques. 6) CD C" ' ’1 > ’1 p4 Q.) A summary. It appears from the review of literature presented in this chapter that the following tentative conclusions are justified. It is to be noted, however, that the tentative conclusions are based on trends as well as statistically significant findings and are to be in- terpreted as being only indicative of the findings in general. 1. The effectiveness of programed instruction as an instructional technique has been shown at every level of instruction and in a variety of subject matter fields. Programed instruction appears to be at least as effective as lecture-recitation in many situations but results are inconclusive since there were many uncontrolled variables in the experi- ments reported. 2. It appears that there is no significant difference in either a 7)Robert Goldbeck, James Shearer, Peggie Campeau and Hary Nillis. Lategrating Proggamed Instruction with Jonventional Classroom Teaching. washington, D. C. U. 3. Office of Education, Department of Health, Education, and Welfare; December 1932. 29 p. 7!; q , . . j ‘ Donald J. Jessart. "some Thoughts on Programeu Instruction in fibtnematics.“ School, Science and mathematics 6Q: 235-283; April 1994. 37 learning tine or in the amount learnel between linear and branching pro- grams. 3. It appears that students learn equally well when either con- structed responses or multiple choice responses are required. Constructed responses require more time for the student to complete the prcgr n and might have a possible aivantage in learning material which must be re- called rather than nerely be recognized at a later time. 4. The data indicate that overt responding is not a requirement for learning from autoinstructional programs. However, there is some indication that stuients with average mental ages avert responses are required. A longer time is needed to complete a program when overt rather than covert responses are requirei. . It appears that there i: no significant difference in mastery of material when the material is presents: on a nachine as compared to presentation in 3 pr gramei textbook. Jhen material is presented on a machinejthe stwdent cannot look aneai; out where is no evidence to indi— 1 cate how lanaging lookin* ateai is to the learning process, or if looking ahead is {a aging at all. Machine presentation of material can be im- portant in investigation of the learning process since the order of pre- sentation of material to students can he controllei. o. The data inflicate that it is effective to give additional in- formation in the reopense part of each frame. It also appears that it 18 more effective when the respons s oresentel as a complete thou ht (1! FJ n l - by repeating the relevant part c the stimulus frane rather than giving the response as a single word or phrase. 7. It appears that students at all levels of ability can learn “he“ Programed material is use}. There is sone indication that students of - , _. . . , . . average and below average ability HSBJ a different type of subject Q 3o material in mathematics than students of above average ability in order to learn effectively. 8. The data indicate that students are generally receptive to programed instruction but do lose interest in the subject and become bored after a period of time. No suggestions are offered as to how to avoid student boredom with programei material and still to permit the student to maintain his own pace. 9. writers do not advocate using programed instruction as the sole means of instruction. Teaching machines and programed instruction are seen as ways of implementing instruction, multiplying a teacher‘s effectiveness and taking some of the drudgery out of the teacher's job. There are many unanswered questions concerning programed instruction and its potentialities need to be investigated further. CHAPTER III THE DEVELOPMENT OF THE PROGRAMED MATERIALS Introduction. This chapter cites the literature relating to the construction of programed material and describes how the programed ma— terial was developed for this study. Also included in this chapter is a sample of the programed material used by the students. Literature pertaining to the construction of programed materials. There are many books and articles pertaining to program construction. The book by Lysaught and Jilliamsj, the two volumes by Markle, Eigen and Komoski2 and the department “Faulty Frames” found in the bulletin Egg: gramed Instruction3 are, in the writer's opinion, very valuable in helr- ing a person learn the basic principles of programing. The publications 5 by Cram“, Mechner , Rigney and Fryé, and Green7 also give helpful sug— 1Jerome P. Lysaught and Clarence M. Williams. A Guide to Pro- gramed Instruction. New York: John Niley and Sons, 1962. 180 p. 2Susan M. Varkle, Lewis D. Jigen and P. Kenneth Komoski. A Pro— gramed Primer on Programing. Volumes I and II. New York: Center for Programed Instruction, 1961. 67 p. 3P. Kenneth Komoski (Ed.). "Faulty Frames." Programed Instruc— tion. Volumes I, II and III. David Cram. Qgplaining "Teaching machines” and Programing. San Francisco: Fearon Publishers, 1961. 857p. Francis Mechner. A Teaching machine Prggram cn Programmed In- struction. New York: Basic Systems, Inc., 1951. / o , , ,_, ,, . . . . Joseph V. Rigney and ndward B. Fry. ”current Teaching-machine Erograms and Programming Techniques.“ Audio—Visual Communication Review: DuPplement 3; May-June 1941. 122 p. Edward J. Green. The Learning_Process and Programmed Instruction. Dkfiv Yerk: Holt, Rinehart and Winston 1§62. 118 p. 39 40 gestions on the concepts and techniques of programing. Phrkle, Eigen, and Komoski and mechner have constructeo programs to present the tech- niques of programing. Rigney and Fry10 have presented programing styles and techniques by example. The techniques presented in the above publi- cations fulfil the useful functions of stating the principles of program— ing which are thought to be important at the present time and examining the features of programs from which students have learned what the pro— gramer has stated they should have learned. However, a prospective pro- gramer will not find a set of rules telling him how to write a successful program in a particular subject area. The organization of a program is determined partly by the basic principles of programed instruction but is also determined by the subject matter to be programed, the programer's analysis of the concepts and skills to be programed, his ideas as to the sequencing of the subject matter and his assumptions concerning the learn- ing process. Therefore, programing cannot be considered as simply the decomposition of a textbook into finer detail. Writers generally agree that prospective programers must first establish their assumptions concerning the learning process. Methods or techniques of programing are categorizei according to these assumptions. Regardless of the method of programing advocated, there is general agree— ment that learning is an active process rather than a passive one, that better learning results when the learner is provided with immediate know- ledge of results so that correct responses can be reinforced and incor- rect ones can be extinguished and that the establishment of well defined 8 shrkle, sijen ani nomoski, :2. Cit. -‘ l ’Mechner, 32, cit. 10;. digney and Fry, 3p. cit. 41 behavioral goals are necessary for an efficient learning situation. Be- yond these points of agreement, there are basically two views of the learning process in relation to programing. One View is that the learn— ing process is linear in nature, proceeding in small steps from the simple to the complex, and that mastery of each small step is necessary before the learner proceeds to the next step. These principles are advocated by linear programers. The second view is that instructions is essentially a communication process in which the communication is successful if the learner chooses the correct alternative and unsuccessful if the wrong al— ternative is chosen. The alternatives must be natural choices of the leer-er, and suitable branches must be provided for each of the wrong al- ternatives in order to correct the communication process. The latter view is implemented by intrinsic programers. Linear and intrinsic pro- graming are often considered as the only procedures for generating pro- grams. However, as the field of programed instruction has developed, many variations and combinations of these methods have appeared. It is recognized that programs must reflect the kind of learning that is to take place, and since several kinds of learning are required in a particular subject area, a program may make use of several different programing tech- niques. The prospective programer needs to define the purpose and specific {goals of the subject matter to be programed. He must decide on the gross amount of naterial to be covered, analyze the concepts and skills, decide YKNJ the program is to be related to the teaching situation where the pro- gram is to be used, and decide on how much detail he wishes to include. The concepts and goals must be translated as precisely as possible into \ 4-« OJ.“ - 1 1 . 1 ‘ ' b615718 o- an final oenaVior the students are to oe able to display. The ‘ r . fl. , , . . . \ progiamer has defined the composition of his program once ne has statei : -_—-fl-I" J...‘ _ " ' .L.‘ To what the learner should be able to do upon completion of the program, what discriminations the learner should be able to make and what ques- tions the learner should be able to answer. The guide published by Wiley - 11 and sons, Inc., suggests that the programer prepare a posttest for each unit before doing any writing as one means of helping decide what kind of terminal behavior the learner should have. The programer also needs to determine the previous background students should have if they are to master the program. The programer must keep the goals, terminal behavior and previous background of the students in mind if he is to write purpos— ively and avoid including irrelevant items. The preceding statements bring up the important point of the back— \ ,. q. . 