• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.1-24
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• 2008

The purpose of this study is to uncover weaknesses in the constructivism in mathematics education and to search for ways to complement these deficiencies. We contemplate the relationship between the capability of construction and the performance of it, with the view of the 'Twofold-Structure of Mind.' From this, it is claimed that the construction of mathematical knowledge should be to experience and reveal the upper layer of Mind, the Reality. Based on the examination on the conflict and relation between the structuralism and the constructivism, with reference to the 'theory of principle' and the 'theory of material force' in Neo-Confucianist theory, it is asserted that the construction of mathematical knowledge must be the construction of the structure of mathematical knowledge. To comprehend the processes involved in the construction of the structure of mathematical knowledge, the epistemology of Michael Polanyi is studied. And also, the theory of mathematization, the historico-genetic principle, and the theory on the levels of mathematical thinking are reinterpreted. Finally, on the basis of the theory of twofold-structure, the roles and attitudes of teachers and students are discussed.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.129-142
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• 2004

These days, constructivism has become a central theory in mathematics education. A essential concept in constructivism is 'construction' and the meaning of construction of mathematical knowledge is a core issue in mathematics educational field. In the basis of Dewey's epistemology, this article is trying to explicate the meaning of construction of mathematical knowledge. Dewey, Kant and Piaget coincide in construction of knowledge from the viewpoint of the interaction between mind and environment. However, unlike Dewey's concept, Kant and Piaget are still in the line of traditional realistic epistemology. Dewey's concept of construction logically implies teaching-learn learning principles. This can be named as a principle of genetic construction and a principle of progressive consciousness.

• School Mathematics
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• v.18 no.3
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• pp.571-587
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• 2016

Nam(2008a) suggested that the role of teacher for helping students to learn mathematical structures should be the manifestor of tacit knowledge. But there have been lack of researches on embodying the manifestation of tacit knowledge. This study embodies the manifestation of tacit knowledge by showing that exemplification is one way of manifestation of tacit knowledge in terms of goal, contents, and method. First, the goal of the manifestation of tacit knowledge through exemplification is helping students to learn mathematical structures. Second, the manifestation of tacit knowledge through exemplification intends to teach students mathematical structures in the tacit dimension by perceiving invariance in the midst of change. Third, the manifestation of tacit knowledge through exemplification intends to teach students mathematical structures in the tacit dimension by constructing explicit knowledge creatively, reflection on constructive activity and social interaction. In conclusion, exemplification could be seen one way of embodying the manifestation of tacit knowledge in terms of goal, contents, and method.

• School Mathematics
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• v.12 no.2
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• pp.151-176
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• 2010

This research aims to conduct the teaching experiment based on the constructivism to elementary preservice teachers and report on how they construct and develop the mathematical knowledge on ratio concept. Furthermore, this research aims to examine the significances and difficulties of "constructivist teaching experiment" which are conceived by elementary preservice teachers. As the results of this research, I identified the possibilities and limits of mathematical knowledge construction by elementary preservice teachers in the "constructivist teaching experiment". And the elementary preservice teachers pointed out the significances of "constructivist teaching experiment" such as the experience of prior thinking on the concept to be learned, the deep understanding on the concept, the active participation to the lesson, and the experience of learning process of elementary students. Also they pointed out the difficulties of "constructivist teaching experiment" such as the consumption of much time to carry out the constructivist teaching, the absence of direct feedbacks by teacher, and the adaption on the constructivist lesson.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.1-12
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• 2003

