• Journal for History of Mathematics
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• v.20 no.4
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• pp.153-174
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• 2007

The concept of Function is not just a single concept but an integrated concept that includes various mathematic topics such as arithmetics, geometry and so on. Therefore, the concept of function is the basic principal underlying mathematics. Moreover, we should think of function as conceptual expedient for understanding the phenomena in the variously changing real world. Therefore in this article, I would like to consider the concept of an integrated function through historical investigation. Especially, from the middle ages to the 19th century, representation which related to the function has been evolved, and therefore, I will consider function as an integrated concept through changing the concept of function.

• Education of Primary School Mathematics
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• v.1 no.1
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• pp.3-22
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• 1997

본 연구는 첫째로는 수학교육에서 패턴이 강조되는 이론적 근거를 찾고자 역사적 맥락에서 수학의 성격변화를 탐색하였다. 수학의 성격 변화를 통하여 수학은 수의 탐구, 기하의 탐구, 운동ㆍ변화ㆍ공간의 탐구, 수학 연구의 도구에 대한 탐구로 그 영역을 점차 확대하여 왔으며, '수학은 패턴의 과학이다'라는 정의는 수학이 폭넓어짐에 따라 수학이 무엇인가에 대한 수학의 본성에 접근하는 논의라고 할 수 있다. 이러한 수학에 대한 새로운 관점은 수학교육의 새로운 방향 모색에 시사하는 바를 살펴보고, 특히 수학교실의 변화에 따른 패턴의 강조를 살펴보았다. 둘째로는 수학적 패턴을 밝힘과 동시에 수학 교육에서 수학적 패턴 분석의 틀을 마련하고자 수학적 패턴의 유형화를 시도하였다. 패턴의 속성에 따른 유형화와 패턴의 생성 방식에 따른 유형화를 통하여 수학적 패턴의 유형을 마련하였다. 초등학교 수학에서 다루어지는 패턴은 어떠한 것인가를 현행 4학년 수학교과서 및 익힘책에 제한하여 유형화한 틀로서 조사 분석하였다. 셋째로는 수학적 패턴에 관한 지도 방안의 모색으로서, 지도의 기본 방향을 설정하고 수학적 패턴에 관한 교수 전략을 마련하였다. 교수전략은 크게 패턴에서의 규칙 찾기, 패턴을 변형ㆍ확장하기, 자신의 새로운 패턴 만들기, 패턴을 수학적으로 설명하기로 나누고, 각각에 3-4개의 세부 전략과 세부 전략에 따른 예를 제시하였다.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.229-241
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• 2009

This paper provides a review of the historical development story of the NCTM 1989 Standards based on perspective of history of U. S. mathematics education and research in the 1970s and 1980s. In contrast to other nations, the U. S. has always favored local over national control of education. But by 1983, mounting evidence of failures of U. S. education moved the authors of A Nation at Risk to recommend strengthened requirements, rigorous Standards, and higher expectations for all students. In response to A Nation at Risk, the NCTM began to develop the nation's first educational Standards. This paper satisfies the readers who desire to know the entire development story of the first Standards.

• 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 for History of Mathematics
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• v.17 no.3
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• pp.1-12
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• 2004

In the Analysis, there have been many cases of confusion on topological structure and uniform structure because they were dealt in metric spaces. The concept of metric spaces is generalized into that of topological spaces but its uniform aspect was much later generalized into the uniform structure by A. Weil. We first investigate Weil's life and his mathematical achievement and then study the history of the uniform structure and its development.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.177-188
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• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• Journal of Educational Research in Mathematics
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• v.17 no.1
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• pp.1-31
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• 2007

Negative numbers have been one of the most difficult mathematical concepts, and it was only 200 years ago that they were recognized as a real object of mathematics by mathematicians. It was because it took more than 1500 years for human beings to overcome the quantitative notion of numbers and recognize the formality in negative numbers. Understanding negative numbers as formal ones resulted from the Copernican conversion in mathematical way of thinking. we first investigated the historic and the genetic process of the concept of negative numbers. Second, we analyzed the conceptual fields of negative numbers in the aspect of the additive and multiplicative structure. Third, we inquired into the levels of thinking on the concept of negative numbers on the basis of the historical and the psychological analysis in order to understand the formal concept of negative numbers. Fourth, we analyzed Korean mathematics textbooks on the basis of the thinking levels of the concept of negative numbers. Fifth, we investigated and analysed the levels of students' understanding of the concept of negative numbers. Sixth, we analyzed the symbolizing process in the development of mathematical concept. Futhermore, we tried to show a concrete way to teach the formality of the negative numbers concepts on the basis of such theoretical analyses.

• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.99-114
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• 2009

Although they are interested in Linear Algebra not only in science and engineering but also in humanities and sociology recently, a study of teaching linear algebra is not relatively abundant because linear algebra was taken as basic course in colleges just for 20-30 years. However, after establishing The Linear Algebra Curriculum Study Group in January, 1990, a variety of attempts to improve teaching linear algebra have been emerging. This article looks into series of studies related with teaching matrix. For this the method for teaching the concepts of matrix in relation to historico-genetic principle looking through the process of the conceptual development of matrix-determinants, matrix-systems of linear equations and linear transformation.

• The Journal of the Korea Contents Association
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• v.14 no.6
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• pp.499-512
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• 2014

Architecture is usually seen as a product of art and technology. However, most historical buildings also exemplify various sophisticated principles of mathematics. Outstanding examples of architecture around the world such as Seokguram, Daewoongjun of Bulguksa, Muryangsujeon of Buseoksa, and the Parthenon provide students with a great opportunity to study their underlying mathematical properties and principles. The activity of identifying and investigating such mathematical principles in historical buildings enables students to realize that mathematics is a practical subject, and thus provides justification for the study and importance of mathematics. For the purpose of this study historical architecture was reviewed with this in mind in order to develop STEAM education materials focused on elementary school mathematics. The result of this study is as follows: first of all, appropriate examples of historical architecture were selected on the basis of the 2009 revised curriculum's content and teaching goals. These involved chapters on 'proportion', 'symmetry', 'movement of figures', 'building blocks', and 'triangles'. Secondly, a meta-analysis was performed on the historical buildings that clearly illustrate mathematical principles. Thirdly, STEAM education materials focused on elementary mathematics using architectural examples were developed which made actual application in classrooms possible. And lastly, surveys of professional groups were conducted to verify whether the produced materials were suitable teaching resources.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.59-72
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• 2007

There are three kinds of order of instruction in mathematics, that is, historical order, theoretical organization and lecturing organization-order. Simply speaking, each lecturing organization-order is a combination of two preceding orders. The problem is how to combine between them. In a recent paper, we concretely considered this problem for the case of the concept of angle. The present paper analogously discuss with the concept of vectors. To begin with, we investigate theoretical organization and historical order of the concept of vectors as materials for the construction of its lecturing organization-order. It enables us to establish 4 stages in historical order of the concept of vectors proper to its theoretical organization. As a consequence, we suggest several criteria and forms for constructing its lecturing organization-order.