12 ground of the programer. ACCQFJlng to Lysaught and williams understand— ing of a subject is necessary and basic to programing it successfully. According to the author's guide published by Hiley and Sons, Inc.: It is assumed that he [the programer\ knows the subject thoroughly and has had experience in teaching it. If this is not the case, it is highly unlikely that he is qualified to write the program. m~11+ L , nigen suggests the team approach to writing programs. The team members should include a subject matter specialist, someone who has had experience teaching the subject at the grade level for which the program is intend— ed, a curriculum specialist, someone knowledgeable in the problems of 11A Guide for Wiley Author 8: In the Preparation of Linear Auto- ZDostructional Programs. New York: John Wiley and Sons, Inc., 1962. 6 p. 12 Lysaught and billiams, pp, cit. 13A L ”uide for Wiley Authors, 2p. git., p. 3. 4 Lewis D. Eigen. Paper presented at symposium "Teaching Machines arml mathematics Programs: The Interaction of Content and Programming SpeciiLList in Developing Self—instructional Programs." Reprint from the flerican .‘~Tathematical ‘elonth‘ly 69: 558-561; June-July 1962. ’43 programing and who understands the psychological background of program- ing, and someone who can write clear and precise English. Each team member may possess more than one of these skills. Mills15 suggests that the person doing the programing depends on what kind of material is being programed. If the organization of the subject matter is to be radically revised on the basis of a better understanding of its nature, then it would be preferable for the scholar in the subject to learn the techni— ques of programing and write the prev 0 ram with the advice of a programing technician. It may be feasible, on the other hand, to train technicians as programers if writing the program consists largely of translating . . . . . _ 16 eXisting curricular material into program form. Barlow refers to the translation of existing curricular material into program form as expedi- ency programing and while he admits that this is sometimes effective, . . . . 17 claims that it is far short of what can be done. It seems to Barlow that even to do expediency programing it is as easy and more efficient for a content specialist to learn to program than for a programing specialist to attempt to gain any real mastery of academic areas with which he previously had little or no familiarity. As Green states: It has been truly said that it is easier to teach a physicist programming than it is to teach a programmer physics. For this reason, the person responsible for teaChing the gaterial is the Person who should do the programmingo1o 1 I f. “V o P‘ o 5Annice L. hills (od.). Prggrammed Learning and the educational Process. A Summary of a Conference held by the Thomas Alva Edison FOgndation and Grolier Inc. New York: Thomas Alva Edison Foundation, 1910 2"” I). 16John A. Barlow, Paper at symposium ”Teaching Machines and Math— cmatics Programs: The Interaction of Content and Programming Specialists 1J1 Developing Self—instructional Programs." Reprint from the American Idenim-:-maticai Monthly 69: 552-555; June—July 1952. WEE, p- 554. 18Green. 22. gig” p. 151. After the programer has constructed an outline of the subject mat- ter to be programed and has defined the goals and objectives in terms of the learner's behavior, he is ready to start writing frames. A frame usually presents information to a student, requires him to make a re— sponse, and provides him with immediate knowledge of results. However, sometimes frames are constructed which require a student response but do not present any additional information. Frames such as these are for review purposes or occur as terminal items in a sequence to check whether the student has mastered the lesson up to that point. In linear program- ing, only a small amount of new information is presented in each frame, so the student acquires knowledge in small steps. The size of the step is not measured by the amount of time taken to complete the frame but is defined in terms of almost errorless progress toward mastery of the ma- terial. Prompts and cues are provided to promote correct responding and these are faded as the sequence progresses. Thus, a sequence of frames presenting a particular concept moves from the introductory item to items with prompts and finally to terminal items where the stuient responds with no prompts. Consecutive steps of a program may be very similar, the only difference being ‘hat prompts are being faded. A sequence of as many frames as necessary is written to develop a concept. The student must respond to the new information given in the frame in a way which indicates that he understood the most important part of the information. ,A small step does not require that the response be small. Sometimes r _\ ‘1- _o "A gI "\ _ .-..— u‘u \ 1" __', " :A L‘ _ 4‘ _ “_“ _ . 1 4 A .3 ‘ik:ltl‘hml in;>:..t1\n is Mt.~n in on: F‘Sj«.ofi zant If the Irate. x~... .11.. 4.. o: .-17 : J-..‘. ~ :- -r~n, v-- '--...~ - .. w - LUV; \- 1‘ ‘J‘I‘g '- 1 -‘t.’,.”;’_: t» it or“‘1.- i ‘_."' is ’:‘ . 1:"..Tt-V'i . H? .( EL' 1t sf“; 1 3,5313.- 19 ' . . ‘H -. K‘ .-J. .- ,- n "w -_ i n , . Lewis D. digen. construction oi nrames of an automated Teach- BIKE Program. New York: Center for Programei Instruction, 1953. Q5 witz20 reported an experiment using two forms of a program in pa chology. In one form this confirming response was presented as a complete sentence in which the omitted word or phrase was underlined. In the other form the confirming response was a single word or phrase. The posttest scores showed no significant difference between the two groups in knowledge of terminology. However, the group where the confirming response was pre— sented in a complete sentence did excel 151 iificantly in ability to apply the principles learned. Briggs and Angellé1 feel that one of Skinner's most significant contributions has been his urg iQ that learning not be J- 1 left to chance, but that it oe tated and fostered by logical ar— F10 facil ran ement of material and bv the use of prompts and cues to enhance cor- rect responding. They al so point out that while most authorities agree that some form of =rrm ting “r cueing is needed and that success in the task shoul be attainable in order to av'oid the frustration of failu: there is disagreement concerning how easy the responses should be, how strongly the exper ilerter should guide the responses and what kind of arrangement of naterj.als forms an optimal sequence. The beginning programer, in writing the first draft of a program, J. ' is quite likely to be verbose and use steps .'hich are too difficult and too few for the subject matter. The author's guide published by Niley 9? and Sons, Inc. suggests that the most important prinCiple in writing I the first draft is conci ise ness, since it is difficult to eliminate items ? ‘ J~nn 3. "rn bolt? and eroa ra B navitz. ”The iffect of ReceiVin; in}: 3‘" l“';flg dspzrc: -o Jontstt i* -r-grammed “aterial.” I2ir1al of Sducatinnai £9-3a13h 53 533—575. Jun,-)13y 12/“. o ’1Leslie o. Briggs an} Dav'i iQ ell. ”ongrra ed Instruction in ~A'16MC“ sod Catheaatics.“ Aev'ew of dlucational desearch 33: 353—373; A udlde for mile‘ Aubn>ro, op. cit. 46 at a later point in the program, but it is quite easy to put in addi— tional items. It is possible to construct frames to which the learner will respond correctly even though he has not observed the critical in— formation carefully. In other words, the programer has not selected a significant response word. Klaus states: The most frequently made writing error of all was to assume that the learning took place while reading rather than while responding. Too often the frame is written first and then an effort is made to find a word or two which can be left out and used as the response. Je found the best way to write a frame is to begin with the response aimed for, and then develop the remainder of the frame with that goal in mind, adding only as many words to the frame as necessary.‘ The programer discovers where he needs additional frames and where the program is worded so that it is not clear to the learner when he tests and revises his program. After each revision, the programer should try out his program on a few students. The programer must discover every difficulty the learner has so that he can eliminate it before further testing. Several writers suggest that a record be kept of all student responses since incorrect responses are often the best clue as to how to revise the material. The program is tested and revised as many times as necessary, using students each time who have not previously been ex- posed to the material. Finally, a full pilot class is run on the com— plete program and a comprehensive revision done. Programing in this manner is a tedious and time consuming process of composing frames, try- ing them out and revising them. Lysaughtzu estimates that programers at Recordak Corporation spend twenty to thirty minutes per item including 2 . 3DaVid Klaus. "Programming: A Re-Smphasis on the Tutorial Approach." Audio—Visual Instruction 6: 130—142, 148; April 1961. 2h Lysaught and Williams, op. cit. s I’ v :1; .1: p o Laura. an)” .. ._ . 