• School Mathematics
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• v.18 no.4
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• pp.839-856
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• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Korean Journal of Logic
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• v.10 no.1
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• pp.99-107
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• 2007

최근 김세화는 "프로슬로기온" 3장에 나오는 논증을 새롭게 해석하는 방안을 제시했다고 주장한다. 그에 따르면, 그가 제시한 논증 III 은 3장에 대한 기존의 해석과 다르며, 3장에 대한 또 다른 가능한 해석인 논증 IV보다도 더 낫다. 여기서 나는 논증 III은 기존의 해석과 견주어 볼 때 새롭다고 하기 어려우며, 나아가 그가 원하는 결론을 얻고자 한다면 도리어 논증 III보다 논증 IV를 택해야 함을 보인다.

• The Mathematical Education
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• v.55 no.1
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• pp.91-106
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• 2016

The aim of this study was to analyze characteristics of teachers' knowledge about reductio ad absurdum. In order to achieve the aim, this study conducted didactical analysis about reductio ad absurdum through examining previous researches and developed a questionnaire with reference to the results of the analysis. The questionnaire was given to 34 high school teachers and qualitative methods were used to analyze the data obtained from the written responses by the participants. This study also elaborated the framework descriptors for interpreting the teachers' responses in the light of the didactical analysis and the data was elucidated in terms of this framework. The specific features of teachers' knowledge about reductio ad absurdum were categorized into five types as a result. This study raised several implications for teachers' professional development for effective mathematics instruction related to reductio ad absurdum.