이차함수에서 두 변량사이의 관계 인식 및 표현의 발달 과정 분석: 민선의 경우를 중심으로
A student’s conceiving a pattern of change between two varying quantities in a quadratic functional situation and its representations: The case of Min-Seon
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The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of ‘derivative’ as a tool to express the relationship with employing a concept of ‘rate of change.’ The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, y=x^2. In conclusion, we argue that covariational approach could not only facilitate students’ construction of an initial function concept, but also support their understanding of the concept of ‘derivative.’
Abstract
The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of ‘derivative’ as a tool to express the relationship with employing a concept of ‘rate of change.’ The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, y=x^2. In conclusion, we argue that covariational approach could not only facilitate students’ construction of an initial function concept, but also support their understanding of the concept of ‘derivative.’
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