47 initial writing, sequencing and first revision following field testing. It would seem that full time teachers would not have the time to devote to programing by this technique. Preparation of the programgdgmaterials for this study. The ma- terial to be programed for this study covered the topics of elementary algebra treated in the first ten chapters of Sparks' workbook—text.25 This text treats the topics in a traditional manner and is primarily con— cerned with manipulative techniques and the basic facts and concepts which are necessary to understand these techniques. Since this text had been chosen as the best one available to meet course objectives when. independent study was used, the writer decided to use essentially the same approach in programing the topics. Since the treatment of these topics would be extended in later courses and since there was a limited amount of time in which to cover the material, the writer decided to limit the treatment of ideas to that found in the workbook. This meant that much of the material to be programed was basic factual material or manipulative techniques which could be hr ken Iu“n in It 3;; 51 t“ th: Cgit r that 2 lite?“ wri rim c>ulT ha fritten which would provide adequate instruction for the basic factual material and manipulative techniques to be covered. Therefore, a linear program was written for this study. The programed material was written to provide all the necessary ixistruction on the topics included. It was written for the student who needs to rel;arn and review these basic ideas. It was recognized that VKDSt Of the students using this material would have some previous back— 25 Fred J. Sparks. A Survey of Basic Mathematics: a Text and Tark— W. New York: Redraw—Hill, 1930. 257 p. 49 ground in algebra. However, students using the material would have re- ceived low scores on the mathematics placement test, indicating an in- adequate background, so the material was written assuming that students were only able to do addition, subtraction, multiplication and division with positive integers. The writer believes that many difficulties in algebra stem from an inadequate understanding of the processes and tech- niques of arithmetic. Therefore, a review of arithmetic was included in the programed material. Thus, the programed material may be used by stu- dents who have no previous background in algebra. In order to define the purposes and specific goals of the material to be programed and the organization of the program, the writer first a- dopted the suggestion made in the author's guide published by Wiley and Sons, Inc.26 of preparing posttests on each unit. The writer then made notes regarding the elements of knowledge of subskills necessary for a student to perform the desired terminal behavior. These elements and skills were then sequenced in a logical order. The procedures were fol— lowed before any frames were constructed. In the actual construction of the frames, the writer followed, for <1e27 . . . 29 the most part, the suggestions of Marl , Lysaught and Williams J and the department "Faulty Frames" found in the bulletin Programed Instruc— onzl9 tir . Copying frames, emphasis and textual clues, small steps and much repeatition were used. The frames were first written on 5 by 3 inch sheets (if paper in longhand. Responses were written on the back of each sheet. 26 A Guide for diley Authors, LE° Ci . 27 Markle, op. cit. Lysaught and Tillians, 3p. cit. AP, I ”Komoski. "Faulty Frames." 2p. cit. — .— : -_- _.-_.__ L' Except for review and test frames, only a small amount of material was to be included in each frame. Use of the small sheet of paper helped keep the writer aware of the fact that each frame was to contain only a small amount of material and emphasized the need for conciseness. At the end of each unit, the writer reviewed the frames. The frames were then typed on ditto masters and stapled together in sections of approxi— mately 140 frames. Some errors were discovered after the material had been duplicated. Most of these were discovered in time for hand cor- rection. Students were most understanding when errors were discovered after they had received the material and informed the writer of what they believed to be errors. The responses usually required are con- structed ones since recall memory is more important in mathematics than recognition memory. The answers to problems are more complete than those usually found in a textbook or workbook and are even more complete than those generally found in programed material. This was done to give a student additional help with the intermediate steps of a complex prob. lem. Sometimes additional information was given in the response, and students often had to explain why they had chosen a certain process or technique. There are some problems where there is no correct answer. In responses to problems of this nature, students were encouraged to give counter examples as well as definitions to indicate why it was im- possible to solve the problem. The responses given were often quite lengthy even though the amount of new material presented in the frame was small. This was due to the inclusion of all the stels needed for the solution of a complex problem. Sample of the programed material used by the students. To illus- trate the programed materials constructed by the writer and used in this StUdY. the instruction sheet and frames 73 - 140 of the third chapter, 50 Operations with Polynomials, are included here. These frames represent about two hours of student working time. In the programed material pre- pared for this study, the frames are listed on the right side of each page and the corresponding confirming responses on the left of the page. In many instances, the confirming response is presented as a phrase or complete sentence rather than as a single word. The confirm— ing responses for frames 73, 81, 100 and 105 illustrate this. The con— firming responses for frames 100 and 105 also illustrate that in many instances where the solution to a problem is called for)the problem is repeated and followed by steps in the solution. Sometimes review in- formation or additional information is included in the confirming re— sponse. Illustrations of this are the responses for frames 103, 111 (c) and 122 (a). The confirming responses are more complete than those usually found in a textbook or workbook and are even more complete than those generally found in programed material. Not only are most of the steps required for the solution to a problem given, but often alternate solu— tions are included. These last two statements are illustrated by the confirming responses for frames 76, “9, 101, 1C7, 114 (e), 122 (d), 125 and 132. Frames such as 76, 83, 87, 107 and 115 show that students were sometimes asked to give a reason for a certain process or technique. Part of the time, as in frames 83 and 115, the processes or techniques ‘used are legitimate ones. Sometimes, as is illustrated by frames 76, 87, and 107 the processes and techniques cannot be justified by the laws of algebra. Examination of the confirming responses for frames 76, 87 arui 107 show that students could use definitions or counter examples to indicate why processes or techniques could not be justified. 51 Interested individuals will find further illustrations such as the examples mentioned above in the complete programed material. All of the programed material constructed for this study is filed as a Supple- ment to the Thesis in the library at Michigan State University and in the reference room of the College of Education at Michigan State Uni- versity. Instructions A series of questions and incomplete statements appear on the following pages. You are to answer the questions or fill in the blank or blanks. The information needed is contained in the statement or in previous statements. Read each frame completely before writing your answer. You must read carefully to make sure your answer is the correct one. Clues such as underlined words and the first letter of missing words are often given. Pay attention to these. Compare your answers to the correct one. The correct one is given to the left of the next statement. It is recommended that you use an index card or a piece of paper to hide the answer until you have decided what the answer should be. You will probably learn more as reading an answer is not the same as constructing one yourself. The eye is quicker than the will power of the most honest. If you make an error, make sure that the given answer makes sense to you before proceeding to the next frame. For continuity of thought, take a few minutes at the beginning Aof each work session to reread a few frames immediately preceding your last answer. 73- In general, (am)(an) = am+n if m and n are numbers. wnat‘kind (Remember a[1 is defined only if n is .) See frame 15 if necessary. '73. m and n must be positive inte- 7%. In m“, m is called the . gers as a has been defined so far only when n is a positive integer. 7““ 'base 75. Note that the law of exponents given in frame 73 involves the 75. 76. 77. 78. 52 X5+9 X14 No. so the law given in frame 73 can't be used. 'I‘ryx=2andy=1. Youcan see the two results are not equal. x3(y2) = x-x'X°y°y° or there are three factors of x and two factors of y. xy5 = X°y°y'y'y°y or there are five factors of y and one factor of x. Since the same factors are not involved, the two cannot be equal. 2+ +6 9 5r3 z p7r9 «onomial -27X5y ZS \ A \ / f) C) I A ’3 (-?/<-’21r 1 )&~ 1‘ a ‘ = Q 1 , 4 .BFEBq 14 76. The bases are 222 the same 77. 78. same base and this law holds only when the bases are the same. x5(x9) = ’2 Does x“(y2) = xys? Give a reason for your answer. 9 To multiply p”r3 by psr6 we have to use the commutative and associative laws. 1: p2r3(p5r6) = pzp’1r3r6) by these laws. m Now we can use the law (a ) n men a (a ) = a as we nave the same base and positive exponents. 6 5(r3 ) = 2 Thus, p p r (-3x2yuz)(9x3y2zu) can be multi- plied together in the same man— ner. Each of these quantities consists of a single term and so each is called a In multiplying monomials, we use the commutative and associa- tive laws to change the order of the factors and to regroup the factors. Then we can use the laws of multiplication. A1. H11. (-jxfiy‘zf(9x3y'zfi) can be re- grouped and reordered to read 2 3 4 2 4 (~3)(9)(X °X’)(J 'y )(Z°z ). Complete the multiplication. Multiply —?pq)r2 by -4p2q5r2. 