Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

This is an outcomes based program evaluation which used a nonequivalent control-group design to determine the effectiveness of the implementation of Applications of Mathematics 10 in British Columbia public schools. The Experimental Group (10 classes, N = 154) and Control Group (13 classes, N = 232) were selected as intact classes from a population of schools offering Applications of Mathematics 10 (Experimental Group) and Principles of Mathematics 10 and Mathematics 10A (Control Group) in the 1998/99 school year. The criteria used to evaluate this program consisted of: (1) a comparison of teaching methodology used in the 23 classes participating in the study based upon teacher surveys (pre-test and post-test) and logbooks kept by the teachers reporting the methodology used in each class; (2) a comparison of student achievement in the three courses based upon student achievement scores (pre-test and post-test) on multiple choice mathematics assessments; and, (3) a comparison of student attitudes towards mathematics in the three courses based upon student attitude scores (pre-test and post-test) on two surveys. Teachers in the Experimental and Control groups reported using different teaching strategies (but similar assessment strategies) in their respective classes. The Experimental Group teachers reported using teaching methodologies more consistent with the desired constructivist treatment than did the Control Group teachers. Using analysis of variance and subsequent post-hoc multiple comparisons of pre- and post-test means it was determined that student achievement scores in the Control Sub-Group, Principles of Mathematics 10 (pre-test M = 17.5, SD = 5.1; post-test M = 23.0, SD = 6.8), were significantly higher (pre- and post-test) than the Experimental Group scores (M = 12.6, SD = 4.2; post-test M = 14.8, SD = 4.8) and the Control Sub-Group scores, Mathematics 10A, (pre-test M = 10.6, SD = 3.9; post-test M = 12.8, SD = 4.6). The Experimental Group scored significantly higher than the Mathematics 10A sub-group on the pre-test assessment, but not the post-test assessment. It was also determined that student attitude toward mathematics scores in the Control Sub-Group, PM 10 (pre-test M = 13.2, SD = 3.0; post-test M = 12.8, SD = 3.2), were significantly higher (pre- and post-test) than the Experimental Group scores (M = 10.1, SD = 2.8; post-test M = 10.0, SD = 3.0) and the Control Sub-Group scores, 10A, (pre-test M = 9. 1, SD = 2.6; post-test M = 8.4, SD = 2.9). The Experimental Group scored significantly higher than the 10A sub-group on the post-test attitude toward mathematics assessment, but not the pre-test assessment. It was concluded that the Applications of Mathematics 10 implementation is a qualified success and that this model of delivering mathematics instruction should be pursued. / Graduate

There has been very little research into play production in schools, as distinct from drama in education and theatre in education, and none at all with specific attention to the Eastern Cape. The proliferation of dramatic productions in the schools of the Eastern Cape during the 1960s and 1970s coincided with the establishment at Rhodes University of a Department of Speech and Drama. The particular interest of this Department in the educational aspects of dramatic work of all kinds led naturally to a desire to investigate what was being done, and had been done, in the schools in the area. Added to this, interest in the history of the Eastern Cape has been stimulated by the building of the 1820 Settlers' Monument, which was opened in 1974, to mark the hundred and fiftieth anniversary of the arrival of the British Settlers. In order to set the social and political scene for the beginnings of cultural activity in the schools, I have given a brief account of the historical events leading up to the English settlement in the Eastern Cape. Because the evolution of the towns has affected that of the schools, an account of this development has been included¹. To prevent this work from becoming unwieldy, the detailed investigation of the cultural milieu has been limited to that of two frontier towns and two seaports, as being the most representative in the Eastern Cape². So much that was done in the schools had grown out of the ideas brought from Britain and its public schools that it was necessary also to look at the basis upon which the schools in the Eastern Cape were founded, and the lines along which their ethos developed. To facilitate a consideration of the work done in play production and related activities over a period of approximately a hundred and fifty years, I have separated the account into four natural historical divisions: from 1820 until the turn of the century; 1900 to 1918; the period between the two world wars; and that which follows the Second World War. Of these, the first three have been considered from the historical point of view; but with regard to the years between 1940 and 1977 it seemed more interesting and profitable to examine specific trends and developments in dramatic activity within the schools. I wished, further, to find more detailed information about what is happening in the schools at present than could be gathered from school magazines and the local press. For this purpose, two questionnaires were sent to the schools. The evaluation of these will be found in Part III and in Appendix B. The investigation was confined to the English and parallel medium schools in the area. The catalogue of plays produced since 1860 which is given in Appendix E is not necessarily exhaustive, though as comprehensive as it was possible to make it. It has been drawn up from the information in school archives and the press, as well as that given in the answers to the questionnaires, but there are occasions when these sources do not give titles of plays (this is especially the case with one-act plays) and there are also times when productions may not have been reported, or magazines are missing. It is not the purpose of this thesis to give details of the best production procedures. Teacher-directors may find these in many excellent books on the subject, some of which have been suggested in Appendix F. ¹While not strictly part of the subject under investigation, a consideration of musical activity is relevant to developments in drama . A short section on music has therefore also been included in Appendix A. ²My researches have pointed to the fact that there is an interesting field for further investigation in the smaller towns such as Cathcart and Uitenhage. (Pref. p. ii-iii)

