예비 중등 수학교사의 비례추론 이해
Prospective secondary mathematics teachers’ understanding of proportional reasoning
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초록
중등 예비수학교사가비례추론을 어떻게이해하는지 파악하고비례추론과제를 해결하는데있어서어떤전략을어떻게 활용하는지를 살펴보았다. 선행연구에서 개발된 질문지를 수정, 검토하여 서울 소재 교원양성기관에 재학 중인4명의 예비교사를 인터뷰하였으며, 녹취록을 바탕으로 비례추론에서 예비교사가 보이는 사고의 특징들에 대해 분석하였다. 분석 결과로, 첫째, 예비교사들은 비와 비율의 용어를 혼동하고 혼용하였는데 특히 비율을 단순히 분수로 인식함으로써 기준량을 항상 전체로인식하는 경향을 보였다. 둘째, 비례상황의 의미를 파악하는것이 비례추론의 핵심임에도 불구하고 비례상황을 의미를 기초로 한 추론을 발전시키지 못하는 것으로 나타났다. 두 양을 관련지음으로써 얻어지는 속성의 의미를 잘 파악하지 못하며, 비례식 등호의 의미도 명확하게 설명하지 못하는 것으로 나타났다. 특히 수치를 다루지않는 질적추론문제에서이러한경향이명확하게나타나는데, 이는예비교사가 비례상황을 인식할 때피상적인단어들을이용하기때문으로밝혀졌다.
Abstract
This study examined the understanding of proportional reasoning of prospective secondary mathematics teachers and the strategies they employ in solving tasks pertaining to this topic. The questionnaire developed in the previous study was revised and reviewed, and four preservice teachers enrolled in a teacher education institution in Seoul were interviewed. The transcripts of these interviews were analyzed to identify the characteristics of preservice teachers’ thinking in proportional reasoning. The results of the analysis indicated that, initially, the preservice teachers exibited confusion regarding the distinction between the terms “ratio” and “proportion.” Notably, they demonstrated a tendency to perceive the referece quantity as a whole at all times, interpreting the ratio as a function. Secondly, it appeared that they did not develop reasoning based on the meaning of the proportional situation, despited the fact that grasping the meaning of the proportional situation is the fundamental aspect of proportional reasoning. This was particularly evident in qualitative reasoning tasks that did not involve numbers, as the preservice teacher used superfical terms to recognize proportional situations, even though grasping the meaning of proportional situations is central to proportional reasoning.
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