The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Manifestation examples of group creativity in mathematical modeling

수학적 모델링에서 집단창의성 발현사례

  • Jung, Hye Yun (Department of Mathematics Education, Graduate School of Seoul National University) ;
  • Lee, Kyeong Hwa (Department of Mathematics Education, Seoul National University)
  • Received : 2018.09.05
  • Accepted : 2018.10.27
  • Published : 2018.11.30
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Abstract

The purpose of this study is to analyze manifestation examples and effects of group creativity in mathematical modeling and to discuss teaching and learning methods for group creativity. The following two points were examined from the theoretical background. First, we examined the possibility of group activity in mathematical modeling. Second, we examined the meaning and characteristics of group creativity. Six students in the second grade of high school participated in this study in two groups of three each. Mathematical modeling task was "What are your own strategies to prevent or cope with blackouts?". Unit of analysis was the observed types of interaction at each stage of mathematical modeling. Especially, it was confirmed that group creativity can be developed through repetitive occurrences of mutually complementary, conflict-based, metacognitive interactions. The conclusion is as follows. First, examples of mutually complementary interaction, conflict-based interaction, and metacognitive interaction were observed in the real-world inquiry and the factor-finding stage, the simplification stage, and the mathematical model derivation stage, respectively. And the positive effect of group creativity on mathematical modeling were confirmed. Second, example of non interaction was observed, and it was confirmed that there were limitations on students' interaction object and interaction participation, and teacher's failure on appropriate intervention. Third, as teaching learning methods for group creativity, we proposed students' role play and teachers' questioning in the direction of promoting interaction.

Keywords

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[그림 1] 수학적 모델링(정혜윤 외, 2018) [Fig. 1] Mathematical Modeling(Jung et al., 2018)

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[그림 2] 학생들에게 제공된 활동지의 예 [Fig. 2] Examples of activity sheet provided to students

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[그림 4] 실세계 탐구 단계에서 관찰된 A조의 상호보완적 상호작용 사례 [Fig. 4] Example of mutually complementary interaction observed in the real-world inquiry stage of group A

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[그림 5] 문제에 영향 미치는 요인 찾기 단계에서 관찰된 A조의 상호보완적 상호작용 사례 [Fig. 5] Example of mutually complementary interaction observed in the factor-finding stage of group A

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[그림 6] B조의 모델링 과정에서 관찰된 상호보완적 상호작용과 갈등 기반 상호작용의 연결 사례 [Fig. 6] Example of connection between mutually complementary and conflict-based interaction observed in the modeling process of group B

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[그림 7] 단순화하기 단계에서 관찰된 B조의 갈등 기반 상호작용 사례 [Fig. 7] Example of conflict-based interaction observed in the simplification stage of group B

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[그림 8] 단순화하기 단계에서 관찰된 A조의 메타인지적 상호작용 사례 [Fig. 8] Example of metacognitive interaction observed in the simplification stage of group A

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[그림 9] 수학적 모델 도출 단계에서 관찰된 A조의 메타인지적 상호작용 사례 [Fig. 9] Example of metacognitive interaction observed in the mathematical model derivation stage of group A

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[그림 10] 수학적 모델 도출 과정에서 관찰된 B조의 비 상호작용 사례 [Fig. 10] Example of non-interaction observed in the mathematical model derivation stage of group B

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[그림 3] 수학적 모델링 과정에서 관찰된 상호작용과 모델링 과정의 표현틀 [Fig. 3] Representation framework of interaction and modeling process observed in mathematical modeling process

[표 1] 각 유형의 상호작용이 수학적 모델링에 미치는 효과 [Table 1] Effects of each type of interaction on mathematical modeling

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