Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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A case study on analyzing mathematical errors of low-achieving students in translation tasks among linear function representations and developing 'Looking tasks'

일차함수 표상 간 번역 과제에서 저성취 학생의 수학적 오류 분석 및 Looking 과제 개발 사례 연구

  • Received : 2026.03.03
  • Accepted : 2026.03.23
  • Published : 2026.03.31
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Abstract

The purpose of this study was to analyze mathematical errors appearing in translation tasks among linear function representations for two low-achieving eighth graders, and to develop 'Looking tasks' and questioning strategies that facilitate the process of forming those errors into mathematical meaning. To this end, an instrumental case study was conducted in which analytic tasks were developed based on the learning trajectory of Ahn and Oh (2021), each student's errors were analyzed through iterative diagnosis, and customized 'Looking tasks' were designed and implemented. The results revealed that both students followed unique learning trajectories differing from the general one, and new types of errors not previously reported in the literature were identified. 'Looking tasks' and questioning strategies designed according to the looking-back principle, developmental node appropriateness principle, and self-correction principle facilitated the process of forming the students' errors into mathematical meaning, with task sequencing playing a particularly important role in error resolution. These findings suggest that in-depth diagnosis is necessary for analyzing errors of low-achieving students, and that developing customized tasks based on each student's developmental node and error characteristics is essential.

본 연구는 중학교 2학년 저성취 학생 2명을 대상으로, 일차함수 표상 간 번역 과제에서 나타나는 수학적 오류를 분석하고, 이를 수학적 의미로 형성하는 과정을 촉진하는 Looking 과제 및 발문을 개발하는 것을 목적으로 한다. 안후상과 오영석(2021)의 학습 경로를 기반으로 분석 과제를 개발하고, 반복적 진단을 통해 학생별 오류를 분석한 후 맞춤형 Looking 과제를 개발·적용하는 도구적 사례 연구를 수행하였다. 연구 결과, 두 학생은 일반적 학습 경로와 다른 고유한 경로를 보였으며, 선행연구에서 보고되지 않은 새로운 오류 유형이 발견되었다. 되돌아보기 원리, 발달 지점 적합성 원리, 자기 수정 원리에 따라 설계된 Looking 과제와 발문은 오류를 수학적 의미로 형성하는 과정을 촉진하였으며, 과제 순서의 수정이 오류 해결에 중요한 역할을 하였다. 이는 저성취 학생의 오류 분석에 심층적 진단이 필요하며, 학생의 발달 지점과 오류 특성에 기반한 맞춤형 과제 개발이 중요함을 시사한다.

Keywords

References

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