• Journal of Intelligence and Information Systems
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• v.1 no.1
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• pp.1-22
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• 1995

본 연구에서 퍼지인식도(Fuzzy Cognitive Map) 개념을 기초로 하여 (1) 특정 문제영역에 대한 전문가의 인과관계 지식(causal knowledge)을 추출하는 알고리즘을 제시하고, (2) 이 알고리즘에 기초하여 작성된 해당 문제영역에 대한 여러 전문가들의 인과관계 지식을 계층별로 분해하여, (3) 해당 계층간의 양방향 추론이 가능한 추론메카니즘을 제시하고자 한다. 특정 문제영역에 있어서의 인과관계 지식이란 해당 문제를 구성하는 여러 개념간에 존재하는 인과관계를 표현한 지식을 의미한다. 이러한 인과관계 지식은 기존의 IF-THEN 형태의 규칙과는 달리 행렬형태로 표현되기 때문에 수학적인 연산이 가능하다. 특정 문제영역에 대한 전문가의 인과관계 지식을 추출하는 알고리즘은 집합연산에 의거하여 개발되었으며, 특히 상반된 의견을 보이는 전문가들의 의견을 통합하여 하나의 통합된 인과관계 지식베이스를 구축하는데 유용하다. 그러나, 주어진 문제가 복잡하여 다양한 개념들이 수반되면, 자연히 인과관계 지식베이스의 규모도 커지게 되므로 이를 다루는데 비효율성이 개재되기 마련이다. 따라서 이러한 비효율성을 해소하기 위하여 주어진 문제를 여러계측(Hierarchy)으로 분해하여, 해당 계층별로 인과관계 지식베이스를 구축하고 각 계층별 인과관계 지식베이스를 연결하여 추론하는 메카니즘을 개발하면 효과적인 추론이 가능하다. 이러한 계층별 분해는 행렬의 분해와 같은 개념으로도 이해될 수 있다는 특징이 있어 그 연산이 간단명료하다는 장점이 있다. 이와같이 분해된 인과관계 지식베이스는 계층간의 추론메카니즘을 통하여 서로 연결된다. 이를 위하여 본 연구에서는 상향 또는 하향방식이 추론이 가능한 양방향 추론방식을 제시하여 주식시장에서의 투자분석 문제에 적용하여 그 효율성을 검증하였다.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.263-279
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• 2015

The introduction of real numbers is one of the most difficult steps in the teaching of school mathematics since the mathematical justification of the extension from rational to real numbers requires the completeness property. The author elucidated what questions about real numbers can be unanswered as the "institutional didactic void" in school mathematics defining real numbers as the union of the rational and irrational numbers. The pre-service teachers' explanations on the extension from rational to real numbers and the raison d'$\hat{e}$tre of arbitrary non-recurring decimals showed the superficial and fragmentary understanding of real numbers. Connecting school mathematics to university mathematics via the didactic void, the author discussed how pre-service teachers could break the illusion of transparency about the real number.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.771-796
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• 2013

The purpose of the study is to analyze the phenomenon of private education and to get the countermeasures of it. To do this, we approached the phenomenon of private education from the game theory, which is famous in economics. As result, we could make the mathematical model. One is a model consisted of two-person. This is a mathematical model simplifying the competition within the school. The problem of private education can be solved by the disconnection with private education and exam of school in this model. The other is a model consisted of three-person. This is a mathematical model simplifying the interscholastic competition. The problem of private education can not only be solved by the disconnection with private education and exam of school, but can be also solved by the specificity of school education in this model. We will hope that our study can give an aid in deciding an educational policy.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.1-8
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• 2005

In this paper, we describe H. Hopf's life and works from the historical point of view. We have a very brief mention of history and results prior to Hopf. He raised the question of the topological implications of the sign of curvature. We discuss his contributions in the field of Riemannian geometry.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.745-752
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• 1998

