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Understanding what a proof is: a classroom-based approach

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Abstract

Being unaware of the assumptions underlying a deductive argument is widespread among learners and is a major stumbling block to their understanding of proof. Thus, the basic idea of the present paper is that at some points in the course of secondary education there should be classroom-based interventions addressing this difficulty and making the axiomatic organization of mathematics a theme. Students should be made aware that there are axioms in mathematics, what their role is and how mathematicians come to agree about which axioms should be accepted. An axiom which is not yet accepted is simply a hypothesis. A hypothesis is evaluated by deductively drawing consequences and by investigating whether these consequences agree with experience or should be accepted for other reasons. The teaching intervention discussed in this paper exemplifies this idea by way of the example of ancient attempts at modelling the path of the sun, the so-called “anomaly of the sun”. It is investigated to what extent the teaching intervention fostered students’ understanding of the conditionality of mathematical/astronomical statements, that is, of the fact that the truth of these statements is dependent on the initial hypotheses.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany

    Hans Niels Jahnke & Ralf Wambach

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  1. Hans Niels Jahnke
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  2. Ralf Wambach
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Correspondence to Ralf Wambach.

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Jahnke, H.N., Wambach, R. Understanding what a proof is: a classroom-based approach. ZDM Mathematics Education 45, 469–482 (2013). https://doi.org/10.1007/s11858-013-0502-x

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