각기둥의 정의 만들기에 관한 지도 사례 연구 -초등학교 5학년을 대상으로-

A Scheme of the Instruction of Prism Definition for 5th Grade Students

이 연구에서는 각기둥의 정의 만들기 활동을 위한 학생용 활동지를 개발하여 초등학교 5학년 학생들에게 실행하고 그 결과를 분석하였다. 정의 만들기 수업에서 핵심은, 학습지에 차례로 제시되는 비(非) 예들이 포함되지 않도록 기존의 정의를 수정하여 새로운 정의를 만드는 것이었다. 연구 결과로, 학생들이 각기둥의 성질을 어떻게 인식하며, 비(非) 예를 제거하는 과정에서 각기둥의 정의에 사용되는 성질들로 무엇이 부각되는지를 알 수 있었다. 더불어 정의 만들기 활동을 통한 학생들의 수학적 정의에 대한 인식의 변화를 확인할 수 있었다.

The purpose of this study is to suggest an effective plan for teaching the definition of prism by integrating and analyzing the theories related to the instruction of definitions. The subjects in this study to realize these objectives were as follows. First, it looks to theoretical backgrounds regarding the instruction of the definition of solid by functions of definition in mathematics education. Second, it explores the instructional way to form the definition of solid through function of definition, by analyzing the unit of solid in the 6th grade. Third, after conducting the real practice with the 5th graders who before learn solid in 6th curriculum, according to plan of instruction, it examined student's response and testify its effectiveness, and then propose a teaching scheme which is designed to be useful based on the outcomes. In terms of theoretical background, it investigated the precedent research in relation to the instruction of the definition that mathematical definition is not given perfectly but the process of making knowledge that mathematization activity is necessary. It investigated the effects of the instruction of definitions, based on the effects of teaching and interviews with the 5th graders, and analysis of student's handout. The followings were the results of this study. First, 'Making Definitions' activities through remove counterexample process was possible to analytic thinking not intuitively thinking, and it effects the extend of awareness in definition that definition is not fixed but various. Second, it need the step of organize terms that is useful on solid's definition through activate of background knowledge. Third, it is effective that explore characters of the solids after construct the solids. Fourth, interactive discussion that students correct their mistakes each other through mathematical communication and they can think developmental is useful on making definition more than individual study.