• Journal of Educational Research in Mathematics
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• v.9 no.2
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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.

• School Mathematics
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• v.1 no.2
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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'.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.83-100
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• 2007

Normality is one of the most common assumptions made in sampling and statistical inference procedures without suffering from lack of attention. Its results may lead to an invalid conclusion. We present several testing procedures that can be used to evaluate the effects of departure from normality using concrete examples by hand or with the aid of Minitab. The goal is to influence prospective teachers in order to learn statistical concepts and techniques for testing normality on the basis of the didactical theory.

• Research in Mathematical Education
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• v.13 no.4
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• pp.349-377
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• 2009

In this work we present a study undertaken with in-service mathematics teachers of primary and secondary school where we describe and analyze the didactical competences needed to implement an innovative design in geometry applying Van Hiele's models. The relationship between such competences and an ideal teacher profile is also studied. Teachers' epistemology is established in terms of didactical competences and we can see that this epistemology is an element that helps us understand the difficulties that teachers face in practice when implementing an innovative curriculum, in this case, geometry based on the Van Hiele theory.

• East Asian mathematical journal
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• v.31 no.4
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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.

• The Mathematical Education
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• v.54 no.4
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• pp.365-383
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• 2015

Factorization asks the recognition of the structure of polynomials, compared to polynomial expansion with process characteristic. Therefore it makes students experience a lot of difficulties. This study aims to figure out causes of the difficulties by identifying students' cognitive characteristics in factorizing in the perspective of 'structure sense'. To do this, we gave six factorizing problems of three types to middle school students and selected six participants as interviewees based on the test results. They were classified into two categories, structure sense and non-structure sense. Through this interview, we figured out the interviewee's cognitive characteristics and the causes of difficulty in the perspective of structure sense. Furthermore, we suggested some didactical implications for encouraging structure sense in factorizing by identifying assistances and obstacles for recognition of structures.

• East Asian mathematical journal
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• v.35 no.2
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• pp.259-275
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• 2019

The researches on the didactic transposition in mathematics education have been conducted almost for 35 years in Korea. Those studies have been quite usually interested in the extreme phenomena such as Topaze Effect, Meta-Cognitive Shift, etc. However, the understanding on the meaning and roles of contextualization and decontextualization in the theory of didactic transposition is needed theoretically in mathematics education and also practically in school mathematics. In particular, for the purpose of managing the efficient instruction on the class, the proper and plentiful role and application of the contextualization is very important in the aspect of the teacher as well as the learner respectively. By this reason, this study investigates the meaning and role of reflection based on the concept of contextualization.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.699-722
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• 2015

Based on Lagrange's general theory of algebraic equations, by applying the solution of the equation using the relationship between roots and coefficients to the high school 1st grade class, the purpose of this study is to recognize the significance of symmetry associated with the solution of the equation. Symmetry is the core idea of Lagrange's general theory of algebraic equations, and the relationship between roots and coefficients is an important means in the solution. Through the lesson, students recognized the significance of learning about the relationship between roots and coefficients, and understanded the idea of symmetry and were interested in new solutions. These studies gives not only the local experience of solutions of the equations dealing in school mathematics, but the systematics experience of general theory of algebraic equations by the didactical organization, and should be understood the connections between knowledges related to the solutions of the equation in a viewpoint of the mathematical history.

• School Mathematics
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• v.4 no.1
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• pp.15-27
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• 2002

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them. Definitions use din academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about let·els of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.