2 . . . In —?pq3r , the coeffiCient 18 The exponent of p is 83. 84. 85. 536. ’37. 853. coefficient is -2 exponent of p is 1 (-1)(12)(m2)(n.n)(p5.p) = -12m'n2p6 yes because the bases are the same and the exponents are positive integers. 5+7 12 3 = 3 9 factors of 4 “9 28 No because since we don't have the same base we cannot use the law given in frame 73. If you're in doubt, multiply it out and compare the results. (3'35)(X‘x2)(y7'y)(23'22) .3gx3y825 or 729x3y8z5 H 82. 83. 84. 86. 87. <-m2np5>(12np> = __________ = In frame 73, we stated that w n . a'°a‘ 2 am 1 when m and n are positive integers. Can we use this law to multiply 35 by 37? Why? 5. 3 37 = The product is 314. This makes sense if we 7interpret the mean— ing of 35 37. 35 = 3(3><3><3)<3) or means that there are 5 factors of 3. 7 = 3(3)<3)(3)(3><3>(3) or means that there are 7 factors of 3. Hence, 35°37 means that 5 fac— tors of 3 are multiplied by 7 factors of 3 which means that 12 factors of 3 are multiplied together. Twelve factor? of 3 can be Jritten as 3 In QB'QD, how many factors of h are present? / 3. o 4’ h = g (Write using an exponent) 05(2)) :2 {Express using exponents) Dues 73°56 = 359? why? ? 2 ’ 3xy7z3)(35x'yz ) = = I 24 : (+2)+ d these both mean c2)” means 90. 91. 92. 93. 94. 54 2(2)(2)(2) OP +2(+2)(+2)(+2) (-2)(-2)(-?)(-2) -32 means —3(3> or -<3)(3) or -1(3)(3) and any of these equal -9 (-3)(-3) and this equals 9 -f=-oxmowm=-m (a) -(3)(3)(3)(2)(2)(2) = -(27)(8) = -216 (a) 53+; = 58 (b) (.7)!HS = (-7)9 (C) (9)(-8) = -72 (d) <9)(4) = 36 (e) -(9)(8 = - r) -(-64)(1) = 54 A 7,7110 95. - 2LL does not equal either of the above. _ 27 means the same as _(2)4 and both of these mean _1(2)(2)(2)(2) or this can be written -2(2)(2)(2). 9 _ 3“ means and this equals 2 (-3) means and this equals 4 Evaluate - 7 / o>«3%§) (b) (.3)3(-2)3 If it is possible, express each of the following results using exponents. If the result can't be expressed as a number to a power, evaluate it. Evaluate: (a) 53'55 (m tpfimfi (o cmkafi (m than? e>-¥efi w>-owkaf (m @2847 m>scmkefl What does {—szy)3 mean? 55 (s) (-32)(-1) = 32 (h) 5(49)(—1/8) = - 2%: 95. (-5x2y)(-5x2y)(-5X2y> 96. 96. _5(-5)(_5)(X2.XZ.X2)(y.y.y) = 97. —125 xéy3 or (.5)3x6y3 97. (2mun32)(2mun32)(2mun32)(2man32)98. / this equals 16m1on1224 98. (m3)(m3) 99. lo I), 99. p7<5) = o”3 or 1oo. L (PS)(P5)(P5)(95) : D5+5+5+5 2 p20 Complete the multiplication. (-5x2y><-sx2y)<—sx2y) = (QmanBZy‘L means . This equals . Let us see if there is a law we can use to raise a quantity to a power. Examine (m3)2 - (m3)2 means In words, we could say that raising m3 to the second power i? equigalent to multiplying m by m . q o (m*)(mj} can be evaluated by the law given in frame 73. So m3(m3) = m3+3 = *6 ‘1‘ . No?e\that mB+3 is the same as m2 3, because 3+3 = 2(3). In other words, when a monomial is raised to a power, multiply— igg the exponents gives the same result as writing the meaning of the quantity and then doing the indicated multiplication. (p5)4 = Stated in general terms if m and n are positive integers th en (am)n : amn. _. _ 11 A (x )J * ~ (p)5 = = 100. 102. 103. 134. (x11)3 = x3<11) = 101. (p)5 : (p1)5 : p5(1) : Is to cube x11 or 102. to raise x11 to the third power or 11 11 11 x (x )(x ). aided the exponents 103. because am'an = am+n if m and 104. n are positive exponents. Note: the bases must be the same to apply this law. or x11(x’) means eleven factors of x multiplied by three factors of x which means that there are fourteen factors of x. Fourteen fac CtPI‘SO L 7». 1' vritten as x14. multiplication 195. 1 A} 34(6) — 3‘4 106. (x11)3 means to do what opera- tion? If you said that you were to multiply meaning that you were to multiply 11 by 3, you are WRONG. When exponents are multiplied, you have performed the opera- tion of raising to_powers. T91 mu tiply x11 by x3, that is )what did you do with the (exponents? what gives you the right to say that x11(x3) : x11+3 : This law states that we may add the exponents when the bases are the same in order to perform the operation of (3“)6 = 25.29 -.. —. In evaluating (3p 2LI’qu), we can :rite out the meaning of this and proceed to multiply the fac- tors. r"or ex mple 53p2 q3): means (3; or )(3p qr )(39 qr ) By the associative and commutative laws this can be written 3<3><3)(:2~ which equals pZ‘p2)(q°q°Q')(r3'r3'r3) 33333 6 or 27p q3r9. 106. 198. _s Q 57 (x2"23)u (x2)7(y)7(23)u 107. No. The lay (ab) 1 a b applies only when the base is composed of factors. 138. o The base (a“+b) is not comLosei of factors as factors must be multiplied. You can two results are not Try a = 2 and b = 1. see the equal. <3>5555 H35 35b5 20 J .7) (-2) ( 3) 2(21LL )2 109. 113. Instead of writing out the meaning of the given statement, m n wp can app ly the law (a ) = a xhen m and n are positive exponents after we have applied another law. .1 e need the fact that (ab)n anbn. By this law we can write that (x 2yz3)b’= . . n n n Note that the law (an) = a b only aor lies when n is a n3=i- tixe .nt”ger and when the 1 ant:. t; raise? to the power is can. posel of factors. 11 ca gs :«rite that (a 2+0)3 (a') + (b) ? shy? 7%r8t apply the law (ab)n = a p n and pgen apply the law (a” - ' '7 to find the value of (3a'bcu)5. ' ? Evaluate (-2p3q4)" 1 Did you write -22(p3)2(q4)2 for the last problem? If yod did it is wrong. The error is in the coefficient. "3 The correct coefficient is (-2)7 as an exponent affects the let— “r syibol which in— y preceles it and in thB exp ‘nent 2 a” rything inothe paren— -se‘. demember—7 :“i (-2 2 mean the same and are equal. (D 59 7 I 9 11?. (.3)L"(x“)‘L = 31x' 111. 2 2 f 2 2 111. (a) (~52 (p3) (qJ) (r5) = 112. (b) (-1)6(a3)°6(c5)6 = a18b12030 4 4 4 8 4 16 2 (c) <—1> (y > (z > = - Z3 Remenber in parts b and c that -a means —1(a). .7? .2 a 1+ 112. -(3mn )(3mn )(-2m“n ) or 113. {-1)(3mn2)(3mn4)(-2s3nw) These equal 3 9 q u (-1)(3)(3)(-?’.)(»’n'm°m )(rf'n‘m ) r a or 19mjnv 113. -(—p q )(9; q ) : 9p 1 11+. fl20 114. (a) 1 115. (.) (.2)15 (C) 52..«6 - S8 201 Svaluate (-Yx ) . Evaluate: (a) {-5p3q6r52 (b) (-a3b2c5>0 Q 4 (C) by” 2” Evaluate -(3mn2)2(-2m3n*). Write out the meaning of this statement before you try to simplify. Instead of writing u the mean- ing of -(3 n”) (-Zm n ) we could square 3mn and then perform the multiplication. 1 Doing this, -(an2Q2(-2m3n:) = -(Qan )(_2n’n ) and this is (-1>(9)<-2)(m2.m3)(n“.n“) or 13msnd. -(~r2q>3(-3pa2)2 = = Perform the following operations and simplify. c a (a) (3’) Leave in exponent form. (b) IL”? 5 Leave in exponent form. 9 o o ' (C) (5)w(5)) Leave in exponent form. I 1 Q ’) 0 ’3 (i) (3*D“Q5r)”(394qr5>’ A o 1 ’) (e) —(-?xy))7(-xjy4)j So far we have multiplied to- gether quantities which consist— ed of factors. Now let us con- sider multiplication when terms are involved. 115. 116. 117. 118. 119. 120. 121. 59 9 (d) (38P6q10r”)(33P6q3r15) = 11 12 13 1 3 p q ’r 7 (e) -(1:-2]7X7y21)(-X9y12) = -(_128x7y21)(-X9312) = / .128xhy33 by the distributive law 3a(a2)+3a(33) 3 +9512 3a -2P3(3P2)+(-2;3)(73) = -6p5—1bp4 You may have written —6p5+-14p4 as your answer. This is correct However, we generally use only one sign between terms since adding a negative is the same as subtracting a positive, we can write 5 -6p -1Upu. 2 i . —x3y (42°>-x3y2(-3xy)-x3y2<5y3>12o. 9 11 = ~4x5yw+3xv 3 ”Bx 9mn3(3m2n)+9mn3(hmn:)+0nn3(-m3)121. ° 6 1 = 27% n++36mkn .QmLLn3 / :‘rw ”q ’3 -poq2+39’q)_6qu’-2p+qj by the 127. distributive law. Combining similar terms, we have, M5 ~P6 q2— Dq ZPQ Q3 116. 117. 118. 119. We multiplied 3(4+7) by two different nethods. In one case, we said 3<4+7) = 3(11) = In the other case, we said 3(4+7)= 3 4+3 7 Why can we make this last statement? The distributive law states that a(b+c) = ab + ac providing a, b and c are rational numbers. Usin" the distributive law, 3a(a“+3a) = Complete your answer to the last frame. 3 2 -2P (3P +7P) = = The distributive law can be ex— tended to read a(b+c+d) = ab+ac+ad a(b+c+d+e) = ab+ac+ad+ae a(b+c+d+. .+n) = ab+ac+ad+. +an Using the distributive law, 3) 3) 2 2 _x3y (OX —3xy+5y 9mn3(3m? n+4flnn —m 2 a 2 2 2 -PQ (PS-3P Q>+2PBQ(-3P q -Pq ) = dimplify the folloZing. (a) (3Xy 3z5>< 32 y% 6) (b) —3xw3(4x2_7xw2+5wu-9) (c) <—2psqgw>“ (d) -3xy2(x3+x2y)+2y3(—4x3fl “y2 ) 122. 123. 12h 125 O \ L) (a) /,3-5 11 -ox y 2 you ion't need to use the dis— tributive law here as only factors are involved. _.L F0 b) (b) Use the distributive law here, ’) ’) ’8 -12x3wJ+21x“w5_15xw7+27xw) (c) Use the law (ab)n = anbn to get 1 1 o 1 ' 4 1 2 4 4 -2) (25) (q 1 (w) . Now use that (am)n = amn and get 20 9 a 16p q w (d) Use the distributive law. 1 ’2 ’3‘ ’3 -3x4y2_3x3y’-8x’y1+9y5 which 1 1 equals —3xuy2_11x’yj+8y5 l! (2a+3)b+(2a+3)30 2ab+3b+6ac+9c (Ba—2)Na+(3a-2)1 12a2-3a+3a_? : 12a"_5a-2 7’ A (3P-2q)p'+(3r-2q)4pq+(3p_2q) 1i4, (~3q2) = q 2 2 2 2 o 2 T ? 393+1Op q-17p1/+3q“ 124. 125. The distributive law can also be extended to (a+b)(c%d). Let (a+b) = N, then (a+b)(c+d) becomes N(c+d). By the distri- butive law N(c+i) = Nc+Nd. Since N : a+b, Nc+Ni becomes (a+b)c + (a+b)d which equals ac+bc+ad+bd. Using the distributive law, (2a+3)(b+30) = (Ba-2)(4a+1) = "D ’D (39—2q1(P‘+4pq-3q ) = Since multiplication is com- mutative 9 ? BP-Zq)(3r+4r). 130. This equals (3y+4r)3p+(3;+4r)4r 2 , fl 2 2 9p +24pr+1or 131. (2x+y)(2jl;f1(2x+y7 \J) associatiVe 1 15?A+J>2A+(/.+J)vj (2<+y) = 13?. 1§x2+2xy+2xy+yij (2x+y) = ? 9 O o (4x +Qxy+y’)?x+(hx +®xy+y“)y : 3 o 3x’+12x2y+6xy“+y3 (a) 134. ’ 2 7 o 9 43 rfultiply in1 collect sililar ter15. (n-2n)2 neans Use the iistributive law tv expand (n—Zn)(m-2n). L) (m—Zn)(m_2n) I : . 2 (3p+4r) means . This equals = . 