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<p>This research provided insights into the mathematical achievement of a cohort of tertiary mathematics students. The context for the study was an entry level mathematics course, set in an engineering programme at a tertiary institution, the Cape Peninsula University of Technology (CPUT). This study investigated the possibilities of providing a bridge between the assessment of students by means of tests scores and a taxonomy of mathematical objectives, on the one hand, and the critical analysis of student produced texts, on the other hand. This research revealed that even in cases of wrong solutions, participant members' responses were reasonable, meaningful, clear and logical.</p>

M.Ed. (Subject Didactics) / Please refer to full text to view abstract

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2007. / Twelve years into a democracy, South Africa still faces many developmental challenges. Since 2002 Universities of Technology in South Africa have introduced Foundational Programmes/provisions in their Science and Engineering programmes as a key mechanism for increasing throughput and enhancing quality. The Department of Education has been funding these foundational provisions since 2005. This case study evaluates an aspect of a foundational provision in Mechanical Engineering, from the beginning of 2002 to the end of 2005, at a University of Technology, with a view to contributing to its improvement. The Cape Peninsula University of Technology (CPUT), the locus for this case study, is the only one of its kind in a region that serves in excess of 4.5 million people. Further, underpreparedness in Mathematics for tertiary level study is a national and international phenomenon. There is thus a social interest in the evaluation of a Mathematics course that is part of a strategy towards addressing the shortage in Engineering graduates. This Evaluation of integration of the Foundation Mathematics course into Foundation Science, within the Department of Mechanical Engineering at CPUT, falls within the ambit of this social need. An integrated approach to curriculum conception, design and implementation is a widely accepted strategy in South Africa and internationally; this approach formed the basis of the model used for the Foundation programme that formed part of this Evaluation. A review of the literature of the underpinnings of the model provided a theoretical framework for this evaluation study. In essence this involved the use of academic literacy theory together with learning approach theory to provide a lens for this case study. The research methodology used was largely qualitative, with both qualitative and quantitative methods used for purposes of triangulation. The evaluation was conducted of four key aspects of integration of foundation mathematics into foundation science, namely conception, design, implementation and impact. This provided the framework for the main argument of this thesis, namely that conceptual and design flaws in the integration modelled to student learning of Mechanics concepts (in Foundation Science) not being effectively supported. The final section of the study outlines recommendations for improvement of the foundation mathematics course. It also identifies areas for future research. / National Research Foundation (NRF)

Thesis (MEd)--University of Stellenbsoch, 2001. / ENGLISH ABSTRACT: The primary concern of the study is how pre-service teachers perform after they have been exposed to a section of a linear algebra course based on the problem-centred approach. The students were in their final (3rd ) year of a teacher education course at a college of education which prepares them to teach mathematics at high school level. Sixty students, who formed the experimental group, were exposed to a linear algebra section, which was underpinned by the tenets of the problem-centred approach. The control group comprised of 60 students of similar mathematical background and they were taught the linear algebra section in the conventional way. The main study is preceded by an overview of the history of the teaching of linear algebra and this overview rendered that certain aspects of linear algebra were historically taught in context. Furthermore an analysis of current secondary school mathematics curricula indicated that there are components of linear algebra present in these syllabi. To test whether there was any significant effect of the experimental course, both groups were subjected to the same linear algebra test items at the end of the experimental period. The null hypothesis tested was: there will be no significant difference between the achievement scores of the experimental and control groups. A simple statistical two-tailed test for the difference between two means was done. This test confirmed the rejection of the null hypothesis at the 0,01 level of significance. It is thus accepted that the superior achievement of the experimental group was due to the intervention - approaching aspects of linear algebra through the problem-centred approach. To get an indication of the strategies the experimental group followed to solve linear algebra problems, an analysis was done of the written work of the students. This analysis showed that students applied an absolute calculation strategy to seek solutions to the problems. The study had the following limitations: 1. The students were not representative of the pre-service secondary teachers in South Africa. Only students from the developing population group were involved. 2. The students were not randomly assigned to the experimental and control group. They were in their normal college classes . . Notwithstanding the above limitations it is recommended that: 1. The problem-centred approach, which support the ideals of outcomes-based education, be applied to a major part of the South African school and college of education mathematics syllabi. 2. Appropriate assessment procedures consonant with the problem-centered approach are installed. 3. Adequate support systems are put in place to support teacher transition from the conventional to the problem-centred approach. / AFRIKAANSE OPSOMMING: Die primêre fokus van die studie is die effek van In lineêre algebra kursus, aangebied volgens die probleem-gesentreerde benadering, op kollege onderwysstudente. Die studente was in hulle finale (3de) jaar van In kursus aan In onderwyskollege wat hulle voorberei om wiskunde op hoërskoolvlak te onderrig. Die eksperimentele groep, bestaande uit 60 studente, het aspekte van lineêre algebra geleer, onderrig volgens die probleem-gesentreerde benadering. Die kontrolegroep, bestaande uit 60 studente met omtrent dieselfde wiskunde agtergrond, het dieselfde lineêre algebra geleer, onderrig volgens die konvensionele metode. Die hoofstudie is voorafgegaan deur In oorsig van die geskiedenis van die onderrig van lineêre algebra, wat getoon het dat dat sekere aspekte van lineêre algebra histories in konteks onderrig is. In Ontleding van die huidige hoërkool wiskundekurrikulum toon dat dit komponente van lineêre algebra bevat. Om die impak van die eksperimentele kursus te bepaal, het beide groepe aan die einde van die eksperimentele periode dieselfde lineêre algebra toetsitems voltooi. Die volgende nul-hipotese is getoets: Daar is geen beduidende verskil tussen die prestasies van die eksperimentele en die kontrole groepe nie. In Eenvoudige tweevlerk statistiese toets vir die verskil tussen twee gemiddeldes is gedoen. Die toets bevestig die verwerping van die nul-hipotese op die 0,01 vlak van beduidendheid. Dit word dus aanvaar dat die beter prestasie van die eksperimentele groep toegeskryf kan word aan die intervensie, naamlik die leer van lineêre algebra volgens die probleem-gesentreerde benadering. Om "n aanduiding te kry van die strategieë wat die eksperimentele groep gebruik het in die oplos van lineêre algebra probleme, is die geskrewe werk van die studente ontleed. Die ontleding het getoon dat studente 'n absolute rekenstrategie gebruik het om oplossings vir die probleme te soek. Die studie het die volgende beperkings: 1. Die studente was nie verteenwoordigend van sekondêre onderwysstudente in Suid Afrika nie. Slegs studente uit die onwikkelinggroep was betrokke. 2. Die studente is nie willekeurig aan die eksperimentele en kontrole groepe toegewys nie. Hulle was in hul gewone kollege klasse. Ondanks die bogenoemde beperkings, word daar aanbeveel dat: 1. Die probleem-gesentreerde benadering, wat die beginsels van uitkomsgebaseerde onderwys ondersteun, behoort in die wiskunde kurrikulum vir skole en onderwyserskolleges gebruik te word. 2. Gepaste assesseringsmetodes, soos in die probleem-gesentreerde benadering gebruik, moet toegepas word. 3. Doeltreffende ondersteuningstelsels moet geïmplementeer word om onderwysers te ondersteun in huloorgang na die probleem-gesentreerde benadering.

