• Journal for History of Mathematics
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• v.23 no.2
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• pp.59-74
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• 2010

Though considering of philosophy of mathematics can be optional to theoretical mathematicians, that of philosophy of mathematics-education is supposed to be indispensible to mathematics-educators. So it is natural for mathematics-educators to ask what kind of philosophy might be more desirable for mathematics-education. In this context, this essay reviews two kinds of major philosophy of mathematics, Platonism and formalism. However it shows that humanism could be more plausible alternative philosophy of mathematicseducation. In the course of entailing such a result it introduces an episode of lecture for Laplace-transformation as a speculative evidence from experience.

• Journal of Elementary Mathematics Education in Korea
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• v.4 no.1
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• pp.39-55
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• 2000

The purpose of this research is to analyse Korean elementary mathematics curriculum taking a philosophical view of mathematics education. In this research, 1 will analyze not only the current elementary mathematics curriculum but also the past ones. There have been intermittently quantitative and external analysis so far to comprehend the elementary mathematics curriculum. But, I thought we also need qualitative and internal comprehension and examined the curriculums through a philosophical analysis. Generally, mathematics curriculums at every period have their own mathematical philosophy consciously or tacitly. And, the school mathematics is the practice of mathematics curriculum based on that mathematical philosophy. Mathematical curriculum reflects both the philosophical aspect in mathematical philosophy that forms the background of the mathematical curriculum and the sociological aspect in real-class that is the output of the curriculum. With this view, the logic of social constructivism can be an appropriate way that leads mathematical philosophical analysis and sociological analysis in mathematics education. So, I comprehend the tendency of the Korean elementary mathematics curriculum from the first to the seventh through the philosophical views. In view of the results so far achieved, after the second half of the 20th century, the Korean mathematical curriculums mainly have the tendency from the Ideology of progressive educator (the first) to of technological pragmatist (the second), from that of old humanist (the third and forth) to progressive educator (the fifth and sixth), and lastly that of social constructivism (the seventh).

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.599-615
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• 2015

Teachers' philosophies have not been emphasized enough in the current teacher education curriculum even though teacher's philosophy palys a critical role in schools and classrooms. The examination on pre-service teachers' teaching philosophies is necessary to improve teacher education curriculum so that teaching philosophies are often discussed in the courses of 'pedagogical content knowledge' as well as 'general education.' Therefore, the current study investigated 44 pre-service teachers' teaching philosophies, their sub domains, and relationships among the sub domains. The previous studies regarding mathematics teacher's teaching philosophy were more about 'teacher's belief' and employed deductive inference approach using surveys or questionnaires. These studies commonly pointed out that there were three major domains of 'belief on mathematics itself,' 'belief on teaching mathematics,' and 'belief on learning mathematics.' As these three domains of teacher's philosophy has been strengthened, there were very few studies examining the other potential domains of teacher's teaching philosophy. According to the findings of the present study, which employed inductive inference approach and pre-service teachers' free essay writing assignment, 'belief on teacher's role in mathematics classroom,' 'belief on the purpose of mathematics education,' and 'motivation to be a mathematics teacher' were additionally illuminated as sub domains of teacher's teaching philosophy. Moreover, the interrelationship among the sub-areas of teacher's teaching philosophy was disclosed. Specifically, 'belief on the purpose of mathematics education' and 'motivation to be a mathematics teacher' influenced the other sub domains. This implies that the relationships among the sub domains of teacher's teaching philosophy were more likely to be causal and vertical relationships rather than independent and parallel relationships. Finally, the findings from the current study provide implications indicating how pre-service teachers' teaching philosophies might be established in mathematics education courses for future research and education.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.59-74
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• 2015

It is an increasing research area to explore mathematics learning from discursive perspectives. However, there have been little studies conducted on why and how discursive perspectives in mathematics learning were adopted and developed. Especially, not much discussion has been done on the later Wittgenstein's philosophical stance in terms of the relationship between language and thought as a background of discursive approach to learning mathematics. This study aims to explore the later Wittgenstein on language to get better understanding about discursive approaches to mathematics learning. For the attainment of this aim, first the later philosophy is compared with the former philosophy in depth. Then the later philosophy is discussed focusing on how his point of view on the world and the language have been changed. After providing an account of his later philosophy, it is clarified that what is discursive approaches to learning mathematics and how this philosophy brace the approaches. This research concludes with implications and limitations, as well as suggestions for future researches.

