CAN STUDENTS CONSTRUCT NON-CONSTRUCTIVE REASONING? IDENTIFYING FUNDAMENTAL SITUATIONS FOR PROOF BY CONTRADICTION
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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?
This work was partially supported by JSPS KAKENHI Grant Number 17H00147.
Place; Umeå, SWEDEN Date; 3-8 July, 2018
Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education
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