• 한국학교수학회논문집
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• 제11권2호
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• pp.249-283
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• 2008

본 연구의 목적은 고등학생들이 가지고 있는 극한에 대한 개념 정의와 개념 이미지를 조사해보고 어떤 부적절한 개념 이미지를 가지고 있는지 알아보는데 있다. 또한 관련 개념에 대한 문제를 해결하는 과정에서 어떤 오류를 범하는지도 알아보았다. 연구대상은 인문계 고등학교 이공계열 여학생 121명 이었으며 연구방법은 질문지 검사를 통하여 이루어졌다. 무한수열의 극한의 경우 11%, 무한급수의 경우에는 5%의 학생만이 교과서의 형식적 정의와 유사한 개념정의를 가지고 있었다. 학생들이 보여준 오류유형은 모두 6가지로 나타났으며 학생들은 문제를 푸는 과정에서 무한수열의 극한에 비하여 무한급수의 합에 대한 정의와 성질들을 이해하고 적용하는 것을 더 어려워했다.

• 대한수학교육학회지:수학교육학연구
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• 제12권4호
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• pp.557-579
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• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.