The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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How middle-school mathematics textbooks of Korea and the US support to develop students' statistical reasoning

한국과 미국 중학교 교과서의 통계 영역 수학과제가 제시하는 통계적 추론에 대한 학습기회 탐색

  • Received : 2019.01.31
  • Accepted : 2019.02.27
  • Published : 2019.02.28
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Abstract

This study attempts to examine statistical tasks in the middle-school mathematics textbooks of Korea and Connected Mathematics 3 [CMP] of the US in terms of an opportunity-to-learn for statistical reasoning. We utilized an analytical framework consisting of types of context, statistical reasoning level, cognitive demand of the tasks, and types of student response. The findings from the task analysis suggested that Korean textbooks focused on finding answers by applying previously learned algorithms or formulas and thus provided students with very limited opportunities to experience statistical reasoning. Also, the results proposed that the mathematical tasks in statistics unit of CMP3 offer more essential and complex tasks that promote students' conceptual understanding of various statistical ideas and statistical reasoning in a meaningful way.

Keywords

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[그림 1] A교과서의 상황과제분석 예시 [Fig. 1] An analysis of a context-task in textbook A

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[그림2] CMP3의 상황과제분석 예시 [Fig. 2] An analysis of a context task in CMP3

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[그림 3] 통계적 추론 촉진하지 않는 상황과제 예시 (C 교과서, 2014, p. 171) [Fig. 3] A Context-task that does not promote statistical reasoning (Textbook C, 2014, p. 171)

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[그림 4] 대푯값 과제(C교과서, 2014, p. 160) [Fig. 4] A task for finding mean, median and mode (Textbook C, 2014, p, 160)

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[그림 5] 같은 유형의 과제 반복(A교과서, 2018, p. 265) [Fig. 5] Similar tasks repetition (Textbook A, 2018, p. 265)

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[그림 6] 답만 요구하는 과제 (C교과서, 2014, p. 158) [Fig. 6] A task that requires only answers (Textbook C, 2014, p. 158)

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[그림 7] 유의미 맥락 과제 (CMP3-8, 2014, p. 88-92) [Fig. 7] Relevant and essential context tasks (CMP3-8, 2014, p. 88-92)

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[그림 8] 통계적 추론 과제 (CMP3-8, 2014, p. 82-84) [Fig. 8] Tasks for promoting statistical reasoning (CMP3-8, 2014, p. 82-84)

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[그림 9] 상관관계 과제 (CMP3-8, 2014, p. 85-86) [Fig. 9] A mathematical task for correlations (CMP3-8, 2014, p. 85-86)

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[그림 10] High-level 과제 (CMP3-7, 2014, p. 67) [Fig. 10] High-level Tasks (CMP3-7, 2014, p. 67)

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[그림 11] High-level 과제 (CMP3-7, 2014, p. 67) [Fig. 11] High-level tasks (CMP3-7, 2014, p. 67)

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[그림 12] CMP3 통계 과제 (CMP3-7, 2014, p. 35-37) [Fig. 12] Tasks in CMP3 (CMP3-7, 2014, p. 35-37)

[표 1] 2015 교육과정 수학 교과역량(교육부, 2015) [Table 1] 2015National curriculum:mathematical competencies(Ministryof Education, 2015)

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[표 2] 중학교 1-3학년 통계영역 성취기준(교육부, 2015) [Table 2] Grade level expectations for grades 7-9 statistics (Ministry of Education, 2015)

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[표 3] 한국과 미국의 중학교 통계영역 내용 비교 [Table 3] Mathematical ideas in statistics in the curriculum of Korea and the US

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[표 4] 통계의 Big Ideas (Kader, et al., 2013) [Table 4] Big Ideas for statistics (Kader, et al., 2013)

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[표 5] 분석틀 [Table 5] A framework for data analysis

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[표 6] 2015 개정 교육과정 중학교 1학년 교과서 통계 단원 구성 [Table 6] Topics of statistics in textbooks for grade 7 (2015 Curriculum)

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[표 7] 2009 개정 교육과정 중학교 3학년 교과서 통계 단원 구성 비교 [Table 7] Topics of statics in textbooks for grade 9 (2009 Curriculum)

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[표 8] CMP3 통계 단원 구성 [Table 8] Topics of statics for CMP3

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[표 9] 수학교과서의 수학과제 개수 [Table 9] The number of mathematical tasks in the textbooks

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[표 10] 한국 교과서 상황과제의 통계적 추론 [Table 10] Context-tasks promoting statistical reasoning suggested in Korean textbooks

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[표 11] 한국 교과서 수학과제의 인지적 노력수준 [Table 11] The levels of cognitive demand of the mathematical tasks in the Korean textbooks

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[표 12] CMP3 통계 상황과제의 인지적 노력수준 [Table 12] The levels of cognitive demand of context tasks in CMP3

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[표 13] CMP3 상황과제의 학생의 응답유형 [Table 13] Context tasks in CMP3: Type of student response

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