• Journal for History of Mathematics
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• v.33 no.2
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• pp.115-132
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• 2020

Social awareness of mathematics and academic attitudes toward the value of mathematics education has kept changing according to the intellectual, political and religious contexts. In this article, we examine how mathematics was defined and recognized in liberal arts education of the Roman Empire and early medieval Western Europe. This study analyzes how mathematics was described in encyclopedic works written in the Roman era after the mid-second century BC and in the Western European monasteries and cathedral schools after the fifth century. Ancient Greek mathematics took a clear place in liberal arts education through encyclopedia writings and prepared a mathematics curriculum for medieval universities. I hope this study will contribute to understanding the origin and context of the mathematics curriculum of medieval universities.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.93-108
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• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Journal for History of Mathematics
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• v.30 no.6
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• pp.327-339
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• 2017

Recently industry goes through enormous revolution. Related to this, major changes in applied mathematics are occurring while coping with the new trends like machine learning and data analysis. The last two decades have shown practical applicability of the long-developed mathematical theories, especially some advanced mathematics which had not been introduced to applied mathematics. In this concern some countries like the U.S. or Australia have studied the changing environments related to mathematics and its applications and deduce strategies for mathematics research and education. In this paper we review some of their studies and discuss possible relations with the history of mathematics.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.73-88
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• 2007

In this paper, we study the symmetry of figures in elementary geometry. First, we investigate the historical and mathematical background of symmetry of figures and we explore the suitable teaching and learning methods for symmetry in elementary geometry. Also we study the major problem of geometry education that occurring in elementary school.

• Journal for History of Mathematics
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• v.32 no.2
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• pp.79-93
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• 2019

Choi Yoon Sik is a person who can not be omitted when discussing the history of mathematics in Korea. He is a mathematician who led Korean mathematics community after liberation from Japan. However, he took interests in mathematics education in middle and high school also. Choi Yoon Sik should be remembered as a leading person not only in the history of mathematics but also in the history of mathematics education in Korea. Choi Yoon Sik thought that histo-genetic principle, intuitive principle, and practical principle are important in mathematics education by help of Okura Kinnosuke's view, with hope to reform the mathematics education in Korea. He also argued that mathematics has educational values.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.65-78
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• 2006

The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law $\frac{v_1}{sin{\theta}_1}=\frac{v_2}{sin{\theta}_2$ through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.509-523
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• 2005

This study empirically examines motivations of entering college of education and academic problems that pre-service teachers encounter under the curricular activities. We analyze the phenomena of professional development under the four categories: motivation toward entering college of education, pedagogical content knowledge, subject matter knowledge and future vision. We conducted survey for the S university students first and interviewed 3 selected participants. Almost 50 students from college of education participated answering to the surveys. Using SPSS package, there was no significant difference between freshmen, sophomore and junior students in any category Male students responded more positively than female students in all the categories. To explore survey results deeply, we selected 3 students from sophomore and junior levels and 2 extra senior students to conduct interviews. The interpretation of the data described how their academic problems unfold partly because they seek another major and how their professional development take place carrying out practicum activities. Most of the interviewees felt that their academic lives were affected motivations of entering college of education and difficulties of studying subject matter knowledge. At the end, several suggestions are added for future research.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.23-34
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• 2012

The International Congress of Mathematicians (ICM) will next be held in Seoul, Korea from August 13th to 21st 2014. The ICM, currently hosted by the International Mathematical Union, has a history spanning a period of one hundred years and is traditionally held every four years. Felix Klein has often been credited with formulating the concept of the ICM, however George Cantor not only initially propagated the idea of forming a mathematical society in Germany, but also proposed organizing an international mathematical union. This study has endeavored to investigate the early period of development of the ICM. Specifically, this paper has studied the development of early 20th century mathematics through changes in the formulaic language of the ICM, the number of participants, the number of presentations, the nationality of plenary speakers, and the changes in sessions.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.25-40
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• 2010

We first seek a principle of cognitive development processes by reviewing and summarizing Piaget's cognitive development theory, constructivism and Dubinsky's APOS theory, and also the epistemology on logics of 墨子 and 荀子. We investigate Chapter 8 方程 on the theory of systems of linear equations, of the Nine Chapters, one of the oldest ancient Asian mathematical books, from the viewpoint of our principle of cognitive development processes. We conclude the educational value of the chapter and the value of the research on Asian ancient mathematical works and heritages.