• 대한수학교육학회지:수학교육학연구
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• 제9권2호
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• pp.473-491
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• 1999

The learning of mathematics happens in some situations. It is natural that students should learn mathematics in more appropriate situations. But, so far It has been hardly studied about concrete situation and milieu where math can be successfully taught. In today's math education, the situation of education as a external circumstance become realized more and more importantly with influence of open education. But they don't embody situation as an internal circumstance where the intrinsic concept of mathematics can be obtained. We started this thesis from this tried to answer it on the basis of Brousseau's question, have theory about the didactical situations. One of the purpose of this study is to understand the theory of didactical situations, which focuses on how we can elaborate situations which really make a mathematical notion function. In this study, It is attempted clarify some concepts of the theory of didactical situations. The other is to discuss about what the theory of didactical situations suggests us in math zeducation. The method of math teaching and learning and the teacher's role were discussed in the viewpoint of Brousseau's theory. Finally, We elaborated and presented some didactical situations which make the notion of the area of rectangle.

• 한국수학사학회지
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• 제20권2호
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• pp.89-108
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• 2007

많은 학생들에게 소수의 곱셈은 의미 있게 학습, 지도되지 못한다. 이와 관련하여, 이 글에서는 Dewey, Vergnaud, Brousseau의 관점에서 소수 곱셈의 본질은 비와 비례관계의 인식에 있음을 드러내었다. 이를 토대로 한국과 일본 교과서에서 소수곱셈을 다루는 방식을 비교하고 그 특징을 살펴본 후, 우리나라 교과서에서 소수곱셈을 보다 의미 있게 전개하기 위한 제언을 하였다.

• 한국수학사학회지
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• 제16권3호
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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.

• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.417-431
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• 1999

In this study, I consider Brousseau's theory of didactical situation focused on 'the development process of situations', and analyze some examples of didactical situation related to instruction of 'decimal' concept. To elaborate situations which really make a mathematical notion function, we have to analyze the essence of the notion, and to construct the situation which can be developed to situations of 'action-formulation-validation - institutionalization'. From this view, it can be said that the instruction of decimal concept in our country mainly lies in the situations of 'action' and 'institutionalization'. we have to provide more situations of 'formulation' and 'institutionalization' which can connect 'action' and 'institutionalization'.

• 대한수학교육학회지:수학교육학연구
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• 제16권1호
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• pp.43-58
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• 2006

이 연구의 목적은 브루소가 소개한 교수학적 계약에 관해 논의하는 것이다. 브루소는 수학과 수업 자체를 게임으로 모델 화하고 있는 바, 그 게임에는 나름대로 교사와 학생들이 지켜야 하는 여러 가지 숨겨진 규칙으로서의 교수학적 계약이 존재한다. 브루소는 수학과 수업의 어떤 숨겨진 규칙을 표현하기 위해 그것을 도입하였다. 그 규칙들은 암묵적이고 호혜적인 것으로, 특히 학생들이 위반하기 전에는 드러나지 않는다. 브루소는 교수학적 계약을 조작적으로 정의하기 위해 그것을 교사의 행동과 그것에 대응하는 학생의 행동으로 정의하였으나, 심리적 및 인식론적 차원에서 정의하지는 않았다. 그러나 교사의 교수 행동은 자신의 신념 체계와 인식론의 영향을 받는 만큼, 그에 대한 논의도 필요하다. 또, 브루소는 교사가 교수학적 계약을 위반하는 경우에 대해서도 충분히 논의하지 않고 있다.

• East Asian mathematical journal
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• 제31권4호
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• pp.569-585
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• 2015

Many mathematics teachers in characterization high schools have been troubled to teach students because most of the students have weak interests in mathematics and they are also lack of preliminary mathematical knowledges. Currently many of mathematics teachers in such schools teach students using worksheets owing to the situation that proper textbooks for the students are not available. In this study, we referred to Chevallard's didactic transposition theory based on Brousseau's theory of didactical situations for mathematical teaching and learning. Our lessons utilizing worksheets necessarily entail encouragement of students' self-directed activities, active interactions, and checking the degree of accomplishment of the goal for each class. Through this study, we recognized that the elaborate worksheets considering students' level, follow-up auxiliary materials that help students learn new mathematical notions through simple repetition if necessary, continuous interactions in class, and students' mathematical activities in realistic situations were all very important factors for effective mathematical teaching and learning.

• 대한수학교육학회지:수학교육학연구
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• 제11권1호
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• pp.223-238
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• 2001

Decimal fractions are the practical system of notations representing real numbers. The set of decimal fractions with the definition of comparison of decimal fractions and the identification of their double representations is essentially the field of real numbers. Therefore, we have to clarify the concept of decimal fractions. However, there are problematics that the aquisition of the concept of decimal fractions is not easy. In this paper, we attempt to eradicate the problematics relevant to the acquisition of decimal fractions discussed above and find the desirable direction of instruction of meaning for mathematical symbols: The case of decimal fractions. In J. Hiebert & decimal fractions. First of all, we clarify the essence of them - ratio, operator and linearity. And we compare and analyse the theories about decimal fractions of Resnick, Drexel, Brousseau and Hiebert and the contents of texts about decimal fractions in Korea. Finally, we suggest the efficient instruction methods which are faithful to the essence of decimal fractions and choose some methods among them to plan the classroom instruction and implement the methods in the classroom.

• 대한수학교육학회지:학교수학
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• 제4권3호
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• pp.483-494
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• 2002

A Situation-problem, one of the problems in school mathematics, plays a role as the starting point of teaming mathematics. It leads to construct knowledge which is a tool for solving the problems. Whether the problem is a situation-problem or not, it depends upon how to use that problem. Since posing situation-problems is accompanied by prior analysis and planning for teaching in the class, it is a difficult task. This paper focuses on the characteristics of situation-problems and on how their characteristics are realized in the process of classroom instruction. For this purpose, it analyzes the context of classroom instruction to which the 'puzzle problem' model suggested by Brousseau is applied. The model is considered as a typical situation-problem, which aims at proportionality and linearity. In addition, this paper suggests various sources of information that are useful in posing the situation-problems related to the ratio concepts.

• 한국수학사학회지
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• 제15권1호
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• pp.15-42
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• 2002

Dialectical Methods is the form in which thinking and being developed, according to Hegel. Every given definition removes itself necessarily and goes over to its contrary definition. The mutual struggle brings us to a new definition, which is richer and more concrete insofar as it embraces the original definition, but on a higher level. The purpose of this study is to enhancing student's creative thinking in mathematics by dialectical methods. The conclusions drawn from the results obtained in this study are as follows, First the introduction of dialectical methods to mathematics education had been made by Lakatos, Brousseau, Freudenthal. Second, the dialectical teaching methods in mathematics are developed from dialectical methods: the step of affirmation - the step of negation - the step of sublation. Third, the students who team mathematics by dialectical teaching methods are creative in its implications.

• 한국수학사학회지
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• 제26권4호
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• pp.259-275
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• 2013

It has been proposed since modern times that we need to consult the history of mathematics in teaching mathematics, and some modifications of this principle were made recently by Lakatos, Freudenthal, and Brousseau. It may be necessary to have a direction which we consult when modifying the history of mathematics for students. In this article, we analyse the elements of the cognitive interest in Hamilton's discovery of the quaternions and in the history of discovery of imaginary numbers, and we investigate the effects of these elements on attention of the students of nowadays. These works may give a direction to the historic-genetic principle in teaching mathematics.