An Analysis of Third Graders' Representations and Elaborating Processes of Representations in Mathematical Problem Solving

초등학교 3학년 학생의 수학적 문제 해결에서의 표상과 표상의 정교화 과정 분석

  • Lee, Yang-Mi (Daejeon Heungryong Elementary School) ;
  • Jeon, Pyung-Kook (Department of Mathematics Education, Korea National University of Education)
  • Published : 2005.11.01

Abstract

This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.

Keywords