거북 행동을 통한 함수 그래프 구성
Construction of function graphs through turtle motion
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참고문헌
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초록
동일한 함수 그래프를 접근하는 방법은 다양하다. 물리 교과에서는 중력상태에서 물체의 운동으로 포물선을 정의하고 있으며 수학 교과에서는 수식을 이용한 이차함수로 포물선을 정의한다. 본 연구에서는 교육과정에 나타나는 함수 그래프를 국소적이며 내재적인 거북 행동의 관점에서 접근하고 분석한다. 또한 교육과정에 나타나지 않지만 수학사에서 중요한 의미를 가지는 몇몇 곡선에 대하여 같은 방법으로 곡선을 구성하고자 한다. 그리고 pre-calculus의 관점에서 고등학생의 지식을 바탕으로 곡선의 길이와 넓이를 구하는 수학화 활동을 소개한다.
Abstract
There are different perspectives on a function graph. For instance, a parabola is defined by movement of a ball in physics and by quadratic function in mathematics. This study deals with the turtle motion, which is local and intrinsic, and the construction of function graphs with mathematical experiments in a microworld. This paper concerns with a function graph which is in the curriculum or in the history of mathematics. In view of pre-calculus, we introduce activities of mathematization about formalizing of length and area of function graphs without knowledge of calculus.
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