• 한국수학교육학회지시리즈A:수학교육
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• 제44권4호
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• pp.627-651
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• 2005

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.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제18권3호
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• pp.203-216
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• 2015

본 연구는 초등학교 6학년 수학 영재 학생을 대상으로 ACODESA 방법을 적용한 문제해결 과정에서 나타나는 표상 사용의 유형을 분석하였다. 수업 설계는 다양한 표상의 조직화된 사용을 강화시키는 ACODESA 방법에 따라 이루어졌으며 40분 동안 4차시에 걸쳐 수업이 진행되었다. 자료 분석을 위해 동영상 촬영, 학생과의 인터뷰 등을 수집하여 녹취록을 작성하였고, Despina(2011)의 표상 사용유형에 따라 표상의 변화를 분석한 결과 추가형, 정교화, 그리고 제한형이 나타났다. 이러한 연구 결과를 통해 문제해결 과정에서는 개인적 표상이 소그룹별 토론과 확인의 과정을 거쳐 제도적 표상으로 생성될 수 있는 수업 설계가 필요함을 알 수 있었다.