한국수학교육학회지시리즈A:수학교육 (The Mathematical Education)

  • 제56권4호
  • /
  • Pages.387-405
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  • 2017
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  • 1225-1380(pISSN)
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  • 2287-9633(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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거리함수와 속력함수의 관계에서 거리함수의 상수항에 대한 학생들의 인식과 표현

A Study of Students' Perception and Expression on the Constant of Distance Function in the Relationship between Distance Function and Speed Function

  • 투고 : 2017.09.21
  • 심사 : 2017.11.27
  • 발행 : 2017.11.30
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초록

The purpose of this study is to investigate the change of students 'perception and expression about the motion of object following distance function $={x \atop 3}$ and distance function $y=\frac{x^3}{3}+3$ according to the necessity of research on students' perception and expression about integral constant. In this paper, we present the recognition and the expression of the difference of the constant in the relationship between the distance function and the speed function of the students, while examining the process of constructing the speed function and the inverse process of the distance function. This provides implications for the relationship between the derivative and the indefinite integral corresponding to the inverse process. In particular, in a teaching experiment, a constructive activity was performed to analyze the motion of two distance functions, where the student had a difference of the constant term. At this time, the students used the expression 'starting point' for the constants in the distance function, and the motion was interpreted by using the meaning. This can be seen as a unique 'students' mathematics' in the process of analyzing the motion of objects. These scenes, in introducing the notion of the relation between differential and indefinite integral, it is beyond the comprehension of the integral constant as a computational procedure, so that the learner can understand the meaning of the integral constant in relation to the motion of the object. It is expected that it will be a meaningful basic research on the relationship between differential and integral.

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참고문헌

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