証明と論駁を通じての数学的知識の生成
証明と論駁を通じての数学的知識の生成
In this paper we present a framework for describing mathematical activity in which mathematical knowledge is developed through proofs and refutations. The framework is constructed by adding the component generation of mathematical knowledge to our previous framework of conjecturing (or working on given statements), proving, and refuting (e.g. discovering counterexamples). We illustrate the framework with a hypothetical example in which secondary school students tackle a mathematical proof task using dynamic geometry software.
mathematics, knowledge, proof, refutation, dynamic geometry software, geometry, education
405-406
Japan Society of Mathematical Education
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
4 November 2017
Komatsu, Kotaro
22446313-5c59-4d33-a7c2-94684615e98f
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Komatsu, Kotaro and Jones, Keith
(2017)
証明と論駁を通じての数学的知識の生成.
In 日本数学教育学会第50回秋期研究大会発表集録.
vol. 50,
Japan Society of Mathematical Education.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
In this paper we present a framework for describing mathematical activity in which mathematical knowledge is developed through proofs and refutations. The framework is constructed by adding the component generation of mathematical knowledge to our previous framework of conjecturing (or working on given statements), proving, and refuting (e.g. discovering counterexamples). We illustrate the framework with a hypothetical example in which secondary school students tackle a mathematical proof task using dynamic geometry software.
Text
Komatsu&Jones_generate_math_knowledge_JSME_2017
- Accepted Manuscript
More information
Accepted/In Press date: 4 October 2017
Published date: 4 November 2017
Venue - Dates:
50th Autumn Conference of Japan Society of Mathematical Education, Aichi University of Education, Kariya, Japan, 2017-11-04 - 2017-11-05
Alternative titles:
Generation of mathematical knowledge through proofs and refutations
Keywords:
mathematics, knowledge, proof, refutation, dynamic geometry software, geometry, education
Identifiers
Local EPrints ID: 415518
URI: http://eprints.soton.ac.uk/id/eprint/415518
PURE UUID: d9b5605f-085c-429b-a0e5-fbd888b7d9be
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Date deposited: 14 Nov 2017 17:30
Last modified: 15 Mar 2024 16:49
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Contributors
Author:
Kotaro Komatsu
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