This pilot study was aimed at investigating with the aid of a two-tier multiple choice questionnaire, the misconceptions held by pupils in standards 8 and 10 as well as first year Biology students in the area of senior secondary school genetics. It was found that certain of the children's preconceived ideas were altered by tuition while others were unaffected by either age or tuition and consequently warranted the name misconceptions. Four misconceptions were identified in this study and these were seen to be at the root of the difficulties experienced in genetics. They involved plants being seen to be unable to reproduce sexually, an inability to relate meiosis to genetics, a tendency to cling to the Punnett square algorithm when solving genetics problems despite a lack of understanding of the underlying processes and a failure to see the role of chance in genetics. These misconceptions were seen to have arisen because of certain preconceived ideas which hamper the formation of a suitable conceptual framework. The adoption of suitable teaching strategies appears to be the most likely method of rectifying the problem. However, before this can be regarded as conclusive, further research into the concept development of specific aspects such as sexual reproduction, needs to be done. Studies to investigate the most suitable teaching strategy should also be carried out as well as an investigation into the structure of the curriculum

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This study was designed to determine the relative effectiveness of teaching a unit on wave-motion and sound at the grade nine and ten levels, using two different methods of instruction. One hundred twenty students enrolled in the grade nine and ten General Science courses at the Balmoral Junior Secondary School in School District No. 44 (North Vancouver), took part in the investigation. The students were grouped into three levels of scholastic aptitude within each grade, and also, into two methods sections. Two questions were investigated in this study. First, do significant differences exist between the mean scores on the final test of the various grade and methods groups? Secondly, for which of these groups is the unit suitable? In order to answer the first question, the final scores were studied by an analysis of covariance with scholastic aptitude, knowledge of General Science, and prior knowledge of the material in the unit being the variables controlled. The second question was investigated by first adjusting the final scores of all the subjects for differences between them on the three factors assumed to influence their performance in this study. The performance of each group was then compared with the criterion that 75 per cent of the students in a group should make a mark of 50 per cent or better on the final test in order for the unit to be judged suitable for that group. All the differences between the means of the two grade groups, and the three levels of scholastic aptitude within these two grades, were found to be non-significant at the one per cent level of significance. On the other hand, the differences between the means of the methods groups, demonstration-experiment and student-experiment, were found to be significant at the one per cent level. Of the two methods groups, the highest adjusted mean score was obtained by the demonstration-experiment group. All the groups satisfied the requirement of suitability that 75 per cent should obtain a mark of 50 per cent or better on the final test. / Education, Faculty of / Graduate

