삼각형의 내심과 외심의 증명에 관한 교과서의 논증 분석

Abstract

In this article, we investigate the argument structure of the proof about the incenter/circumcenter of the triangle written in textbooks. A total of 10 textbooks for middle school mathematics 2, corresponding to the 2015 revised curriculum, were analyzed with the layout of arguments suggested by Toulmin. From the local argument perspective, we found that the following two structural features could limit acceptability of the argumentation to students. First, in arguing the congruence of two triangles to prove the uniqueness of the incenter/circumcenter, the structural location of three geometrical facts was stated inappropriately. Second, some warrants need to be provided when considering the learning trajectory of students. From the global argument perspective, we found that the following two structural features could limit acceptability of the argumentation to students. First, arguments for right-angled and obtuse triangles and some sub-local argument structures were omitted. Second, the definition of the incenter/circumcenter of the triangle was not included in the argumentation structure. These findings suggest that textbook writers need to consider whether linguistic phrases for provig are logically structured, whether enough warrants are provided for current learners, whether sub-argument structures are fully examined, and whether statements about the existence and uniqueness of inscribed/circumscribed circles are embedded in the argument.