Abstract
This paper explores the understanding which students who are training to be secondary mathematics teachers have of elementary concepts in mathematical analysis. Research to date has tended to concentrate on students' knowledge and understanding prior to university entrance or in the first year of undergraduate mathematics courses. The design of this research, similar in style to a viva voce, involved probing students' conceptual understanding of convergence and continuity and associated reasoning. The report tentatively concludes that even mathematically well qualified students have difficulties with some elementary concepts and that students with engineering backgrounds allow the 'dynamic' image to dominate their engagement with the concepts.
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