The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Students' cognition and a teacher's questioning strategies in the error-finding activity of the concept of irrational numbers

무리수 개념의 오류 찾기 활동에서 학생 인식과 교사의 발문 전략

  • Received : 2023.01.06
  • Accepted : 2023.01.29
  • Published : 2023.02.28
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Abstract

The purpose of this study is to examine not only students' cognition in the mathematical error-finding activity of the concept of irrational numbers, but also the students' learning stance regarding the use of errors and a teacher's questioning strategies that lead to changes in the level of mathematical discourse. To this end, error-finding individual activities, group activities, and additional interviews were conducted with 133 middle school students, and students' cognition and the teacher's questioning strategies for changes in students' learning stance and levels of mathematical discourse were analyzed. As a result of the study, students' cognition focuses on the symbolic representation of irrational numbers and the representation of decimal numbers, and they recognize the existence of irrational numbers on a number line, but tend to have difficulty expressing a number line using figures. In addition, the importance of the teacher's leading and exploring questioning strategy was observed to promote changes in students' learning stance and levels of mathematical discourse. This study is valuable in that it specified the method of using errors in mathematics teaching and learning and elaborated the teacher's questioning strategies in finding mathematical errors.

본 연구는 무리수 개념의 수학 오류 찾기 활동에서 학생의 인식뿐 아니라, 오류 활용에 관한 학생의 학습 태도와 수학적 담론 수준의 변화를 초래하는 교사의 발문 전략을 살펴보는 데 목적이 있다. 이를 위해 133명의 중학교 학생을 대상으로 오류 찾기 개인별 활동, 모둠 활동과 추가 면담을 수행하여, 학생의 인식과 학생의 학습 태도와 수학적 담론 수준의 변화를 위한 교사의 발문 전략을 분석하였다. 연구 결과, 학생들의 인식은 무리수의 기호 표상과 소수 표상에 집중하며 수직선 위의 무리수의 존재성은 인식하지만 도형을 활용한 수직선 표현에는 어려움을 겪는 경향이 있었다. 또한 학생의 학습 태도와 수학적 담론 수준의 변화를 촉진하기 위해 교사의 유도적-탐구적 발문 전략의 중요성을 관찰할 수 있었다. 본 연구는 수학 교수·학습에서 오류의 활용 방법을 구체화하고, 수학 오류 찾기에서 교사의 발문 전략을 정교화하였다는 점에서 가치가 있다.

Keywords

Acknowledgement

This work was supported by the College of Education, Korea University Grant in 2022; This work was a revision of Na's master thesis (2023).

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