• Title/Summary/Keyword: 수학적 표현

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On the Pedagogical Significance of Mathematical Representations (수학적 표현의 교수학적 의의)

  • Kim, Young-Kuk
    • The Mathematical Education
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    • v.47 no.2
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    • pp.155-168
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    • 2008
  • The theory of representation, which has been an important topic of epistemology, has long history of study. But it has diverse meaning according to the fields of argument. In this paper the author set the meaning of mathematical representation as the interrelation of internal and external representations. With this concept, the following items were studied. 1. Survey on the concepts of mathematical representations. 2. Investigation of pedagogical significance of the mathematical representations, taking into account the characteristics of school mathematics. 3. Recommendation of principles for teaching representation to cope with the problems that are related with cause of disliking each domain of the secondary school mathematics. This study is expected to enable the development of teaching methods to help students strengthening their ability to comprehend mathematical sentences.

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An Analysis of Mathematical Communication in Elementary Mathematics (초등수학의 수학적 의사소통에 관한 분석)

  • Ahn, Byoung-Gon
    • Journal of Elementary Mathematics Education in Korea
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    • v.15 no.1
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    • pp.161-178
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    • 2011
  • For the students who live in the knowledge-information oriented society, thinking rationally and training mathematical communication ability are necessary. I represented three ways of teaching-learning related to mathematical communication in revised 2006 curriculum of elementary mathematics. In this study, based on three matters from devised curriculum, I have done survey-analysis of mathematical representation and characteristics of contents of major theses about mathematical communication published after 2007 curriculum revision, for further mathematical communication teaching.

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A study on the transition of the representations of numbers and mathematical symbols in Joseon mathematics (조선산학의 수학적 표현의 변천에 대한 고찰 - 수와 연산, 문자와 식 영역을 중심으로 -)

  • Choi, Eunah
    • Communications of Mathematical Education
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    • v.28 no.3
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    • pp.375-394
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    • 2014
  • The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

Mathematically Gifted Students' Justification Patterns and Mathematical Representation on a Task of Spatial Geometry (수학영재들의 아르키메데스 다면체 탐구 과정 - 정당화 과정과 표현 과정을 중심으로 -)

  • Lee, Kyong-Hwa;Choi, Nam-Kwang;Song, Sang-Hun
    • School Mathematics
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    • v.9 no.4
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    • pp.487-506
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    • 2007
  • The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

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An Analysis of Students' Mathematical Communication Competency focused on Fraction Division (분수의 나눗셈에 대한 초등학생의 수학적 의사소통 능력 분석)

  • Pang, Jeong Suk;Kim, Yoon Young;Sunwoo, Jin
    • Education of Primary School Mathematics
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    • v.25 no.2
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    • pp.179-195
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    • 2022
  • Mathematical communication competency, one of the six mathematical competencies emphasized in the latest mathematics curriculum, plays an important role both as a means and as a goal for students to learn mathematics. Therefore, it is meaningful to find instructional methods to improve students' mathematical communication competency and analyze their communication competency in detail. Given this background, this study analyzed 64 sixth graders' mathematical communication competency after they participated in the lessons of fraction division emphasizing mathematical communication. A written assessment for this study was developed with a focus on the four sub-elements of mathematical communication (i.e., understanding mathematical representations, developing and transforming mathematical representations, representing one's ideas, and understanding others' ideas). The results of this study showed that students could understand and represent the principle of fraction division in various mathematical representations. The students were more proficient in representing their ideas with mathematical expressions and solving them than doing with visual models. They could use appropriate mathematical terms and symbols in representing their ideas and understanding others' ideas. This paper closes with some implications on how to foster students' mathematical communication competency while teaching elementary mathematics.

암반공학 분야에서 수치해석의 적용성에 관하여

  • 이희근
    • Tunnel and Underground Space
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    • v.10 no.3
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    • pp.257-270
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    • 2000
  • 사물의 거동, 현상에 대한 해석을 실시함에 있어 해석적 해법에 대비한 수치적 해법의 장점은 재질의 성질이 불균질하고 이방성이며 구조물의 형태가 기하학적으로 복잡할 뿐만 아니라 경계조건이 복잡하여 수학적인 표현이 어려울 때 그 해석을 가능케 해 주는 것이라고 볼 수 있다. 이러한 수치 해석법의 대표적인 것으로 유한요소법과 경계 요소법을 들 수 있다.(중략)

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Characteristics of Students' Problem Solving Using Additive Strategy in Ratio and Proportion Tasks (비와 비례 과제에서 가법적 전략을 사용하는 학생의 문제해결특징 : 중학생 2명의 사례 연구)

