중학교 증명 수업에서 학생들의 연역적 추론 분석: 의사소통(commognition) 관점을 중심으로1)

Abstract

This study developed a teaching-learning method by focusing on the deductive reasoning and analyzed the characteristics of mathematical discourse in the light of the framework descriptors of the level of mathematical justification based on Sfard’s commognition perspective, in order to provide the implication for proof teaching by encouraging students to experience deductive reasoning as a thinking process. To achieve the aim, 8 lessons were implemented using the teaching-learning method developed by this study and the students’ features related to deductive reasoning were explored based on the descriptors. As a result, at the lessons about the mathematical justification there was a commognitive conflict between students using empirical justification and deductive justification, in the process of checking premises for deductive justification, students reached axiomatic-formal justification with partial and procedural characteristics. At the lessons of implementing mathematical justification for the properties of parallelogram, the students made a chaining relationships by eliciting conclusions from the premises, connected several steps of justification, and defined by the deductive organization of properties. It can be said that they used the meta-rule of axiomatic- formal justification. The result suggests that deductive reasoning could be taught to middle school students by taking appropriate pedagogical strategies. In the process of justifying, students realized the existence of axiom and its meaning as a promise, understood the chaining relationships derived from axioms. In addition, in the process of justifying visual mediators were used an important tool that drove deductive reasoning and the terms ‘proof’ and ‘definition’ were informally emerged even though have not been taught at the lessons.