2x+y)3 means . This can be written [12x+y)(2x+yi] (2x+y) because law. [£7x+y)(?x+y] (2x+y) = .9 _ — —— of the Perinorm the indie Ht 3 operations and sinjliiy. (a) (@a-jb)(a2-ab-2b4) (b) 3x_2)(2x+3) ? (C) (By—3) 4 2 6 2 3 (1) (9p +6; q3+4q )(Bp -Zq’) (e) (7a W+3o3)( a -3s3) a If (3x-2)(2x+3) = 6x3+Sx-6, we may say that §3x_2) is a or fixt+(-2q3) = 27p6-8q9 (e) (734+8b3)7au+(7au+3b3)(-8b3) R / = 49a'-6hbo factor 135. 2 . a +2a. a 18 a factor of 136. o +2a 3+2 137 m3 138. 9 a2 because a3°a” = a5 139. a2 1&0. a(a+2) : , . 2 a is a of a +2a. o 2 Name another lactor of a +2a. If m is one factor of mu, the other factor is 5 If a3 is one factor of a , then the other factor is because 3' e aB'aZ = as, then inc a5 = \J) a 12 Y because . 62 Product is Maj-7a”b-5ab“+6b (b) (3x-2)2x+(3x—2)3 = 6x2+5x—6 (C) (2y-3)(2y-3) = uy2_ 12y+9 (d) (9pu+5p2q3+4q6)3p2+(9h4+6p2 q3+4q6>(-2q3) = 27p6-8q9 (e) (7a”+8b3)7a”+(7a”+sb3)(-sb3) R / = 219314—64bo 134. factor 135. a(a+2) = . a is a 0L a2+2a. 2 . 2 135. a +2a. a is a factor of 136. Name another lactor of a +2a. 2 a +2a. 136. a+2 137. If m is one factor of mg, the other factor is 137. m3 138. If a3 is one factor of a5, then the other factor is because 13?. a2 because a3°32 = a5 139. Since aB-a2 = a5, then ugly-:— : 0 a3 ") 7 y because . L‘. 63 Summary. It appears from the review of literature pertaining to the construction of programed materials presented in this chapter that the following tentative conclusions are justified. 1. There is no set of rules telling how to write a successful pro- gram in a particular subject area. The organization of a program is de— termined partly by the basic principles of programed instruction but is also determined by the subject matter to be programed, the programer's analysis of the concepts and skills to be programed, his ideas as to the sequencing of the subject matter and his assumptions concerning the learn- ing process. 2. The person who does the programing should be familiar with the subject matter and have had experience teaching it. 3. The frames of a program require a student response and provide him with immediate knowledge of results. The frames also present infor— mation to the student except for frames occurring as terminal items in a sequence. Terminal frames in a sequence are to check whether the student has mastered the lesson up to that point; consequently, no new information is presented in these frames. 4. Programers must be careful to construct frames to which the learner will respond correctly only when he has observed the critical information carefully. Programers must also be careful not to be verbose or to use steps which are too difficult and too few for the subject matter. Also included in this chapter is a description of how the programed materials were developed for this study. The important characteristics Of the frames and confirming responses of the material constructed for this study are pointed out. In order to illustrate these characteristics and to illustrate the manner in which one topic was developed, a sample 0f the programed material used by the students is included. CHAPTER IV ORGANIZATION AND IMPLEMENTATION OF THE STUDY Introduction. This study was designed to compare the relative ef- fectiveness of the programed materials prepared by the writer and the self-help and tutor method in the teaching of the course Mathematics 082 at Michigan State University. The present chapter describes the two in- structional methods used in this study, the students in the study, the samples that were used for making the comparisons and the administration of the materials. Mathematics 082. Mathematics 082 is a noncredit high school alge- bra course offered by the Mathematics Department at Michigan State Univer- sity in order that students may remove a college entrance deficiency. One year each of high school algebra and geometry or the equivalent and a satisfactory score on the mathematics placement test are prerequisite .for all courses in mathematics Department which carry college credit. The mathematics placement test is one of a series of orientation tests 'which.all new undergraduate students must take before registering at the Ikrtversity. This test was designed by staff members of the Mathematics Department and is revised periodically. The test consists of thirty items ccwering topics generally found in the first year and a half of kfiéflz school algebra. Students scoring fourteen or above on the test may register for an appropriate mathematics course. Students scoring less than.1kmirteen must take an arithmetic test. Those failing the arithmetic test;:mist register for arithmetic improvement and remain in it until they 6M 65 can pass an arithmetic retest. Upon passing the arithmetic test, these students must satisfactorily complete Mathematics 082 or score fourteen or above on a retake of the mathematics placement test before they can register for any mathematics course carrying college credit. Students who fail the mathematics placement test are eligible for retesting pro- viding at least one term has elapsed since the previous time they took the test. The course of study for Mathematics 082 is designed to provide a student with knowledge and understanding of certain basic algebraic facts and manipulative techniques which are necessary if one is to continue the study of mathematics. The topics covered are: the four fundamental operations with negative numbers and polynomials; the use of parentheses; factoring; fractions; linear and fractional equations; simultaneous linear equations; and ratio, proportion, and variation. Sparks' text-workbook is used as the basic text and the forementioned topics are treated in its first ten chapters. One member of the Mathematics Department is designated as adminis- trator of Mathematics 082 each term it is offered. He is responsible for scheduling examinations, making up the examinations, and assigning grades. He is assigned several graduate assistants. The graduate assistants are .responsible for covering the tutorial sessions and proctoring the exami- nations. Three progress tests during the term and a final examination are used to evaluate the students. The staff member in charge determines the scale for determining grades. Even though Mathematics 082 is a non- credit.course, students are graded A, B, C, D, or F in order to indicate their knowledge of the course of study. k 1 - Fred W. Sparks. A Survey of Basic Mathematig§; A Text and werk_ 299k for College Students. New York: McGraw-Hill, 1960. 257 p. a, 66 The self-help and tutor method. Mathematics 082 is offered regu- larly on a self-help and tutor basis. In this method, no regular classes are scheduled. Students enroll using regular enrollment procedures and are informed as to the time and place of the initial class meeting. This meeting is conducted by the staff member designated as administrator. At the initial meeting, each student receives printed information ex— plaining the self—help and tutor method and the course requirements. The staff member gives further explanation, clarifies details, and answers questions concerning this information. Students are told (1) to obtain a copy of the workbook.text2 and to complete the first ten chapters, (2) to plan to spend a minimum of eight hours a week in independent study, and (3) to obtain help with specific problems and with ideas which are not clear at the tutorial sessions. Nine hours of tutorial help are available each week and a student may come to as many of these as he feels is necessary. The times and places of the tutorial sessions and the times and places of the examinations are announced. In order to be admitted to the final examination, the workbook must be turned in for checking at least one week before the final examination with a minimum of the odd- numbered problems in the first ten chapters completed. The student re- ceives a ticket with the returned workbook and this ticket admits him to the final examination. Students in the study. The students in this study were (1) those who enrolled in Mathematics 082 at Michigan State University in the winter term, 196# and took all four examinations during the term; and (2) those Who enrolled in Mathematics 082 at Michigan State University in the Spring term, 1964 and took all four examinations during the term. The 2mm, 257 p. ‘ 67 regular academic year at Michigan State University is divided into three terms or quarters of approximately ten weeks of instructional time. Winter term, 1964 covered the time from January 6, 1964, through March 21, 1964. Spring term, 1964, included the time from March 30, 1964, through June 13, 1964. The initial contact with the students in the winter term was the first class meeting of Mathematics 082 on January 9, 1964. This meeting was conducted by the writer. These students had enrolled using regular enrollment procedures and expected that the course would be offered on the self-help and tutor basis. The students did not know the investiga- tor at the time of registration, nor did they know that they were to be a part of a research project on the teaching of Mathematics 082. At the first class meeting, the investigator explained that this term Mathematics 082 would be offered in two different ways. Two groups would be formed. One group would be conducted essentially the same as in the past. This group would use the self-help and tutor method which has been described on page three of this chapter. The only difference was that students would meet five days a week to work on the material and were instructed that they should spend a minimum of three additional hours a week in in— dependent study. This difference was deemed necessary in Order to insure that students using the workbook would spend, at a minimum, approximately the same amount of time working on the material as the students using the Programed material. The other group would use the programed materials prepared by the writer. Students using the programed materials would zmeet five days a week also but would work on the materials only during this time. Both sections were to meet from 4-5 p.m. every day. The pur— pOses of the research project were also explained. Fifty-eight students indicated an interest in participating in the research project and these 68 students were divided into two groups by the use of random numbers. DrOp- outs decreased the number of students in each group as the term progressed. Figure 1 shows the number of students in the study during the winter term, 1964. FIGURE 1 WINTER 58 students enrolled in J? 1 Course Mathematics J] . 