  • Park, Jung-Sook
    • School Mathematics
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    • v.10 no.4
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    • pp.603-623
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    • 2008
  • The purpose of this research was to gain a better understanding of the characteristics of students' mathematical representations using additive strategy in ratio and proportion tasks. The additive strategy is the erroneous one used most often among the strategies reported in solving ratio and proportion tasks. It is a problem solving strategy that preserves the difference from one ratio to another. Students' additive strategies were categorized into four parts: subtracting without considering units of quantities, comparing the numbers that represent the whole subtracted from the part and same part, adding the difference, and subtracting the difference. In order to change from additive strategy to multiplicative strategy, the researcher asked to find out the unit quantity and found the characteristics of students' mathematical notations in the following: Firstly, the students made the number which they wanted by multiplying and adding same numbers. Secondly, they represented the mid-points between natural numbers. Thirdly, they related $a{\div}b$ to decimal number, not $\frac{a}{b}$. Fourthly, they were inclined to divide the larger number with the smaller number without understanding the context of the problem. These results are interpreted as showing that lower level of performance in the dividing operation with the notations of fraction hinders the transformation from additive strategy to multiplicative strategy.

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Mathematical expression systems of Xiangshu Zhouyi Theory in traditional times (중국 전통시기 역학의 수학적 해석체계)

  • YOON, SEOKMIN
    • The Journal of Korean Philosophical History
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    • no.35
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    • pp.385-413
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    • 2012
  • This thesis is a study on the relation of between Xiangshu Zhouyi Theory and mathematics, Zhouyi Theory as the one of the study of Chinese classics, was formed by Zhouyi' Eight Diagrams, the theory of Yinyangwuxing and the knowledge of natural science in Han dynasty. 'Xiangshu' had been regarded as the important concept and theory in the history of Zhouyi Theory From the beginning of Han dynasty to the end of Qing dynasty. At this developing of this Periodical Change, 'Xiangshu' had been endoded in the expression system of mathematics. This thesis considers binary system and surplus nembers, multiple and progression, magic square and circular constant, a proportional expression from Zhouyi Theory point of view. Xiangshu Zhouyi theory got the answer of these questions like the origin of Zhouyi, interpreting Guayao-word and Cosmology by using those expression systems of mathematics. Besides mathematics, Xiangshu Zhouyi theory was also related to astronomy, medicine, etc. Xiangshu Zhouyi theory had kept the pace with the general development of natural science. This thesis from the premise that Xiangshu Zhouyi theory kept the pace with natural science, summing up the mathematical expression system in the history of Zhouyi theory, proves that Xiangshu Zhouyi theory had developed according as the conditions of natural science.

유전 알고리즘과 군집 분석을 이용한 확률적 시뮬레이션 최적화 기법

  • 이동훈
    • Proceedings of the Korea Society for Simulation Conference
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    • 1998.10a
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    • pp.62-64
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    • 1998
  • 유전 알고리즘은 전통적인 등반 알고리즘을 이용하여 구하기 어려웠던 최적화 문제를 해결하기 위한 강인한 (Robust) 탐색 기법이다. 특히 목적함수가 (1)여러 개의 국부 최대치를 가지거나 (2)수학적으로 표현이 불가능하거나 어렵거나 (3) 목적함수에 교란항이 섞여 있을 경우도 우수한 탐색 능력을 갖는 것으로 알려져 있다. 본 논문에서는 군집성 분석(cluster analysis)을 이용하여 군집화함으로써 유전 알고리즘을 이용하여 나타나는 다양한 해집합을 형성하는 개체군을 그룹화하고, 각 군집에 부여된 군집 적합도에 따라서 최적해를 구함으로써 최적값에 근접시킬 수 있는 탐색 알고리즘을 제안하였으며, 시뮬레이션의 출력이 특정한 테스트 함수의 형태로 나타난다고 가정한 경우에 확률적으로 나타나는 시뮬레이션 모델의 출력을 최대화하는 문제에 대하여 적용하고 분석하였다.

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A Study on The Electronic Potential Occurrance Principle and Measurement by Stimulation of Multi-Link Neuron (다중 링크된 뉴런에서의 자극에 의한 전위발생 원리와 측정에 관한 연구)

  • 김석환;허창우
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 1998.05a
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    • pp.300-307
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    • 1998
  • 인간의 몸에서 발생하는 여러 생체반응을 이해하고 계측한다는 것은 매우 힘든 일이다. 그러나 분명히 존재하고 있는 물리화학적 변수들간의 상호관계를 정성적으로 묘사함으로써 생체반응을 설명한다. 본 논문에서는 인체의 기능을 추론 및 공학적 이론을 토대로 생체변수간의 관계를 수학적으로 표현하고 컴퓨터 시뮬레이션을 수행해 수리적으로 해석함으로써 인체의 각종현상을 정량적으로 예측한다.

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