間接証明の構造の理解に関する研究 ―理解の様相を捉える枠組みの構成―

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　　Currently in Japan all high school students learn indirect proof.  Indirect proof is expected to train the logical thinking ability of learners.  Previous studies about indirect proof have not been able to properly associate the structure of indirect proof with understanding, despite it’s importance.  Thus, the purpose of this paper is to construct a theoretical framework that understanding of the structure of indirect proof.  There are three main theoretical frameworks in this paper: a model of indirect proof (Antonini & Mariotti, 2008), deduction system of classical logic (NK), a framework of understanding of the structure of deductive proofs (Miyazaki et al., 2017).  As a result of textbook analysis using NK, we identified the following the structure of indirect proof (meta-theory specific to indirect proof): the low of contrapositive (proof by contraposition), introduction and cut of negation & cut of double negative OR introduction and cut of negation & disjunctive syllogism & low of the excluded middle (proof by contradiction).  In addition, we revealed that the learner needs to interpret the above inference rules using the set theory symbols and diagrams.  Based on this result, each level of a framework of understanding of the structure of deductive proofs are reconstructed in order to make it applicable to indirect proof.