• Research in Mathematical Education
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• v.5 no.2
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• pp.127-132
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• 2001

Mathematics holds a key position among many subjects of school education. Besides having an instrumental value, mathematics for the general public has been underestimated. Thus, in this paper we examine how western educational theorists have emphasized the value of mathematics as humanities form of education. First of all, we discuss Platonism as a philosophical basis of the ancient Greek mathematics education. Next, we examine the thoughts of Froebel, who provided the theoretical basis for the public education since 19th century, and discuss the value of mathematics teaching in their humanistic educational thoughts. Also, we examine the humanistic value of mathematics education in Dewey\\`s educational philosophy, which criticized the traditional western ethics and epistemology, and established instrumentalism. In this paper, we recognize the humanistic values of mathematics education through the historical examination of the philosophies of mathematics education.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.69-76
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• 2003

In this article, We explained the historical origin and significance of decimal fraction, and draw some educational implications based on that. In general, it is accepted that decimal fraction was first invented by a Belgian man, Simon Stevin(1548-1620). In short, the idea of infinite decimal fraction refers to the ratio of the whole quantity to a unit. Stevin's idea of decimal fraction is significant for the history of mathematics in that it broke through the limit of Greek mathematics which separated discrete quantity from continuous quantity, and number from magnitude, and it became the origin of modern number concept. H. Eves chose the invention of decimal fraction as one of the "Great moments of mathematics."The method of teaching decimal fraction in our school mathematics tends to emphasize the computational aspect of decimal fraction too much and ignore the conceptual aspect of it. In teaching decimal fraction, like all the other areas of mathematics, the conceptual aspect should be emphasized as much as the computational aspect.al aspect.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.53-68
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• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

• Journal of the Korean Society of Earth Science Education
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• v.10 no.2
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• pp.214-225
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• 2017

The first accurate estimate of the Earth's circumference was made by the Hellenism scientist Eratosthenes (276-195 B.C.) in about 240 B.C. The simplicity and elegance of Eratosthenes' measurement of the circumference of the Earth by mathematics abstraction strategies were an excellent example of ancient Greek ingenuity. Eratosthenes's success was a triumph of logic and the scientific method, the method required that he assume that Sun was so far away that its light reached Earth along parallel lines. That assumption, however, should be supported by another set of measurements made by the ancient Hellenism, Aristarchus, namely, a rough measurement of the relative diameters and distances of the Sun and Moon. Eratosthenes formulated the simple proportional formula, by mathematic abstraction strategies based on perfect sphere and a simple mathematical rule as well as in the geometry in this world. The Earth must be a sphere by a logical and empirical argument of Aristotle, based on the Greek word symmetry including harmony and beauty of form. We discuss the justification of these three bold assumptions for mathematical abstraction of Eratosthenes's experiment for calculating the circumference of the Earth, and justifying all three assumptions from historical perspective for mathematics and science education. Also it is important that the simplicity about the measurement of the earth's circumstance at the history of science.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.135-148
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• 2011

Middle school mathematics treats axiom as mere fact verified by experiment or observation and doesn't mention it axiom. But axiom is very important to understand the difference between empirical verification and mathematical proof, intuitive geometry and deductive geometry, proof and nonproof. This study analysed textbooks and surveyed gifted students' conception of axiom. The results showed the problem and limitation of middle school mathematics on the treatment of axiom and proof.

• Journal for History of Mathematics
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• v.33 no.4
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• pp.223-236
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• 2020

We examine how the formulas of the area and the circumference of a circle related to pi in the ancient Egyptian and the Old Babylonian fields of mathematics have been controversial. In particular, the Great Pyramid of Khufu, Ahmes Papyrus Problem 48 and Moscow Mathematical Papyrus Problem 10 have raised extensive controversy over π. We propose the pi-theory of the Great Pyramid of Khufu as a dynamic symmetry based on Euclid's rectangle. In addition, we argue that the ancient Egyptian or Old Babylonian mathematics influenced Solomon's Molten Sea, Plato and Archimedes' pi.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.493-511
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• 2014

In this paper, we study the major mathematical history appeared in the elementary school mathematics textbooks. School mathematical history described in the texts reflects the axial age, and deals with mathematical transculture from the ancient Greek into Europe without the Islamic mathematics. We discuss about them through out the elementary school textbooks and give some directions for the problems.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.45-56
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• 2007

The aims of the study were to review the transcriptions of the famous cuneiform tablet 'Plimpton 322' and interpret the meanings of the numbers. Since the tablet was found, many scholars tried to interpretate the relation among numbers. Neugebauer & Sacks, Buck, and Robson's finding are reviewed. This tablet must be the most well known and taken as an important role to complete a proof of the Pytagoras' theorem before the development of Greek Mathematics.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.275-284
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• 2010

Deliberate self-harm (DSH) is the act of deliberately harming your own body, such as cutting or burning yourself, without suicidal intent. It has especially become a problem among adolescents and college-age students in institutional settings such as boarding schools, Greek houses, detention centers and hospitals. We focus on contagion of DSH among adolescents and young adults by creating a deterministic epidemiological model. We study the impact of actual peer pressure, virtual peer pressure (the Internet) and treatment analytically in terms of a basic reproduction number through stability analysis of a system of ordinary differential equations. All parameters are approximated and results are also explored by simulations. The model shows that DSH is present in an endemic state in the population considered, and the control strategies are discussed.