• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.121-134
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• 2011

Stevin is known as the inventor of decimal fractions, even though many mathematicians had the concept of decimal fractions and used it before Stevin. Why? To respond to such a question, we studied about its significance which 'La Disme' had in the history of mathematics. These can be summarized as its notational aspect, the manner of developing the book, the conceptual revolution and the practical purpose. And the chapter and verse of are little known when compared to its reputation. So in this paper we considered its contents in detail and discussed some didactical implications in relation to teaching and learning of decimal fractions in elementary school : importance of place values, similarity of calculation to natural numbers, using common fractions to justify, emphasis on the applications of decimal fractions, relation to measuring units, necessity of teaching number sense, using notational aspects.

• Journal for History of Mathematics
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• v.22 no.1
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• pp.41-52
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• 2009

Dutch mathematician Simon Stevin published De Thiende(The Tenth) in 1583. In that book Stevin suggested new numerical notation which could express all numbers. That new notation was decimal fraction system. In this article I will argue that Stevin invented new decimal fraction system with two main purposes. The explicit purpose was to invent a new system which could be used easily by practical mathematicians. The implicit purpose which cannot be found in De Thiende alone but in his other writings was to break the Aristotelian tradition which separated geometry and arithmetic which dealt continuous magnitude and discrete numbers respectively.

• Journal for History of Mathematics
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• v.28 no.5
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• pp.249-262
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• 2015

Simon Stevin, a mathematician active in the Netherlands in early seventeenth century, parlayed his mathematical talents into improving navigation skills. In 1605, he introduced a technique of calculating the distance of loxodrome employed in long-distance voyages in his book, Navigation. He explained how to calculate distance by 8 different angles, and even depicted how to make a copper loxodrome model for navigators. Particularly, Stevin clarified in the 7th copper loxodrome model on the unique features of equiangular spiral curve that keeps spinning and gradually accesses from the vicinity to the center. These findings predate those of Descartes on equiangular spiral curve by more than 30 years. Navigation, a branch of actual mathematics devised for the survival of sailors on the bosom of the ocean, was also the first step to the discovery of new mathematical object.

• 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.

• School Mathematics
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• v.4 no.4
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• pp.643-655
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• 2002

In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.595-605
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• 2014

Infinite decimals have an infinite number of digits, chosen arbitrary and independently, to the right side of the decimal point. Since infinite decimals are ambiguous numbers impossible to write them down completely, the infinite decimal representation accompanies unavoidable opaqueness. This article focused the transparent aspect of infinite decimal representation with respect to the completeness axiom of real numbers. Long before the formalization of real number concept in $19^{th}$ century, many mathematicians were able to deal with real numbers relying on this transparency of infinite decimal representations. This analysis will contribute to overcome the double discontinuity caused by the different conceptualizations of real numbers in school and academic mathematics.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.445-458
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• 2010

This study intends to investigate the process of the development of quantity concept and how to deal with the quantity calculus in elementary school, and to find out the implication for improving the curriculum and mathematics textbooks of Korea. There had been the binary Greek categories of discrete number and continuous magnitude in quantity concept, but by the Stevin's introduction of decimal, the unification of these notions became complete. As a result of analyzing of the curriculum and mathematics textbooks of Korea, there is a tendency to disregard the teaching of quantity and its calculus compared to the other countries. Especially multiplication and division of quantity is seldom treated in elementary mathematics textbooks. So these should be reconsidered in order to seek the direction for improvement of mathematic teaching. And Korea's textbooks need the emphasis on the quantity calculus and on constructing quantity concept.