• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.229-248
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• 2006

In creative society, fluency in technology means the ability to reformulate knowledge, to express oneself creatively and appropriately, to produce and generate information in computer environment. Fluency in technology is essential for mathematics education with a point of constructivist view. In this paper, we study the meaning of fluency in technology, related to mathematics education. For this purpose, we suggest Papert's constructionism as a theoretical background and consider the principle of 'Learning through design' for fluency in technology. And we consider some principles for designing a mathematical microworld and implement a mathematical microworld for fluency in technology. With this microworld, we consider the after-school-program where students have participated a design activity.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.296-310
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• 2023

In this paper, we derive the Γ-limit of functionals pertaining to some optimal material distribution problems that involve a variable exponent, as the exponent goes to infinity. In addition, we prove a relaxation result for supremal optimal design functionals with respect to the weak-∗ L^∞(Ω; [0, 1])× W^1,p0 (Ω;ℝ^m) weak topology.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.213-228
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• 2002

We know that curriculum is, first of all, related to teaching materials, namely, contents. Therefore, when we think of mathematics curriculum, we must take account of characteristic of mathematics. Vygotsky has studied the development of scientific concepts and everyday concepts. According to Vygotsky, scientific concepts grow down through spontaneous concepts; spontaneous concepts grow upward through scientific concepts. And mathematics is a representative of subjects dealing with scientific or theoretical concept. Therefore, his study provides scientific basis for mathematics curriculum design. In this context, Davydov notes that everyday concepts are developed through empirical abstraction, while scientific concepts require a theoretical abstraction. And Davydov constructed the curriculum materials for the teaching of number concept. Davydov's curriculum is an example of reflecting Vygotsky' theoretical view and his view about the types of abstraction. In particular, it represents mathematical characteristic of a 'science' by introducing number concept through quantitative relationship and use of signs. In conclusion, stance mathematical concepts have scientific characteristic, mathematics curriculum reflects this characteristic.

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.231-246
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• 2001

Local linear smoothing enjoys several excellent theoretical and numerical properties, an in a range of applications is the method most frequently chosen for fitting curves to noisy data. Nevertheless, it suffers numerical problems in places where the distribution of design points(often called predictors, or explanatory variables) is spares. In the case of univariate design, several remedies have been proposed for overcoming this problem, of which one involves adding additional ″pseudo″ design points in places where the orignal design points were too widely separated. This approach is particularly well suited to treating sparse bivariate design problem, and in fact attractive, elegant geometric analogues of unvariate imputation and interpolation rules are appropriate for that case. In the present paper we introduce and develop pseudo dta rules for bivariate design, and apply them to real data.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.27-32
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• 2001

The paper describes some principles how we design the mathematics curriculum through mathematical Modelling. since the motivation for modelling is that it give us a cheap and rapid method of answering illposed problem concerning the real world situations. The experiment was focussed on the possibility that they can involved in modelling problem sets and carry modelling process. The main principles could be described as follows. principle 1. we as a teacher should introduce the modelling problems which have many constraints at the begining situation, but later eliminate those constraints possibly. principle 2. we should avoid the modelling real situations which contain the huge data collection in the classroom, but those could be involved in the mathematics club and job oriented problem solving. principle 3. Analysis of modelling situations should be much emphasized in those process of mathematics curriculum principle 4. As a matter of decision, the teachers should have their own activities that do mathematics curriculum free. principle 5. New strategies appropriate in solving modelling problem could be developed, so that these could contain those of polya's heusistics

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.353-374
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• 2005

Recently, there have been many changes in researches of mathematics education. There is a growing number of researchers who are interested in empirical researches. According to the these changes, there is also an emphasis on methodology of mathematics education. This means that many researchers try to conduct an research using scientific approach. Therefore, new types of research developing mathematics courses recently has evolved as follows: teaching experiment, hypothetical loaming trajectory, design science, developmental research. The aim of this study is to reflect on developmental research in RME and to induce desirable directions for developing our mathematics courses. In order to attain these purposes, the present paper reflects the philosophy of RME, aim, procedure, data collection, data analysis, and justification of developmental research with illustrating a exemplar Based on these reflections, it is discussed that it needs to construct the mathematics curriculum connecting theory and practice in mathematics education, to report the process of developing mathematics courses faithfully, and to develop real mathematics courses after conducting basic developmental researches in order to take scientific app- roaches for developing mathematics courses.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.15-29
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• 1999

The purpose of this study is to investigate various mathematics education improvement or reform movements of Western Europe countries (United Kingdom, Germany, etc.) and the United States of America, to see the effects of those movements on Korean mathematics education circle, and to find a direction of Korean mathematics curriculum design. The third Korean mathematics curriculum was most affected by the new mathematics movement of the United States of America. This movement was emphasizing abstract structure, logical rigorousness and discovery learning of mathematics, which was fired from late fifties. Korean mathematics education circle imported the new mathematics early seventies from USA, but serious problems had been found at that time in USA. This study has pointed out that new math oriented Korean mathematics curriculum was not proper and the new mathematics itself was disastrous for most Korean students' learning. The study also points out that they hurried too much introducing the new mathematics and publishing new mathematics oriented textbooks but they had not sufficient teacher training programs. In our future mathematics curriculum reform, we have to remember such a historical lesson.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.63-82
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• 1997

In experimental situations where n two or three level fac-tors are involoved and n observations are taken then the D-optimal first order saturated design is an $n{\times}n$ matrix with elements $\pm$1 or 0, $\pm$1, with the maximum determinant. Cononical forms are useful for the specification of the non-isomorphic D-optimal designs. In this paper we study canonical forms such as the Smith normal form the first sec-ond and the jordan canonical form of D-optimal designs. Numerical algorithms for the computation of these forms are described and some numerical examples are also given.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.489-504
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• 2005

In this paper, we design a environment in computers and mathematics education. For this purpose, we study two different points of view about relations between computers and mathematics education. As theoretical background, we also study constructionism and microworld. Next, we introduce functionization as a basic principle for computers and mathematics education. The concept of functionization focuses on the variation of mathematical objects, and it is a basic concept of both mathematics and computer science. We consider the concept of functionization as a paradigm for the research and practice of the computers and mathematics education. We also present the concept of functionization as a principle for designing a computer environment. Finally, we use the concept of functionization to integrate two famous microworlds, LOGO and DGS by introducing such objects as tiles and folding nets. Combining LOGO and DGS, we design a new microworld that can be used under the internet environment. We present tiles and folding nets to introduce how the concept of functionization is used to design a new microworld and to integrate two microworids.