• Communications of Mathematical Education
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• v.12
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• pp.125-139
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• 2001

올해부터 7차 수학 교과과정에서 중학 1학년 학생을 대상으로 7단계 수학이 시작되었다. 7차 수학교육은 단계형, 수준별 학습을 명시적으로 도입하였다. 교육과정은 수학교사의 교수학적 전문 능력을 요구하고 있다. 따라서 각 학교와 수학교사들은 7차 수학 교과과정을 수행하기 위하여 적절한 교수 방법 및 운용 계획 등을 찾고 있다. 수학 교과과정이 성공적인 모든 교실 수업으로 실현되기 위하여 교육과정, 교육 상황, 과제들을 살펴보았다. 중등수학 교육과정의 유연성 및 교수학적 측면을 이해하기 위한 배경과 과제를 소개한다.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.57-71
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• 2010

Similarity between concept and concept, principle and principle, theory and theory is known as a strong motivation to mathematical knowledge construction. Metaphor and analogy are reasoning skills based on similarity. These two reasoning skills have been introduced as useful not only for mathematicians but also for students to make meaningful conjectures, by which mathematical knowledge is constructed. However, there has been lack of researches connecting the two reasoning skills. In particular, no research focused on the interplay between the two in didactic transposition. This study investigated the process of knowledge construction by metaphor and analogy and their roles in didactic transposition. In conclusion, three kinds of models using metaphor and analogy in didactic transposition were elaborated.

• School Mathematics
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• v.11 no.4
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• pp.707-722
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• 2009

Various theories of mathematics education which have been considered by many European researchers particularly, in France, recently are introduced. The Anthropological Theory of the didactic discussed by Chevallard will be briefly introduced. Then the praxeology as Anthropological model according to Chevallard's theory will be discussed. The necessity of Anthropological Theory, its background of development through transition process of didactic, and its basic elements will be discussed further. Additionally, teaching limit of sequences in high school mathematics will be suggested according to the theory.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.203-221
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• 2017

The purpose of this study is to suggest didactical principles for using mathematical teaching aids and to applicate didactical principles in a relation with curriculum. First, we meta-analyzed related literature to suggest didactical principles for using mathematical teaching aids. And we suggested didactical principles as follows: principle of activities, principle of instruments, principle of learning. Using mathematical teaching aids with didactical principles in mind would help avoiding situations in which mathematical teaching aids are only used as interesting tools. Second, we concretized the meaning to applicate didactical principles and use mathematical teaching aids in a relation with curriculum. We considered domain, key concept, function, achievement standard, which were presented in the curriculum of mathematics, and suggested concrete activities. Third, we produced two designs for lessons on incenter and circumcenter of triangle and linear function's graph using mathematical teaching aids.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.469-489
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• 2017

Teachers are the primary agent of didactic transposition. In the process of transposing mathematical knowledge presented in mathematics curriculum and textbooks to mathematical knowledge for teaching in a classroom, teachers are significantly influenced by not only teachers' personal factors but also circumstances and constraints existing inside and outside of classrooms. Therefore, to understand teachers' didactic transposition, we need to analyze influence of institutional and socio-cultural factors on teachers' didactic transposition process. Identifying factors and constraints influencing teachers' didactic transposition provides important opportunities to have a deeper understanding of teachers' didactic transposition and develop their classroom practices. This study analyzed secondary mathematics teachers' perspectives on didactic transposition by exploring factors influencing their didactic transposition process using their reflective journal about their classroom practices. As a result, we identified the five factors influencing participating teachers' didactic transposition. We also found that different teachers had different extent of influence of five factors on their didactic transposition. Based on the results, we discussed ways to help mathematics teachers' didactic transposition.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.891-907
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• 2010

This study analyzed the Fundamental Theorem of Calculus from the historical, mathematical, and instructional perspectives. Based on the in-depth analysis, this study suggested an alternative way of teaching the Fundamental Theorem of Calculus.

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

• Communications of Mathematical Education
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• v.13 no.1
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• pp.337-360
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• 2002

그래프 능력을 바탕으로 한 함수의 그래프 표현은 함수 교수 ${\cdot}$ 학습상 중요한 위치를 차지한다. 그러나 부적절한 함수 그래프 과제 교수 ${\cdot}$ 학습 방법은 학생들의 지식 구성, 이해 과정에 영향을 주면서 수학적 오류를 형성하게 하였다. 그러므로 체계적인 오류 분석을 기반으로 한 좋은 교수학적 프로그램을 통해 수학적 오류를 예견하고 학습 과정에서 그것을 잘 처치, 활용하는 것이 효과적인 함수 교수 ${\cdot}$ 학습을 위해 요구된다. 본 연구에서는 지필 환경하에서 함수 그래프 과제를 수행한 학생들에게서 일반적으로 나타나는 수학적 오류를 점검하고, 새로운 교육용 테크놀러지 환경하에서 이러한 수학적 오류가 변화되는 과정을 살펴보고자 하였다. 첫 번째 연구 문제를 위해 고등학생 119명을 대상으로 양적 연구를 실시하였으며, 함수에 대한 개념 이미지로부터의 오류가 가장 많이 나타났음을 확인할 수 있었다. 두 번째 연구문제를 위해 고등학생 2명을 대상으로 사례 연구를 실시하였는데, 그 결과 기존의 수학적 오류가 새로운 교수학적 환경하에서 변화, 극복되는 것을 확인할 수 있었다.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.377-394
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• 2022

Criticism has been raised that the way of teaching weights in the 3rd and 4th graders of elementary school is different between the 2015 revised math curriculum and the 2015 revised science curriculum, causing confusion among elementary school teachers and students. This study tried to confirm the social recognition that should be considered in the process of didactic transformation which means transformation from knowledge to used into knowledge to taught and to compare the variations of didactic transformations differently according to didactic intentions. The research analyzes and synthesizes the root of the meaning of weight, weight in the international standard system of units SI, weight implemented in Korean mathematics curriculum and textbooks, Singaporean mathematics curriculum and textbooks, USA mathematics curriculum and textbooks, and Korean science curriculum and textbooks. Through this analysis, a pedagogical perspective on how to define and teach weight in elementary school as knowledge to be taught was derived.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.459-478
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• 2013

Didactic transposition refers to an adaptive treatment of mathematical knowledge into knowledge to be taught. This study intends to investigate how mathematical knowledge was modified in mathematics textbooks and lessons. This study identified examples of didactic transposition in mathematics textbooks and lessons in Korea and those in the U.S., The examples identified were FOIL method, trigonometry using s, c, t in writing style, order of operations(PEMDAS), area of a circle and circumference, order of prefixes in the metric system, trigonometry(SOH, CAH, TOA), operations on integer, and regular polyhedra. These examples were classified into the two categories, one for mnemonics, and one for concreteness and intuitiveness. Then a survey was conducted for in-service teachers in Korea and those in the U.S. to evaluate the appropriateness and the necessity of didactic transposition. Lastly, the potential didactic phenomena, meta-cognitive shift which may occur with these examples were discussed.