• Title/Summary/Keyword: mathematical representation

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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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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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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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On Mathematics Education Major Students' Conception of Characteristics of Mathematical Knowledge (수학적 지식의 특성요소에 대한 수학교육전공 대학생의 인식 상황)

  • Kim, Young-Kuk
    • The Mathematical Education
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    • v.51 no.2
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    • pp.161-171
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    • 2012
  • Generally mathematics is regarded as a subtle subject to grasp their true meaning. And teacher's personal conceptions of mathematics influence greatly on the teaching and learning of mathematics. More over often teachers confess their difficulties in explaining the true nature of mathematics. In this paper, applying the theory of epistemology, we tried to search factors that must be counted important when trying to understand the true nature of mathematics. As results, we identified five characteristics of mathematical knowledge such as logical reasoning, abstractive concept, mathematical representation, systematical structure, and axiomatic validation. Next, we tried to investigate math education major students' conception of mathematics using these items. To proceed this research we asked 51 students from three Universities to answer their opinion on 'What do you think is mathematics?'. Analysing their answers in the light of the above five items, we got the following facts. 1. Only 38% of the students regarded mathematics as one of the five items, which can be considered to reveal students' low concern about the basic nature of mathematics. 2. The status of students' responses to the question were greatly different among the three Universities. This shows that mathematics professors need to lead students to have concern about the true nature of mathematics.

An approach to modeling a bionic self organization and functional expression

  • Yokoi, Hiroshi;Kakazu, Yukinori
    • 제어로봇시스템학회:학술대회논문집
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    • pp.334-339
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    • 1992
  • This study is concerned how to construct a model of life as physical/ mathematical representation. This model is called here a bionic model and vibrating potential field is introduced as fundamental world background of the model. Namely, required information creating/ processing/ controlling are done on this field. Especially this paper reports how to realize the simulation of a bionic self organization and its functional expression based on the mutual actions among a set of life units.

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A mathematical approach to motion planning for time-varying obstacle avoidance (시변 장애물 회피 동작 계획을 위한 수학적 접근 방법)

  • 고낙용;이범희;고명삼
    • 제어로봇시스템학회:학술대회논문집
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    • pp.388-393
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    • 1990
  • A robot manipulator and an obstacle are described mathematically in joint space, with the mathematical representation for the collision between the robot manipulator and the obstacle. Using these descriptions, the robot motion planning problem is formulated which can be used to avoide a time varying obstacle. To solve the problem, the constraints on motion planning are discretized in joint space. An analytical method is proposed for planning the motion in joint space from a given starting point to the goal point. It is found that solving the inverse kinematics problem is not necessary to get the control input to the joint motion controller for collision avoidance.

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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.

A Study of the Representation and Algorithms of Western Mathematics Reflected on the Algebra Domains of Chosun-Sanhak in the 18th Century (18세기 조선산학서의 대수 영역에 나타난 서양수학 표현 및 계산법 연구)

  • Choi, Eunah
    • Journal of the Korean School Mathematics Society
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    • v.23 no.1
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    • pp.25-44
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    • 2020
  • This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

Pre-Service Primary Teachers' Mathematical Investigation Through Transforming Mathematical Games (수학적 게임 변형을 통한 초등 예비교사의 수학적 탐구 경험)

  • Lee, Dong-Hwan
    • Journal of Educational Research in Mathematics
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    • v.26 no.1
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    • pp.143-157
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    • 2016
  • This study aims to find out the feasibility and effectiveness of mathematical games as a way to provide primary pre-service teachers with doing mathematics. The game had induced the active participation of elementary pre-service teachers. Through transforming the game, the teachers have been able to experience of mathematical problem posing and generating mathematical representation. Based on this, we discuss the role of mathematical games as a method of pre-service teacher education.

Use of Petri Nets to the Information Systems (페트리넷의 정보 시스템의 응용)

  • 차균현
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.19 no.3
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    • pp.28-36
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    • 1982
  • Petri nets have been used for medeling a wide variety of systems from computer to social systems. This paper disusses Petri nets in the context of mathematical representation and its associated bag theory. The method of modeling systems such as event-condition, computer progranm computer operation and PERT chart is discribed and their Petri net representation are presented. Finally Petri net representation of tunnel diode oscillator circuit and the analysis of the circuit using Petri net are discussed with the program and results.

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