Mmari, Geoffrey R. V2021-02-202021-02-201973Mmari, Geoffrey R. V (1973) A study of the understanding of mathematical ideas and concepts among Tanzania secondary school pupils , PhD Thesis , University of Dar es Salaam, Dar es Salaamhttp://41.86.178.5:8080/xmlui/handle/123456789/14870Available in print form, EAF collection, Dr. Wilbert Chagula Library (THS EAF QA11.M45)The research study covers work done during a span of four and a half years beginning in July 1968. As the title of the dissertation suggests, the primary objective of the study was to find out the extent to which pupils at the Form two level of Secondary school education understand mathematical concepts and ideas. Form two is selected because it appears to be the major water-shed, both historically and in current practice. After two years of secondary school work, there is a tendency for schools and pupils to separate the strong from the weak in mathematics and other sciences. The Dissertation is presented in five chapters accompanied with tables, figures, and followed by appendices. There are nine appendices, twenty-five tables, and sixty-three figures. In the research design these being Chapter One attempts to provide a background to the study by stating the nature of the problem and the necessity for the study. Terms used in the rest of the study are defined and the setting in Tanzania provided. The problem is seen to be one of improving performance in mathematics by improving the quality of teaching to enhance understanding of the mathematical concepts and ideas. The basis for improving and understanding of mathematical concepts is seen to be research into pupils' pattern of understanding with a view to identifying the concepts found difficult by them. Chapter Two examines the literature around the problem to be examined and related problems. It is found that not many studies have been done in Tanzania to investigate pupils' understanding of mathematical concepts. Research carried out elsewhere was found useful in providing both theoretical and practical reference for this study. In Chapter two methods of data collection are reviewed. Research designs of other researchers are studied, and relevant approaches adapted for this study. A full account is given of the factors used in the research design, these being: geographical location of the schools, sex of the pupils, management of the schools, residential status of the schools, and type of mathematical programmes offered in each school. Chapter Three is devoted to discussion on collection of data. A list of topics covered during the first two years by each programme is given and followed by a list of topics common to all three. The list is used in constructing the testing instrument. Altogether 47 schools were earmarked for the test but 42 actually participated. A total of 1,624 pupils were involved, of whom 722 were on Traditional Mathematics, 552 on Entebbe Mathematics and 350 on School Mathematics for East Africa (SMEA) programmes. Of the 1,624 pupils, 661 were in Government Schools, 728 in Voluntary Agency Schools, and 235 in Private Schools (including Seminaries). The total sample included 745 pupils in boys’ schools, 510 pupils in girls’ schools and 369 pupils in coeducational schools. Finally, of the total, 1,213 were in Boarding schools while 411 were in Day schools. Private Schools; Boys, Girls and Coeducation Schools Chapter Three gives the re-arranged order of topics for the Final test as well as the complete Test itself. The reliability and validity of the Test are discussed in this chapter. The coefficient of reliability was found to be 0.7097, using the Kunder-Richardson Formula 20. The coefficient of validity is calculated from data obtained in Terminal and Annual examinations in mathematics. These coefficients range between 0.39 and 0.52. Chapter Three is devoted to discussion on collection of data. A list of topics covered during the first two years by each programme is given and followed by a list of topics common to all three. The list is used in constructing the testing instrument. Altogether 47 schools were earmarked for the test but 42 actually participated. A total of 1,624 pupils were involved, of whom 722 were on Traditional Mathematics, 552 on Entebbe Mathematics and 350 on School Mathematics for East Africa (SMEA) programmes.us Of the 1,624 pupils, 661 were in Government Schools, 728 in Voluntary Agency Schools, and 235 in Private Schools (including Seminaries). The total sample included 745 pupils in boys’ schools, 510 pupils in girls’ schools and 369 pupils in coeducational schools. Finally, of the total, 1,213 were in Boarding schools while 411 were in Day schools. Private Schools; Boys, Girts and Coeducation Schools Chapter Three gives the re-arranged order of topics for the Final test as well as the complete Test itself. The reliability and validity of the Test are discussed in this chapter. The coefficient of reliability was found to be 0.7097, using the Kunder-Richardson Formula 20. The coefficient of validity is calculated from data obtained in Terminal and Annual examinations in mathematics. These coefficients range between 0.39 and 0.52. In Chapter Four an analysis of results is presented. The following hypotheses were tested: the null hypothesis that there is no difference in achievement between schools following different programmes, the null hypothesis that there is no difference in achievement between pupils in schools run by different managements, the null hypothesis that there is no difference in achievement due to sex, and the null hypothesis that there is no difference in achievement between pupils due to the boarding status of the school. These hypotheses were tested by calculating the F-values and t-values at the 1 per cent level of significance. Results show that the only hypotheses rejected are that there are no differences in achievement between SMEA and Traditional programmes and between Girls and Coeducational schools. The other hypotheses cannot be rejected: that there is no difference in achievement between Government, Voluntary Agency and Private Schools; Boys, Girls and Coeducational Schools; Boarding and Day Schools. Solo Also presented in Chapter Four, is a full Item Categorization. Six categories are considered. First category covers manipulative abilities items. Second category covers items testing knowledge and understanding of formulas, theorems and mathematical terms. Third category items test ability to translate sentences into algebraic or graphic representation. Fourth category items test ability to draw conclusions from given data. Fifth category items test ability to recognize which facts or processes are necessary for the solution of a problem, and to use these accurately in the solution. The sixth category of items test ability to visualize forms and relationships in three-dimensional space and to apply knowledge of algebra, plane geometry, or trigonometry to them. An analysis of performance in the different categories shows that in all programmes, pupils have not sufficiently mastered the fundamental algebraic operations. There is also lack of sufficient understanding of formulas, theorems and mathematical terms. Ability to translate sentences into algebraic or graphic representation is lacking among many pupils irrespective of programme followed. Although performance on some items was satisfactory, it was observed that pupils lack reasonable ability to draw conclusions from given data. Finally, it was observed that there is an indication that ability to recognize which facts or processes are necessary for the solution of a problem and to use these accurately in the solution has not been adequately observed. In Chapter Five, Conclusions based on analysis of results are made. For ease of presentation, the conclusions are analysis. Recommendations based on the statistical evidence and on survey of studies elsewhere are given at the end of the chapter. These recommendations also cover areas of further research. A complete bibliography of eighty-one sources cited in the study is given. This is followed by Appendices and Figures, whose titles appear in the table of contents and are self-explanatory.enMathematicsStudy and teaching (Secondary)TanzaniaThesis