• Communications of Mathematical Education
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• v.15
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• pp.1-7
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• 2003

수학사 및 수리철학에 관한 연구는 교사양성 대학에서 더욱 강조되어야 할 부분임에도 불구하고 그에 관한 연구가 미진하다. 자연대의 수학과는 수학 그 자체가 중요하겠지만, 교사양성 대학에서는 수학 내용자체 뿐만 아니라, 수학의 역사적인 측면과 수학에 관한 인식론적인 측면이 함께 요구되어 진다. 절대적인 것으로 인식되어 온 수학에 대한 잘못된 선입견은 수학교육에도 심각한 악영향을 끼칠 수 있다. 그러나 괴델의 불완전성 정리 등으로 인해 수학에서의 논리체계는 더 이상 절대적이지 않다는 것을 알 수 있다. 본 연구에서는 숱한 오류들의 극복을 통해 발전해 온 수학사적인 측면과 그로 인하여 수학에 관한 인식론적 변화를 수학에서의 큰 사건들을 중심으로 살펴보고자 한다. 구체적으로 유클리드 기하에서 비유클리드 기하의 발견, 칸토어의 무한한 역설의 발생, 역설을 극복하기 위한 수학기토론의 탄생, 괴델의 불완전성 정리로 이어지는 과정들을 살펴보고, 그로 인해 도출되어지는 수학교육적 시사점을 논의해 보며, 이르르 바탕으로 교사양성 대학에서의 수학사 및 수리철학 강좌의 운영 방안을 제시한다.

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.495-508
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• 2005

This study focused on what philosophy of education based on theory of Dewey has to be involved in teacher professional development program. In this view, an attempt was made to identify characteristics and ultimate goal of professional development program. Finally, this paper also discussed the design and the process of the professional development program based on the principles of reflective thinking and psychological observation by Dewey in order to connect theory with practice as a model which is for conducting professional development program for a group of mathematics teachers.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.33-52
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• 2004

The paper is analyzed the mathematics curriculum of Korea and the philosophy of the mathematics education in the history of mathematics education. We have found that the various philosophy of Western mathematics education have led us to various views of the mathematics curriculum of Korea. This change of the mathematics curriculum in Korea have important implications to the didactics of mathematics. This study tried to find out the direction of outlook on the mathematics education in the future.

• School Mathematics
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• v.5 no.2
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• pp.151-165
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• 2003

So far there have been intermittently quantitative and syntactic analyses of the past elementary mathematics curriculums to comprehend elementary mathematics education in Korea. However, we think we also need qualitative and semantic analyses to comprehend and examine the past elementary mathematics curriculums exactly and so to look out on our future elementary mathematics education. Generally, school mathematics curriculum reflects both the philosophical aspects of mathematics itself that form the background of the philosophy of mathematics education and the sociological aspects in real mathematics class that could be the output of the curriculum. With this view, the logic of the social constructivism can be an appropriate way that leads mathematical philosophical analysis and sociological analysis in mathematics education. With this kind of method of analysis we got the results that: the past Korean elementary mathematics curriculums mainly have the tendency from the ideology of the progressive educator(the 1st) to of the technological pragmatist(the 2nd), from that of the old humanist(the 3rd and 4th) to the progressive educator(the 5th and 6th) again, and lastly that of social constructivism(the 7th).

• Journal of Educational Research in Mathematics
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• v.16 no.3
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• pp.179-198
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• 2006

In This Paper, I call Johnson & Lakoff (1980; 1999)'s Experientialism or Experiential Realism or, Embodied Realism, Nunez(1995; 1997)'s Ecological Naturalism as Experientialism and try to investigate the possibility of their Experientialism to be a philosophy of mathematical education. This possibility is approached in the respect with the problem of objectivism and relativism. I analyzed the epistemological background of embodied cognition first and then mathematical epistemology of experientialism. Experientialism shares its Philosophical position partly with Dewey and Merleau-Ponty. Experientialists deny the traditional hypothesis of philosophy as such separability of subject and object, and of body and rationality and also They have better position of epistemology than that of Hamlyn, and of Social Constructivism. Therefore, They guarantee wider range of mathematical universality than Hamlyn and Social constructivist. I conclude that the possibility of Experientialism to be a philosophy of mathematical education depends on the success of its supporting the practical study on mathematics education.

• Communications of Mathematical Education
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• v.9
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• pp.327-333
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• 1999

21세기를 바로 앞두고, 우리 나라 수학 교육의 과거와 현재의 실태, 즉 수학교육의 목적, 교수 내용, 교수 방법, 평가 등을 철학적 관점과 심리학적 관점에서 역사적으로 재조명해 보는 것은 새로운 2000년대를 앞두고 의미 있는 일이 될 수 있다. 또한 이를 바탕으로 21세기에 우리 나라 수학 교육이 나아가야 할 방향을 세계적인 추세와 관련하여 제시해 보고자 한다.