9 4 } 30 students QB“ “J 28 students 1 in control in experimental group Agroup 2 students 1 student dropped out before end of_6_weeks dropped out before end of 6 weeks 7 students I 6 students 5 dropped out before dropped out before end of 8 weeks 1 cm of dyeeka Durw- 3 students dropped out before end of 10 weeks 18 students 21 students in in Experimental (i_______ji Control group C group E1 \ )Kf’ 2m .- ._ - . -‘ -| Comparisons Made The sample using the self_help and tutor method was designated as the control group and will be referred to throughout the thesis as C. Originally, there were six women and twenty—four men in control group C. Two women and ten men dropped during the term, so the sample used in 69 making the comparisons was composed of four women and fourteen men. The material shown in Tables I and II was obtained from a questionnaire each student was asked to fill out at the first class meeting. Table I shows TABLE I STUDENT AGE AND PAST EXPERIENCE IN MATHEMATICS 082 Group Average Age Took Mathematics 082 before in years No Yes C 19.3 8 10 E1 19.9 8 13 E2 19.6 4 9 the average age and past experience in Mathematics 082 of the students in the samples used in making the comparisons. Table II shows the high school mathematics courses taken by the students and the number of students who had taken each course. One stu- dent reported having taken five high school mathematics courses and hav- ing received grades of C or better in all of them. Six students reported having taken three high school mathematics courses and eleven reported having taken only ninth grade algebra and plane geometry. The sample using the programed material during winter term, 1964 was designated as experimental group E, and will be referred to through- out the thesis as E1. This designation is used in order to distinguish between the E1 group, the winter term experimental group, and the 32 group, the spring term experimental group. Originally there were five women and twenty—three men in experimental group, E1. Seven men dropped during the term, so the sample used in making the comparisons was com- POsed of five women and sixteen men. Tables I and II show the average 70 TABLE II PAST EXPERIENCE OF STUDENTS IN HIGH SCHOOL MATHEMATICS COURSES Group Alg. Alg. Pl. 801. Trig.D Other68 I I1 112 Geom. 3 Geomfl C 18 7 18 1 1 0 E1 20 8 17 2 3 4 32 1 3 5 11 1 2 1 -’ L ——.——— 1Algebra I or ninth grade algebra. 2Algebra II or a gecond year of high gchool algebra. 3Plane Geometry. Solid Geometry. Trigonometry. General Mathematics, Practical Mathematics or Business Mathematics. Table III shows the grade distribution in the various courses as reported by the students in group C. TABLE III GRADE DISTRIBUTION FOR HIGH SCHOOL MATHEMATICS COURSES - GROUP C Grade —IJAlg. AlgI——~—=:PII Sol.4£=: TrigI§=====Sifizfig==: I1 II2 Geom.3 Geom. A 2 0 0 O 0 0 ———— B 2 1 5 0 0 0 C 13 4 10 1 1 O D 1 2 3 0 0 0 ____ 1 , . 2 Algeora I or nin h grade algebra. , Algebra II or a gecond year of high chool algebra. Plane Geometry. Solid Geometry. Trigonometry. General Mathematics, Practical Mathematics or Ensiness Mathematics. age, past experience in Aathematics 082, the high school math matics Courses taken, and the number of students who had taken each course. This information was obtained fro» a questionnaire which each student completed 71 at the first class meeting. One student reported having taken only one year of ninth grade algebra. One student had taken ninth grade algebra and a course in General Mathematics. A third student reported having taken three years of General Mathematics, and a fourth that he had taken ninth grade algebra and two years of Practical Mathematics. All the other students had taken ninth grade algebra and plane geometry. Seven of these students reported having taken a third high school mathematics course and three students had taken two additional courses. One student reported that he had taken five different courses but had received grades of D in four of them including two years of algebra and a C in the fifth course. Table IV shows the grade distribution in the various courses as reported by the students in group E1. TABLE IV GRADE DISTRIBUTION FOR HIGH SCHOOL MATHEMATICS COURSES — GROUP E1 Grade Alg. Alg. Pl. Sol. Trig.§ Otherg I1 112 Geom.3 Geom._fi__r A 3 0 2 0 0 2 B 6 1 7 O 0 1 C 7 5 6 o 2 1 D 4 2 2 2 1 0 Algebra I or nin h grade algebra. uzAlgebra II or a econd year of high gEhOOl algebra. Plane Geometry. Solid Geometry. Trigonometry. General Mathematics, Practical Mathematics or Business Mathematics. No investigation was made of the drOpouts from the groups that existed during this study. However, approximately one half of the total dropouts notified the investigator that they would be unable to complete the course. Insufficient time and the pressure of courses taken for credit were the most common reasons. However, one student who dropped 72 from Group E1 between the sixth and eighth weeks, reported that he had then retaken the Mathematics Placement Test and had passed it. This stu- dent had attended the class sessions regularly for six weeks and had com- pleted the first 800 frames of the programed material. He had taken tests A and B which occurred at the end of the third and sixth weeks and re- ceived grades of B and C respectively. According to the questionnaire, this student completed at the first class meeting, he had registered for Mathematics 082 the previous term. He also reported having completed one year of ninth grade algebra with a grade of B and one year of plane geometry with a grade of C in high school. The initial contact with the students in the spring term was the first class meeting of Lhthematics 082 on April 2, 1964. Students in- dicating an interest in Mathematics 082 at registration were told to go to the Mathematics Department office. There students signed a sheet in- dicating their interest and were informed as to the time and place of the first class meeting. Nineteen students came to this meeting and were designated as an experimental group and will be referred to throughout the thesis as E2. The investigator explained that programed materials would be used for instruction, that this was part of a research project, and that the class would meet every day from-4-5 p.m. There were some drOpouts as the term progressed. Figure 2 shows the number of students in the study during spring term, 1964. All the students in E2 were men. There were nineteen students in the cnfiuginal group. Six of these dropped during the term leaving thirteen students in the sample usei in making the comparis:ns. The average age and the past experience in bathematics 032 of these students are found in Table I. Table II shows the high school mathematics courses taken by the Students and the number of students who had taken each course. This in- 73 formation was obtained from a questionnaire each student completed at the first class meeting. One student reported having taken only ninth grade algebra. Another student reported having taken ninth grade algebra and Business Mathematics. Five students had taken one year of algebra and one year of geometry. Four students reported three courses and two students had taken four high school mathematics courses. Table V shows the grade distribution in the various courses as reported by the students in group E2. TABLE V GRADE DISTRIBUTION FOR HIGH SCHOOL MATHEMATICS COURSES — GROUP E2 Grade Alg. Alg. Pl. Sol. Trig. Othe I1 II2 Geom.3 Geom.“ A 0 0 0 0 0 0 B 4 1 2 0 1 0 C 9 4 9 1 1 1 D 0 0 0 0 0 0 =‘ “— 1Algebra I or nin h grade algebra. .2Algebra II or a gecond year of high gchool algebra. .Plane Geometry. Solid Geometry. Trigonometry. General Mathematics, Practical Mathematics or BuSiness Mathematics. Administration of Mathematics 082 during the winter term. The groups C and E1 were selected at the first class meeting on January 9, 1954. The groups were separated before being given specific information on the instructional method and course requirements and the writer gave instructions to each of these sections individually. In group C, the investigator followed an outline given to each student in explaining the self-help and tutor method and the course requirements. Students were told (1) to obtain a COpy of the workbook—textB, (2) to plan to spend a ‘ 3Ibid., 257 p. 74 FIGURE 2 19 students enrolled in Course Mathematics 082 5 students drOpped out before end of:6 weeks _J .c—...... D.— .- ri..-m- .-..... 1 student‘ dropped out before 1 end of 8 weeks {7 13 students. . 1 18 students _ii"-“-__“._f%,in experimental in control group E2 group C /1\ I. I m L.._.