The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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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

이차함수에서 두 변량사이의 관계 인식 및 표현의 발달 과정 분석: 민선의 경우를 중심으로

  • Received : 2015.08.28
  • Accepted : 2015.11.05
  • Published : 2015.11.30
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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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References

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