The purpose of this study was to ascertain those services and resources generally considered to be the essential parts of a mathematics learning center for students in two-year colleges by determining perceptions held by mathematics students and instructors toward these services and resources. A questionnaire sent to the mathematics department chairperson in all two-year colleges revealed 25 colleges had comprehensive mathematics learning centers (offer tutoring, testing, calculators, counseling, computer terminals, reference books, and filmstrips/slides/tapes services). Questionnaires for algebra students and their instructors were then sent to the names supplied by 19 colleges with comprehensive mathematics learning centers. Of the 837 student respondents, 38% indicated they had used the center. The most number of students had used the tutoring service. Each service was rated for the student feelings about the amount of time they used it and the help they received for satisfying their mathematical needs. The students ranked tutoring, testing, calculators, counseling, reference books, computer terminals, and filmstrips/slides/tapes services from highest to lowest respectively, for helpfulness in learning mathematics. Students gave various reasons for not using the center with 48% of the nonusers stating they knew about it but did not need to use it. The nonusers also checked the services they assumed would be of worth to them in their study of mathematics. All student responses were compared by age, college load, and outside job hours groups. Of the 33 instructor respondents, 94% recommended the tutoring service to students. The instructors rated the services for their feelings about the amount of input into each service and the support they received from each service in teaching algebra. Many instructors felt they had no input. They ranked the services for overall support provided in teaching algebra. Guidelines were formulated for the development of a college mathematics learning center. Based on this study, the conclusions were: (1) Tutoring is the most essential service. (2) Testing and calculators are very essential services. (3) The other services were less essential with computer terminals next to lowest and filmstrips/slides/tapes lowest. (4) Filmstrips/slides/tapes were more essential to instructors than to students.

The purpose of this study was to ascertain the value, as determined by student achievement, of using a discovery method of teaching mathematics in a college freshman mathematics course for non-mathematics and non-science majors.

This study examines how mathematical modeling activities within a collaborative group impact students' `value creation' through mathematics. Creating `value' in this study means to apply one's knowledge in a way that benefits the individual and society, and the notion of `value' was adopted from Makiguchi's theory of `value creation' (1930/1989). With a unified framework of Makiguchi's theory of `value', mathematical disposition, and identity, the study identified three aspects of value-beauty, gains, and social good-using observable evidence of mathematical disposition, identity, and sense of community. Sixty students who enrolled in a college algebra course participated in the study. The results showed significant changes in students' mathematics dispositions after engaging in the modeling activities. Analyses of students' written responses and interview data demonstrated that the modeling tasks associated with students' personal data and social interactions within a group contributed to students' developing their identity as doers of mathematics and creating social value. The instructional model aimed to balance the cognitive aspect and the affective skills of learning mathematics in a way that would allow students to connect mathematical concepts to their personal lives and social lives. As a result of the analysis of this study, there emerged a holistic view of the classroom as it reflects the Makiguchi's educational philosophy. Lastly, implications of this study for research and teaching are discussed.

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