Pre-service teachers' handling of linear algebra in a problem-centred approach

George, Salimma (2001-03)

Thesis (MEd)--University of Stellenbsoch, 2001.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/52413
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