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A study on understanding of infinite series

무한급수의 이해에 대한 연구

  • Oh, Hye-Young (Department of Mathematics Education, Incheon National University)
  • Received : 2020.04.29
  • Accepted : 2020.06.27
  • Published : 2020.09.30

Abstract

The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

무한급수 개념은 학부의 전공 수학 교육과정의 중요한 주제이다. 여러 세기 동안 그것은 학습자에게 직관에 반대되는 장애를 제공했을 뿐만 아니라 해석학 연구의 중심적 역할을 해 왔다. 수학의 역사에서 무한급수 개념에 대한 이해가 미적분학 발달의 기초가 되었듯이 현재의 학생들에게 무한급수 개념에 대한 이해는 전공 수학을 학습하는 데 꼭 필요하다. 무한합의 개념을 가진 학생 대부분은 무한급수의 수렴 판정 같은 수학적 내용은 어려워하지 않으나 무한급수 개념을 부분합의 열을 이용해서 구성하는 것은 어려워한다. 이에 본 연구에서는 무한급수 개념을 구성하는 방법을 APOS 이론과 발생적 분해의 관점에서 부분합 스키마를 이용하여 분석하고자 한다. 질적 연구를 통해 급수 개념의 구성 방법을 점검해서 무한급수 지도 개선에 대한 유용한 교육적 시사점을 얻고자 한다.

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