The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Investigating how the tasks' characteristics change according to modifying the textbook tasks and implementing the lesson by secondary preservice teachers: Focused on the mathematical modeling perspectives

중등 예비교사의 교과서 과제 변형 및 수업 실행 중 나타난 과제의 특징 변화: 수학적 모델링 관점을 중심으로

  • Received : 2024.07.02
  • Accepted : 2024.08.08
  • Published : 2024.08.31
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Abstract

It is difficult for mathematics teachers to develop mathematical modeling tasks and implement mathematical modeling lessons for their students. These difficulties serve as a reason why mathematical modeling lessons are not implemented well in school mathematics. In this study, we aimed to examine how preservice mathematics teachers (PMTs) modify mathematical modeling tasks in mathematics textbooks as a way to develop mathematical modeling tasks and how they implement the mathematical modeling lesson. In particular, we focused on how the openness and reality reflected in the task and the mathematical modeling process change as PMTs modify the tasks. We collected data through PMTs' evaluation reports on analyzing textbook tasks, task modification, lesson plans and implementations, peer evaluation, and self-evaluation. Then, we analyzed these data according to the case analysis process. The findings revealed that when PMTs modified the textbook task, they focused on and improved the openness and the defining variables and the model stages of mathematical modeling process. However, when PMTs implemented lesson, the openness and the defining variables and the model stages of mathematical modeling process were restricted again. PMTs did not focus on other stages. Based on these results, the theoretical and practical implications of the study was discussed.

수학 교사가 수학적 모델링 수업을 위해 과제를 개발하고 수업을 설계하여 실행하는 데에는 많은 어려움이 있으며, 이와 같은 어려움은 학교수학에서 수학적 모델링 수업이 잘 실행되지 않는 원인으로 작용한다. 본 연구에서는 이와 같은 교사의 어려움을 개선하기 위하여, 중등 예비교사들이 수학 교과서 실세계 맥락 과제를 수학적 모델링 과제로 변형하고, 변형된 과제를 적용하여 수업을 실행하는 과정을 살펴보았다. 특히, 과제 변형과 수업 실행 과정에서, 수학적 모델링 과제의 특징이라고 할 수 있는 수학적 모델링 과정의 각 단계 및 과제의 개방성과 현실성이 어떻게 변화하는지 살펴보았다. 이를 위해, 중등 예비교사 의한 변형 전후 과제, 변형 전 과제 분석 결과 보고서, 과제 변형 보고서, 수업 실행 장면을 녹화, 녹음 및 전사한 자료, 수업 실행에 대한 동료평가와 자기평가를 수집하였으며, 사례 분석 절차에 따라 자료를 분석하였다. 연구 결과는 다음과 같다. 첫째, 예비교사들은 과제 변형 시 개방성과 변수 정의하기 단계 및 수학적 모델 도출하기 단계에 주목하는 경향을 보였으며, 이에 따라 변형된 과제에서는 변형 전과 비교하여 개방성과 변수 정의하기, 수학적 모델 도출하기 단계에 대한 학습 기회가 증진되었다. 둘째, 예비교사의 수업 실행 과정에서 변형된 과제의 개방성과 변수 정의하기, 수학적 모델 도출하기 단계가 다시 제한되는 경향이 나타났다. 셋째, 예비교사들은 위에서 언급한 수학적 모델링 과정의 단계들 외에 나머지 단계에 대하여 과제 변형과 수업 실행 과정에서 크게 주목하지 않았다. 이상의 연구결과를 토대로 예비교사들이 수학적 모델링 과제의 변형과 수업 실행 시 갖는 어려움을 확인하고 향후 수학적 모델링에 대한 예비교사교육의 시사점을 제안하였다.

Keywords

Acknowledgement

This work was supported by Incheon National University Research Grant in 2023.

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