[논문]수학적 모델링 과정을 반영한 교과서 문제 재구성 예시 및 적용

박선영; 한선영

doi:10.7468/mathedu.2018.57.3.289

수학적 모델링 과정을 반영한 교과서 문제 재구성 예시 및 적용
Reconstruction and application of reforming textbook problems for mathematical modeling process 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.57 no.3, 2018년, pp.289 - 309

박선영 (성균관대학교 대학원) , 한선영 (성균관대학교)

Abstract ▼ AI-Helper

There has been a gradually increasing focus on adopting mathematical modeling techniques into school curricula and classrooms as a method to promote students' mathematical problem solving abilities. However, this approach is not commonly realized in today's classrooms due to the difficulty in developing appropriate mathematical modeling problems. This research focuses on developing reformulation strategies for those problems with regard to mathematical modeling. As the result of analyzing existing textbooks across three grade levels, the majority of problems related to the real-world focused on the Operating and Interpreting stage of the mathematical modeling process, while no real-world problem dealt with the Identifying variables stage. These results imply that the textbook problems cannot provide students with any chance to decide which variables are relevant and most important to know in the problem situation. Following from these results, reformulation strategies and reformulated problem examples were developed that would include the Identifying variables stage. These reformulated problem examples were then applied to a 7th grade classroom as a case study. From this case study, it is shown that: (1) the reformulated problems that included authentic events and questions would encourage students to better engage in understanding the situation and solving the problem, (2) the reformulated problems that included the Identifying variables stage would better foster the students' understanding of the situation and their ability to solve the problem, and (3) the reformulated problems that included the mathematical modeling process could be applied to lessons where new mathematical concepts are introduced, and the cooperative learning environment is required. This research can contribute to school classroom's incorporation of the mathematical modeling process with specific reformulating strategies and examples.

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핵심어	질문	논문에서 추출한 답변
	학생들이 수학의 유용성을 인식하고 실생활에서 수학을 활용하는 능력을 향상시킬 수 있도록 돕는 수학적 모델링 과정을 반영하여 교과서 문제를 재구성하고 적용하는 연구의 연구문제는?	1) 2009 개정 교육과정 수학 교과서의 실생활 문제는 수학적 모델링 과정의 단계를 어느 정도로 다루고 있는가? 2) 학교 수학 교과서의 문제를 수학적 모델링 과정을 반영한 문제로 재구성하는 방안은 무엇인가? 2-1) 학교 수학 교과서의 문제를 수학적 모델링 문제로 재구성하는 근거 및 예시는 무엇인가? 2-2) 학교 수학 교과서의 문제를 수학적 모델링 문제로 재구성한 예시를 적용한 수업에서 학생들의 문제 해결 과정 및 태도는 어떠한 특징을 보이는가?
	수학적 문제해결력을 향상시키는 구체적인 방안으로 주목받는 것은?	수학적 문제해결력을 향상시키는 학교 교육 과정 및 수업을 위한 구체적인 방안으로서 수학적 모델링에 대한 관심이 지속적으로 증가하고 있다. 우리나라 2015 개정 수학 교육과정에는 문제해결 역량의 하위 요소로 수학적 모델링이 도입되었고(교육부, 2015), 전미수학교사협의회 (NCTM: National Council of Teachers of Mathematics) 에서 발간하는 저널 『Mathematics Teaching in the Middle School』에서는 수학적 모델링을 2015년의 주제로 선정하여 교사 및 연구자의 다양한 모델링 수업 사례를 다루기도 하였다.
	수학적 모델링을 문제해결의 한 방안으로서 교육과정에 반영하려는 노력은 무엇과 관련이 있는가?	우리나라 2015 개정 수학 교육과정에는 문제해결 역량의 하위 요소로 수학적 모델링이 도입되었고(교육부, 2015), 전미수학교사협의회 (NCTM: National Council of Teachers of Mathematics) 에서 발간하는 저널 『Mathematics Teaching in the Middle School』에서는 수학적 모델링을 2015년의 주제로 선정하여 교사 및 연구자의 다양한 모델링 수업 사례를 다루기도 하였다. 이와 같이 수학적 모델링을 문제해결의 한 방안으로서 교육과정에 반영하려는 노력은 수학 교육의 궁극적인 목표와 관련이 있다. 모든 학생들은 미래의 세계 시민으로서 각자의 일상생활이나 직업 상황에서 부딪히게 되는 다양한 수학적 문제 상황에 대비해야 하며(NCTM, 2000), 그 상황이 수학적 지식을 활용하여 해결할 수 있는 문제임을 스스로 인식하고, 여러 가지 해결 전략 중에서 가장 효과적인 전략을 선택하여 적용할 수 있는 능력을 갖추어야 한다(Sutherland, 2006).

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