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The need for proof and proving: mathematical and pedagogical perspectives. (English) Zbl 1247.97021

Hanna, Gila (ed.) et al., Proof and proving in mathematics education. The 19th ICMI study. Berlin: Springer (ISBN 978-94-007-2128-9/hbk; 978-94-007-2129-6/ebook). New ICMI Study Series 15, 215-229 (2012).
Summary: This article first examines why mathematics educators need to teach proof, as reflected in the needs that propelled proof to develop historically. We analyse the interconnections between the functions of proof within the discipline of mathematics and the needs for proof. We then take a learner’s perspective and discuss learners’ difficulties in understanding and appreciating proof, as well as a number of intellectual needs that may drive learners to prove (for certitude, for causality, for quantification, for communication, and for structure and connection). We conclude by examining pedagogical issues involved in teachers’ attempts to foster necessity-based learning that motivates the need to prove, in particular the use of tasks and activities that elicit uncertainty, cognitive conflict and inquiry-based learning.
For the entire collection see [Zbl 1234.00015].

MSC:

97E50 Reasoning and proving in the mathematics classroom
97D30 Objectives and goals of mathematics teaching
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