• Title/Summary/Keyword: 수학적 개념

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The Operational Approach and Structural Approach to the Mathematical Concepts - Focusing on exponential function and logarithmic function - (수학적 개념에 대한 조작적 접근과 구조적 접근 - 지수함수와 로그함수를 중심으로 -)

  • Kim, Bu-Yoon;Kim, So-Young
    • Communications of Mathematical Education
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    • v.21 no.3
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    • pp.499-514
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    • 2007
  • In modern mathematic education, the development of mathematical ability based on the understanding of mathematical concepts has been emphasized in curriculum and teaching methodology. Also, in schools, most math teachers stress the importance of mathematical concepts in doing math well. Thus, in this paper, we outlined the development of mathematical concepts through the literature survey. And then, based on the Sfard's definition of mathematical concepts, which classifies math concepts into the operational approach and structural approach, we analyzed the math concepts of exponential function and logarithmic function units in three highschool math textbooks. As the result, we found that the textbook authors used different approach for the same concepts, and, at the same time, they used both approaches to help develop the students' math concepts.

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College Students' Conceptions of Mathematics: A Comparison of Korean Students and American Students (대학생의 수학 개념: 한국 학생과 미국 학생의 비교)

  • JKang, Ok Ki
    • Journal of Educational Research in Mathematics
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    • v.13 no.1
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    • pp.1-12
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    • 2003
  • 이 논문은 수학적 개념의 뜻과 과 중요성을 살펴본 다음, 연구자가 소속되어 있는 한국의 대학생과 연구자가 연구년 동안 강의한 바 있는 미국의 대학생이 갖고 있는 수학적 개념의 수준에 대하여 조사하여 보고, 그 차이점을 비교하여 수학교육의 개선을 위한 시사점을 찾아보고자 하였다. 본 연구는 수학적 개념을 수학적 지식의 구성, 수학적 지식의 구조, 수학적 지식의 현상, 수학을 행하기, 수학적 아이디어의 가치 인식, 구성으로서의 학습, 유용한 노력으로서의 수학으로 분류하고 각 개념에 대한 양국 학생들의 인식 정도를 설문조사 방식으로 조사하였다. 본 연구에서 한국 학생들은 수학적 개념에 대한 7개의 영역 중에서 '수학적 지시의 현상', '수학을 행하기'를 제외한 5개의 영역에서 더 높은 수준을 보였다. 앞으로 한국의 수학교육은 수학을 실제로 행하는 활동을 더욱 강조하여야 할 것이다.

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Cyberhuman: The Interaction Autonomous Agents in Dynamic Environment (사이버인간: 동적 환경에서 능동 에이전트간 상호작용)

  • Bae, Kyung-Pyo;Park, Jung-Yong;Shin, Dong-Seung;Park, Jong-Hee
    • Proceedings of the Korean Information Science Society Conference
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    • pp.96-98
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    • 1998
  • 객체와 객체, 객체와 환경(공간 객체) 사이의 상호작용을 Field 라는 개념을 도입하여 개념적으로 장 이론이라는 방법론으로 객체들간의 상호작용을 해석하였다. 구체적으로 환경은 공간에 대한 수학적 개념으로 정의하고 객체와 환경사이의 상호작용은 해석하였다. 구체적으로 환경은 공간에 대한 수학적 개념으로 정의하고 객체와 환경사이의 상호작용은 일련의 상호 의존적 사실들로 표현하였다. 따라서 공간에 대한 수학적 개념과 힘의 역동 개념을 동원해서 객체와 환경이 주어진 상황에서 나타나는 구체적인 행동을 기술한다. Vector, Algebra, Topology 등과 같은 물리학적 및 수학적 개념을 도입하여 객체 상호작용을 해석하기 위한 과학적 이론 시스템 개발에 활용할 가능성을 제시하였다.

