• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.249-283
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• 2008

The purpose of the study was to investigate the definitions and concept images of Infinity and limits for high school students. In addition, the error patterns of the students were also investigated. The participants were 121 girls highschool students and survey method was used to co11ed data. Only 11 % and 5% of the participants revealed the definitions similar to the standard textbook definitions in limits of infinite sequences and infinite series respectively. The participants showed 6 types of error patterns and had more difficulties in understanding and applying concepts and properties of infinite series than those of infinite sequences.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.469-482
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• 2008

This study analysed difficult points on the understanding of infinity when the concept is considered as actual infinity or as potential infinity. And I consider examples that the concept of actual infinity is used in texts of elementary and middle school mathematics. For understanding of modem mathematics, the concept of actual infinity is required necessarily, and the intuition of potential infinity is an epistemological obstacle to get over. Even so, it might be an excessive requirement to make such epistemological rupture from the early school mathematics, since the concept of actual infinity is not intuitive, derives many paradoxes, and cannot offer any proper metaphor.

• School Mathematics
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• v.12 no.1
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• pp.1-15
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• 2010

The study presented in this paper, which serves as a pilot study for a future comprehensive project, was to investigate how students deal with the concepts of infinity and limit. Based on the communicational approach to cognition, according to which mathematics is a kind of discourse, we tried to identify the characteristics of students' discourse on the topics. Four American and four Korean students were interviewed in English on limits and infinity and their discourse was scrutinized with an eye to common characteristics as well as culture, age, and education-related differences.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2007.10a
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• pp.49-50
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• 2007

• The Mathematical Education
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• v.39 no.1
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• pp.37-47
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• 2000

Number concept is basic in mathematics education. But it is very complex and is not easy to understand real number concept, because of its infinity. This study tried to show that what percents of secondary school mathematics teachers in Korea understood the properties of real number, such as cardinality, continuity, relation with real line, and infinity, which were written by verbal language.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.57-68
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• 2005

무한, 극한, 연속, 미분가능과 같은 중요한 수학적 개념을 이해하는 것은 대학수학 교양과정의 미분적분학 수강생들에게 필수적이다. 이들 개념의 이해 수준을 부록1, 2, 3을 통해 알아보고 평가를 분석한다. 평가결과는 이해도가 낮은 학생들을 위한 새로운 교수법이 필요성을 알게 하고 수학적 기본개념의 이해를 증진시키는데 정의의 정확한 이해를 돕고 구체적인 예제를 제시하는 교수법 개발에 수학교수의 노력을 필요로 한다.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.1-24
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• 2009

In this paper we have inferred the influence of Zeno on the construction of the potential infinite of Aristotle based on arguments of Zeno's paradoxes. When we examine the potential infinite of Aristotle as the basis of the ancient Greek mathematics, we can see that they did not permit the concept of the actual infinite necessary for calculus. The reason Why they recognized the potential infinite, denying the actual infinite as seen in Aristotle's physics could be found in their attempt to escape the illogicality shown in Zeno's arguments. Accordingly, this paper could provided one of reasons why the ancient Greeks had used uneasy exhaustion's method instead of developing the quadrature involving the limit concept.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.1-8
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• 2004

In this paper we try to research in the influences which the concepts of infinity have made to our life, and how they have led the trend of the times through studying on the process of changes of concepts of infinity. Also we intend to make a research in how the shift of paradigm on the view of life have been changing under the circumstances in which the concepts of infinity have been accepted as an actual meaning.

• Journal for History of Mathematics
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• v.9 no.2
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• pp.54-57
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• 1996

• The Science & Technology
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• s.497
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• pp.61-63
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• 2010