HОW DO PRIMARY SCHOOLS MATHEMATICS PRESERVICE TEACHERS CONSIDER MATHEMATICAL PROOFS AND MATHEMATICAL ARGUMENTATION (PERSONAL REFLEXION)

Daniel A. Romano

doi:10.7251/НСК1311 046Р

Authors

Daniel A. Romano Универзитет у Бањој Луци Природно-математички факултет

DOI:

https://doi.org/10.7251/НСК1311%20046Р

Keywords:

proof, argumentation, cognitive unity and meta-cognitive unity

Abstract

Starting from a general discussion on mathematical proof, a structural analysis wascarried out in this presentation, leading to the construction of a model within whichdirect and indirect proofs can bedescribed and how our students consider these proofs. The model shows itself a good interpreting tool to identify and explaincognitive and didactic issues, as well to precisely formulate research hypothesesconcerning students'

difficulties withdirect and indirect proofs. We discuss the theoretical construction of 'cognitive unity’ and ‘meta-cognitive unity’, which may give reason of success and difficulties in indirect proofs.

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