• Journal for History of Mathematics
• /
• v.31 no.2
• /
• pp.73-91
• /
• 2018

This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

• Communications of Mathematical Education
• /
• v.25 no.1
• /
• pp.1-19
• /
• 2011

HPM(History and Pedagogy of Mathematics) become an important issue to us now. Study on old Korean mathematics books were made recently. We study mathematics books in Kyujanggak in this article. Horng Wann-Sheng 洪萬生, an math. historian and a member of editorial board of Historia Mathematica, visited Kyujanggak, the royal library of Joseon Dynasty. After his visit, he published a paper, "The first visit to mathematics books in Kyujanggak 奎章閣收藏算書初訪"(2008 Kyujanggak 32, p. 283-293). In his paper, he also raised several research problems on the history of Korean mathematics. In this paper, we analyze his paper "The first visit to mathematics books in Kyujanggak" and give some answers to those raised problems on Korean mathematics. Also we correct some misunderstanding of Horng on some facts. Especially, we make it clear that the author of SinJungSanSul(New Arithmetics 新訂算術) was not Lee Sang-Seol(李相卨), whom Horng considered as the author, but Lee Gyo-Seung(李敎承) through the correct translation of its preface and an article about its copyright lawsuit. And we added some pathways how Chinese mathematics books were imported by Joseon. We introduce the case of Hong Dae-Yong(洪大容) in detail.

• Journal for History of Mathematics
• /
• v.24 no.4
• /
• pp.97-118
• /
• 2011

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.

• School Mathematics
• /
• v.3 no.2
• /
• pp.249-265
• /
• 2001

In this information-oriented society of the 21st century, our education should combine the knowledge from the past and present in order to have students be ready to solve “the problems in the future”. But nowadays, our social situation makes much importance of the “cramming” education just for the College Scholastic Ability Test rather than the “whole man” education for making creative citizens of the future society. So does mathematics education. In a high school, mathematics education should be toward these aims: recognizing the value of math, applying mathematical principles to actual lives, promoting students' thinking ability. Also, it should focus on teaching higher level of mathematical knowledge which includes more logical and abstract idea so that students can prepare for the global society of the future. This study is about development and utilization of the teaching materials for mathematics class which usually deviates from the routine right after the Scholastic Ability Test finished. These materials are the result of a complete survey of the 3rd graders and their teachers and designed to use for 30 periods of class from after-the-test-finished to graduation. The materials consist of a history of mathematics, puzzles, magic number squares, and so on. Remarkably different from the current textbooks which deal with sets, equations, functions, these materials proved to be useful for their variety and attraction. Consequently, the materials are considered to keep the 3rd graders from forgetting mathematics even after the Scholastic Ability Test, and to help them recognize that mathematics is a kind of basic and cultural study and a tool of daily lives.

• Journal of Elementary Mathematics Education in Korea
• /
• v.15 no.1
• /
• pp.77-93
• /
• 2011

Jisuguimundo(地數龜文圖) is a magic hexagon created by Suk-Jung Choi in his book about three hundreds years ago in Korea. Recently attention is focused on jisuguimundo, and it is known that jisuguimundos exist when magic number is from 77 to 108, however a general method making jisuguimundos is not known so far. Up to now, methods of making jisuguimundos using computers are known. In this study, a method making jisuguimundos is suggested using pairs of two numbers with sum p and q ($p{\neq}q$) alternately when magic number is from 88 to 92, and from 94 to 98, without using computer in elementary math class as a task for problem solving. Mathematical theory is introduced for this method, and jisuguimundos are presented which are found out through this method. Elementary students are expected to make their own jisuguimundo using this method.

• Communications of Mathematical Education
• /
• v.23 no.3
• /
• pp.643-682
• /
• 2009

There is no doubt that the national competitiveness, in 21st century, definitely depends on how effectively it has been producing high-qualify human resources. It is inevitable that we are required to produce outstanding people who are going to make the use of highly developed scientific technology. Every country has already set to concentrate their all efforts in cultivating competitive human resources, enabling it to strengthen its national competitiveness. We Korea, in order to keep up with it, have arranged legal and systematic basis and are putting spurs to producing competent human resources under the 영재교육진흥법 및 시행령, which took effect from March, 2002. With the lack of experience and short history of Gifted Education, however, it is true that we still have many problems in promoting it in reality, We are asked to improve it by finding out what problems we have in whole area of Gifted Education, such as defining conception, choosing target students, structuring system and managing students afterwards. Therefore, this study, especially focusing on Math of Gifted Education is to investigate the present situation of Gifted Education and to examine what we should do for administering Gifted Education in effective ways.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2010.05a
• /
• pp.401-404
• /
• 2010

Researches on prodigies and education for those have recently been progressing in many fields. Education for the gifted, which was basically on Math and Science on the start, now includes Intelligence, Invention, Cultural Sciences, Art, and so on. With the progression towards extremely developed information society, interests in and importance on the courses for the talented get more and more focused. The problem is, however, choosing the gifted and educating them is not an easy matter, since the history of Intelligence Technology is relatively short and it is hard to identify prodigies and categorize what kinds of courses they need. Also, from 2010 "Science Education Institute for the Gifted" freshmen draft, paper-based admission test has been discarded and teacher-recommendation through long-term observation introduced. Therefore needs have been increasing for quality selection methods including observation records, recommendation letters, and portfolios. Reformation on teaching and creative selection methods has been accentuated because of lack of academic base for selecting candidates for education for the gifted. Because of all those mentioned above, reliances for the selection processes during the last three years and the one in 2010, observation records, recommendations and portfolios included, have been analyzed and evaluated. Several factors which can be used instead of paper-based tests were coordinated. Based on it, it was highly possible and has been successful to draft all the applicants in cognitive, sentimental, and creative fields.

• Journal for History of Mathematics
• /
• v.22 no.2
• /
• pp.27-52
• /
• 2009

This article discusses the contributions of the leader Oswald Veblen, who was the president of AMS during 1923-1924. In 2006, Korea ranked 12th in SCIE publications in mathematics, more than doubling its publications in less than 10 years, a successful model for a country with relatively short history of modern mathematical research. Now there are 192 four-year universities in Korea. Some 42 of these universities have Ph.D. granting graduate programs in mathematics and/or mathematical education in Korea. Rapid growth is observed over a broad spectrum including a phenomenal performance surge in International Mathematical Olympiad. Western mathematics was first introduced in Korea in the 17th century, but real significant mathematical contributions by Korean mathematicians in modern mathematics were not much known yet to the world. Surprisingly there is no Korean mathematician who could be found in MaC Tutor History Birthplace Map. We are at the time, to have a clear vision and leadership for the 21st century. Even with the above achievement, Korean mathematical community has had obstacles in funding. Many people thinks that mathematical research can be done without funding rather unlike other science subjects, even though they agree fundamental mathematical research is very important. We found that the experience of early American mathematical community can help us to give a vision and role model for Korean mathematical community. When we read the AMS Notice article 'The Vision, Insight, and Influence of Oswald Veblen' by Steve Batterson, it answers many of our questions on the development of American mathematics in early 20th century. We would like to share the story and analyze its meaning for the development of Korean Mathematics of 21st century.