Teaching introductory calculus: approaching key ideas with dynamic software

Abstract

While, commonly across the world, selected key ideas of the Calculus are introduced to students in the final years of schooling, and are thence built upon as students take a full course in Analysis at University, there remains much to learn about how best to introduce such ideas and how to develop and expand the ideas at University level. This paper reports on the work of a European-funded project involving four countries in which the potential of dynamic software was exploited in the teaching of topics such as infinite processes, limits, continuity, differentiation and integration. Amongst the approaches adopted in the project, problem-solving situations were developed through which students, while their knowledge may initially be inadequate, could approach intuitively the central mathematical notion in ways that are consistent with formal mathematical definitions. Amongst the implications of the project, in terms of the debate about what is suitable preparation for students embarking on a course of analysis at University level, are that it might be useful to think in terms of two categories of learning activity – the first is introducing student to relevant concepts and the second focuses on the teaching of theorems. These two categories entail a different design of learning activity.

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ORCID for Keith Jones: orcid.org/0000-0003-3677-8802

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