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極限槪念의 指導改善과 그 適用에 關한 硏究 : 高校數學을 中心으로 for High School Mathematics
孫璨錫,李衡基 부산대학교 사범대학 과학교육연구소 1977 科學敎育硏究報 Vol.4 No.-
Ⅰ. Purpose The purposes of this study were twofold: ① to improve the way of education of analysis in high school which has been inclined toward only applications of the result of fragments of knowledge obtained by intuitive method. ② to provide professional suggestions for practicing the education of analysis more effectively in high school by using the logic of ε-N and ε-δ rather than intuitive method. Ⅱ. Procedure The method used for this study was as follows: ① introducing the continuity of real numbers and the greatest lower bound and the least upper bound of a set of real numbers. ② introducing the definition of convergent sequence and investigating propositions of sequence by the logic of ε-N. ③ introducing the definition of limits of functions and investigating propositions for limits of functions by the logic of ε-δ. ④ investigating relationships between limits of sequences and limits of functions. ⑤ introducing the theory related to the definition and the proposition of continuous functions. ⑥ clarifying the definition of the definite integral and investigating integrability on continuous functions. ⑦ interpreting and analyzing the problems of limit concept from the points of view of mathematic education of present high school. ⑧ improving and applying limit concept in high school mathematics. Ⅲ. Conclusions Through methods above it was attempted to focus on the followings. ① narrowing the gap between high school mathematics and college mathematics. ② extending widely the theory of analysis. ③ increasing reading power by oneself for the advanced theory.