• 대한수학교육학회지:수학교육학연구
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• 제20권2호
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• pp.145-161
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• 2010

본 연구에서는 수학적 지식이 구명되고 형식화되는 과정을 '수학화(mathematization)'와 '곁가지의 수학화(byproduct mathematization)'란 개념으로 정의하고 분석하였다. 수학화는 수학적 개념들 간의 내적연결성 및 당위성을 경험하도록 교수 학습 활동을 구성하는데 있어 하나의 모델이 된다. 그리고 구체적 예로 '삼각함수의 연속성에 대한 수학화'와 '삼각함수의 덧셈정리의 곁가지의 수학화'를 구성하였다. 이러한 수학화는 교사의 전문성 신장을 위한 학문적 배경 지식을 주며, 가르칠 지식에 대한 다양한 지도 관점을 제공한다.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권2호
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• pp.159-167
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• 2005

As the 7th mathematics curriculum reform in Korea was implemented with its goal based on Freudenthal's perspectives on mathematization theory, the research on the effect of mathematization has been become more significant. The purpose of this thesis is not only to find whether this foreign theory would be also applied effectively into our educational practice in Korea, but also to investigate how much important role teachers should play in their teaching students, in order that students accomplish the process of mathematization more effectively. Two case studies were carried out with two groups of middle-school students using qualitative-research method with the research instrument designed by the researcher. It was found that we could get the possibility of being able to apply effectively this theory even to our educational practice since the students engaged in their mathematization using the horizontal mathematization and the vertical mathematization in geometry. Also, it was mentioned that teachers' role was so important in guiding students' processes of mathematization, although mathematization is the teaching-learning theory, stimulating students' activities. Since the Freudenthal's mathematization applied in the thesis is so meaningful in our educational practice, we need more various research about this theory that helps students develope their mathematical thinking.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권3호
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• pp.353-373
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• 2010

This research was to help slow learners to be motivated and to make their outcome productive, using GSP based on the mathematization theory for learning mathematics, as a way of encouraging the learner-centered approach. With 2 of the second graders in a high school, who had not yet understood trigonometric functions in their first grade period, 7 units of lesson plans were designed for the research. The results showed that first, understanding real life contexts and analyzing properties by observation, and experiment using GSP, to build the concept of trigonometric functions could be a foothold on which learner's organization and outcome from a horizontal mathematization led to vertical mathematization. Despite the delay during the level-up-stage for a while, the learners could attain the vertical mathematization stage and moreover the applicative mathematization through effective use of GSP and the interaction between the learners or a teacher and the learners. Second, using GSP was a vertical tool of connecting horizontal mathematization with vertical mathematization in forming the concept of trigonometric functions and its meaning could be understood by their verbalizing and presenting the outcomes through their active performance. Using GSP is helpful for slow learners to overcome learning difficulties, based on the instructional materials designed by Realistic Mathematics Education.

• 한국수학사학회지
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• 제17권4호
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• pp.17-26
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• 2004

본 논문은 모더니즘이 가지는 핵심적인 성격이 ‘수학화’에 있다고 주장하고 특히 18세기를 중심으로 수학화가 어떻게 전개되었는지 소개하는 데 있다. 뿐만 아니라 ‘수학화’에 따르는 문제점을 지적하려 한다.

• East Asian mathematical journal
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• 제26권4호
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• pp.487-507
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• 2010

We study mathematization of natural thinking and some materials developed in geometric construction of regular n-polygons. This mathematization provides a nice model for illustrating interesting approaches to trigonometric functions and trigonometric ratios as well as their inter-connections. Thereby, results of this paper will provide the procedure of the development for these concepts in natural way, which will be helpful for understanding background knowledges.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권3호
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• pp.273-290
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• 2008

This article provides how to implement the use of Realistic Mathematics Education (RME) in a teaching a function at a school to improve the equity based on the gender in students' mathematization for their mathematical thinking using technology. This study was planed to get research results using the mixed methodology with qualitative and quantitative methodologies. 120 middle school students participated in the study to bring us data about their mathematical achievement. Through the data analysis used by ANCOVA for the qualitative method, the students with the experiment of the mathematization based on technology excelled the other groups of students who were not provided with technology or both of them. Through the data analysis used by the constant comparative method for the qualitative data, the technology environment had helped the female students manipulate learning trends easily, strong construction on horizontal mathematization, depending on discussion with peers, and more reflexive thinking using a calculator. This means that teachers can put careful assignment on each category of mathematization regarding the gender. The study results in a lot of resources for teachers to use into their teaching mathematics for improving students' equity in interactive technology environment.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권1호
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• pp.97-122
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• 2007

This article provides how to implement the use of Realistic Mathematics Education (RME) in a teaching a function at a school to improve students' mathematization for their mathematical thinking using technology, This study was planed to get research results using the mixed methodology with quantitative and qualitative methodologies. 120 middle school students participated in the study to bring us data about their mathematical achievement and disposition. Through the data analysis used ANCOVA, the students with the experiment of the mathematization and technology excelled the other groups of students who were not provided with technology or both of them. In analysis of the questions of the achievement test, the problems for vertical mathematization were presented harder for the students than the other problems for horizontal and applicative mathematization. The technology environment might have helped students manipulate the application of real-life problems easier. This means that teachers can put more careful assignment on vertical mathematization using technology. We also explored that learning and teaching under RME using technology encouraged students to refine and develop their informal functional concept and pursue higher thinking of formalization. The study results in a lot of resources for teachers to use into their teaching mathematics for improving students' mathematical thinking.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권1호
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• pp.17-29
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• 2020

본 연구의 목적은 수학화 과정에서 교사와 학생 간의 상호작용 양상에 따른 교사의 담론 구조를 분석하는 것이다. 이러한 목적 달성을 위해 학생들의 참여를 촉진하는 교수법을 20년 이상 실행한 경력 교사의 한 학기 수업 44차시 중에서 수학화 과정에서 교사와 학생 간의 서로 다른 상호작용 양상을 보이는 대표적인 경우 각각 1차시 수업을 비교분석하였다(근거 이론). 분석 결과, 학생들의 참여 양상을 고려한 교사의 담론 구조는 수학화 과정 경험에 도움을 준 것으로 볼 수 있었다. 이러한 결과를 바탕으로 향후 학생들과의 상호작용 양상에 따라 수학화 과정을 경험할 수 있도록 도움을 주기 위한 교사의 역할을 구체화함으로써 수학화를 위한 교실 담론 개발에 도움을 줄 수 있을 것이다.

• 한국수학사학회지
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• 제25권2호
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• pp.71-95
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• 2012

현재 수학교육에서 큰 흐름을 이루고 있는 수학적 모델링, 수학화, 문제해결을 살펴보았다. 먼저, 1990년대 이후 수학교육에서 활발히 연구되기 시작한 수학적 모델과 수학적 모델링을 살펴보았다. 그리고 1970년대 Freudenthal가 주장한 수학화를 분석하여 수학적 모델링과 비교분석하였다. 또한, 1980년대 이후 수학교육의 중심이 된 문제해결도 살펴보고, 이를 수학적 모델링과 비교분석하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권2호
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• pp.149-160
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• 2010

Composition of functions are important tool for producing associativity in mathematical model. However it is not properly treated in dealing together with the other operation, the addition +, of functions defined on real numbers. In this note, we will study mathematization of the construction of nearring axiom from relationships between the addition + and the composition $\circ$ of functions, comparing with those between the addition + and the multiplication of functions. Furthermore, we will suggest some helpful teaching methods of these mathematization in the secondary school mathematics.