What should be the object of research with respect to the notion of mathematical proof?

zakaria ndemo, david Mtetwa, david Mtetwa, Fred Zindi, Fred Zindi

Abstract


Abstract

Despite its central place in the mathematics curriculum the notion mathematical proof has failed to permeate the curriculum at all scholastic levels. While the concept of mathematical proof can serve as a vehicle for mathematical thinking, studies have revealed that student teachers have a superficial understanding of mathematical proof. There is overwhelming evidence that students experience serious challenges in proof and proving. Evidence of students’ difficulties in handling the concept of mathematical proof include: not knowing how to begin the proving process, the proclivity to use empirical verifications for tasks that call for axiomatic methods of proving, resorting to rote memorization of uncoordinated fragments of proof facts.  Several studies have been conducted with the aim of addressing students’ fragile grasp of mathematical proof.  However, the majority of such studies have been based on convincement issues, that is, research activities have involved students reflecting and validating arguments supplied by the researchers.  Even with those few studies (particularly in the local Zimbabwean context) that have tried to involve students in proof construction, the tendency has been to concentrate on the front instead of the back of mathematics thereby compromising the voice of the student teachers. What therefore should be the object of research in view of students’ weak command of the concept of mathematical proof?  There is a dearth in research studies into students’ thinking processes around mathematical proof especially in the Zimbabwean undergraduate mathematics learning that are grounded in students’ own proof attempts. Hence, research intended to identify critical elements of students’ knowledge of the notion of proof should be informed by students’ actual voices, that is, their own proof attempts.  Research activities meant to pursue this goal should show an inclination towards the back of mathematics.


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DOI: http://dx.doi.org/10.11591/edulearn.v12i4.9558

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