• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.427-440
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• 2004

Freudenthal의 수학화 이론에 대한 지금까지의 대부분의 연구는 이론의 탐색에 집중하고 이에 따른 학습 지도 방안과 자료개발에만 역점을 두었던 것이 그 한계점으로 지적되어져 왔다. 이에 본 연구자는 실제 이 이론이 어떻게 학습 현장에 적용될 수 있는지에 대해 첫째, Freudenthal의 수학화에 의한 도형 지도에서 학생이 어떻게 수학화를 이루어 가는지를 조사하였고, 둘째, 학습의 주체자인 학생들의 능동적인 활동을 강조한 수학화 과정에서 교수의 주체자인 교사는 학생들의 수학화가 원만히 이루어지게 하기 위하여 어떤 역할을 수행하게 되는지를 중학교 1학년 학생을 대상으로 사례연구를 실시하여 조사하였다.

• Journal of Educational Research in Mathematics
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• v.20 no.2
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• pp.145-161
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• 2010

Concepts in mathematics have been formulated for unifying and abstractizing materials in mathematics. In this procedure, usually some developments happen by necessity as well as for their own rights, so that various interesting materials can be produced as byproducts. These byproducts can also be established by themselves mathematically, which is called byproduct mathematization (sub-mathematization). As result, mathematization and its byproduct mathematization interrelated to be developed to obtain interesting results and concepts in mathematics. In this paper, we provide explicit examples：the mathematization is the continuity of trigonometric functions, while its byproduct mathematization is various trigonometric identities. This suggestion for explaining and showing mathematization as well as its byproduct mathematization enhance students to understand trigonometric functions and their related interesting materials.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.323-345
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• 2015

This study is intended to establish and apply a program created with RME for mathematising instruction and learning and identify how it influences on the mathematical thinking process in the field. In order to deal with this study inquiries, related theories have been analyzed establishing a program for mathematising instruction and learning method based on a model of them and RME theory principles and re-organizing education courses for instruction on the fields concerned. Study subjects were limited to two classes consisting of fifth graders in S elementary school located in the city of Daegu and divided them in an experiment group and a control group. An experiment group was given a mathematising learning method applied with RME, while a control group had a class with regular methods of learning and instruction during the period of experiment. As a summary of aforementioned results of the study, mathematising learning method applied with RME had an effect on improving mathematical thinking ability for students and also on promoting mathematising outcome through a repetitive experience in each procedure obtained on a regular basis.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.99-115
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• 2007

The purpose of this study was to look into whether this mathematising learning utilizing realistic context has an effect on the mathematical thinking. To solve the above problem, two 5th grade classes of D Elementary School in Seoul were selected for performing necessary experiments with one class designated as an experimental group and the other class as a comparative group. Throughout 17 times for six weeks, the comparative group was educated with general mathematics learning by mathematics and "mathematics practices," while the experimental group was taught mainly with mathematising learning using realistic context. As a result, to start with, in case of the experimental group that conducted the mathematising learning utilizing realistic coherence, in the analogical and developmental thoughts which are mathematical thoughts related to the methods of mathematics, in the thinking of expression and the one of basic character which are mathematical thoughts related to the contents of mathematics, and in the thinking of operation, the average points were improved more than the comparative group, also having statistically significant differences. The study suggested that it is necessary to conduct subsequent studies that can verify by expanding to each grade, sex and region, develop teaching methods suitably to the other content domains and purposes of figures, and demonstrate the effects. In addition to those, evaluation tools which can evaluate the mathematical thinking processes of children appropriately and in more diversified methods will have to be developed. Furthermore, in order to maximize mathematising for each group in each mathematising process, it would be necessary to make efforts for further developing realistic problem situations, works and work sheets, which are adequate to the characteristics of the upper and lower groups.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.17-26
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• 2004

This paper claims that an essential characteristic of modernism is mathematization, and introduces how mathematization was deployed in the eighteenth century. It also points out problems caused by mathematization.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.187-209
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• 2008

In this paper we analyze various russian studies related with differentiated mathematics education. Especially we work on the studies published in 1980-1995 years. As a result, we find that many studies are carried out with various view points in different directions, draw out essential variables, embodiment methods of differentiated mathematics education in Russia.

• The Mathematical Education
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• v.62 no.1
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• pp.23-34
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• 2023

The rationalizing denominators presented in the mathematics textbooks is being used in various places of school mathematics curriculum. However, according to some previous research on the rationalizing denominators in school mathematics, it seems that there is no clear explanation as to why rationalizing denominators is necessary and why it should be used. In addition, a previous research insists that most students know how to rationalize denominators but do not understand why it is necessary and important. To confirm this, we examined the rationalizing denominators presented in the 2015 revised mathematics curriculum as school mathematics. Then we also examined the rationalizing denominators algebraically as academic mathematics. In detail, we conducted an analysis on the rationalizing denominators presented in randomly selected three mathematics textbooks and teacher guidebooks for middle school third grade. Then the algebraic meaning of the rationalizing denominators was examined from a proper algebraic structure analysis. Based on this, we present alternative definitions of the rationalizing denominators which is suitable for school mathematics and academic mathematics. Finally, we also present the mathematical contents (irrationals of the special form can be algebraically interpreted as numbers in the standard form) that teachers should know when they teach the rationalizing denominators in school mathematics.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.71-95
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• 2012

Nowadays, the big issues on mathematics education are mathematical modeling, mathematization, and problem solving. So, this paper looks about these issues. First, after 1990's, the researchers interested in mathematical model and mathematical modeling. So, this paper looks about mathematical model and mathematical modeling. Second, it looks about Freudenthal' mathematization after 1970's. And then, it compared with mathematical modeling. Also, it looks about that problem solving focused on mathematics education since 1980's. And it compared with mathematical modeling.

• School Mathematics
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• v.8 no.2
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• pp.161-176
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• 2006

Some adequate programs for mathematising are necessary to pre-service mathematics teachers, if they can guide their prospective students in secondary school to make a mathematising. They should be used to mathematising. In this paper, mathematising teaching units for the inquiry into number partition models with constant differences are designed for this purpose. They guide a series of process to make nooumenon for organizing phainomenon which is organized already through number partition model. Especially the new nooumenon and the process of obtaining it are discussed. But it is restricted when the numbers for partitioning are natural numbers, and elements and their differences are integers. Through these teaching units, pre-service mathematics teachers can experience and practice secondary mathematising, as they go through the procedures which are similar with those of mathematicians making theorems.

• School Mathematics
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• v.8 no.4
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• pp.417-439
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• 2006

Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.