Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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An Analysis of Problem-Posing Tasks in 7th grade Mathematics Textbooks Based on 2015 National Mathematics Curriculum

2015 개정 교육과정에 따른 수학교과서 문제제기 과제 분석 : 중학교 1학년을 중심으로

  • Received : 2019.05.01
  • Accepted : 2019.05.08
  • Published : 2019.05.15
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Abstract

This study analyzed how problem-posing tasks included in Korean middle school mathematics textbooks were distributed in terms of content area, task type, and context of task to investigate that the mathematics textbooks are giving students ample opportunities for problem-posing activities. The analysis of 10 mathematics textbooks for first grade in middle school according to the revised mathematics curriculum in 2015 found that the problem-posing tasks contained in the textbooks are insufficient in quantity and not evenly distributed in terms of content areas. There were also more problem-posing tasks with relatively moderate constraints than those with strong or weak constraints in terms of mathematical constraints. In addition, there were more problem-posing tasks that were not requiring students to make a new context, and more often camouflage contexts were used. Based on this, implications for improving mathematics problem-posing tasks in mathematics textbook were suggested.

이 연구는 우리나라 중등 수학교과서가 학생들에게 문제제기 활동의 기회를 충분히 주고 있는지 확인하기 위하여 2015 개정 수학과 교육과정에 따른 중학교 1학년 수학교과서의 문제제기 과제를 내용 영역, 과제 유형, 과제 맥락 등의 측면에서 분석하였다. 2015년 개정 수학과 교육과정에 따른 중학교 1학년 수학교과서 10종을 분석한 결과, 교과서에 포함된 문제제기 과제의 수는 적은편이며, 내용 영역별로 과제가 고르게 분포되어 있지 않았다. 문제제기 과제의 수학적 제약의 정도에 따라 분석한 결과, 수학적 제약 조건이 강하거나 약한 과제보다는 상대적으로 중간 정도의 제약 조건을 가지는 문제제기 과제가 더 많았다. 맥락 구성 요구에 따른 분석 결과, 학생들에게 새로운 맥락을 요구하지 않는 문제제기 과제가 더 많았고, 이러한 과제들은 주로 가장된 맥락을 사용하고 있었다. 이러한 결과를 바탕으로 수학교과서에서의 문제제기 과제 활용을 위한 시사점을 제시하였다.

Keywords

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[그림 III-1] 수학 과제 개수 구분 사례(류희찬 외, 2018, p. 180)

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[그림 III-2] SC 코드로 분류된 과제(고호경 외, 2018, p. 132)

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[그림 III-3] NC2 과제로 분류된 과제(이준열 외, 2018, p. 105)

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[그림 IV-1] 동일한 수학적 관계 혹은 구조를 가지는 질문 제기하기 과제(유형2)(이준열 외, 2018, p. 89)

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[그림 IV-2] 주어진 정보에 기반을 둔 질문 제기하기 과제(유형4)(류희찬 외, 2018, p. 284)

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[그림 IV-3] 새로운 맥락의 구성을 요구하는 과제(김원경 외, 2018, p. 114)

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[그림 V-1] 적절하고 본질적인 맥락을 가지는 문제제기 과제 (김구연, 전미현, 2017, p. 308의 [그림 IV-11]에서 저자 수정)

<표 III-1> 내용 영역에 따른 중학교 1학년 수학교과서에 포함된 수학과제 개수

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<표 IV-1> 내용 영역에 따른 중학교 1학년 수학교과서 문제제기 과제 분포

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<표 IV-2> 수학적 제약에 따른 중학교 1학년 수학교과서 문제제기 과제 분포

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<표 IV-3> 맥락 구성 요구에 따른 중학교 1학년 수학교과서 문제제기 과제 분포

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