• Journal for History of Mathematics
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• v.20 no.3
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• pp.105-126
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• 2007

The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

• The Mathematical Education
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• v.51 no.4
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• pp.455-469
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• 2012

Given the importance of mathematical connections in instruction, this paper analyzed the objects and the methods of mathematical connections according to the lesson flow featured in 20 elementary lessons selected as effective instructional methods by local educational offices in Korea. Mathematical connections tended to occur mainly in the introduction, the first activity, and the sum-up period of each lesson. The connection between mathematical concept and procedure was the most popular followed by the connection between concept and real-life context. The most prevalent method of mathematical connections was through communication, specifically the communication between the teacher and students, followed by representation. Overall it seems that the objects and the methods of mathematical connections were diverse and prevalent, but the detailed analysis of such cases showed the lack of meaningful connection. These results urge us to investigate reasons behind these seemingly good features but not-enough connections, and to suggest implications for well-connected mathematics teaching.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.547-563
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• 2005

There have been many papers reporting that the axiomatic approach in Abstract Algebra is a big obstacle to overcome for the students who are not trained to think in an abstract way. Therefore an instructor must seek for ways to help students grasp mathematical concepts in Abstract Algebra and select the ones suitable for students. Mathematics faculty and students generally consider Abstract Algebra in general and quotient groups in particular to be one of the most troublesome undergraduate subjects. For, an individual's knowledge of the concept of group should include an understanding of various mathematical properties and constructions including groups consisting of undefined elements and a binary operation satisfying the axioms. Even if one begins with a very concrete group, the transition from the group to one of its quotient changes the nature of the elements and forces a student to deal with elements that are undefined. In fact, we also have found through running abstract algebra courses for several years that students have considerable difficulty in understanding the concept of quotient groups. Based on the above observation, we explore and analyze the nature of students' knowledge about $Z_n$ that is the set of congruence classes modulo n. Applying the genetic decomposition method, we propose a model to lead students to achieve the correct concept of $Z_n$.

• Research in Mathematical Education
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• v.17 no.2
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• pp.133-152
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• 2013

In this research, we investigated students' understanding of the definitions of sequence of continuous functions and its uniform convergence. We selected three female and three male students out of the senior class of a university and conducted questionnaire surveys 4 times. We examined students' concept images of sequence of continuous functions and its uniform convergence and also how they approach to the right concept definitions for those through several progressive questions. Furthermore, we presented some suggestions for effective teaching-learning for the sequences of continuous functions.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1311-1327
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• 2010

We introduce the concept of cyclic morphisms with respect to a morphism in the category of pairs as a generalization of the concept of cyclic maps and we use the concept to obtain certain sets of homotopy classes in the category of pairs. For these sets, we get complete or partial answers to the following questions: (1) Is the concept the most general concept in the class of all concepts of generalized Gottlieb subsets introduced by many authors until now? (2) Are they homotopy invariants in the category of pairs? (3) When do they have a group structure?.

• The Mathematical Education
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• v.47 no.3
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• pp.373-386
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• 2008

In highschool probability education, this study analyzed conflicts between intuitive concept and formal definition which originates from the process of establishing the concept of statistical independence. In judging independence, completely different types of problems requiring their own approach was analyzed by dividing them into two types. By doing so, this study researched a way to view independence as an overall idea. That is purposed to suggest a solution to a conflicts between intuitive concept and formal definition and to help not to judge independence out of wrong intuition. This study also suggests that calculation process which leads to precise perception of sample space and event be provided when we prove independence by expressing events with assembly symbols.

• Journal of the Korean Mathematical Society
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• v.8 no.2
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• pp.47-50
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• 1971

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.213-228
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• 2002

We know that curriculum is, first of all, related to teaching materials, namely, contents. Therefore, when we think of mathematics curriculum, we must take account of characteristic of mathematics. Vygotsky has studied the development of scientific concepts and everyday concepts. According to Vygotsky, scientific concepts grow down through spontaneous concepts; spontaneous concepts grow upward through scientific concepts. And mathematics is a representative of subjects dealing with scientific or theoretical concept. Therefore, his study provides scientific basis for mathematics curriculum design. In this context, Davydov notes that everyday concepts are developed through empirical abstraction, while scientific concepts require a theoretical abstraction. And Davydov constructed the curriculum materials for the teaching of number concept. Davydov's curriculum is an example of reflecting Vygotsky' theoretical view and his view about the types of abstraction. In particular, it represents mathematical characteristic of a 'science' by introducing number concept through quantitative relationship and use of signs. In conclusion, stance mathematical concepts have scientific characteristic, mathematics curriculum reflects this characteristic.

• Communications of Mathematical Education
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• v.16
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• pp.139-147
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• 2003

While the statistical concept 'order statistics' has a great number of applications in our society ranging from industry to military analysis, it is not necessarily an easy concept to understand for many people. Adding some interesting simulation activities of this concept to the probability or statistics curriculum, however, can enhance the learning curve greatly. A hands-on and a graphic calculator based activities of a missile simulation were introduced by Kim(2003) in the context of order statistics. This article revisits the two activities in his paper and point out a dilemma that occurs from the violation of an assumption on two deviation parameters associated with the missile simulation. A third activity is introduced to resolve the dilemma in the terms of a kernel density estimation which is a nonparametric approach.

• Korean Journal of Child Studies
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• v.35 no.6
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• pp.93-110
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• 2014

The purpose of this study was to examine the effects of cookbook making activities on young children's mathematical concept and writing development. The participants were comprised of 50 five-year-old children from two intact classes from a kindergarten in Gyeonggi province, and they were divided into an experimental and a comparison group. The experimental group participated in cooking activities and produced cookbooks as extension activities whereas the comparison group carried out only cooking activities. The results indicated that the children in the experimental group received statistically higher scores in mathematical concept- and writing-tests, suggesting that cookbook making activities are a useful educational tool for enhancing young children's mathematical concepts and facilitating their writing development.