This study is concerned with Grade 7 students' conceptual and procedural understandings of division. Although division is formally introduced in Grade 3 or 4, late intermediate students frequently have difficulty understanding both the concepts and the procedures associated with division. The classroom case study was chosen as the method of investigation for this study. Because the researcher was also the enrolling teacher of the group of 22 Grade 7 students, the conditions of the study were as similar as is possible to regular classroom instruction. The investigation followed a unit of study in division of whole numbers and decimal fractions from the pretest, through instruction, to the posttest. The researcher elicited students' understandings of division in computational and problem-solving situations in a variety of ways. Students wrote a pencil-and-paper pretest which was designed to reveal understandings. Areas of interest identified by the pretest were then investigated through small group and whole class discussions. Instruction was based on eliciting and confronting students' beliefs regarding division, and on strengthening conceptual understanding of both division and decimal fractions. Students viewed division procedurally, attaching little meaning to the processes associated with the division algorithm. Approximately one fourth of the students were uncertain about the meaning of the two forms of notation, and most read "b ÷ a" as "b goes into a." When asked to use manipulative materials to reflect a division question, some students were unable to do so independently. It was found that students relied heavily on the partitive model of division. Although some students demonstrated an understanding of quotitive division, these students also tended to rely on partition and turned to quotition only when it became apparent that partition was not appropriate. This reliance on partition influenced the students' ability to solve story problems requiring division. Students were able to solve story problems which fit the partitive model: the divisor is a whole number and is less than the whole number dividend. In situations where this was not true, students had difficulty. In these cases, students reversed the terms of the question or chose an operation other than division. These results led to an investigation of students' beliefs about division. The belief that "division always makes smaller" was common. This belief stems from partition with whole numbers where it is true. A related belief held by students is that the divisor must be smaller than the dividend. An exception is the case where this would necessitate a divisor less than one. In this case, students preferred a larger whole number as the divisor. Division by a number less than one was seen as illegitimate. Division involving decimal fractions was generally difficult for students. Weak place value concepts, coupled with a belief that whole numbers and decimal fractions were two separate and unrelated number systems, contributed to difficulty when solving problems. Students had few representations for decimal fractions which compounded their difficulty. The dominance of partition and the tendency to overgeneralize whole number rules appear to be partly responsible for this. When solving problems students showed little evidence of planning or looking back. Generally they found the numbers in the problem and performed the operation that seemed appropriate. Decisions about operations were often driven by the relative size of the numbers in the problem and by the beliefs mentioned earlier. Because they omitted the looking back phase of problem solving, students rarely accounted for remainders and did not recognize when an answer was unreasonable. Implications for instruction resulting from this study centre on the assessment of students' understanding of division. This can be accomplished in the regular classroom setting through pencil-and-paper tests, small group work, whole class discussions, and individual interviews. Beliefs which may interfere with learning must be revealed and confronted. Asking students to defend and justify their thinking is part of this process. Students' reliance on partition and their procedural view of division suggest changes in the way in which division is introduced in the early intermediate years. Delaying the formal introduction of the division algorithm to Grade 5 would allow more students time to develop their conceptual understanding of partition and quotition. Students should focus on estimation and reasonableness of responses. Introduction of division involving decimal fractions, including numbers less than one, could be accomplished by using manipulative materials and calculators. Contexts in which the divisor is greater than the dividend should also be introduced in the early intermediate years. Procedures, when finally introduced, should be linked to the concepts. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

An exploratory investigation into the effect of co-operative group learning, involving tutoring, on the achievement and attitudes of 174 grade eight pupils in new mathematics is described. Three volunteer teachers and six volunteered mathematics classes were involved. Five hypotheses concerning test performance and one concerning attitudes were advanced. Using the scores obtained in the mathematics sections of the Stanford Achievement Test (Advanced) and an entering behaviour test of prior mathematics learning, to establish similarity of the groups, instruction was carried out over a period of twelve weeks. A retention test was given two months later. Attitude scores from data collected by Semantic Differential before and after the experiment were analysed using a model for multidimensional analysis of Semantic Differential attitude data (McKie and Foster, 1972). Achievement in algebra learning and retention reached the .05 level of statistical significance, favouring the experimental group. No differences for treatment occurred for instructor effects, instructor by group interaction or attitudes at the .05 level of statistical significance. Conclusions for further research and practice are drawn. / Education, Faculty of / Graduate

The purpose of this investigation was to evaluate the effect of two modes of exposition of tenth-grade incidence geometry on logically evaluated problem solving ability. To achieve this purpose two classes of tenth-grade geometry students were chosen to be the experimental and control groups. The two treatments, which were of nine class hours duration per group, and were both taught by the investigator, involved the use of a set theoretic symbolic-nonrepresentational mode for the experimental group, and a pictorial-representational mode for the control group. The content of the treatments was Euclidean incidence geometry. At the termination of the treatment a criterion test was administered to both groups. The criterion test was composed of two types of problems- Type NR problems, which were believed to be most successfully solved by a symbolic-nonpictorial analysis, and Type R problems, which were believed to be most successfully solved by a pictorial analysis. Two hypotheses, of null form, were considered: that the mean scores of both groups on Type NR problems would be equal and that the mean scores of both groups on Type R problems would be equal. Both hypotheses were tested by means of an appropriate t-statistic at the .05 level of significance. Analysis of the data indicated that both null hypotheses were not to be rejected. A difference in means on Test NR of the control over experimental group was observed at the .20 level of significance. The implication of the analysis of the data and the restrictions imposed by the limitations of the study is that the pictorial-representational exposition was as effective as the experimental symbolic-nonrepresentational exposition for Type NR problems and for Type R problems. Since the pictorial-representational mode of exposition is generally considered standard practice in the teaching of tenth grade geometry it should be continued for the present. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

