This study investigates some students’ and teachers’ beliefs about the role of homework in mathematics in Sweden. By interviewing eight adolescent students and two experienced mathematics teachers the study discusses the role of homework in relation to learning, teaching, achievements, and relationship between students, teachers and parents. The results suggest that (a) students and teachers have similar beliefs and perspective on homework (b) students and teachers believe in the use of homework to increase mathematics test results (c) homework breeds relationship and communication between students, teachers, and parents (d) the quality and quantity of homework is essential, and that (e) well developed relationship between parents, students, and teachers is essential to create successful students who appreciate homework.

Doctor Educationis / One of the educational ideas used in mathematics education to improve mathematics achievement in schools is examination-driven teaching. Its effects have sparked intense debates in different didactic circles regarding its usefulness as a teaching technique. More specifically, researchers have consistently debated whether examination-driven teaching is a good or a bad approach that can be used beneficially for learners’ achievement. In South Africa, the urgent need to uplift the low performances of high school learners in Mathematics has led to a development of a project which is a partnership with the Western Cape Education Department (WCED) and the University of the Western Cape (UWC). This project used examination-driven teaching in the context of a continuous professional development to improve learners’ mathematics scores. Five secondary schools that were opportunistically sampled in the province of the Western Cape were exposed to examination-driven teaching. For evaluation, the project yearly developed and implemented high-stakes Grade 10 end-ofyear mathematics examinations, and the data subjected to analysis were learners’ mathematics scores for 2012, 2013 and 2014. A quantitative approach employing Rasch procedures and some statistical procedures were used to analyse the data. The study intended to answer the following questions: 1) Do learners’ achievement scores in a high-stakes Grade 10 mathematics examinations improve over time when an examination-driven teaching approach is being used as intervention? 2) Does socio-economic status of schools influence mathematics performances in the case of using examination-driven teaching ? 3) Are there differences over time in the achievement of learners in the two different papers comprising the examination? / Okitowamba, O. (2015) Tracking learners’ performances in high-stakes Grade 10 mathematics examinations. PhD thesis. University of the Western Cape. Bellville. http://hdl.handle.net/11394/5655.

>Magister Scientiae - MSc / The aim of the thesis is to research the difficulties that first year mainstream mathematics students at UWC experience when solving Related Rates problems in calculus. In chapter 2, an in-depth study was made of the nature of Related Rates problems by studying a number of examples. The findings of this study are summarized in section 2.12. The study adopted the same model of the solution of all types of Related Rates that was used by Martin (2000) for the solution of geometric Related Rates problems. In chapter 3 of this thesis, many examples were used to illustrate how the seven step solution procedure of the Standard Solution model is applied. In the literature review in chapter 4, the underlying concepts which underpin Related Rates problems are identified and specific examples of research on each of these concepts are given. For example, the review of the literature on word problems is done comprehensively and covers extensively the range of issues involved in this topic. Drawing on the work in chapter 2 on the nature of Related Rates problems, it is explained in chapter 5 why this study is underpinned by Constructivism as a theoretical basis. Chapter 6 of the thesis is devoted to answering the 3 research questions posed in chapter 1. The thesis contains many worked examples of Related Rates problems which can be used by the lecturers assigned to the MAT105 course.

The problem with which this investigation is concerned is that of determining whether utilizing self-help groups for remedial mathematics students would improve their course completion rates, achievement, and attitudes toward learning mathematics. The methods of determining the success/failure of self-help groups in this study were the Z-test from inferences concerning two proportions, the t-test from inferences concerning the difference between two independent means, and the t-test from inferences concerning the difference between two dependent means. The participants of the study were chosen from the students enrolled in "daytime" mathematics classes at Tarrant County Junior College - Northeast Campus, Hurst, Texas. The experiment was conducted over two semesters and the data combined for statistical analysis. There were one hundred four students involved in the study. Fifty-two students comprised each of the experimental and control classes. The term self-help group was utilized to describe a small group of two-to-fifteen people who engaged in discussion of responsibility, standards, confession, lay leadership, and action. The students did not study mathematics in self-help group sessions. The group meetings dealt with anxieties, attitudes, and commitment that may be associated with mathematics in general. To investigate the hypotheses of this study, data was collected to calculate the percentage completion rates, the means of the final exams taken by students, and the differences of the Semantic Differential scores given to students in the experimental class at the beginning and the end of the semester. This data was utilized for statistical analysis to determine if the experiment was successful. The report concludes that self-help groups did not significantly improve course completion rates, achievement, or attitudes of students toward learning mathematics. Forty-four per cent of the students that completed the experimental class participated in self-help groups.

The learning difficulties prevalent among mathematics students are widely documented. This case study explores the difficulties experienced by National Certificate (Vocational) Level 2 mathematics students at a Technical and Vocational Education and Training (TVET) College in Gauteng in the learning of functions. The primary research question was: What conceptual and procedural knowledge difficulties do NC(V) L2 students experience when learning the concept of functions in mathematics? Qualitative data was generated from the students (n=17) through lesson observations, test responses and interviews. The convenient sample of students all belonged to one L2 mathematics class. The findings revealed that the students experience conceptual knowledge difficulties in terms of defining a function, identifying functions, translating between representations of functions, and interpreting the behaviour of a function. The findings also revealed procedural knowledge difficulties prevalent among the students. The errors that students committed in this regard included factorisation errors, structural errors, misapplication and modification of the rules. In general, the findings indicated that the students in this sample lack procedural knowledge and conceptual understanding of functions. The lesson observations revealed a prevalence of several misconceptions regarding functions among the students which were seemingly not recognised nor remedied by the teacher. The teacher’s instructional practices thus appeared to be among the possible sources of the difficulties that the students experience in the learning of functions. This finding was also confirmed by the students during the interviews. Shaky foundations from previous grades were also a factor. / Dissertation (MEd)--University of Pretoria, 2020. / Science, Mathematics and Technology Education / MEd / Unrestricted

