The University of Southampton
University of Southampton Institutional Repository
Warning ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

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
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
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. pp. 405-406 .

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
Available under License Creative Commons Attribution.
Download (267kB)

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
ORCID for Keith Jones: ORCID iD orcid.org/0000-0003-3677-8802

Catalogue record

Date deposited: 14 Nov 2017 17:30
Last modified: 21 Nov 2021 09:21

Export record

Contributors

Author: Kotaro Komatsu
Author: Keith Jones ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×