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The Study on the Process of Undergraduate Students' Generating Counter-Examples and Proposing True Statements  

Oh, Hye Mi (Bopyung high school)
Kwon, Oh Nam (Seoul National Univ. Dept. of Math. Edu.)
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Journal for History of Mathematics / v.26, no.5_6, 2013 , pp. 401-416 More about this Journal
There has been increasing interest in recent years in the pedagogical importance of counter-examples that focuses on pedagogical perspectives. But there is no research that undergraduate students' generating counter-examples and proposing the true statements. This study analyze 6 undergraduate students' response to interview tasks and the process of their generating counter-examples and proposing true statements. The results of interviews are that the more undergraduate students generate various counter-examples, the more valid they propose true statements. If undergraduate students have invalid understanding of logical implication and generate only one counter-example, they would not propose true statements that modify the given statement, preserving the antecedent. In pre-service teacher's education and school mathematics class, we need to develop materials and textbooks about counter-examples and false statements.
Counter-example; proof; implication;
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