• School Mathematics
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• v.8 no.2
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• pp.123-138
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• 2006

The fraction concept consists of various meanings and is one of the more abstract and difficult in elementary school mathematics. This study intends to analyze the fraction concept from historical and psychological viewpoints, to examine the current elementary mathematics textbooks by these viewpoints and to seek the direction for improvement of it. Basic ideas about fraction are the partitioning - the dividing of a quantity into subparts of equal size - and about the part-whole relation. So these ideas are heavily emphasized in current textbooks. However, from the learner's point of view, situations related to different meanings of fraction concept draw qualitatively different response from students. So all the other meanings of fraction concept should be systematically represented in elementary mathematics textbooks. Especially based on historico-genetic principle, the current textbooks need the emphasis on the fraction as a measure and on constructing fraction concept by unit fraction as a unit.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.309-331
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• 2007

Mathematics education starts from learning the concept of number. How the children at the beginning of school age learn the concept of natural number is therefore important for their future mathematics education. Since ancient Greek period, the concept of natural number has reflected various mathematical-philosophical points of view at each period and has been discussed ceaselessly. The concept of natural number is hard to define. Since 19th century, it has also been widely discussed in psychology and education on how to teach the concept of natural number to the children at the beginning of school age. Most of the works, however, were focused on limited aspects of natural number concept. This study aims to show the best way to teach the children at the beginning of school age the various aspects of natural number concept based on activistic perspective, which played a crucial role in modern mathematics education. With this purpose, I investigated the theory of the activistic construction of knowledge and the construction of natural number concept through activity, and activistic approaches about instruction in natural number concept made by Kant, Dewey, Piaget, Davydov and Freudenthal. In addition, I also discussed various aspects of natural number concept in historical and mathematical-philosophical points of view. Based on this investigation, I tried to find out existing problems in instructing natural number to primary school children in the 7th National Curriculum and aimed to provide a new solution to improve present problems based on activistic approaches. And based on activistic perspective, I conducted an experiment using Cuisenaire colour rods and showed that even the children at the beginning of school age can acquire the various aspects of natural number concept efficiently. To sum up, in this thesis, I analyzed epistemological background on activistic construction of natural number concept and presented activistic approach method to teach various aspects of natural number concept to the children at the beginning of school age based on activism.

• Communications of Mathematical Education
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• v.32 no.1
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• pp.37-57
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• 2018

In the early days, the use of concept maps in mathematics education focused on how to represent mathematical ideas in the concept map. In recent years, however, concept maps have proved beneficial for improving problem solving ability. Conceptual diagrams can be used for collaboration among students, tools for exploring problems, tools for introducing problem structures, tools for developing and systematizing knowledge systems. In this study, we focused on the structure analysis of mathematical problems using Concept Map based on the analysis of previous research. In addition, we have devised a method of using concept maps for problem analysis and a method of analysis of systematic mathematical problem structure. The method developed in this study was found to have significant value by applying to the university scholastic ability test.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.163-172
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• 1995

G.Lumer [8] introduced the concept of semi-product space. H.M.El-Hamouly [7] introduced the concept of fuzzy inner product spaces. In this paper, we defined fuzzy semi-inner-product space and investigated some properties of fuzzy semi product space.

• 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.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.679-686
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• 2022

In this study, the concept of lacunary statistical convergence is studied in G-metric spaces. The G-metric function is based on the concept of distance between three points. Considering this new concept of distance, we examined the relationships between GS, GS_θ, Gσ₁ and GN_θ sequence spaces.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.469-482
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• 2008

This study analysed difficult points on the understanding of infinity when the concept is considered as actual infinity or as potential infinity. And I consider examples that the concept of actual infinity is used in texts of elementary and middle school mathematics. For understanding of modem mathematics, the concept of actual infinity is required necessarily, and the intuition of potential infinity is an epistemological obstacle to get over. Even so, it might be an excessive requirement to make such epistemological rupture from the early school mathematics, since the concept of actual infinity is not intuitive, derives many paradoxes, and cannot offer any proper metaphor.

• 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.

• East Asian mathematical journal
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• v.39 no.2
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• pp.119-139
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• 2023

Most of calculus and real analysis are concerned with the study on continuous functions. Because of self-sustaining concept caused by everyday language, continuity has difficulties. This kind of viewpoint is strengthened with that teacher explains continuity by graph drawn ceaselessly and so finally confused with mathematics concept which is continuity and connection. Thus such a concept image of continuity becomes to include components which create conflicts. Therefore, we try to analyze understanding of continuity on university students by using the concept image as an analytic tool. We survey centering on problems which create conflicts with concept definition and image. And we investigate that difference of definition in continuous function which handles in calculus and analysis exists and so try to present various results on university students' understanding of continuity concept.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.101-119
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• 2017

This paper is a follow up study of [2]. In this paper we analyse the contents of middle school mathematics textbooks published in the 1st National Curriculum Period centered on the concept 'straight line' and discuss how they are different from contemporary mathematics textbooks in view of connectedness of contents, mathematical terms, textbook as a learning material vs. teaching material, relationship between contents of national curriculum and textbooks, and some topics related to direct proportion, function, method of equivalence as a method for solving simultaneous linear equations and so on. The results of our analysis and discussion suggest implications for reforming mathematics curriculum and developing mathematics textbooks.