Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof

Kanellos, Ioannis, Nardi, Elena ORCID: https://orcid.org/0000-0002-7145-6473 and Biza, Irene ORCID: https://orcid.org/0000-0003-1727-3884 (2018) Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof. Mathematical Thinking and Learning, 20 (4). pp. 277-294. ISSN 1098-6065

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Abstract

In this paper, we propose an enriched and extended application of Harel and Sowder’s proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students’ emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14–15) secondary students. We capture these students’ first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students’ multi-faceted and evolving competence in, and appreciation for, proof and proving.

Item Type:	Article
Uncontrolled Keywords:	proof schemes,proof and proving,first encounter with proof,secondary mathematics
Faculty \ School:	Faculty of Social Sciences > School of Education and Lifelong Learning
UEA Research Groups:	Faculty of Social Sciences > Research Groups > Research in Mathematics Education
Depositing User:	Pure Connector
Date Deposited:	05 Mar 2018 10:30
Last Modified:	07 Mar 2024 04:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/66431
DOI:	10.1080/10986065.2018.1509420

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