중학교 1학년 학생들의 비례 추론과 공변 추론의 관계 비교·분석

Abstract

To understand the relationship between students’ proportional reasoning and covariational reasoning, clinical interview was conducted with four 7th grade students. Students participated in four interviews each of which took about three-four hours. The analysis of the data suggests the following results: First, all four students conceived ratio as ‘internalized ratio’ but how they reasoned with the ratio concept were somewhat different, which were categorized into three different types of proportional reasoning. Secondly, there were differences in how the four students conceived two quantities in graph construction and interpretation tasks. Specifically, two of the four students showed ‘coordination of values’ level, one showed ‘chunky continuous covariational reasoning’, and the other showed ‘smooth continuous covariational reasoning’. Thirdly, there was little relationship as to how students conceived ratio and how they reasoned with quantities in function task. All four students perceived the continuity of function in various ways. We have finalized our study by suggesting students' ways of partitioning and iterating of two quantities in proportion and function tasks as potential theoretical constructs to distinguish how students reason.