___ ,__ __ ___1 Comparisons made J‘ .a -me “H minimum of three additional hours a week on independent study, (3) to complete a minimum of the odd-numbered problems in the first ten chapters, and (4) that they could obtain help with specific problems and with ideas which were not clear at the tutorial sessions. Nine hours of tutorial help were available each week from graduate assistants in a tutoring room set up by the Mathematics Department. A student could attend as many of these sessions as he felt was necessary. The times and places of these tutorial sessions were announced. Three examinations were to occur at the end of the third, sixth, and eighth weeks. The tOpics in the first four chapters are the four fundamental operations with negative numbers and Polynomials, and factoring. These topics were to be covered on the first examination. Chapters five, six and seven cover the topics of 75 fractions, linear and fractional equations, and simultaneous linear equations. These topics were to be covered on the second examination. EXponents and radicals are the tOpics found in the eighth chapter, and this material was to be covered on the third examination. final ex. amination was to cover the topics which had not been previously tested, as well as covering previous topics. The students were informed that the workbook would have to be turned in for checking at least one week before the final examination with at least the odd-numbered problems in Chapters 1 — 10 completed in order to be admitted to the final. The times and places of the examinations were announced. The investigator next introduced the person who would be present at each class session and would be responsible for taking attendance, maintaining order, and administering the examinations. This person was a senior undergraduate who was not majoring or minoring in mathematics or a related field. It was assumed that a person with this background would not be able to answer many of the questions about the subject mat- ter that students in the study might ask. This was deemed necessary in order to compare the relative effectiveness of the instructional materials. In group E each student received printed material explaining the 1. use of programed material and the course requirements. A sample of the programed material they would be using was also included. The investiga- tor discussed the purposes and objectives of programed material and gave further explanation on the use of this material. It was explained that the programed material contained all of the information needed for rele- vant learning of the topics found in the first ten chapters of the work- book and it was emphasized that programed material is not a test even though it might look like one. Students were told that (1) the programed material would be furnished and contained all the information needed on 76 the topics to be covered so it was not necessary to purchase a text, (2) the programed material would be available at each class session, (3) the programed material would be given to them in sections and they could ob- tain additional material as they needed it, and (4) overt responses were to be used. Three examinations and a final were scheduled. These ex— aminations covered the same topics and occurred on the same dates as did those for group C. The time and place of the class meetings and examina- tions, the number of examinations, and the topics to be covered on each examination were announced. The programed material contained 1,067 frames. The students were to complete 511 frames for the first test, through frame 886 for the second test, through frame 968 for the third test, and the re- mainder for the final. Although the students were informed of the number of frames they were required to complete for each test, they obtained ma— terial as they needed it in sections containing approximately 140 frames. No mention was made of tutorial help as none was available to the students using the programed material. The investigator answered questions con- cerning the use of the programed materials and the course requirements. The investigator next introduced the person who would be present at each class session and would be responsible for taking attendance, maintaining order, and administering the examinations. This person was also responsible for distributing and collecting the programed materials at each class session and announced corrections in the material when er- rors were found too late for hand correction. Since group 31 did not meet in the same room as group C to work on the material, this person was not the same individual as the one present at the group C class sessions. However, this person was also a senior undergraduate who was not majoring Or minoring in mathematics or a related field. It was assumed that a person with this background would not be able to answer many of the ques— 77 tions about the subject matter that students in the study might ask. Administration of Mathematics 082 during the spring term. At the first class meeting, group EZ was given the same printed information and the same instructions by the investigator as the students in group E1 received at the first class meeting. The same number of examinations were scheduled with the same time interval between them as were scheduled for group E The students were given all the material they would need 1. for each test in the class session immediately following each examination. Thus, they received the first 511 frames at the first work session, through frame 886 at the session immediately following the first test, etc. Students worked on the material only during the class sessions. The investigator was present at each class session in order to take attendance and maintain a satisfactory study environment. Students in E2 were allowed but not encouraged openly to ask questions. The writer did not offer any additional explanatory material but answered only the specific question asked and encouraged students to try and answer the question themselves from the information given in the programed ma- terials. There were no lectures on group discussions. Comparisons made. Figures 1 and 2 show the samples used in making two of the comparisons. Figure 3 shows the samples used in making the third comparison. Comparisons were made of the performance of students in these samples for all four examinations. FIGURE 3 39 students in experimental groups E1 and E? FWJQ " 1:1 control group L.._.—_..___ ......._1 O E I. -- .—-——-- —-—._._._— _~ --- __.1 Comparisons made 78 Summary. This chapter has described the organization and im— plementation of the study. The instructional methods used in this study, the students in the study and the samples that were used for making the comparisons have been described. In addition, detailed descriptions of the administration of Mathematics 082 for the winter and spring terms of 1964 have been included. These descriptions show that the number and length of class periods, the examinations and the scheduling of the ex- aminations were the same for all groups. These descriptions also pointed out how the administration of Mathematics 082 differed for the experimen- tal and control groups. These differences were: (1) the experimental groups used programed material only during the class sessions; (2) the control group took care of their own materials and could work on them outside of class; and (3) no tutorial help was available for students in the experimental groups but tutorial help was available on an individual basis for students in the control group. CHAPTER V RESULTS AND FINDINGS OF THE EXPERIMENT Introduction. One purpose of this study was concerned with the relative effectiveness of programed materials and the self-help and tutor method for teaching students in the course Mathematics 082. Student a- chievement on tests constructed to measure knowledge and understanding of certain basic algebraic facts and manipulative techniques was com— pared to determine the relative effectiveness of the programed materials and the self-help and tutor method. The purposes of this chapter are: (1) to describe the tests used; (2) to discuss the statistical methods used; and (3) to give the results of the statistical treatment of the data. Tests used in the study. The tests used in this study were: (1) the College Qualification Numerical Test, (2) the Michigan State Univer- sity Reading Test, and (3) four tests constructed by the writer. The College Qualification Numerical Test and the Michigan State University Readirmg Test are two of a battery of orientation tests given to students before: they register for the first time. The scores on these tests for each :>f the students in the study were obtained from Evaluation Services at Mic higan State University. The four tests constructed by the writer were axhninistered each term by the person in charge of the group. These tests 81%? to be found in the Supplement to this thesis. The tests were scored but the writer in the manner explained later in this chapter. Effiklege Qualification Numerical Test. The College Qualification Tests are a series of three ability tests developed for use by colleges in admission, placement, and guidance procedures. The Numerical Test is one of these. It contains fifty items including items from arithmetic, algebra, and geometry. The items were designed to test understanding of concepts and manipulation of ideas rather than computational proficiency. The emphasis is on power rather than on speed. Thus, although there is a time limit, almost all students who have the ability to answer the test items have an adequate time to answer all the items. Information concerning the reliability and validity of the College Qualification Numerical Test is reported in the test manual.1 A group of freshmen at two state universities was used in the reliability study. Estimates of reliability were obtained by comparing differences between scores on the odd and the even items of the test. The reliability co— efficients were reported separately for men and women and ranged from .89 to .93 for the various forms of the test. The validity coefficients are reported separately for men and women for individual institutions. Al- though descriptive information concerning each group studied is provided with the validity coefficients, anonymity of the institution is maintained. The grade point average at the end of the first term was used as the focus for the prediction studies. The validity coefficients for the Numerical Test in a four-year state university located in the North Cen- tral region of the United States range from .47 to .55. The test appears to be al;good predictor of the first term grade point average. This state- ment.i£s substantiated for students at Michigan State University by a study 1 George A. Bennett, Majorie S. Bennett, flimburn L. Mallace, and glexander G; Uesman. College Qualification Test Manual. New York: SyChOlOgical Corporation, 1961. 