이 논문은 수학적 개념의 뜻과 과 중요성을 살펴본 다음, 연구자가 소속되어 있는 한국의 대학생과 연구자가 연구년 동안 강의한 바 있는 미국의 대학생이 갖고 있는 수학적 개념의 수준에 대하여 조사하여 보고, 그 차이점을 비교하여 수학교육의 개선을 위한 시사점을 찾아보고자 하였다. 본 연구는 수학적 개념을 수학적 지식의 구성, 수학적 지식의 구조, 수학적 지식의 현상, 수학을 행하기, 수학적 아이디어의 가치 인식, 구성으로서의 학습, 유용한 노력으로서의 수학으로 분류하고 각 개념에 대한 양국 학생들의 인식 정도를 설문조사 방식으로 조사하였다. 본 연구에서 한국 학생들은 수학적 개념에 대한 7개의 영역 중에서 '수학적 지시의 현상', '수학을 행하기'를 제외한 5개의 영역에서 더 높은 수준을 보였다. 앞으로 한국의 수학교육은 수학을 실제로 행하는 활동을 더욱 강조하여야 할 것이다.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.1-14
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• 2005

Piaget는 인류가 지식을 구성해 온 방식과 유사한 방식으로 어린이들도 자신들이 학습해야 할 지식을 학습할 수 있다고 가정한다. Kamii는 이 가정을 확인하고자 하는 열망으로 실험교수법을 이용한 수학수업을 실시하였다. 본 고에서는 Kamii가 얻은 결과 중 곱셈에 대한 결과를 발생론적 인식론 입장에서 논의가 이루어 질 것이다. 이 논의는 어린이들이 구성해 가는 지식이 선대인들이 사용하던 지식과 유사하다는 점과 어린이들이 구성해 가는 지식이 완성된 지식의 형태를 갖출 수 있다는 점을 중심으로 이루어진다. 또한, 그 결과로부터 전통적인 수학 교수법에 변화가 있어야 함을 발생론적 인식론을 적용한 수학 수업의 특징과 비교하면서 시사점을 논의하고자 한다.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.443-455
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• 2002

정보화시대를 맞아 어느 때보다도 활발히 전교과에 걸쳐 학생의 의사소통의 능력을 향상하기 위한 다양한 방법이 모색되고 있다. 학교현장의 수학교육자는 수학교수-학습에서 어떤 상호작용이 일어났는지, 특히 다루기 쉬운 도구로써 계산기가 주어졌을 때 어떻게 학생의 지식 발달이 언어적 상호작용에서 이루어지는지를 알아야 한다. 본 연구는 이러한 학생의 상호작용을 분석할 때 필요한 분석도구를 개발하는 것이다. 예비연구와 본 연구를 통해 언어적 상호작용의 구성요소가 세 영역, 즉, 지식구성 진술, 사회적 상호작용 진술, 그리고 교사의 교육어 진술에서 개발되었다. 본 연구에서 개발한 자료를 이용하여 특히 학생의 지식 구성 발달에 따른 상호작용의 구성요소의 특징을 파악하고 이에 필요한 언어적 상호작용의 역할과 활성화 방안을 모색하는 연구가 가능하다.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.355-369
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• 2009

Though there is no agreement on the definition of analogical reasoning, there is no doubt that analogical reasoning is the means of mathematical knowledge construction. Mathematicians generally have a tendency or desire to find similarities between new and existing Ideas, and new and existing representations. They construct appropriate links to new ideas or new representations by focusing on common relational structures of mathematical situations rather than on superficial details. This focus is analogical reasoning at work in the construction of mathematical knowledge. Since analogical reasoning is the means by which mathematicians do mathematics and is close]y linked to measures of intelligence, it should be considered important in mathematics education. This study investigates how mathematicians used analogical reasoning, what role did it flay when they construct new concept or problem solving strategy.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.79-112
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• 2016

The purpose of this research is to find the effects of learner-centered instruction based on constructivism (LCIC) on their knowledge generation level and reasoning ability. To look for them, after fraction units are re-planed for implementing LCIC, instructions using it provide students in a class. From the data, some conclusions can be drawn as follows: LCIC has more positive influence of students on recall ability, generation ability, and reasoning ability than tractional instruction method. With the data it can be said that the interaction exists between learners' reasoning ability and generation level.

• 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.