• School Mathematics
• /
• v.11 no.1
• /
• pp.111-129
• /
• 2009

This paper is about didactical transposition, which is to transpose academic knowledge into practical knowledge intended to teach. The research questions are addressed as follows. 1. Are the 13 mathematics textbooks of the 10-Na level indisputable regarding with the didactical transposition, in terms that the order of arrangement and the way of explaining the knowledge of trigonometric functions being analyzed and that its logical construction and students' understandings are considered? 2. Can some transpositions for easier use of didactical manipulative, for more practical and for more principle based be proposed? To answer these questions, this research examined previous studies of mathematics education, specifically the organization of the textbook and the trigonometric functions, and also compared orders of arranging and ways of explaining trigonometric functions from the perspective of didactical transposition of 13 versions of the 10-Na level reorganized under the 7th curriculum. The paper investigated what lacks in the present textbook and sought a teaching guideline of trigonometric functions(especially about sector and graph, period, characters of trigonometric function, and sine rule).

• School Mathematics
• /
• v.16 no.2
• /
• pp.285-301
• /
• 2014

Because a development figure is treated restrictively in elementary school, not only there are brought out the concept image, but also the definition of the development figure in textbook in not unique. Furthermore, since the comparison and analysis of 'definition element' between the materials in textbook are nor carried out, its educational value as well as the teaching for concepts and objectives does not give rise to public discussion. In this note, we will investigate the definition and teaching of the development figure in Korea and Japan. And through three viewpoints of its definition and related debate, we will consider the fundamental understanding and objectiveness of a development figure, and suggest its mathematical application. This study will promote teachers's critical and didactical insight for the didactical transposition.

• Journal of Educational Research in Mathematics
• /
• v.8 no.2
• /
• pp.475-484
• /
• 1998

In this paper, we give descriptions that the choices made in the Knowledge modelling or representation in Computer Evironments can modify the meaning of this knowledge through a process similar to that of the didactical transpostion. Thus, they are likely to have effects on learning. These problems and phenomena are consequences of general constraints of computer and an algorithms built-in computers. Students may not learn the knowledge intended by teacher. Teacher is always on the alert for the changable mathematical knowledge in computer-based environments. It is an important role of teachers in new teaching and learning environment.

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

• Journal of Elementary Mathematics Education in Korea
• /
• v.19 no.4
• /
• pp.563-588
• /
• 2015

In elementary school, didactical transposition is inevitable due to several reasons. In mathematics, addition and multiplication are taught as binary operations, subtraction and division are taught as unary operations. But in elementary school, we try to teach all the four operations as binary operations by didactical transposition. In 'Mastering' the concepts of the four operations, the way of concept introduction is dealt importantantly. So it is different from understanding the four operations. In this study, we analyzed the four operations of natural numbers and fractions from two perspectives: concept understanding (how to introduce concepts and how to choose an operation) and connection between the operations. As a result, following implications were obtained. In division of fractions, students attempted a connection with multiplication of fractions right away without choosing an operation, based on the situation. Also, to understand division of fractions itself, integrate division of fractions presented from the second semester of the fifth grade to the first semester of the sixth grade are needed. In addition, this result can be useful in the future textbook development.

• Journal of Elementary Mathematics Education in Korea
• /
• v.14 no.3
• /
• pp.827-842
• /
• 2010

In this paper, actual didactical transposition and dramatization of designing patterns presented in 4th grade mathematics curriculum is critically reviewed. Patterns in designing patterns are not wallpaper patterns generally. The method of designing new patterns using unit given pattern are not the same as the method of designing wallpaper patterns. In the viewpoint of not designing wallpaper patterns, the context of designing new patterns using unit given pattern is said to be putting transparent stickers. In this paper, on the premise of this characteristics, the shape of unit given pattern, the method of designing new patterns using unit given pattern, and the rule of putting unit given patterns continually are critically discussed. The shape of unit given pattern have to be square actually. In designing new patterns using unit given pattern, if the regularities of designing new patterns can be presented, any regularity is fine. Even though the relationship between new patterns and wallpapers designed by using unit given pattern is not clear, in that these two patterns can not be unrelated, designing new patterns using unit given pattern could be an example of wrong elementarization(Freudenthal, 1973).

• East Asian mathematical journal
• /
• v.31 no.4
• /
• pp.569-585
• /
• 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.

• School Mathematics
• /
• v.4 no.1
• /
• pp.111-125
• /
• 2002

In this study, we studied some examples using GSP(Geometer's SketchPad) in the process of problem solving that is explained by G. polya. After reconsidering examples, we tried to show that using GSP can help student's intuitive thinking, investigative activities, reflective thinking. Especially, in the three phase of problem solving(understanding the problem, devising a plan, looking back), mathematics teachers may using GSP in order to helping student's understanding. Besides, we tried to suggest the direction to use GSP more adequately in the teaching and Beaming mathematics. First of all, Mathematics teachers using GSP in their class must have ideas how to use it. And they have to be careful on the didactical transposition of mathematical knowledge in the computer-based learning. They also have to lead students move from activities with GSP materials to carrying out the problem solving plan and reflection activities.

• Journal of Educational Research in Mathematics
• /
• v.15 no.4
• /
• pp.445-459
• /
• 2005

Statistics education is considered within the mathematics curriculum and, thus, can be integrated into other areas of mathematics. However, statistical concepts and thinking skills have to be considered as very different from those of other areas. It is possible to make statistics more meaningful for the learner by making definitions or explanations of concepts in textbooks more clear and consistent. In 'Math I' and 'Probability & Statistics' of the 7th curriculum, the definitions of sample standard deviation are different, which might confuse students. In this study, firstly, some issues relevant to sample standard deviation concept are discussed through the analysis in terms of didactical situation and curriculum. Secondly, the characteristics of sample standard deviation concept as a scholarly knowledge are examined. Finally, the characteristics of didactic transposition of sample standard deviation concept in Japanese, American, and British textbooks are investigated and some suggestions are elicited.

• School Mathematics
• /
• v.15 no.4
• /
• pp.759-783
• /
• 2013

Both curriculum and textbooks play an important role in the process of didactical transposition from mathematics as a science to school mathematics. The 2009 revised national curriculum for mathematics introduced the system of grade-band, so its achievement criteria for mathematical contents tend to be addressed more and less generally in the curriculum. We need to investigate whether the achievement criteria were applied meaningfully in elementary textbooks for mathematics. This study aims to recognize the connection between the curriculum and the textbooks and make a suggestion for composing the following curriculum and its textbooks. To do this, we analyzed the mathematics textbooks for 1~2 grades in relation to the mathematical contents as per reconstructed one of curriculum achievement criteria, the mathematical terms and symbols, and the mathematical processes -mathematical problem solving, mathematical reasoning, mathematical communication. Based this analysis, futhermore, this study includes some didactical discussions and implications for development of mathematics textbooks in 3~4 and 5~6 grade-bands.