Current literature emphasizes the need to attempt new approaches in the teaching of Social Studies. Jerome S. Bruner in his book The Process of Education (1961), claims that the main objective of a school must be to "present subject matter effectively, - that is with due regard not only for coverage but also for structure." Only by teaching the fundamental structure of a subject is that subject comprehensible to the student. Bruner says: "Intellectual activity anywhere is the same, whether at the frontier of knowledge or in a third grade classroom. What a scientist does at his desk or in his laboratory .... is the same order as what anybody does when he is engaged in like activity if he is to achieve understanding. The difference is in degrees, not in kind. A schoolboy learning physics is a physicist, and it is easier for him to learn physics behaving like a physicist than by doing something else." Professional geographers advocate the inductive method of teaching so that pupils discover the structure of geography in the same way as it is understood by the professional geographer. The teaching then should be experimental and intellectually stimulating, leading from geographical data supplied to reach the desired principles and generalisations. To-day children at various levels of efficiency, learn the inductive method in their study of chemistry, biology, and similar sciences. In theory - if not always in practice- they study in laboratories, consider hypotheses, analyze examples, draw tentative conclusions, and make cautious generalisations. Similar inductive procedures have increasingly marked the work of professional geographers, sociologists and political scientists. In short, pupils should be taught to become amateur geographers, performing similar (not identical) tasks of those scholars working on the frontiers of knowledge. Paraphrasing Jerome Brune, "If children are going to learn geography, they must do things the way geographers do them." This is the whole essence of the laboratory approach - it is a successful way to teach geography because it is essentially the way geographers operate, During the last four years I have conducted a continuing experiment into the development of an approach to better geographic teaching. This experiment has attempted to evaluate the relative effectiveness of a laboratory approach to the teaching of geography. The word "laboratory" suggests exploration and adventure on a rather direct, personal basis. Thus, the laboratory approach provides the opportunity for active study at firsthand basis and direct involvement of the students. It makes provision for the students to do something on their own - using their thinking ability and with their own hands. This is the basis of inquiry-oriented approaches and the new strategies, now being increasingly used in the domain of social studies. But this direct experience does not mean that the laboratory approach in social studies education ignores reading and highly symbolic abstract experiences. The laboratory approach offers much more to the students than listening to the teacher or studying the textbook. It represents a significant means for communicating non-verbal experiences and knowledge to the students. For example, laboratory methods train individuals to develop their observational power, and help them acquire skills. Along with these, the atmosphere in the laboratory promotes the desire to share experiences. It develops the ability of working together, provides for individual, creative activity and heightens pupil motivation. Studies of instructional practices suggest that teaching processes and materials should be coordinated in a systematic manner. We should, as teachers, spend a great deal of time and effort in planning to that teaching materials are directly related to a systematic study of a problem. In recent years, considerable emphasis has been placed on individualization of learning. The laboratory approach maximizes the opportunity for individualization of learning, provides for creativity, and originality. The use of laboratory strategies and materials other than dry words and textbooks are significant in making social studies education real and concrete. The laboratory approach is not a panacea but it offers an opportunity to make the teaching of geography more interesting and exciting. It has proven possible in courses in physical science to have students perform simple experiments in order to come closer to understanding the methods of science. I see no conceivable reason why this can't be done in social science. In the Laboratory Approach students and teachers plan together and share materials, an important part of learning -teaching process. Besides fostering the achievement of the cognitive and effective objectives of teaching social studies the Laboratory Approach develops various kinds of skills -communicative, creative, acquisitive, organizational and manipulative. This course is based on the view that the traditional emphasis on expository teaching of Geography by lecture and rote memorization must be replaced by an emphasis on the use of inductive methods through which students learn to use the materials and modes of thought of geographers. In the course itself, the inductive approach is used, laboratory type studies are used throughout in which principles are applied to materials in the structuring of lessons. The uses of aerial photos described here are desirable in that the tool, the photo, is considered a means not an end. The exercises force the student to face situations which require him to generalize. He must make an orderly study of the land use of the area shown in the photograph and then organize the data for the purpose of generalization. The student also gains an appreciation of the problems of the map maker as well as a better understanding of the cultural and physical patterns of the area included in the photograph. This learning logically provides motivation for seeking similar patterns in the areas contiguous to that studied as well as to distant areas. The elements of geography teaching emphasized in this experimental work are the elements of geographic field study; observation and recording of information, selection of required data from that which has been observed and recorded and then analyzation, synthesization and interpretation of all this selected data in order to formulate a generalization. The ideas offered here are merely samples of kinds of experiments possible in the social studies Laboratory Approach. A flexible approach and a capitalizing on what takes place in both the classroom and the community may develop entirely different ways to involve the student in acting and reacting. "New frontiers" in any category of academic disciplines emerge from territory already explored. Those time-tested and solid foundations of the social studies which have served well in the past obviously must not be cast aside in favor of untested educational programs and designs. What are "new frontiers" for some, accordingly, may be old and comfortable territory for others. Some of the concepts and observations set forth in this paper, therefore, are not necessarily new, although many school systems for one reason or another may not have given them consideration or trial. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate