초등학교 6학년의 수학적 논증 활동에서 나타나는 반박 유형 및 대응 방안 분석
Analysis of rebuttals and corresponding responses in sixth-grade students’ mathematical argumentation
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초록
본 연구의 목적은 초등학교 6학년 학생들의 수학적 논증 활동에서 나타나는 반박 유형과 반박에 대한 대응 양상을분석하고, 이를 토대로 수학 수업에서의 논증교육 실천방안을 탐색하는것이다. 이를위해 직육면체의부피 개념을주제로 Lakatos의 방법론에 따라 수업을 설계하고, 경기도 소재 초등학교 6학년 학생 8명을 대상으로 연구를 수행하였다. 학생들의 논증 활동 과정을 녹음·녹화 후 전사하여 질적으로 분석한 결과, Verheij의 다섯 가지 반박 유형 중보장에 대한 반박을제외한네가지유형이확인되었다. 반박에대한대응은(1) 추가자료나 논거제시, (2) 조건 제한을 통한 한정, (3) 주장 수정 또는 철회의 세 가지 방식으로 나타났다. 분석 결과를 바탕으로 초등 수학 수업에서반박 중심논증활동의적용가능성과시사점을논의하였다.
Abstract
The 2022 revised mathematics curriculum emphasizes the development of students' abilities to communicate effectively about mathematical thinking and strategies, as well as to reason logically based on conjectures and justifications. Accordingly, the purpose of this study is to explore practical approaches to teaching mathematical argumentation in the classroom by analyzing the types of rebuttals and corresponding responses that appear during sixth-grade students' mathematical argumentation activities. For this purpose, a lesson was designed based on Lakatos’s methodology, focusing on the concept of the volume of rectangular prisms. The study was conducted with eight sixth-grade students from an elementary school located in Gyeonggi Province. Students’ activities were audio- and video-recorded, transcribed, and qualitatively analyzed. The results revealed that among the five types of rebuttals proposed by Verheij, four excluding rebuttals against the warrant were observed during the lessons. In response to rebuttals, students employed three major strategies: (1) presenting additional data or supporting arguments, (2) limiting claims through specifying conditions, and (3) modifying or withdrawing original claims. Based on these findings, this study proposes the applicability and educational implications of rebuttal-centered argumentation activities in elementary mathematics classrooms.