• Communications of Mathematical Education
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• v.32 no.2
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• pp.131-146
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• 2018

Differentiation with integration is an important subject which is widely applied in mathematics, natural science, and engineering. Derivative is an important concept of differentiation. But students don't understand its concept well and concentrate on acquiring only the skill to solve the standardized calculus problem. So they are poor at understanding of the concept of differentiation. In this study, after making a survey of differentiation on college students, we try to analyze errors which appeared in solving differentiation problem and investigate mathematics process of limiting process inherent in the derivative and historical development about derivative. Thus, we try to analyze the understanding of differentiation and present the results about this.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.575-596
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• 2007

This study investigates preservice teachers' development of subject-matter knowledge and pedagogical content knowledge in teaching function concept. This development takes place in the pedagogical mathematics courses in which the theory of constructivism and cooperative learning theory are aligned. Pre and post courses test were administered to examine the development and the follow-up interviews were conducted to gain more details. Analysis of the written questionnaire results and interview transcripts reveal that their limited concept image can be extended and developed in depth through pedagogical mathematics courses that apply reformed teaching methods.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.441-457
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• 2014

This study starts with the idea that Korean mathematical word 'byon' which means 'side' of polygons or angles is very ambiguous. The purpose of this study is to make the concept and range of 'byon' clear and to suggest the ideas which can help children understand the concept of 'byon'. For this, various dictionary and the past Korean mathematics curriculums are reviewed. As a result, two attributes 'byon' has are identified and some reasons which block children from understanding 'byon' are detected in its introduction method of mathematics text books and inkhorn of the mathematical term. Finally, two different ideas for helping children understand the concept 'byon' are suggested based on the conclusion of this research.

• The Mathematical Education
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• v.40 no.2
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• pp.241-252
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• 2001

Many high school students are having difficulties for studying advanced mathematics concepts. It is more complicated than in junior high school and they are losing interest and confidence. In this paper, advanced mathematics concepts are not just basic concepts such as natural numbers, fractions or figures that can be learned through life experience but concepts that are including variables, functions, sets, tangents and limits are more abstract and formal. For the students to understand these ideas is too heavy a burden and so many of the students concentrate their efforts on just memorizing and not understanding. It is necessary to search for a meaningful method of teaching for advanced mathematics that covers deductive methods and symbols. High school teachers are always asking themselves the following question, “How do we help the students to understand the concept clearly and instruct it in a meaningful way?” As a solution we propose the followings : I. To ensure they have the right understanding of concept image involved in the concept definition. II. Put emphasis on the process of making mental representations and the role of intuition. III. To instruct students and understand them as having many chance of the instructional conversation. In conclusion, we studied the meaningful method of teaching with the theory of Ausubel related to the above proposed methods. To understand advanced mathematics concepts correctly, the mutual understanding of both teachers and students is necessary.

• The Mathematical Education
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• v.61 no.2
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• pp.323-338
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• 2022

The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9^th graders and 65 10^th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.57-71
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• 2010

Similarity between concept and concept, principle and principle, theory and theory is known as a strong motivation to mathematical knowledge construction. Metaphor and analogy are reasoning skills based on similarity. These two reasoning skills have been introduced as useful not only for mathematicians but also for students to make meaningful conjectures, by which mathematical knowledge is constructed. However, there has been lack of researches connecting the two reasoning skills. In particular, no research focused on the interplay between the two in didactic transposition. This study investigated the process of knowledge construction by metaphor and analogy and their roles in didactic transposition. In conclusion, three kinds of models using metaphor and analogy in didactic transposition were elaborated.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.287-307
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• 2003

This study analyzed the concept of equal symbol(=) that is the most symbol used in learning of mathematics and investigated students' understanding of that. The equal symbol is endowed with the 'same', 'equal', and 'equivalent' meaning, represented by =, but students interpret the meaning of equal symbol according to the mathematical con text. Thus, we analyzed the equal symbol on the basis of the theory of conceptual fields. In the theory of conceptual fields, concept is a three-tuple of three sets of situation, operational invariants and symbolic representations, and the operational invariants are the concept-in-action and the theorems- in-action. With the analysis contents, we investigated how students read = by korean, what equals in the expression containing = or by what meaning students used =, and which they could correct the error for =. This study imply that we should consider the symbol notation agreed by mathematical society, the meaning, and the situational context that it used, when we teach the mathematics symbols.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.85-101
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• 2017

The purpose of this study is to investigate how elementary school students understand and use the number line relating number concept and what is the main problem in the learning process. For the efficient achievement of this purpose, we investigated how the number line metaphor is related to the number concept and considered the role of the number line on Freudenthal's number concept teaching theory. The test conducted to find the degree of understanding and difficulty on using the number line by actual elementary school students consisted of two questions ; to find appropriate number corresponding to the given number on the number line and to identify contents of chapters about the use of number line on each grade. It was found that many students couldn't solve the problem represented by the number line though they could solve the problem represented by other ways such as number track and pictures. The only difference between the two problems was the way of representation, and they had same contents and structure. This study tried to figure out the meaning of this phenomenon. Also, by using various teaching-learning method (number track, pictures, empty number line, and double number line etc.), this study was aimed to provide the way to help learning 'related number concept' and to solve the difficulty on understanding the number line.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.171-175
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• 2005

In this paper, we introduce the concept of op-idempotents. It is shown that every exchange ring can be characterized by op-idempotents

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.2
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• pp.129-132
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• 2000

We introduce the concept of a fuzzy Vietories topology and we obtain some properties.