CAN STUDENTS CONSTRUCT NON-CONSTRUCTIVE REASONING? IDENTIFYING FUNDAMENTAL SITUATIONS FOR PROOF BY CONTRADICTION

Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education Volume 3 Page 43-50 published_at 2018-07-12
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Title ( eng )
CAN STUDENTS CONSTRUCT NON-CONSTRUCTIVE REASONING? IDENTIFYING FUNDAMENTAL SITUATIONS FOR PROOF BY CONTRADICTION
Creator
Hayata Toru
Source Title
Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education
Volume 3
Start Page 43
End Page 50
Abstract
The purpose of this study is to identify and empirically corroborate a fundamental situation (Brousseau, 1997) for constructing “proof by contradiction.” We identified the four elements of a fundamental situation: i) obtaining strong conviction; ii) negating the given proposition naturally without being aware of the assumption; iii) finding a contradiction easily; and iv) noticing the origin of the contradiction. Based on this study, a new research question arises: How can students construct “proof by contradiction” using teacher support?
Descriptions
This work was partially supported by JSPS KAKENHI Grant Number 17H00147.
Place; Umeå, SWEDEN Date; 3-8 July, 2018
NDC
Education [ 370 ]
Language
eng
Resource Type conference paper
Publisher
PME
Date of Issued 2018-07-12
Rights
Copyright © 2018 left to the authors. All rights reserved.
Publish Type Version of Record
Access Rights open access