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http://dx.doi.org/10.7468/mathedu.2017.56.4.387

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

Lee, Dong Gun (MunJung High School)
Publication Information
The Mathematical Education / v.56, no.4, 2017 , pp. 387-405 More about this Journal
Abstract
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.
Keywords
distance function; speed function; primitive function; indefinite integral; definite integral; integral constant;
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Times Cited By KSCI : 6  (Citation Analysis)
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