• East Asian mathematical journal
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• v.39 no.2
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• pp.167-181
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• 2023

The purpose of this study is to confirm the possibility of whether learning using a math learning platform can be used to expand students' conceptual structure and to consider how to use it. To this end, first-year middle school students studied using a math learning platform. Then, the concept map created was compared and analyzed with the concept map created before learning to examine the change in the concept structure. The results of analyzing the concept map are as follows. First, the change in the hierarchical structure of the concept appeared as the division of the upper concept was subdivided. However, it has also been changed to comprehensively integrate and simplify higher concepts. The term-centered concept structure has changed to content-centered superordinate and subordinate concepts. In the concept structure, subordinate concepts linked to one higher concept were expanded and differentiated. Second, changes in the integrated structure did not form a linkage structure. The expansion of the integrated structure of concepts through learning using the learning platform was influenced by the composition of the learning contents designed in the learning platform.

• School Mathematics
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• v.6 no.4
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• pp.325-344
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• 2004

This study was carried out to investigate effects of the mindmap note-taking for the formation of the mathematical concepts structure and the matjematical creativity. Two classes were randomly chosen for this study from the third grade students of a middle school located in a medium size city. Thirty one lecture hours of the mindmap note-taking on the quadratic equation and functions were administered to the experimental class of 41 students, while same lecture hours of the ordinary instruction on the same contents were administered to the control class of 40 students. It was shown from this experiment that there ware significant evidences of improvement both in the formation of students' mathematical concepts structure and mathematical creativity through the mindmap note-taking lecture. Hence, the mindmap note-taking lecture is suggested for the improvement in the formation of student's mathematical concepts structure and mathematical creativity.

• The Mathematical Education
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• v.42 no.1
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• pp.11-18
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• 2003

One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

• The Mathematical Education
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• v.53 no.1
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• pp.57-73
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• 2014

This study investigated the connections of mathematical thinking of students at the second, fourth, and sixth grades with regard to multiplication, fraction, and proportion, all of which have multiplicative structures. A paper-and-pencil test and subsequent interviews were conducted. The results showed that mathematical thinking including vertical thinking and relational thinking was commonly involved in multiplication, fraction, and proportion. On one hand, the insufficient understanding of preceding concepts had negative impact on learning subsequent concepts. On the other hand, learning the succeeding concepts helped students solve the problems related to the preceding concepts. By analyzing the connections between the preceding concepts and the succeeding concepts, this study provides instructional implications of teaching multiplication, fraction, and proportion.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.397-415
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• 2022

The purpose of this study is to analyze the discourse structure of teachers that can help students participate in class by using mathematical metaphors that can arouse students' interest and motivation. In order to achieve this goal, we observed a semester class of a career teacher who practiced pedagogy that connects students' experiences with mathematical concepts to motivate students to learn and promote participation. Among the metaphors that the study target teachers used in a variety of mathematical concepts and problem-solving processes during the semester, we extracted the two class examples that can help develop teaching methods using metaphors. Representatively selected two classes are one class example using metaphors and, the other class example using metaphors and expanding and applying problems. As a result of analysis, the structure of teacher discourse that uses metaphors and expands and applies problems by linking students' experiences with mathematical content was found to help solve a given problem and elaborate mathematical concepts. As a result of the analysis, the discourse structure of teachers using mathematical metaphors based on communication with students could provide implications for the development of teaching methods for the recovery of mathematics education.

• Education of Primary School Mathematics
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• v.7 no.1
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• pp.43-56
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• 2003

In late 19C, German mathematician Felix Klein declaired "Erlangen program" to reform mathematics education in Germany. The main ideas of "Erlangen program" contain the importance of instructing the concepts of functions and groups in school mathematics. After one century from that time, the importance of concepts of groups revived by Bourbaki in the sense of the algebraic structure which is the most important structure among three structures of mathematics - algebraic structure. ordered structure and topological structure. Since then, many mathematicians and mathematics educators devoted to work with the concepts of group for school mathematics. This movement landed on Korea in 21C, and now, the concepts of groups appeared in element mathematics text as plane rigid motion. In this paper, we state the rigid motions centered the symmetry - an important notion in group theory, then summarize the results obtained from some classroom activities. After that, we discuss the responses of children to concepts of groups.of groups.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.211-223
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• 1997

Lehmann [13] introduced the concept of positive(negative) dependence together with some other dependence concepts. Since then, a great numerous multivariate inequalities have been obtained. For a references of available results, see Karlin and Rinott [12], Ebrahimi and Ghosh [8] and Sampson [14]. Whereas a number of dependence notions exist for multivariate processes (see Friday [10]), recently, Ebrahimi [7] introduced some new dependence concepts of the hitting times of stochastic processes.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.223-234
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• 2005

We introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of quasi-smooth ${\alpha}$- compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.143-153
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• 2004

In [3] and [6] the concepts of smooth closure, smooth interior, smooth ${\alpha}-closure$ and smooth ${\alpha}-interior$ of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth ${\alpha}-compactness$ in terms of these concepts introduced in [3] and [61 and investigate some of their properties.

• The Mathematical Education
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• v.53 no.3
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• pp.329-355
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• 2014

The purpose of this study is to understand the difference of cognitive structure depending on the level of the 6th graders' problem-solving abilities about the division of fraction and to propose a method for improving the 6th graders' understanding about the division of fraction through the word association test. The following is the findings from this study. 1)The lower level students' is, the lower the step that the chunk appeared in cognitive structure is. 2)The basic level students' association frequency between any two concepts was less than the excellent level students and the ordinary level students' it. 3)The basic level students' connection number between concepts was far less than the excellent level students and the ordinary level students' it. 4)The connection between natural number and unit fractions, subtraction of fraction and division of fraction, division of fraction and reduction to common denominator, and division of fraction and common multiple that expected in this study did not appear in the three groups.