컴퓨터의 급속한 보급으로 시각화는 수학 교육자사이의 논의에 자주 등장하는 소재가 되었다. 우리는 다양한 소프트웨어를 사용하여 준비한 수업에 학생들로 임하게는 하지만 거의 그들의 사고 발달과정에는 관심을 갖지 못하고 있다. 이 논문은 구성주의(Constructivism)와 정보처리체계(Information-Processing System)에 입각하여 수학의 시각화를 생각해보고 어떻게 시각화 환경을 준비해야하는지 논해보고자 하였다. 구성주의의 시각화에서는 반영적 추상(reflective abstraction), 반복되는 경험(repeated experience), 그리고 지식 위계성이 학습의 기능 체계를 이루므로 발견적 학습을 통해 학생 스스로 의미를 구성할 수 있도록 Thomas (1992)의 세 가지 제안을 이용하여 수업을 준비할 수 있다. 정보처리체계에서는 지식은 서술적인 것과 과정적인 것으로 나뉘어지고, 시각적 표상을 수록하고 삭제하는 과정과 조작 가능한(manipulative) 환경과의 상호작용으로 기호적 시각으로 표상을 변화하는 과정을 통해 개념을 습득하게된다. 시각화는 스키마와 개념상을 통해서 일어난다. 그래프, 애니메이션, 그리고 다른 시각적 표상 등은 이 개념상에 직접적 효과를 주므로 매우 중요하다. 이런 논란을 바탕으로 교사는 반영적 추상화를 위해 시간을 충분히 제공해야하고, 비슷한 문제를 가지고 여러번 시도를 할 수 있게 하며, 학생을 잘 관찰하여 그들의 지식 위계성을 이해하고 방향을 제시하며, 논리적이고 잘 연결된 시각적 표상을 제공하고, 상징적 사관으로 확장할 수 있게 조작할 수 있는 환경에서 시각화에 대해 학생과 많은 대화를 하도록 수업을 준비해야한다. 그한 예로 타원을 가르치기 위해 몇 가지 테크놀로지를 활용한 시각화 환경을 구성해보았다.ates of bisected bovine embryos by micromanipulator and micropipett were 29.2% and 19.1%, respectively. The rates of non-bisection embryos(46.7%) were significantly higher than those of bisection embryos. 2. The in vitro developmental rates of bisected bovine embryos by micromanipulator, micropipett and pipetting method were 32.4%, 19.4% and 25.6%, respectively.3. The in vitro developmental rates of with and without-zona pellucida of bisected bovine embryos by raicromanipulator were 30.8% and 25.0%, respectively. The rates of nonbisection embryos(53.1%) were significantly higher than those of bisection embryos.랑크톤 군집내 종 천이와 일차생산력에 크게 영향을 미칠 수 있음을 시사한다.TEX>5.2개)였으며, 등급별 회수율은 각각 GI(8.5%), GII(13.4%), GIII(43.9%), GIV(34.2%)로 나타났다.ments of that period left both in Japan and Korea. "Hyojedo" in Korea is supposed to have been influenced by the letter design. Asite- is also considered to

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.411-431
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• 2022

In this paper, implications for future curriculum compilation were sought by analyzing the process and results of compiling books for elementary school mathematics textbooks government published according to the 2015 revised curriculum. The 2015 revised elementary mathematics textbooks government published was operated with a systematic compilation system so that academia and school field experts across the country could demonstrate their expertise. As improvements in content, the unit and time to strengthen basic computational skills were increased, and the mathematical concept and principle introduction method and algorithm presentation method were improved, and the internal connection between contents was strengthened. The learning period was adjusted, such as moving and arranging contents that are difficult for students to understand to the upper semester or the upper grade. In the 1st and 2nd graders, the amount of reading was drastically reduced to suit the students' level of Korean, and sentences and vocabulary were improved, and instructions were briefly revised. As for editing and design improvements, illustrations of each unit's introduction and contextual pictures were presented in detail, and the characters in the textbook were consistently presented across all grades, giving children characters a role to actively participate in learning in the textbook. In the process of compiling, the media, the National Assembly, and civic groups raised opinions that sentences and vocabulary in first-year textbooks are more difficult than students' level of Hangeul education, that reducing textbooks makes it difficult for students to understand. Accordingly, efforts to improve textbook compilation and the results were viewed. Through the overall analysis as above, for future compilation of state-authored textbooks and certified textbooks, a plan to improve textbook compilation for students and teachers and a plan to operate compilation was proposed.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• Journal of Digital Convergence
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• v.14 no.10
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• pp.53-60
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• 2016

This study investigated the effect of visual mathematics education using smartphones and immediate feedback through SNS on students' understanding of basic mathematical concept and academic achievement at the tertiary level. Researchers analyzed the test results of 214 students' mid-term and final examination in 4 classes consisted of 16 weeks' classes with two hours per week. Also their 30 questionnaire survey results were analyzed. The result reveals that classes using smartphones promoted understanding mathematical concepts and induced students' motivation and affirmative reaction. This study implies that an appropriate use of technology will support dynamic visualization of mathematical modeling and its interpretation, which enables students' active participation and deeper understanding.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.35-49
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• 2015

3D-Printing is one of the most innovative technologies that will be widely used in the 21st century. 3D-Printing also serves as an indispensable tool in STEAM education. In this article, we introduce what we have done in our mathematical modeling class in Uni. and recent R&E project under the support of Korean Foundation for the Advancement of Science and Creativity. We planned a model of STEAM education originating from our wish to make tangible models that use mathematical formulas to express the natural beauty of an object. We used a free, open-source software, Sage, to simulate these models online. Then, we created a program that generates a .STL file from these 3D images. This model can help students understand the natural beauty inherent in mathematics and use formulas and technology tools to simulate models in 3D. Finally, we were able to help students to create their own. STL files through a website we developed by adding Sage code into a Sage notebook. Then students can make and hold a 3D object of their very own. This process shows the possibility that mathematics, art and 3D-Printing can be effectively used to achieve the goals of STEAM education.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.261-275
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• 2012

There are some geometry achievement standards presented indistinctly in middle school mathematics curriculum revised in 2011. In this study, indistinctness of some geometric topics presented indistinctly such as symbol $\overline{AB}{\perp}\overline{CD}$ simple construction, properties of congruent plane figures, solid of revolution, determination condition of the triangle, justification, center of similarity, position of similarity, middle point connection theorem in triangle, Pythagorean theorem, properties of inscribed angle are discussed. The following three agenda is suggested as conclusions for the development of next middle school mathematics curriculum. First is a resolving unclarity of curriculum. Second is an issuing an authoritative commentary for mathematics curriculum. Third is a developing curriculum based on the accumulation of sufficient researches.