• Journal for History of Mathematics
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• v.21 no.1
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• pp.157-166
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• 2008

Mathematical communication is an important goal of recent educational reform. The NCTM's Principle and Standards for School Mathematics, consulting an emphasis on mathematical discourse from 1991 Professional Standards for Teaching Mathematics, has a Communication Standard at each grade level. This paper examines Socrates's educational philosophy and the mathematical dialogue in Plato's. Further it examines mathematical dialogues between teachers and students from antiquity through the nineteenth century.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.459-475
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• 2012

Epistemology in which only subject and object of cognition exist can't play a role well in the society. In this paper we analyze structuralism which discusses linguistic and social conditions that make subject of cognition possible and semiologic epistemology's philosophical base with three keywords: subject, structure and discourse. Signification by the signs' relation not object of cognition and construct of subject make meaning of sign in network of signs. The construct exists before subject and subject can exist in the structural order. In understanding and analyzing learning of mathematics, this point of view makes you consider the other problems besides construction by subject.

• School Mathematics
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• v.18 no.3
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• pp.733-747
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• 2016

To describe mathematics learning relying on a priori assumptions about the learners has a risk of assuming the learners as well-prepared subjects. In this study we investigate the epistemological perspective of Gilles Deleuze which is expected to give overcome this risk. Then we analyze the constructivist's epistemology and prior discussions about learning mathematics in the preceding studies accordingly. As a result, a priori assumption on which students are regarded as well-prepared for learning mathematics is reconsidered and we propose a new model of thought to highlight the involuntary aspect of the occurrence of thinking facilitated by the encounter with mathematical signs. This perspective gives a new vision on involuntary aspects of mathematics learning and the learner's confusion or difficulty at the starting point of learning.

• 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.

• 한국정보교육학회:학술대회논문집
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• 2004.08a
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• pp.87-93
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• 2004

본 논문에서는 미래 정보 사회에의 핵심인 정보교육에 적합한 컴퓨터 교육의 방향을 초등교육을 중심으로 논하였다. 이를 위해 관련 선행 문헌연구를 통해 정보사회에서의 컴퓨터 교육의 필요성과 방향을 살펴보고, 현재 7차 교육과정에서의 컴퓨터 교육을 분석하여 문제점을 제기하였다. 또한, ACM과 IEEE의 컴퓨터 과학 분야의 교육과정 연구를 바탕으로 새로운 초등 컴퓨터 교육에서의 교육과정의 방향을 수학적, 과학적, 사회적, 철학적, 통합적 관점으로 고찰하여 제시하였으며, 이를 바탕으로 초등 컴퓨터 교육의 목표와 내용을 재구성하였다. 본 연구는 향후 8차 교육과정의 개편에 있어서 컴퓨터 교육의 발전에 도움을 주리라 기대된다.

• Journal for History of Mathematics
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• v.32 no.6
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• pp.301-313
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• 2019

This paper briefly examines the Book of Changes that is the philosophical background of East Asian ancient mathematics and its collection of complementary(ShíYì), and then examines the structure and contents of GyeSaJeon, which explains the basic principles of Book of Changes as one of ShíYì. GyesaJeon reveals the unique East Asian thought of dealing with numbers in the process of explaining the formation of Eight-Gwae(Bagua) and Sixty-four-Gwae based on Yin-Yang theory. It understands numbers in terms of symbols, not quantitative, and use them to represent characteristics or hierarchy of certain classes, and to explain certain principles. Based on this, the implications of using East Asian mathematics history in the mathematics classroom are discussed.

• School Mathematics
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• v.15 no.4
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• pp.667-682
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• 2013

Though teachers' lesson plays, this article analysed teachers' knowledge for mathematical teaching about mathematical definitions and their pedagogical difficulties in teaching defining. Although the participant teachers didn't transmit definitions to students and suggested possible definitions of the given geometric figure in their imaginary lessons, they didn't teach defining as deductive organization of properties of the geometric figure. They considered mathematical definition as a mere linguistic convention of a word, so they couldn't appreciate the necessity of deductive organization in teaching definitions, and the arbitrary nature of mathematical definitions. Therefore, for learning to teach definitions differently, it is necessary for teachers to reflect the gap between the everyday and mathematical definitions in teachers'education.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.23-30
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• 2005

Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.1-19
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• 2012

Kant defines mathematical cognition as the cognition by reason from the construction of concepts. In this paper, I inquire the meaning and the characteristics of the construction of concepts based on Kant's theory on the sensibility and the understanding. To construct a concept is to exhibit or represent the object which corresponds to the concept in pure intuition apriori. The construction of a mathematical concept includes a dynamic synthesis of the pure imagination to produce a schema of a concept rather than its image. Kant's transcendental explanation on the sensibility and the understanding can be regarded as an epistemological theory that supports the necessity of arithmetic and geometry as common core in human education. And his views on mathematical cognition implies that we should pay more attention to how to have students get deeper understanding of a mathematical concept through the construction of it beyond mere abstraction from sensible experience and how to guide students to cultivate the habit of mind to refer to given figures or symbols as schemata of mathematical concepts rather than mere images of them.

• School Mathematics
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• v.5 no.4
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• pp.521-540
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• 2003

The processes of mathematics development and the results of it are always those of making a conquest of the circumscription by historical inevitability within the historical circumscription. It is in this article that I try to show this processes through the history of calculus. This article develops on the basis of the dialectical materialism. It views the change and development as the facts that take place not by individual subjective judgments but by social-historical material conditions as the first conditions. The dialectical materialism is appropriate for explaining calculus treated in full-scale during the 17th century, passing over ahistorical vacuum after Archimedes about B.C. 4th century. It is also appropriate for explaining such facts as frequent simultaneous discoveries observed in the process of the development of calculus. 1 try to show that mathematics is social-historical products, neither the development of the logically formal symbols nor the invention by subjectivity. By this, I hope to furnish philosophical bases on the discussion that mathematics teaching-learning must start from the real world.