61 p. 81 reported by Dr. A. E. Juola2 of Evaluation Services. He reports that the Numerical Test score appears to be the single score which predicts best the grade in mathematics courses. The Michigan State University Reading Test. The Michigan State University Reading Test is a locally constructed test of reading compre— hension and contains 50 items. This test was revised in 1958. No in— formation is available on the reliability of the test. Information con— cerning the effectiveness of this score in predicting freshman grade point averages is reported by Dr. Juola.3 He writes that the Michigan State Reading Test appears to be almost as good a predictor of freshman grade point averages for three groups of students as the total score of *e Qualification Tests. These three groups were a random l C. \J the three Cclle sample of all freshman ma es, a random sample of all freshman females, and students enrolled in the first term of the three basic subjects of Communication Skills, Natural Science, and Social Science. Correlation coefficients between the total scores on the College Qualification Tests anl total grade point average are reported ranging from .52 to .66. Thus the total so re on the College Qualification Tests shows high pre- dictive validity. The four tests constructed by the writer. The writer constructed four tests designed to measure knowledge and understanding of certain A. bl ic algebraic facts and manipulative techniques. In this thesis test (I) k 2 a .. . - . . . l . . A. a. Juola. The Predictive Jaliditles of the New orientation IEfiyt Battery for Diverse Academic Areas. Evaluation Services, Michigan State University, 1959. 4 p. (Mimeographed.) 3 Ibid., p. 1-4. 82 A refers to the first test, which was given at the end of the third week; test B refers to the second test, which was given at the end of the sixth week; test C refers to the third test, which was given at the end of the eighth week; and test D refers to the final examination, which was given at the end of the term. Some questions on each test were of the objec— tive type in that only one step was required to get an answer. Most of the questions on each test were of the essay type since several steps were required to get an answer. Students were required to show the steps by which they had obtained the answer in questions of the essay type. Tests A, B, and C each had a total of 100 points. Test D had a total of 125 points. The student's final grade in the course was determined by the sum of his scores on these four tests. The faculty member who administers Mathematics 082 for the term is responsible for constructing tests and assigning final grades. There are no departmental examinations available for Mathematics 082. The writer obtained copies of the tests used for Mathematics 032 from two of the staff members. None of the tests obtained from the two staff members could be used in their entirety since none of them had been constructed 'to cover exactly the same topics as tests A, B, C, or D were to cover. 131 addition, the writer obtained a copy of the Mathematics Placement Examination. In constructing tests A, B, G, and D, the writer used as many questions as possible from the tests of the two staff members. Other test questions were selected in two ways. First questions were chosen which were similar to those on the Mathematics Placement Examina— tion. Selection of questions from the posttests which the writer had constructed for each unit before writing the programed material was the second way in which test questions were chosen. When test questions were Chosen in this manner, the writer checked the apprOpriate section of the 83 workbook in order to make sure that it contained several problems of this type. Items ranged from easy to difficult. The majority of the students finished the tests in the time allotted. Tests A, B, C and D for all students during both the winter and spring terms were scored by the writer. Previous to scoring any of the tests, the writer considered each essay type question and assigned the number of points to be given for each step of the solution. Thus a prob— lem having a total value of five points might consist of steps which were assigned values of two, two and one points or of steps which were assigned values of three and two points. The number of points assigned to each step depended on the importance and difficulty of the concept or tech- nique involved. Statistical methods used in this study. For the purpose of the comparison of achievement of the several compared groups of students, a null hypothesis was held. The null hypothesis held for each comparison was that students using the programed material would do no better on the four examinations constructed by the writer than those students who did not use the programed materials; that is, the mean achievements of stu— (Lents in the two samples are equal. The technique illustrated by Palmer 0. Johnson 4 for analysis of variance and convariance with two independent variables for data of a Single classification was used to test the above hypothesis. Twelve such anaJQYses were made in this study. The L1-test of homogenity of estimated variéhnces was significant at the .05 or smaller level in one of these analQVses. However, since the majority of the analyses indicated that the samplxes were drawn from a population having a common standard deviation, Palmer 0. Johnson. Statistical Methods in Research. New York: Prentice—Hall, 1949. pp. 247-230. 84 this comparison was not eliminated from the study. The test of significance used in each analysis was the F_test. When the hypothesis was accepted, it was inferred that the difference be- tween the mean achievements of the students in the two samples could be attributed to chance. Therefore, one method of instruction was assumed (D to be just as effective as the other method. Th hypothesis was rejected when the F-test indicated significance at the .05 or smaller level of confidence. When the hypothesis was rejected, it was inferred that the difference between the mean achievements of the students in the two samples could hardly be due to chance alone. This difference was assumed to have been the result of the instructional methods since in the analysis the two i dependent variables were controlled by a covariance adjustment. To determine which method of instruction had produced this significant dif- ference, the means of the two samples were adjusted for the sample differ- ence on each of the two independent variables in accordance with the tech- nique suggested by'themarS. The method used in teaching the students in the sample having the higher adjusted mean was considered to have been the more effective method of teaching. The independent variables were the score on the College Qualification Numerical Test and the score on the Michigan State University Reading Test. The results of the statistical treatment of the data. Table VI gives the means on each test for each of the samples used in the compari- SOns. Table VII gives the standard deviations on each test for each of the samples used in the comparisons. Tables VIII, IX, and X show the F ratios, the adjusted mean scores ,, 5Quinn MCNemar. Psycholggical Statistics. New York: John filley and Sons, 1949. p. 328. 85 and the difference between adjusted mean scores where the hypothesis was rejected. TABLE VI MEANS FOR EACH TEST FOR EACH 0? THE SAMPLES USED IN THE COMPARISONS '_7§;§fi;__8_' VI=EI 862’- A1 82 c3 D” CQT5 ingg E1 70.810 56.905 31.667 67.524 24.667 28.190 32 82.769 77.308 61.538 77.923 26.308 25.231 0 66.556 57.333 42.667 66.167 26.778 26.556 E1+C 68.846 57.103 36.744 66.897 25.641 27.436 3?+C 73.355 65.710 50.581 71.097 26.581 26.000 42.942 69.654 25.308 26.885 u\ N 0 ._.L \fi 4? Cl] -‘ 7 a 1+ 2+0 72.527 t1) A designates the first test f the term, which was given at the end of the third week of the term. B designates the second test f the term, which was given at the end of the sixth week of the term. C designates the third test,of the term, which was given at the e d of the eighth week of the term. 43 designates the final e' mination. CQT refers to the College Qualification Numerical Test. Reading refers to the Michigan State University Reading Test. Inspection of Table VIII shows that the hypothesis was accepted for all four tests when the 31 group which consisted of 21 students was compared with the C group which consisted of 18 students. The results of the comparisons made of student achievement for the E2 group which consisted of 13 students and the C group are given in Table IX. The hypothesis was rejected in all four comparisons. The adjusted mean for each of these comparisons was higher for the experimental group. From this. one may infer that students using the programed material during the Spring term, 1964, made significantly greater achievement on each of the four tests than the students in the control group. 86 TABLE VII STANDARD DEVIATION FOR EACH TEST FOR EACH OF THE SAMPLES USED IN THE COMPARISONS Group Tests* Read- A B C D CQT ing E1 15.349 21.830 15.899 26.613 7.580 7.287 E2 14.666 12.736 18.661 25.227 8.023 4.492 C 13.901 14.670 19.485 27.498 4.791 5.304 E1+C 14.851 18.868 18.478 27.033 6.530 6.500 72+C 16.322 17.034 21.289 27.195 6.354 5.023 E1+E2+C 15.985 19.598 21.410 27.018 6.939 6.135 T *A, B, C, CQT, and Reading refer to the tests as designated in Table VI. TABLE VIII STATISTICAL COMPARISONS 0F GROUPS 3 AND C ON FOUR TESTS, wINTaR TERM 1964 Test Degrees Freedom F Hypothesis A1 I‘36 IIIII— Iii; I—Ifi aCCeptedfi— 82 36 .019 accepted 03 36 .038 accepted 0” 36 2.742 accepted yA