'n Model vir die konseptuele leer van wiskunde in 'n dinamiese tegnologies-verrykte omgewing by voorgraadse wiskunde-onderwysstudente
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It is no unknown fact that South African learners underachieve in mathematics. Due to the fact that the quality of mathematics teaching is one possible factor that has an influence on learners' mathematics achievement, there are valid reasons questioning the conceptual mathematical knowledge of mathematics teachers. In order to facilitate conceptual understanding teachers themselves must possess profound mathematical knowledge. Apart from the influence of a teacher's knowledge for teaching, teachers' attitudes and beliefs play a meaningful role in the way they teach mathematics. The deficient nature of prospective and practising teachers' knowledge of school mathematics, as well as their attitudes and beliefs towards mathematics has serious implications for the training of prospective mathematics teachers. Literature reveals that a technologically enhanced environment can improve the conceptual learning of prospective mathematics teachers. The purpose of this study was to determine the influence of a dynamic technologically enhanced environment on the attitudes and beliefs, as well as the conceptualisation of prospective mathematics teachers regarding the function concept. In this study, prospective teachers were exposed to Geometer's Sketchpad®, a dynamic software programme providing a powerful learning context that promotes the investigation of algebraic relationships. In order to answer the research question, an explanatory mixed method design was used. In the quantitative part of the study, the Study Orientation Questionnaire in Mathematics and a function test were administered to prospective teachers. In the latter, conceptualisation of the function concept was measured in terms of four competence components, namely interpretation, modelling, translation and reification. In the qualitative part of the investigation semi-structured and task-based interviews were held with a group of prospective teachers. Analysis of the results revealed that the dynamic technologically enhanced environment did not contribute to an improvement of the prospective teachers' attitudes and beliefs. In fact, these decreased visibly. Regarding their conceptualisation, only the reification component showed a practically significant improvement. It therefore appears as if prospective teachers are not being prepared to benefit from the dynamic technologically enhanced environment. A model is proposed for the effective use of such a learning environment. The model involves that diagnostic assessment be made of prospective teachers' basic knowledge of the function concept, their study habits, their attitudes and beliefs with respect to mathematics, as well as their mathematics anxiety. The second component comprises recommendations made to prospective teachers as a result of the diagnostic assessment, as well as continuous support being offered as an integrated part of the mathematics module. Support is offered with respect to cognitive and meta-cognitive skills, affective factors and the creation of an advantageous technologically enhanced learning environment. Despite the restricted value of generalisation of the findings from this study, I still recommend the expansion, refining and implementation of the model so that prospective mathematics teachers can effectively benefit from a technologically enhanced environment. Key words for indexing: mathematics education, mathematics teacher education, teacher knowledge, prospective mathematics teachers, function concept, conceptual learning, tertiary education.
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