Theoretical Perspectives for Analyzing Explanation, Justification and Argumentation in Mathematics Classrooms

수학교실에서 설명, 정당화와 논증 분석을 위한 이론적 관점

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, I show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmin's scheme for argumentation, as elaborated for mathematics education by Kummheuer, provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.