한국수학교육학회지시리즈E:수학교육논문집 (Communications of Mathematical Education)

  • 제37권4호
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  • Pages.569-590
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  • 2023
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  • 1226-6663(pISSN)
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  • 2287-9935(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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대수 문장제를 해결하고 일반화하는 과정에서 드러난 두 중학생의 공변 추론 수준 비교

Comparison of the Covariational Reasoning Levels of Two Middle School Students Revealed in the Process of Solving and Generalizing Algebra Word Problems

  • 투고 : 2023.11.08
  • 심사 : 2023.12.04
  • 발행 : 2023.12.31
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초록

본 사례 연구의 목적은 대수 문장제를 해결하고 일반화하는 과정에서 드러난 두 중학생의 공변 추론 수준을 비교하여 분석하는 것이다. 학교 수학에서 이차방정식을 학습하지 않은 중학생 2명을 대상으로 수업을 진행하였고, 수업이 모두 끝난 뒤 회고 분석 과정에서 속도가 일정하게 변하는 상황을 포함한 대수 문장제의 해결에서 두 학생 간의 차이가 두드러지게 드러났다. 이에 본 연구는 속도의 일정함을 가정하거나 속도가 일정하게 변하는 상황을 포함한 대수 문장제를 해결하거나 일반화하는 과정에서 학생들 스스로 구성한 두 변수에 대해 그들 사이의 변화 관계에 대한 이해 수준을 Thompson과 Carlson(2017)이 제안한 공변 추론 수준에 비추어 비교·분석하였다. 그 결과, 본 연구에서는 대수 문장제의 문제 해결 방식과 그 결과가 표면적으로 유사해 보이더라도 두 학생 간의 공변 추론 수준이 서로 다를 수 있음을 확인하였고, 대수 문장제를 해결하고 일반화하는 과정에서 드러난 유사성을 공변 관점에서 제시하였다. 이를 통해 본 연구는 대수 문장제의 교수·학습에서 문제 상황을 빠르게 식으로 변환하여 해를 찾는 데 주목하기보다 학생 스스로 변화하는 두 양을 찾고 그들 사이의 불변하는 관계를 다양한 방식으로 나타내는 활동이 충분히 다루어질 필요가 있음을 제안한다.

The purpose of this case study is to compare and analyze the covariational reasoning levels of two middle school students revealed in the process of solving and generalizing algebra word problems. A class was conducted with two middle school students who had not learned quadratic equations in school mathematics. During the retrospective analysis after the class was over, a noticeable difference between the two students was revealed in solving algebra word problems, including situations where speed changes. Accordingly, this study compared and analyzed the level of covariational reasoning revealed in the process of solving or generalizing algebra word problems including situations where speed is constant or changing, based on the theoretical framework proposed by Thompson & Carlson(2017). As a result, this study confirmed that students' covariational reasoning levels may be different even if the problem-solving methods and results of algebra word problems are similar, and the similarity of problem-solving revealed in the process of solving and generalizing algebra word problems was analyzed from a covariation perspective. This study suggests that in the teaching and learning algebra word problems, rather than focusing on finding solutions by quickly converting problem situations into equations, activities of finding changing quantities and representing the relationships between them in various ways.

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과제정보

이 논문은 안동대학교 기본연구지원사업에 의하여 연구되었음

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