• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.409-428
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• 2014

The purpose of this study is to examine the features of the curriculum of Chosun-Sanhak(朝鮮算學), the mathematics of Chosun Dynasty in the 17th to 18th century. The results of this study are as follows. First, the goal of education, teaching-learning method and assessment of Chosun-Sanhak in the 17th to 18th century had not changed since the 15th century. Second, the changes in the field of the organization of mathematical contents were observed. Chosun-Sanhak in that time was higher in the hierarchy than in the 15th to 16th century. The share of the equation and geometry had increased and various topics of mathematics had been studied as well. Third, in the field of the characteristics of mathematical contents, the influx of European mathematics and the uniqueness of Chosun-Sanhak had been observed. In conclusion, The 17th to 18th century was the time when Chosun-Sanhak had pursued the identity escaping from the effects of Chinese-Sanhak.

• School Mathematics
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• v.17 no.2
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• pp.179-202
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• 2015

In this research, I explored how to apply the history of mathematics in teacher education and investigated the applicability of Chosun Sanhak (mathematics of Chosun Dynasty) as the program that enriched the mathematical knowledge for teaching of prospective elementary school teachers. This program included not only mathematical knowledge but also socio-cultural knowledge and connection knowledge. Prospective teachers participated in various mathematical activities such as explaining, reasoning and problem solving in this program. The effects of this program are as follows. Prospective teachers learned the subject matter knowledge(SMK) which was helpful in teaching basic concepts and skills of elementary mathematics. Next, this program produced the pedagogical content knowledge(PCK) to prospective teachers by giving ideas how to teach.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.1-12
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• 2009

Zhu Shi Jie's Suan Xue Qi Meng is one of the most important books which gave a great influence to the development of Chosun Mathematics. Investigating San Hak Gye Mong Ju Hae(算學啓蒙註解) published in the middle of the 19th century, we study the development of Chosun Mathematics in the century. The author studied western mathematics together with theory of equations in Gu Il Jib (九一集) written by Hong Jung Ha(洪正夏) and then wrote the commentary, which built up a foundation on the development of Algebra of Chosun in the century.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.7-20
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• 2011

Investigating constructions of equations by Gou gu shu(勾股術) in Hong Jung Ha(洪正夏)'s GuIlJib(九一集), Nam Byung Gil(南秉吉)'s YuSiGuGoSulYoDoHae(劉氏勾股術要圖解) and Lee Sang Hyuk(李尙爀)'s ChaGeunBangMongGu(借根方蒙求), we study the history of development of Chosun mathematics. We conclude that Hong's greatest results have not been properly transmitted and that they have not contributed to the development of Chosun mathematics.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.11-32
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• 2005

This paper is a comprehensive study of mathematics education in the Chosun Dynasty. The basis of this work relies on actual historical records from the period. As shown in the records, mathematics education during the Chosun Dynasty remained at the level of basic arithmetics. The arithmeticians of the Chosun Dynasty did not have an understanding of more complex mathematical thought. But the simple arithmetics of the Chosun Dynasty facilitated the building up of a unique merchant 'middle class.' So this paper examines the development of mathematics in the Chosun Dynasty through middle class. Although the Chosun Dynasty arithmetics occupy a significant part of mathematics history, this paper details why their thought did not evaluate more advanced mathematical theories.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.375-394
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• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.1-16
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• 2007

In the 19th century, Chosun mathematicians studied the most distinguished mathematicians Qin Jiu Shao(泰九韶), Li Ye(李治) Zhu Shi Jie(朱世傑) in Song(宋), Yuan(元) Dynasty and they established a solid theoretical development on the theory of equations. These studies began with their study on Si yuan yu jian xi cao(四元玉鑑細艸) compiled by Luo Shi Lin(羅士琳). Among those Chosun mathematicians, Lee Sang Hyuk(李尙爀, $1810{\sim}?$) and Nam Byung Gil(南秉吉 $1820{\sim}1869$) contributed prominently to the research. Relating to Si yuan yu jian xi cao, Nam Byung Gil and Lee Sang Hyuk compiled OgGamSeChoSangHae(玉監細艸詳解) and SaWonOgGam(四元玉鑑), respectively and then later they wrote SanHakJeongEi(算學正義) and IkSan(翼算), respectively. The latter in particular contains most creative results in Chosun Dynasty mathematics. Using these books, we study the relation between the development of Chosun mathematics and Si yuan yu jian.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.1-9
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• 2012

After disastrous foreign invasions in 1592 and 1636, Chosun lost most of the traditional mathematical works and needed to revive its mathematics. The new calendar system, ShiXianLi(時憲曆, 1645), was brought into Chosun in the same year. In order to understand the system, Chosun imported books related to western mathematics. For the traditional mathematics, Kim Si Jin(金始振, 1618-1667) republished SuanXue QiMeng(算學啓蒙, 1299) in 1660. We discuss the works by two great mathematicians of early 18th century, Cho Tae Gu(趙泰耉, 1660-1723) and Hong Jung Ha(洪正夏, 1684-?) and then conclude that Cho's JuSeoGwanGyun(籌 書管見) and Hong's GuIlJib(九一集) became a real breakthrough for the second half of the history of Chosun mathematics.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.41-52
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• 2009

This study investigates a mathematical subject, 'triangles' in mathematics books of Chosun Dynasty, in special Muk Sa Jib San Bub(默思集算法), Gu Il Jib(九一集), San Hak Ib Mun(算學入門), Ju Hae Su Yong(籌解需用), and San Sul Gwan Gyun(算術管見). It is likely that they apt to avoid manipulating general triangles except the right triangles and the isosceles triangles etc. Our investigation says that the progress of triangle-related contents in Chosun mathematics can fall into three stages: measurement of the triangle-shaped fields, transition from the object of measurement to the object of geometrical study, and examination of definition, properties and validation influenced by western mathematics.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.