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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
Journal for History of Mathematics
Journal Basic Information
Journal DOI :
The Korean Society for History of Mathematics
Editor in Chief :
Volume & Issues
Volume 24, Issue 4 - Nov 2011
Volume 24, Issue 3 - Aug 2011
Volume 24, Issue 2 - May 2011
Volume 24, Issue 1 - Feb 2011
Selecting the target year
Hong Jung Ha's Number Theory
Hong, Sung-Sa ; Hong, Young-Hee ; Kim, Chang-Il ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 1~6
We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l =
are relatively prime and then obtained that for natural numbers
, their greatest common divisor D and least common multiple L,
) are relatively prime and there are relatively prime numbers
with L =
. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.
Gou Gu Shu and Theory of equations in Chosun
Yun, Hye-Soon ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 7~20
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.
Lobachevsky's Philosophy of Mathematics and Non-Euclidean Geometry
Park, Chang-Kyun ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 21~31
In this paper I claim that Lobachevsky's philosophy of mathematics is a kind of reservoir of contemporary philosophy of mathematics. I discuss how his philosophy contributed to the rise of non-Euclidean geometry.
Hilbert and Formalism
Choi, Won-Bae ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 33~43
In this paper I discuss if we can regard Hilbert at the time of Hilbert's program as an instrumentalist. For this I first provide some textual evidences for the instrumentalist interpretation, then examine the three recent criticisms in turn. I argue that the reading Hilbert as an instrumentalist is still tenable in spite of these criticisms.
A Comparing Study of Two Constructivisms on L.E.M.
Oh, Chae-Hwan ; Kang, Ok-Ki ; Ree, Sang-Wook ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 45~59
Constructionists believe that mathematical knowledge is obtained by a series of purely mental constructions, with all mathematical objects existing only in the mind of the mathematician. But constructivism runs the risk of rejecting the classical laws of logic, especially the principle of bivalence and L. E. M.(Law of the Excluded Middle). This philosophy of mathematics also does not take into account the external world, and when it is taken to extremes it can mean that there is no possibility of communication from one mind to another. Two constructionists, Brouwer and Dummett, are common in rejecting the L. E. M. as a basic law of logic. As indicated by Dummett, those who first realized that rejecting realism entailed rejecting classical logic were the intuitionists of the school of Brouwer. However for Dummett, the debate between realists and antirealists is in fact a debate about semantics - about how language gets its meaning. This difference of initial viewpoints between the two constructionists makes Brouwer the intuitionist and Dummettthe the semantic anti-realist. This paper is confined to show that Dummett's proposal in favor of intuitionism differs from that of Brouwer. Brouwer's intuitionism maintained that the meaning of a mathematical sentence is essentially private and incommunicable. In contrast, Dummett's semantic anti-realism argument stresses the public and communicable character of the meaning of mathematical sentences.
On Hilbert's 'Grundlagen der Geometrie'
Yang, Seong-Deog ; Jo, Kyeong-Hee ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 61~86
In this article we introduce old and new references for 'Grundlagen der Geometrie' written by Hilbert and summarize its contents. We then compare the 1902 English translation of the first (German) edition and the 1971 English translation of the 10th (German) edition focusing on the changes of the contents, terminologies, expressions, etc. We then finally discuss about the implications of these changes in translating mathematics classics into modern Korean and in creating mathematics books in modern Korean.
Freudenthal and ICMI
Kim, Sung-Sook ; Khang, Mee-Kyung ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 87~96
Hans Freudenthal made important contributions to algebraic topology and geometry. He also made significant contributions in history of mathematics and mathematics education. In the 1970s, his intervention prevented the Netherlands from the movement of "new math". He had a very important role as a founder of realistic mathematics education and became famous internationally by that. Because he raised the profile of ICMI strongly, Bass used the expression 'Freudenthal Era' for the period that Freudenthal was the president of ICMI. Now many mathematics educator agree to use the Freudenthal Era when they mention about the history of ICMI. In this paper, we present on the life of Freudenthal and his contributions for mathematics education, especially ICMI.
A Study on the comparison of models for teaching the concept of function
Heo, Hae-Ja ; Kim, Jong-Myung ; Kim, Dong-Won ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 97~118
This study aimed finding effective models for the teaching the concept of function. We selected two models. One is discrete model which focuses on the 'corresponding relation of the elements of the sets(domain and range). The other is continuous model which focuses on the dependent relationship of the two variables connected in variable phenomenon. A vending machine model was used as a discrete model, and a water bucket model was used as a continuous model in our study. We taught 2 times about the concept of function using two models to the 60 students (7th grade, 2 classes) living in Taebak city, and tested it twice, after class and about 3 months later. A vending machine model was helpful in understanding the definition of function in the 7th grade math textbook. Also, it was helpful to making concept image and to recalling it. On the other hand, students who used the water bucket model had a difficultly in understanding the all independent variables of the domain corresponding to the dependent variables. But they excelled in tasks making formula expression and understanding changing situations.
Historic Paradoxes of Probability and Statistics Usable in School Mathematics
Lee, Jong-Hak ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 119~141
This paper analysed the mathematical paradoxes which would be based in the probability and statistics. Teachers need to endeavor various data in order to lead student's interest. This paper says mathematical paradoxes in mathematics education makes student have interest and concern when they study mathematics. So, teachers will recognize the need and efficiency of class for using mathematical Paradoxes, students will be promoted to study mathematics by having interest and concern. These study can show the value of paradoxes in the concept of probability and statistics, and illuminate the concept being taught in classroom. Consequently, mathematical paradoxes in mathematics education can be used efficient studying tool.
Discriminant of Polynomial in highschool mathematics curriculum
Choi, Eun-Mi ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 143~155
The discriminant is one of the important concepts in school mathematics according to second degree polynomials. In this paper we survey the history of development to discriminant of any higher degree polynomials and investigate how the discriminant works for determining the graph of polynomials.
The analysis of gender difference on mathematics achievement after learning using CAS on mathematics underachiever
Kim, In-Kyung ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 157~180
This paper analyzed about gender difference in the achievement of underachievers of high school students while learning using technology. Participants were composed of 67 underachievers on first grade in high school located in a metropolitan city. That had never used a mathematics educational calculator before. Target participants were divided into two groups: experiment group that studied activity papers with a CAS calculator. And control group that studied the same activity papers using only paper-and-pencil. The content of the activity papers for the two groups was the same, but the structure differed. The two groups completed mathematics achievement tests both before and after the activity papers. The results are that find out no difference of the mathematics achievement between boys and girls in each group, and that the mathematics achievement of boys in experiment group are better than one of boys in control group, and also girls.
On application of Vygotsky's theory in math education for gifted students
Hong, Jin-Kon ; Kang, Eun-Joo ;
Journal for History of Mathematics, volume 24, issue 4, 2011, Pages 181~200
The focus of gifted education program for math should not only be on how to select gifted students but also on how to magnify students' potential ability. This thesis supports Vygotsky's view, which provides an insight into gifted education field as an 'acquired giftedness' theory. The issues in this thesis suggest proper classroom models for current gifted education program together with moderate classroom atmosphere and optimum role of teachers.