• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.341-349
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• 2001

Infinity is one of the important concept in mathematics, science, philosophy etc. In history of mathematics, potential infinity concept conflicts with actual infinity concept. Reason that mathematicians refuse actual infinity concept during long period is because that actual infinity concept causes difficulty in our perceptions. This phenomenon is called epistemological obstacle by Brousseau. Potential infinity concept causes difficulty like history of development of infinity concept in mathematics learning. Even though students team about actual infinity concept, they use potential infinity concept in problem solving process. Therefore, we must make clear epistemological obstacles of infinity concept and must overcome them in learning of infinity concept. For this, it is useful to experience visualization about infinity concept. Also, it is to develop meta-cognition ability that students analyze and control their problem solving process. Conclusively, students must adjust potential infinity concept, and understand actual infinity concept that is defined in formal mathematics system.

• Research in Mathematical Education
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• v.12 no.1
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• pp.1-26
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• 2008

The concept field is defined as the schema of all equivalent definitions of a mathematics concept. Concept system is defined as the schema of a group concept network where there are mathematics relations. Proposition field is defined as the schema of all equivalent proposition sets. Proposition system is defined as a schema of proposition sets where one mathematics proposition at least is "derived" from the other proposition. CPFS structure that consists of concept field, concept system proposition field, proposition system describes more precisely mathematics cognitive structure, and reveals the unique psychological phenomena and laws in mathematics learning.

• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.405-418
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• 1999

In this paper, we tried to establish the concept of 'Mathematics for Elementary Teachers(MET)'. There are 4 kinds of Mathematics for Teachers(MT). MET is one of tried to establish the concept in contradistinction to school mathematics(SM), mathematics, and Teaching Materials(TM). We suggested the outline of MET by suggesting the parts to which SM, MTs. The concept of MET is established variously according to various views. Here, we mathematics, and TM can not approach.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.67-87
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• 2001

Variable concept plays a crucial role in understanding not only algebra itself but also school mathematics which is algebra-oriented. It solves as an essential means in applying mathematics to the real world because il enables us to describe varying phenomena in the real world. In this study, we examined some matters related to the learning of variable concept in school mathematics. In Particular, we discussed on the teaching of variable concept in the [7-first] stage of the 7th Mathematics Curriculum. We analysed the textbooks in the [7-first] stage and attempted to explain concretely the contents and teaching methods of variable concept which be taught in school mathematics. After reconsidering the practices on variable concept teaching, we pointed out the problems of formalistic teaching method and then proposed the direction in which variable concept teaching should go.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.125-143
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• 2002

The concept of "set" in school mathematics has undergone many changes according to the revision of curriculum and the transition of the paradigm in mathematics education. In the discipline-centered curriculum, a set was a representative concept which reflected the spirit of New Math. After the Back to Basics period, the significance of a set concept in school mathematics has been diminished. First, this paper elaborated several controversial aspects of the terms related to set, such as a collection and a set, a subset, and an empty set. In addition, the changes of the significance imposed to a set concept in school mathematics were investigated. Finally, this paper provided two alternative approaches to introduce and explain a set concept which emphasized both mathematical rigor and learner's psychology.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.305-325
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• 2004

This study is on the teaching-learning of parameter concept in secondary school mathematics. In our school mathematics curriculum, parameter concept is explicitly presented at high school mathematics textbook. But student have difficulty in understanding parameter concept because this concept is implicitly used in the textbook from 7-grade mathematics. Moreover, it is true that mathematics teacher give a little attention to student's understanding of parameter con- cept. In this study, we analyzed concept definition of parameter and the extension of parameter on the basis of preceding research, our mathematical curriculum, mathematical dictionaries. After that, we concluded that parameter is explicitly called in t where x= f(t), y= g(t) and parameter is implicitly treated in the learning of relation between quantities in our mathematical curriculum. We pointed to the importance of parameter concept in the successful learning of school algebra. Specially, when the level of algebra is in the learning of relation between quantities, parameter is the key concept for understanding and representing of families of equations or functions. In mathematics class, students have opportunity to reflect that what the role of each variable(parameter, dependent variable, independent variable etc.) is, and where the information which determines it comes from. It is for mathematical communications as well as learning school algebra. Therefore, mathematics teacher's didactical attention is more needed to student have a good concept image of parameter before they learn explicitly its concept definition.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.57-68
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• 2003

Infinity is very important concept in mathematics. In history of mathematics, potential infinity concept conflicts with actual infinity concept for a long time. It is reason that actual infinity concept causes difficulty in our perceptions. This phenomenon is called epistemological obstacle by Brousseau. So, in this paper, we examine the infinity in terms of mathematical didactics. First, we examine the history of development of infinity and reveal the similarity between the history of debate about infinity and episternological obstacle of students. Next, we investigate obstacle of students about infinity and the contents of curriculum which treat the infinity Finally, we suggest the methods for overcoming obstacle in learning of infinity concept.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.381-403
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• 1998

As a researcher engaged in the mathematical education, mathematics teachers are interested in instructional methods. While it is unlikely that the viewpoints of individual mathematics teachers are reflected in making decisions on instructional purposes and instructional contents, a good many parts of instructional methods on mathematical facts are decided by individual teachers. This means that the role of mathematics teachers is given much weight in the mathematical education. Therefore, the mathematics teachers must not be excluded in all parts of the study of mathematical education. We studied the instructional methods of function concept, a central topic in school mathematics from the following perspectives. First, we examined the characteristics of the three(correspondence-centered, middle, dependence centered) viewpoints about the essence of function concept. And we should that which of them should be the viewpoint of instruction of function concept in school mathematics. Second, we investigated the questions regarding the process of function instruction in school mathematics and presented alternative instruction methods of function concept to solve the questions. Third, we postulated the importance of polynomial function, relating college mathematics in order to present the reason why the polynomial function is importantly treated in functional instruction of school mathematics.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.361-375
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• 2022

In this study, the vocabularies in elementary mathematics textbooks for grade 1-2 were analyzed according to 9-degree of semantic system. Also, the types of vocabulary were analyzed using general academic words, mathematics specific concept words, and mathematics general concept words. As a result, percentages of 1-degree and 2-degree vocabulary was the most in both grade 1 and 2 mathematics textbooks. It also shows that some of general academic words were 3-degree vocabulary and some of mathematics specific concept words were either unregistered or 1-degree vocabulary. In particular, general academic words, which are 3-degree vocabulary, may be unfamiliar to 1^st and 2^nd grade students. Therefore, students should be given the opportunity to guess and understand the contextual meaning of general academic words from the given contexts in textbooks. The frequency of use of mathematics general concept words in grade 2 textbook increased significantly compared to grade 1 textbook. Since mathematics general concept words are academic and technical vocabulary they should be taught explicitly. Based on the results of this study, implications for vocabulary instruction in mathematics textbooks were discussed.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.77-82
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• 2002

This paper is concerned with the mathematical concept displayed in Buddhism, which is reasonable enough to consider as a philosophy and encompasses the concept of infinity as scientific as that of mathematics. The purpose of this paper is to examine the changing process of the Buddhism concept of infinity on the basis of time sequence and to combine this with that of mathematics.