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Proofs and refutations in school mathematics: A task design in dynamic geometry environments

Proofs and refutations in school mathematics: A task design in dynamic geometry environments
Proofs and refutations in school mathematics: A task design in dynamic geometry environments
Although the mathematical activity of proofs and refutations is widely recognised as significant in school mathematics, much remains under-explored about ways of facilitating such activity in the classroom. In this paper, we address this issue by focusing on task design in dynamic geometry environments. In particular, we formulate three principles for the task design and use these to develop classroom tasks. We analyse a task-based interview with a triad of upper secondary school students to show how the designed tasks stimulated their activity of proofs and refutations.
proof, refutation, counterexample, task design, dynamic geometry software, teaching
187-194
DCU Institute of Education and ERME
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Dooley, Thérèse
Gueudet, Ghislaine
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Dooley, Thérèse
Gueudet, Ghislaine

Komatsu, Kotaro and Jones, Keith (2017) Proofs and refutations in school mathematics: A task design in dynamic geometry environments. Dooley, Thérèse and Gueudet, Ghislaine (eds.) In Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education : (CERME10, February1-5, 2017). DCU Institute of Education and ERME. pp. 187-194 .

Record type: Conference or Workshop Item (Paper)

Abstract

Although the mathematical activity of proofs and refutations is widely recognised as significant in school mathematics, much remains under-explored about ways of facilitating such activity in the classroom. In this paper, we address this issue by focusing on task design in dynamic geometry environments. In particular, we formulate three principles for the task design and use these to develop classroom tasks. We analyse a task-based interview with a triad of upper secondary school students to show how the designed tasks stimulated their activity of proofs and refutations.

Text
Komatsu&Jones_proofs&refutations_CERME10_2017 - Accepted Manuscript
Available under License Creative Commons Attribution.
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More information

Accepted/In Press date: 13 March 2017
Published date: 22 December 2017
Additional Information: The copyright page of the full proceedings says "Copyright 2017 left to the authors". As I retain the copyright, I can provide the publication as open access.
Venue - Dates: 10th Congress of the European Society for Research in Mathematics Education (CERME10), Dublin City University, Dublin, Ireland, 2017-02-01 - 2017-02-05
Keywords: proof, refutation, counterexample, task design, dynamic geometry software, teaching

Identifiers

Local EPrints ID: 419652
URI: http://eprints.soton.ac.uk/id/eprint/419652
PURE UUID: c16802b8-9f75-4daf-88c2-a74f660faed3
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 18 Apr 2018 16:32
Last modified: 21 Nov 2021 11:34

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Contributors

Author: Kotaro Komatsu
Author: Keith Jones ORCID iD
Editor: Thérèse Dooley
Editor: Ghislaine Gueudet

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