Many studies have been made concerning the difficulties which business mathematics students have in solving stated problems. Such studies have been made by analyzing the student's errors as they appear on written solutions to problems, and, as a result, many errors are overlooked. Errors in the thinking process, and failure to read the problem a sufficient number of times are responsible for many errors made by students. Such errors are not apparent on written solutions, but would be revealed through oral solutions as recorded on a wire recorder. The purpose of this study, then, is to analyze the errors revealed by a wire recorder, along with errors on written solutions, and to classify and tabulate the errors from both sources.

Research has shown that academic under-performance in higher education can be attributed inter alia to psychosocial difficulties arising from students’ under-preparedness for the rigours of university life, the struggle to accommodate diverse cultural worldviews and poor proficiency in the language of learning and teaching (Chang 1999). As internationalisation of higher education institutions has became more common worldwide, the need for support systems to deal with problems of a multicultural student body has become essential if students are to have equitable opportunities for success. In this regard, Monash South Africa (MSA), an international multicultural higher education institution, introduced a tutor-mentor programme to improve academic outcomes among mathematics students in the Foundation Programme (FP). The impact of this programme was investigated by means of an empirical investigation and framed by a bricolage of learning theories which served as a conceptual framework for the study under the metaphors of acquisition and participation. The literature study showed that tutoring and mentoring programmes tend to be successful pedagogical supports. The empirical inquiry took the form of a mixed-method case study which explored the impact of participation in the tutor-mentor programme on mathematical performance among FP mathematics students at MSA. The participants in the study, which was carried out in two phases, were mathematics students, tutor-mentors and lecturers in the FP. Phase 1 quantitatively explored the extent of effectiveness of the tutor-mentor intervention, using a quasi-experimental non-equivalent control group design. Two formal tests were used to gather data, which were analysed by an analysis of covariance and the Johnson-Neyman technique. Quantitative findings supported the initial assumption of the study: that participation in the tutor-mentor programme as an intervention strategy improved the mathematics scores of FP students at MSA. Phase 2, a qualitative study, used purposive sampling. Data was gathered through focus group and individual interviews, observation, spontaneous conversations and photographs. Interpretation of the quantitative and qualitative data was presented according to the phases and thereafter integrated. Qualitative findings provided information about the dynamics of the tutor-mentor programme in providing academic and psychosocial support to students. Finally, a situation-producing theory was developed from the integrated findings, and recommendations made for improvement of practice. / Educational Studies / D. Ed. (Comparative Education)

Research has shown that academic under-performance in higher education can be attributed inter alia to psychosocial difficulties arising from students’ under-preparedness for the rigours of university life, the struggle to accommodate diverse cultural worldviews and poor proficiency in the language of learning and teaching (Chang 1999). As internationalisation of higher education institutions has became more common worldwide, the need for support systems to deal with problems of a multicultural student body has become essential if students are to have equitable opportunities for success. In this regard, Monash South Africa (MSA), an international multicultural higher education institution, introduced a tutor-mentor programme to improve academic outcomes among mathematics students in the Foundation Programme (FP). The impact of this programme was investigated by means of an empirical investigation and framed by a bricolage of learning theories which served as a conceptual framework for the study under the metaphors of acquisition and participation. The literature study showed that tutoring and mentoring programmes tend to be successful pedagogical supports. The empirical inquiry took the form of a mixed-method case study which explored the impact of participation in the tutor-mentor programme on mathematical performance among FP mathematics students at MSA. The participants in the study, which was carried out in two phases, were mathematics students, tutor-mentors and lecturers in the FP. Phase 1 quantitatively explored the extent of effectiveness of the tutor-mentor intervention, using a quasi-experimental non-equivalent control group design. Two formal tests were used to gather data, which were analysed by an analysis of covariance and the Johnson-Neyman technique. Quantitative findings supported the initial assumption of the study: that participation in the tutor-mentor programme as an intervention strategy improved the mathematics scores of FP students at MSA. Phase 2, a qualitative study, used purposive sampling. Data was gathered through focus group and individual interviews, observation, spontaneous conversations and photographs. Interpretation of the quantitative and qualitative data was presented according to the phases and thereafter integrated. Qualitative findings provided information about the dynamics of the tutor-mentor programme in providing academic and psychosocial support to students. Finally, a situation-producing theory was developed from the integrated findings, and recommendations made for improvement of practice. / Educational Studies / D. Ed. (Comparative Education)

The purposes of this study were (1) to determine the difference between the cognitive style of low and high achieving students in an algebra course in a traditional high school and the cognitive style of low and high achieving students in an algebra course in a high school for dropouts, and (2) to determine the difference between the cognitive styles of low and high achieving males and females in an algebra class in a traditional high school and in a high school for dropouts. It was hypothesized that (1) low achieving mathematics students are more field-dependent than high achieving mathematics students in both the traditional high school and in the high school for dropouts, (2) female students are more field-dependent than male students in the mathematics classes of both schools, and (3) there will be a significant interaction on the achievement variable and the sex variable with respect to field-dependence in both schools.

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