• The Mathematical Education
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• v.42 no.5
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• pp.697-706
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• 2003

In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

• Journal of the Korean School Mathematics Society
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• v.24 no.2
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• pp.217-241
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• 2021

The purpose of this study is to qualitatively examine the effects of graphics representation of trigonometry modelling concerning question generating and idea sharing. The experimental setting(Experiment Group) was one class (N=26) at a public high school. The modelling process was designed as a process-oriented conceptualization divided into three steps i.e., (1) game with idea sharing and question generating, (2) graphic representation, and (3) symbolization in the mathematical applied tasks related to trigonometry function. The result indicates that Graphic Representation with Game Activity increases the opportunity of question generating and idea sharing during experimental work. Also, the results show that the introduction of computer graphics enhances the teaching of mathematical quantity in highschool classrooms.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.175-186
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• 1995

The concept of a fuzzy set, which was introduced in [9], provides a natural framework for generalizing many of the concepts of general topology to what might be called fuzzy topological spaces. The idea of fuzzy topological spaces was introduced by Chang [2]. The idea is more or less a generalization of oridinary topological spaces.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.261-267
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• 2010

Both history of mathematics and education of mathematics is old subject. The question arises wether can these two important subjects can help each other or not. Unfortunately this idea made mathematics society into two groups; one has idea that history of mathematics can help education of mathematics and other group has idea that not only history of mathematics can not help education of mathematics but also it makes some confusion. In this article the author is going to do some comparison and take some conclusion that history of mathematics can make education of mathematics so active and interesting.

• East Asian mathematical journal
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• v.34 no.3
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• pp.317-330
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• 2018

We develop a mathematical model for the obesity dynamics to investigate the long term obesity trend with the consideration of psychological and social factors due to the increasing prevalence of obesity around the world. Many mathematical models for obesity dynamics adopted the modeling idea of infectious disease and treated overweight and obese people infectious and spreading obesity to normal weight. However, this modeling idea is not proper in obesity modeling because obesity is not an infectious disease. In fact, weight gain and loss are related to social interactions among different weight groups not only in the direction from overweight/obese to normal weight but also the other way around. Thus, we consider these aspects in our model and implement personal weight gain feature, a psychological factor such as body image dissatisfaction, and social interactions such as positive support on weight loss and negative criticism on weight status from various weight groups. We show that the equilibrium point with no normal weight population will be unstable and that an equilibrium point with positive normal weight population should have all other components positive. We conduct computer simulations on Korean demography data with our model and demonstrate the long term obesity trend of Korean male as an example of the use of our model.

• School Mathematics
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• v.15 no.3
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• pp.619-632
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• 2013

One area where research is especially needed is their elaboration process and how they elaborate their idea as a group in a mathematical board game re-creation project. In this research, this process was named 'Mathematical Elaboration Process'. The purpose of this research is to understand how the gifted children elaborate their idea in a small group, and which idea can be chosen for a new board game when they are exposed to a project for making new mathematical board games using the what-if-not strategy. One of the gifted children's classes was chosen in which there were twenty students, and the class was composed of four groups in an elementary school in Korea. The researcher presented a series of re-creation game projects to them during the course of five weeks. To interpret their process of elaborating, the communication of the gifted students was recorded and transcribed. Students' elaboration processes were constructed through the interaction of both the mathematical route and the non-mathematical route. In the mathematical route, there were three routes; favorable thoughts, unfavorable thoughts and a neutral route. Favorable thoughts was concluded as 'Accepting', unfavorable thoughts resulted in 'Rejecting', and finally, the neutral route lead to a 'non-mathematical route'. Mainly, in a mathematical route, the reason of accepting the rule was mathematical thinking and logical reasons. The gifted children also show four categorized non-mathematical reactions when they re-created a mathematical board game; Inconsistency, Liking, Social Proof and Authority.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.579-591
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• 2002

New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.167-170
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• 1993

In this paper, X, X$_{1}$, X$_{2}$, .. will denote any sequence of pairwise independent random variables with common distribution, and b$_{1}$, b$_{2}$.. will denote any sequence of constants. Using Chung [2, Theorem 4.2.5] and the same idea as in Chow and Robbins [1, Lemma 1 and 2] we have the following lemma.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.679-687
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• 2001

In this paper, using an idea from the direct method of Hyers, we give the conditions in order for a linear mapping near an approximately additive mapping to exist.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.149-161
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• 2010

We adopt the idea of $C{\breve{a}}dariu$ and Radu to prove the generalized Hyers-Ulam stability of generalized Jordan triple derivation in Banach algebra. In addition, we take account of problems for generalized Jordan triple linear derivation in Banach algebra.