Die rol van leerfunksies vir die bevordering van kritiese denke en prestasie in Wiskunde-onderrig

Thesis (M.Ed.)--North-West University, Vaal Triangle Campus, 2009.The teaching of mathematics frequently comes in the line of fire due to under achievement and a lack of critical thinking. Accordingly educationists and mathematicians continually seek ways to overcome this hurdle. Against this backdrop, this study attempts to determine if the acquiring of learning-functions will improve academic achievement as well as critical thinking in mathematics. By means of a literature study the nature and importance of learning-functions for the development of critical thinking skills and the improvement of academic achievement are highlighted. The literature shows that critical thinking skills such as reasoning, analysis, hypothesising, making of decisions and problem solving are important skills for the mastering of mathematics. The learning-functions decoding of knowledge, synthesis and integration of knowledge, comparison, application of knowledge, generating hypotheses and reflection have been identified as the learning-functions which can develop the necessary skills for the mastering of mathematics. As the research stems from a combined interpretivist-positivist paradigm, the researcher used a combined qualitative and quantitative study. As part of the qualitative research, observation has been used. For the quantitative research the true experimental research method with a post-test control group design was chosen. The focus was on the qualitative collection of data, supported by the quantitative data. Twenty-three first year education students, with mathematics as major subject were used for this study. By means of systematic random sampling the students were assigned, as participants to an experimental and a control group. During contact sessions the participants of the experimental group were subjected for a period of eight weeks to an intervention programme with the focus on guided learning of the learning - functions decoding of knowledge, synthesis and integration of knowledge, comparisons, application of knowledge, generation of hypotheses and reflection. The control group received normal classroom instruction with no focus on guided learning of learning - functions. With the implementation of the intervention programme the experimental group was observed with regard to their progressive development of the application of these learning - functions. To determine any signs of progressive improvement of achievement and critical thinking skills in the experimental group during the implementation of the intervention programme, class tests and assignments were completed. Both the experimental- and the control group wrote the same tests and completed the same assignments. The post -test was a final examination paper which was written after the completion of the intervention by both groups to determine to which extent achievement and critical thinking skills improved within the experimental group. It can be inferred from the results of the empirical research that the guided learning of the learning -functions decoding of knowledge, synthesis and integration of knowledge, comparison, application of knowledge, generating hypotheses and reflective thought in the course of teaching mathematics, appeared to have enhanced learners' academic achievement and critical thinking. From a combination of the prominent findings of the empirical research, together with the knowledge gained from the literature study, justified recommendations were made regarding the learning of learning -functions in order to promote critical thinking and achievement in the teaching of mathematics.Master