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Analysis on the Relationship between the 3rd Grade Middle School Students' Belief about Understanding and Academic Achievement, Mathematical Concepts, Mathematical Procedures (중학교 3학년 학생들의 '단원별 이해도에 대한 신념'과 학업성취도 와의 관계 및 수학적 개념, 수학적 절차에 대한 이해 정도 분석)

  • Kim, Do Yeon;Kim, Hong Chan
    • Communications of Mathematical Education
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    • v.27 no.4
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    • pp.499-521
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    • 2013
  • This paper analyzed the relationship between middle school students' belief about understanding with regard to mathematical concepts, procedures, and applications of the procedures. In order to gain our purpose, the academic achievement results of midterm examination of 139 middle school students and the surveys about their beliefs about understanding, mathematical concepts, and mathematical procedures were collected. And the cross analysis and the frequency analysis of SPSS were conducted. The research results showed that students' belief about understanding are irrelevant to their academic achievements. And the percentage of the students who believe that they understand was almost the same with the percentage of the students who understand the procedures. But there were differences between the percentage of the students who believe that they understand and the percentage of the students who understand the concepts. Through these, it is conformed. Students' belief about understanding does not mean they understand mathematical concepts. They just can solve mathematical problems through mechanical procedures.

Humanity mathematics education: revealing and clarifying ambiguities in mathematical concepts over the school mathematics curriculum (인간주의 수학교육: 수학적 개념의 모호성을 드러내고 명확히 하기)

  • Park, Kyo-Sik;Yim, Jae-Hoon;Nam, Jin-Young
    • Journal of Educational Research in Mathematics
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    • v.18 no.2
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    • pp.201-221
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    • 2008
  • This study discusses how the humanity mathematics education can be realized in practice. The essence of mathematical concept is gradually disclosed revealing the ambiguities in the concept currently accepted and clarifying them. Historical development of mathematical concepts has progressed as such, exemplified with the group-theoretical thought and continuous function. In learning of mathematical concepts, thus, students have to recognize, reveal and clarify the ambiguities that intuitive and context-dependent definitions in school mathematics have. We present the process of improvement of definitions of a tangent and a polygon in school mathematics as examples. In the process, students may recognize the limitations of their thoughts and reform them with feelings of humility and satisfaction. Therefore this learning process would contribute to cultivating students' minds as the humanity mathematics education pursues.

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Analysis of the Equality Sign as a Mathematical Concept (수학적 개념으로서의 등호 분석)

  • 도종훈;최영기
    • The Mathematical Education
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    • v.42 no.5
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    • pp.697-706
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    • 2003
  • In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

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Students' Reinvention of Derivative Concept through Construction of Tangent Lines in the Context of Mathematical Modeling (수학적 모델링 과정에서 접선 개념의 재구성을 통한 미분계수의 재발명과 수학적 개념 변화)

  • Kang, Hyang Im
    • School Mathematics
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    • v.14 no.4
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    • pp.409-429
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    • 2012
  • This paper reports the process two 11th grade students went through in reinventing derivatives on their own via a context problem involving the concept of velocity. In the reinvention process, one of the students conceived a tangent line as the limit of a secant line, and then the other student explained to a peer that the slope of a tangent line was the geometric mean of derivative. The students also used technology to concentrate on essential thinking to search for mathematical concepts and help visually understand them. The purpose of this study was to provide meaningful implications to school practices by describing students' process of reinvention of derivatives. This study revealed certain characteristics of the students' reinvention process of derivatives and changes in the students' thinking process.

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Creep Behavior of Unconsolidated Rock with Mathematical Concept Solution (수학적 개념 해를 적용한 미고결 암석의 Creep거동 해석)

  • Jang, Myoung-Hwan
    • Tunnel and Underground Space
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    • v.28 no.1
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    • pp.25-37
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    • 2018
  • Burger's model was used to analyze creep characteristics of unconsolidated rock. Burger's model should determine four physical parameters from two pairs of data. In this study, physical parameters of Burger's model were determined by applying mathematical concept solution. Creep was accelerated for three years using the determined physical parameters of the Burger's model for unconsolidated rocks. As a result, the creep behavior showed a continuous deformation behavior without convergence. Therefore, in this mine, it is analyzed that the application of U-Beam is more appropriate than roofbolt in terms of stability.

Patterns of mathematical concepts and effective concept learning - around theory of vectors (수학적 개념의 유형과 효과적인 개념학습 - 벡터이론을 중심으로)

  • Pak, Hong-Kyung;Kim, Tae-Wan;Lee, Woo-Dong
    • Journal for History of Mathematics
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    • v.20 no.3
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    • pp.105-126
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    • 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.

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