• Journal of Educational Research in Mathematics
• /
• v.23 no.1
• /
• pp.17-35
• /
• 2013

The purpose of this study was to analyze the extendibility of division algorithm and Euclid algorithm for integers to algorithms for rational numbers based on word problems of fraction division. This study serviced to upgrade professional development of elementary and secondary mathematics teachers. In this paper, fractions were used as expressions of rational numbers, and they also represent rational numbers. According to discrete context and continuous context, and measurement division and partition division etc, divisibility was classified into two types; one is an abstract algebraic point of view and the other is a generalizing view which preserves division algorithms for integers. In the second view, we raised some contextual problems that can be used in school mathematics and then we discussed division algorithm, the greatest common divisor and the least common multiple, and Euclid algorithm for fractions.

• School Mathematics
• /
• v.10 no.2
• /
• pp.297-317
• /
• 2008

This study was designed to gain insight to adopt CAS into secondary level algebra education in Korea. Most inactive usage of calculators in math and most negative effects of calculators on their achievements of Korean students were shown in International studies such as TIMSS-R. A comparative study was carried out with consideration of mathematical backgrounds and technological environments. 8 Korean students and 26 US students in Grade 11 were participated in this study. Subjects' Problem solving process and their strategies of CAS usage in classical Box-problem with CAS were analyzed. CAS helped modeling by providing symbolic manipulation commands and graphs with students' mathematical knowledge. Results indicates that CAS requires shifts focus in algebraic contents: recognition of decimal & algebraic presentations of numbers; linking various presentations, etc. The extent of instrumentation effects on the selection of problem solving strategies among Korea and US students. Instrumentation

• Journal for History of Mathematics
• /
• v.37 no.2
• /
• pp.21-38
• /
• 2024

In this article, we study the historical development of how the main concepts of linear algebra - matrices, vectors, and transformations - arise, are connected then integrated into a category. Also we study how linearity is recognized and integrated into algebraic and geometric viewpoint. Furthermore, we discuss, based on this, the role of linear algebra as a unifying concept in a school mathematics.

• Korean Journal of Optics and Photonics
• /
• v.20 no.6
• /
• pp.319-327
• /
• 2009

We introduce a new design technique by treating a two-group zoom lens system with a wide angle of view. First, the concept of the global optimization is introduced in the initial design stage, and from this, the global design technique is completed by analyzing and summarizing large quantities of modern design data. That is, we define the global structure function to achieve a new conceptual design technique for global optimization. And the function is put in a simple form by referring lots of patent data, manipulated with other algebraic equations, and solved finally such that we obtain the global solution region. The global solution region corresponds to the global optimization and suggests insightful systematized directions for the design of two-group zoom lens systems. These directions are attractive compared to global optimization.

• Journal for History of Mathematics
• /
• v.20 no.3
• /
• pp.105-126
• /
• 2007

The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.503-521
• /
• 2013

For over 20 years, the issue of using an adequate CAS tool in teaching and learning of linear algebra has been raised constantly. And a variety of CAS tools were introduced in many linear algebra textbooks. In Korea, however, because of some realistic problems, they have not been introduced in the class and the theoretical aspect of linear algebra has been focused on in teaching and learning of it. In this paper, we suggest Sage as an alternative for CAS tools overcoming the problems mentioned above. And, we introduce full contents for linear algebra and matrix calculator that Sage was used to develop. Taking advantage of them, almost all the concepts of linear algebra can be easily covered and the size of matrices can be expanded without difficulty.

• Communications of Mathematical Education
• /
• v.18 no.1 s.18
• /
• pp.267-276
• /
• 2004

이 글은 초등학교 학생들을 대상으로 상호변화적(covariational) 개념으로 변화율에 대한 교수실험을 담고 있다. 기하적 문맥에서 함수의 그래프를 자연스럽게 도입하고, 함수의 변화율에 대한 상호변화적 질적 접근의 예를 제시한다. 또한 언어적 명령을 통하여 스스로 함수의 그래프를 만들어보도록 하고 함수의 그래프를 분석하는 경험을 가지게 하여 이후 함수와 그 역함수와의 개념을 마이크로월드에서 경험하도록 하는 환경과 그 역할에 대하여 논의한다. 이 과정을 통한 마이크로월드, 학생, 연구자의 역할과 상호작용을 알아보고 이 후의 대수식의 도입에 대한 문제를 논의한다.

• Proceedings of the KIEE Conference
• /
• 1999.11c
• /
• pp.564-566
• /
• 1999

계측 시스템이나 시스템 식별을 수행할 때 정확히 모델링 되는 플랜트를 가정할 경우, 입출력 신호간 혹은 상태 변수들 사이의 비선형 함수 관계를 유도해 낼 수 있다. 그런데 특히 비선형 함수가 매우 복잡하여 해를 닫힌 형태로 구할 수 없을 경우 고려하는 변수들 양자간의 수학적 모델링을 기반으로 루프내 변수가 방정식의 해로 수렴하는 대수 루프를 구성할 수 있다. 이는 모델을 정확히 아는 시스템에 대하여 출력으로부터 입력을 추정하는 역시스템(inverse system)을 구성하는 것과 유사하다. 이러한 개념을 응용한 간단한 예로 용량형 센서의 입출력 비선형성을 제거해주는 역시스템을 대수 루프를 통하여 구현하였다. 또한 구현한 루프가 항상 유일한 해로 수렴할 수 있도록 하는 조건을 구하였다. 해석된 결과를 바탕으로 구현된 루프가 컴퓨터 시뮬레이션 및 아날로그 회로 실험에서도 잘 동작함을 검증하였다. 시뮬레이션 결과로 보인 잡음에 대한 강인성과 실제 회로 실험 결과는 대수 루프의 구현이 실제 용량형 센서 등에 용이하게 적용될 수 있음을 보여준다.

• Economic and Environmental Geology
• /
• v.53 no.6
• /
• pp.703-713
• /
• 2020

In many geological fields, including hydrogeology, it is of great importance to determine the heterogeneity of the subsurface media. This study briefly introduces the concept and theory of the method that can estimate the hydraulic properties of the media constituting the aquifer, which was recently introduced by Park (2020). After the introduction, the method was applied to the synthetic aquifer to demonstrate the practicality, from which various implications were drawn. The introduced technique uses a global optimization technique called the covariance matrix adaptation evolution strategy (CMA-ES). Conceptually, it is a methodology to characterize the aquifer heterogeneity by assimilating the groundwater level time-series data due to the imposed hydraulic stress. As a result of applying the developed technique to estimate the hydraulic conductivity of a hypothetical aquifer, it was confirmed that a total of 40000 unknown values were estimated in an affordable computational time. In addition, the results of the estimates showed a close numerical and structural similarity to the reference hydraulic conductivity field, confirming that the quality of the estimation by the proposed method is high. In this study, the developed method was applied to a limited case, but it is expected that it can be applied to a wider variety of cases through additional development of the method. The development technique has the potential to be applied not only to the field of hydrogeology, but also to various fields of geology and geophysics. Further development of the method is currently underway.

• Journal of the Korean Society for Railway
• /
• v.12 no.2
• /
• pp.267-275
• /
• 2009

Max-plus algebra is a nonlinear system comprised of two operations, maximization (max) and addition (Plus), which are corresponding to the addition and the multiplication in conventional algebra, respectively. This methodology is applicable to many discrete event systems containing the state transition with the maximization and addition operation. Timetable with connection is one of such systems. We present the method based on max-plus algebra, which can make up timetable considering transfer and analyse its stability and robustness. In this study, it will be shown how to make up the timetable of the urban train and analyse its stability using Max-Plus algebra.