• Journal for History of Mathematics
• /
• v.20 no.4
• /
• pp.61-70
• /
• 2007

Combinatorics, often called the 21 st century mathematics, has turned out a very important subject for the present information era. Modern combinatorics has started from some mathematical works, for example, Pascal's triangle and the binomial coefficients, and Euler's problems on the partitions of integers and Konigsberg's bridge problem, and so on. In this paper, we investigate the origin of combinatorics by looking over some interesting ancient combinatorial problems and some important problems which have started various subfields of combinatorics. We also discuss a little on the role of combinatorics in mathematics and mathematics education.

• Journal for History of Mathematics
• /
• v.15 no.1
• /
• pp.135-146
• /
• 2002

In this paper, we demonstrate that one can teach conditional probability in a manner consistent with many features of the statistics education reform movement. Presenting a variety of applications of conditional probability to realistic problems, we propose that interactive activities and the use of technology make conditional probability understandable, interactive, and interesting for students at a wide range of levels of mathematical ability. Along with specific examples, we provide guidelines for implementation of the activities in the classroom and instructional cues for promoting curiosity and discussion among students.

• Journal for History of Mathematics
• /
• v.14 no.2
• /
• pp.101-114
• /
• 2001

The ancient Egyptians only used fractions of the form 1/n, so any other fraction had to be represented as a sum of such unit fractions and all the unit fractions were different. This study explores some of the history of Egyptian fractions and gives you an algorithm for such representations. There's lots of investigations to do in this area of mathematics suitable for elementary school students and it is also designed as a resource for teachers.

• Journal for History of Mathematics
• /
• v.25 no.3
• /
• pp.119-140
• /
• 2012

This study analyzed the questions related to the content knowledge of mathematics subject for the middle and high school teacher employment examination conducted from the school year of 2009 to 2012 based on the evaluation scope of the mathematics subject content knowledge and evaluation contents which were presented by the Korea Institute for Curriculum and Evaluation(KICE). To achieve the objectives of this study, a total of 105 questions were collected with respect to the questions that appeared on the test over the last 4 years which aimed to evaluate the level of applicants' knowledge related to the contents of mathematics subject. The ratio of the contents covered in the test was assessed based on the scope of evaluation and the items for evaluation among the 9 subjects. Based on the results, suggestions were presented in relation to the operation of the mathematics curriculum for the department of mathematics education at the college of education or the restructuring of the evaluation scope. There was a significant difference in the ratio of items that appeared on the test among the 9 subjects related to the content knowledge of mathematics. Also, there was a remarkable difference in the ratio of items covered in the test among the evaluation scope by subject. The results of analysis on the evaluation content items suggested that 149 items out of 256 items did not appear in the teacher employment examination for 4 years. Based on such results of analysis, this study discussed the need for readjusting the ratio of items covered in the test of content knowledge related to mathematics or the evaluation scope and evaluation content items.

• Journal of Educational Research in Mathematics
• /
• v.25 no.2
• /
• pp.177-188
• /
• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• Journal for History of Mathematics
• /
• v.25 no.3
• /
• pp.77-95
• /
• 2012

The purpose of this study is to draw implication for the teacher education program in association with creativity through analysing teaching behavior for fostering creativity of the mathematics teachers at the primary and secondary schools. In order to do so, a survey was performed by sampling primary, middle, and high school teachers. According to the results, there is significant difference in teachers' behavior for fostering creativity in the perspective of school classification (primary and secondary school), but not gender, region, and career of teachers. In other words, there is significant difference in teaching behaviors for fostering creativity between primary and secondary school teachers, herein the score of teaching behavior of former is higher than latter. Furthermore, the result of teachers' recognition survey on the possibility of fostering students' creativity via education shows that the teachers of primary schools are more relatively positive than those of secondary schools on the matter.

• Journal of Educational Research in Mathematics
• /
• v.24 no.4
• /
• pp.607-622
• /
• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

• Journal for History of Mathematics
• /
• v.21 no.1
• /
• pp.29-44
• /
• 2008

Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

• Journal for History of Mathematics
• /
• v.32 no.2
• /
• pp.61-77
• /
• 2019

The study was conducted based on the 'method of mathematical exploration through history'. In recent school education, 'Probability and Statistics' education has been emphasized, and as a result, the study has conducted a study on permutations. Permutation is used in a variety of fields, and in this study, we looked at the Derangement. The results of this study are as follows. First, analysis was made at current school mathematics level and academic mathematics level for Derangement. Second, the historical development process of derangement was examined. Third, based on this, the research direction of this study was decided to be 'Derangement number's triangle(Rencontres number's triangle)', and the inquiry for education expansion was carried out. Fourth, we have presented data on concrete educational expansion by discovering various mathematical facts of the Derangement number's triangle. We hope that the results of this study will provide meaningful implications for the application of mathematics and the presentation of new inquiry directions.

• The Science & Technology
• /
• v.33 no.10 s.377
• /
• pp.40-42
• /
• 2000

야부우치 기요시는 일본의 대표적 과학사 학자로 중국 과학사 연구와 교육에 평생을 바친 세계적 석학이다. 지난 6월 2일 94세를 일기로 세상을 떠난 그는 한국에도 어지간히 관심을 가져 두 나라를 오가며 여러 차례 계속된 한ㆍ일 세미나에는 꼭 참석하고 강연했을뿐만 아니라 사실상 주도적 역할을 했던 인물이다. 그의 책 가운데 "중국의 과학문명", "중국의 수학", "중국의 천문학"등 세가지가 우리나라에 번역되어 많이 읽히고 있다.