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Pre-service teachers' handling of linear algebra in a problem-centred approach
[摘要] ENGLISH ABSTRACT:The primary concern of the study is how pre-service teachers perform after they havebeen exposed to a section of a linear algebra course based on the problem-centredapproach. The students were in their final (3rd) year of a teacher education course ata college of education which prepares them to teach mathematics at high schoollevel. Sixty students, who formed the experimental group, were exposed to a linearalgebra section, which was underpinned by the tenets of the problem-centredapproach. The control group comprised of 60 students of similar mathematicalbackground 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 linearalgebra and this overview rendered that certain aspects of linear algebra werehistorically taught in context. Furthermore an analysis of current secondary schoolmathematics curricula indicated that there are components of linear algebra presentin these syllabi.To test whether there was any significant effect of the experimental course, bothgroups were subjected to the same linear algebra test items at the end of theexperimental period. The null hypothesis tested was: there will be no significantdifference 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 ofsignificance. It is thus accepted that the superior achievement of the experimentalgroup was due to the intervention - approaching aspects of linear algebra throughthe problem-centred approach. To get an indication of the strategies the experimental group followed to solve linearalgebra problems, an analysis was done of the written work of the students. Thisanalysis showed that students applied an absolute calculation strategy to seeksolutions to the problems.The study had the following limitations:1. The students were not representative of the pre-service secondary teachers inSouth 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-basededucation, be applied to a major part of the South African school and college ofeducation mathematics syllabi.2. Appropriate assessment procedures consonant with the problem-centeredapproach are installed.3. Adequate support systems are put in place to support teacher transition from theconventional to the problem-centred approach.
[发布日期]  [发布机构] Stellenbosch University
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