• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.657-664
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• 2000

A new concept of stability that includes Lyapunov and orbital stabilities and leads to concepts in between them is discussed in terms of a given topology of the function space. The criteria for such new concepts to hold are investigted employing suitably Lyapunov-like functions and the comparison principle.

• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• Research in Mathematical Education
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• v.3 no.1
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• pp.35-56
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• 1999

The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

• The Mathematical Education
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• v.58 no.2
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• pp.319-335
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• 2019

In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.357-370
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• 2015

In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

• The Mathematical Education
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• v.50 no.4
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• pp.429-440
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• 2011

This paper analysed gifted middle students' conception of the definitions of point and line and the uses of definitions in proving. The findings of this paper suggest that the concept of mathematical definitions is very unnatural to students, therefore teachers and textbooks need to explain explicitly the characteristics of mathematical definitions which are different from dictionary definitions using common sense. Also introducing undefined terms in middle school geometry would give students a critical chance to deal with the transition from dictionary definitions to mathematical definitions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.561-572
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• 2018

In this paper we consider the concept of statistical causality in continuous time between flows of information, represented by filtrations. Then we relate the given concept of causality to the equivalent change of measure that plays an important role in mathematical finance. We give necessary and sufficient conditions, in terms of statistical causality, for extremality of measure in the set of martingale measures. Also, we have considered the extremality of measure which involves the stopping time and the stopped processes, and obtained similar results. Finally, we show that the concept of unique equivalent martingale measure is strongly connected to the given concept of causality and apply this result to the continuous market model.

• Korean Journal of Child Studies
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• v.31 no.5
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• pp.63-77
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• 2010

This study was to investigate the differences of 'math talks' between concept-based storybook reading and context-based storybook reading activities. The teachers carried out storybook reading activities with their children using either four concept-based storybooks or four context-based storybooks. Fifty-six storybook reading activities from seven kindergarten classrooms were observed. The data were collected through participant observations and audio recordings. The transcriptions of 'math talks' during storybook reading activity were classified in terms of the levels of instructional conversation, types of mathematizing, and the mathematical processes involved. The results indicated that the 'math talks' during the concept-based storybook reading activity were higher than those of the context-based storybook reading activity in terms of both the instructional conversation and in quantifying and redescribing of mathematizing. However, the 'math talks' during the context-based storybook reading activity were higher than those of the concept-based storybook reading activity in connecting and reasoning of the mathematical processes involved. These findings suggest that early childhood teachers need to improve the level of instructional conversation during math storybook reading activities.

• The Mathematical Education
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• v.46 no.4
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• pp.423-443
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• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.949-957
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• 1997

The purpose of this paper is to establish connection between certain complex of modules of generalized fractions and the concept of cosequence in commutative algebra. The main theorem of the paper leads to characterization, in terms of modules of generalized fractions, of regular (co) sequences.