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
Institute of Education, Dublin City University; European Society for Research in Mathematics Education
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
22 December 2017
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
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).
Institute of Education, Dublin City University; European Society for Research in Mathematics Education.
.
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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
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
Catalogue record
Date deposited: 18 Apr 2018 16:32
Last modified: 15 Mar 2024 19:14
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Contributors
Author:
Kotaro Komatsu
Editor:
Thérèse Dooley
Editor:
Ghislaine Gueudet
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