• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.73-83
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• 2009

Mathematics Olympiad aims to identify and encourage students who have superior ability in mathematics, to enhance students' understanding in mathematics while stimulating interest and challenge, to increase learning motivation through self-reflection, and to speed up the development of mathematical talent. Participating mathematical competition, students are going to solve a variety of types of mathematical problems and will be able to enlarge their understanding in mathematics and foster mathematical thinking and creative problem solving ability with logic and reasoning. In addition, parents could have an opportunity valuable information on their children's mathematical talents and guidance of them. Although there should be presenting diversified mathematical problems in competitions, the real situations is that resent most mathematics Olympiads present mathematical problems which narrowly focus on types of solving problems. In order to diversifying types of problems in mathematics Olympiads and making mathematics popular, this study will discuss a Olympiad for problem solving ability, a Olympiad for exploring mathematics, a Olympiad for task solving ability, and a mathematics fair, etc.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• 전기의세계
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• v.39 no.12
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• pp.21-32
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• 1990

퍼지 논리를 이용한 제어시스템에 관하여 핵심 개념을 중심으로 기술하고자 한다. 요약컨데 이 퍼지제어기의 특징은 1) Parallel(distributed) control 2) logic control 3) linguistic control등이며 퍼지 제어가 효과적일 수 있는 제어대상(plant)로서는 수학적 모델을 적용하기 힘든 시스템으로서 경험적으로 또는 수동적인 방법으로 제어가 잘되고 있는 대상을 들 수 있다. 그 뿐만 아니라 간단한 제어기가 필요한 경우로서 보다 효과적인 제어측 Software를 쓰거나 센서 또는 필터없이 사용가능하고, Inverted Penedulum의 자세 제어처럼 정확성보다는 속도 응답 제어가 요구되는 경우 등에 효과적으로 쓸 수 있는 것으로 알려지고 있다. Fuzzy 제어는 지식 베이스의 규모에서 인공지능형 Expert System보다 Compact하고 선형.비선형 플랜트에 공히 이용될 수 있으며, 설계자는 오퍼레이터와의 접촉을 통해 룰을 구축하므로 사용자가 시스템을 이해하기 쉬운 잇점등이 있기도 한다. 그러나 가장 큰 문제는 구축해 놓은 시스템의 안전성(Stability)를 이론적으로 사전에 검증하기가 어렵고, 같은 제어대상이라 할지라도 추론방법, 소속함수의 형태선택, 룰수 등에 따라 제어성능이 바뀔수 있으나, 무엇이 어떤 영향을 주는지 규명되지 않은점 등 여러가지 연구되어야 할 내용이 많이 있다.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.61-68
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• 2002

통계학은 불확실성(uncertainty)에 대한 연구이다. 베이지안 통계 방법은 불확실성 아래서 통계 추론과 의사 결정 모두를 위한 완전한(complete) 패러다임을 제공한다. 베이지안 방법론은 합리적인 초기 정보와 결합하는 것을 가능하게 만들고, 전통적인 통계적 방법론에 의하여 직면하는 많은 어려움들을 풀 수 있는 coherent 방법론을 제공하면서 엄격한 수학적 기본에 근거하고 있다. 베이지안 패러다임은 일반적인 용어로써 확률이란 단어의 사용을 가장 잘 어울리게 하는 불확실성의 조건부 측도(conditional measure of uncertainty)로써 확률의 해석에 근거한다. 관심있는 것에 대한 통계적 추론은 증거의 관점에서 그 값에 대한 불확실성의 변형으로써 묘사되며, 베이즈 정리(Bayes' theorem)는 이러한 변형이 어떻게 만들어지는 가를 자세히 설명할 수 있다. 베이지안 방법들은 전통적인 통계적 방법론에 접근할 없는 복잡하고, 다양한 구조적 문제들에 응용할 수 있다.

• The Mathematical Education
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• v.51 no.1
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• pp.47-61
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• 2012

Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.

• School Mathematics
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• v.8 no.2
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• pp.107-121
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• 2006

The purpose of this study is to understand various theories of cognitions of mathematics and to compare the difference between students in mathematics education and professors who teach them in their cognition of mathematics. For this purpose, a survey of 'cognitions of mathematics' was done to the students(future teachers) and professors who taught them in the capital area, and the results was statistically analyzed. It shows that professors have almost all of things in common with students in their cognitions of mathematics except some issues such as 'there are usually more than one way to solve mathematical tasks and problems,' or 'It is indispensible for mathematics to be definitional rigor,' which are statistically significant. Many theoretical and empirical grounds were supported for the differences in their responses. The study has, eventually, given valuable suggestions to lead people's attitudes and cognitions of mathematics to a deeper level.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• School Mathematics
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• v.19 no.2
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• pp.289-317
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• 2017

This study aims to explore how Korean middle-school mathematics textbooks on functions provide students an opportunity-to-learn [OTL]. For this purpose, we investigate 3 textbooks in terms of mathematics content and practice, the level of cognitive demands of mathematical tasks, types of student responses, types of context-based tasks, and connections among the tasks. The findings from the data analysis suggest as follows: a) an opportunity-to-learn to connect procedures to functional concepts and new ideas of functions to the existing one is very limited; b) the textbooks seem to provide students an OTL to understand functions as definitions, rules and conventions and to experience repeatedly procedural executions through worked examples and mathematics tasks; c) students may not experience to explain their own ideas/thinking by using mathematical sentence or justify their own cognitive processes; and d) students can be exposed to get a sense of mathematics as a set of fragmented and isolated facts or procedures, rather than to encourage to expand and deepen their understanding of functions.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.19-33
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• 2015

Recently in major industrial areas, there has been a rapidly increasing demand for 'Computational Thinking', which is integrated with a computer's ability to think as a human world. Developed countries in the last 20 years naturally have been improving students' computational thinking as a way to solve math problems with CAS in the areas of mathematical reasoning, problem solving and communication. Also, textbooks reflected in the 2009 curriculum contain the applications of various CAS tools and focus on the improvement of 'Computational Thinking'. In this paper, we analyze the cases of mathematics education based on 'Computational Thinking' and discuss the mathematical content that uses the CAS tools including Sage for improving 'Computational Thinking'. Also, we show examples of programs based on 'Computational Thinking' for teaching Calculus in university.