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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| File | |
| Title ( eng ) |
CAN STUDENTS CONSTRUCT NON-CONSTRUCTIVE REASONING? IDENTIFYING FUNDAMENTAL SITUATIONS FOR PROOF BY CONTRADICTION
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| Creator |
Hayata Toru
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| Source Title |
Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education
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| 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?
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| Descriptions |
This work was partially supported by JSPS KAKENHI Grant Number 17H00147.
Place; Umeå, SWEDEN Date; 3-8 July, 2018
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| NDC |
Education [ 370 ]
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| Language |
eng
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| Resource Type | conference paper |
| Publisher |
PME
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| Date of Issued | 2018-07-12 |
| Rights |
Copyright © 2018 left to the authors. All rights reserved.
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| Publish Type | Version of Record |
| Access Rights | open access |
