[논문]수학적 모델링에서 집단창의성 발현사례

정혜윤; 이경화

doi:10.7468/mathedu.2018.57.4.371

수학적 모델링에서 집단창의성 발현사례
Manifestation examples of group creativity in mathematical modeling 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.57 no.4, 2018년, pp.371 - 391

정혜윤 (서울대학교 대학원) , 이경화 (서울대학교)

Abstract ▼ AI-Helper

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.

주제어

표/그림 (11)

그림 [그림 1] 수학적 모델링(정혜윤 외, 2018) [Fig. 1] Mathematical Modeling(Jung et al., 2018)
그림 [그림 2] 학생들에게 제공된 활동지의 예 [Fig. 2] Examples of activity sheet provided to students
그림 [그림 3] 수학적 모델링 과정에서 관찰된 상호작용과 모델링 과정의 표현틀 [Fig. 3] Representation framework of interaction and modeling process observed in mathematical modeling process
그림 [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
그림 [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
그림 [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
그림 [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
그림 [그림 8] 단순화하기 단계에서 관찰된 A조의 메타인지적 상호작용 사례 [Fig. 8] Example of metacognitive interaction observed in the simplification stage of group A
그림 [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
그림 [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
표 [표 1] 각 유형의 상호작용이 수학적 모델링에 미치는 효과 [Table 1] Effects of each type of interaction on mathematical modeling

질의응답

핵심어	질문	논문에서 추출한 답변
	집단창의성의 개념들에서는 공통으로 무엇이 핵심이 되는가?	집단창의성의 개념은 연구자들에 따라 다양하게 정의 되지만, 집단창의성에 관한 선행연구(김부미, 2018; 김영채, 2007; 유경훈, 2015; Paulus, 2000; Woodman et al., 1993; Zhou & Luo, 2012)를 분석하면, 공통적으로 집단 구성원의 상호작용 속에서 개인이 할 수 있는 것보다 뛰어난 산출을 해내는 집단 수준의 창의적 시너지를 갖는것이 핵심이 됨을 알 수 있다. 이때, 집단 내 상호작용이란 서로의 정보를 교환하고 발전시켜 나가는 과정으로, 사회적 맥락에서의 검증과 구성원들의 합의를 포함한다 (Paulus, 2000; Paulus & Nijstad, 2003, pp.
	English & Sriraman, Gravemeijer에 따르면, 수학적 모델링이란?	수학적 모델링은 실세계 현상에 대한 분석과 해석으로부터 출발하여 수학적 모델을 구성하고 이를 다시 실세계에 적용하는 과정(English & Sriraman, 2010;Gravemeijer, 2002)으로, 학생들의 수학적 사고력 신장과 탐구학습의 기회를 제공할 수 있는 수학교육의 한 방안으로서 그 중요성이 꾸준히 강조되고 있다(정혜윤, 이경 화, 백도현, 정진호, 임경석, 2018). 이에 따라, 국내외의 여러 수학교육 연구자들(김민경, 홍지연, 김혜원, 2010;Bliss & Libertini, 2016; Galbraith & Stillman, 2006;Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) 역시 수학적 모델링 활동과 관련하여 그 의미와 과정, 그리고 역할 및 효과 측면에서 다면적인 논의를 진행해 왔다.
	수학적 문제 해결 시 나타나는 집단창의성 발현과정으로서 상호작용의 상보, 긴장, 발생이라는 세 가지 상태는 각각 어떤 상호작용을 유도하는가?	이에, 최근 집단창의성 발현과정으로서 상호작용 과정에 대한 실제적 연구를 수행하려는 시도가 성지현, 이종희(2017a)에 의해 진행되었다. 이들은 수학적 문제 해결 시 나타나는 집단창의성 발현과정에서의 상호작용으로 상보, 긴장, 발생이라는 세 가지 상태에서의 상호작용을 제시하였는데, 이때 상보적 상태는 구성원의 다양한 사고를 수집하는 상호보완적 상호작용을, 긴장 상태는 사고의 불일치로 인한 갈등 기반 상호작용을, 발생 상태는 새로운 관계의 발견 혹은 연결이 나타나는 메타인지적 상호작용을 유도한다. 이들은 모두 구성원의 정보를 수집, 교환하고 합의해 나가는 과정으로, 집단창의성 발현에 기여하는 맥락을 좀 더 구체적으로 살펴보면 다음과 같다.

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