미적분학 기본정리에 대한 Newton과 Leibniz의 직관 및 발견적 교수법 탐색

Abstract

The purpose of this study was to understand Newton and Leibniz’s intuition and design the heuristic pedagogy on the fundamental theorem of calculus. The history of discovery of the fundamental theorem of calculus, grasped the intuition of Newton and Leibniz were examined and four textbooks analyzed. The history of the discoveries of the fundamental theorem of calculus can be divided into two generations. The period when the fundamental theorem of the calculus was sprouting in the velocity and the distance context, and the period of grasping the relation between the derivative and the derivative in the general functional dimension. Especially, in this study, attention was paid to Newton and Leibniz 's point of view that the fundamental theorem of calculus is taken for granted. Newton formed the intuition of the fundamental theorem of calculus with a viewpoint of the increase of the area and Leibniz formed the intuition of the fundamental theorem of calculus in terms of symbol manipulation. Four textbooks had the problem of dealing with speed and distance as an example for the application of the theorem and proof that it is hard to expect intuition formation. In order to reflect the two - generation classification of the discovery history and Newton's intuition of the fundamental theorem of calculus, and complement the weak points of the textbooks, this study proposed 8 steps of 'heuristic teaching method for intuition formation'.