• Title/Summary/Keyword: 수학적 표현

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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.

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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Visual Sentences for Educational Math Games

  • Chang, Hee-Dong
    • 한국게임학회지
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    • v.8 no.1
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    • pp.32-38
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    • 2011
  • The help or guide sentences of educational math games which use mathematical statements need to represent graphical forms for the learners of the game generation whose cognitive style is graphic first. In this paper, we proposed an object-based visual representation method for mathematical statements. It has object-based description rules to use graphical symbols and mathematical symbols with text words. It is easy to describe or to understand accurately mathematical meaning and is also fast for learners to read for understanding. The proposed method is good for learners of the game generation to get the help as scaffolding for learning math by educational games.

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A Qualitative Case Study about Mathematics Pre-Service Teachers' Ways of Dealing with Math and Linguistic Expressions on Infinity (중등 수학 예비교사의 수학을 다루는 방식과 무한에 관한 언어적 표현 양상에 대한 질적 사례 연구)

  • Jun, Youngcook;Shin, Hyangkeun
    • School Mathematics
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    • v.15 no.3
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    • pp.633-650
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    • 2013
  • The aim of this paper is to explore and understand, using in-depth interviews, the participant's interests and discourse analytic expressions in studying the notion of infinity and limit. In addition we tried to understand how the participant's ways of dealing with math and thinking patterns on the polygons whose boundary is infinite but area is finite as they brought up such examples. Further follow-up questions are posed on the infinite sum of a smallest number close to 0 and the sum of infinite sets of different smallest numbers close to 0. Larger aspects of two pre-service teachers' subjective thinking patterns and colloquial discourses were sketched by contrasting the three posed tasks. Cross case discussions are provided with several suggestions for the future research directions.

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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 6th Graders' Use of Visual Representations in Mathematical Problem Solving (수학 문제 해결과정에서 초등학교 6학년 학생들의 시각적 표현에 관한 연구)

  • Hwang, Hyun-Mi;Pang, Jeong-Suk
    • Education of Primary School Mathematics
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    • v.12 no.2
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    • pp.81-97
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    • 2009
  • Visual representations play an important role for students to understand the meaning of a given problem, devise problem-solving approaches, and implement them successfully. The purpose of this study was to investigate how 6th graders would use visual representations in solving mathematical problems and in what ways such use might affect successful problem solving. The results showed that many students preferred numerical expressions to visual representations. However, students who used visual representations, specifically schematic representations, performed better than those who employed numerical representations. Given this, this paper includes instructional implications to nurture students' use of visual representations in a way to increase their problem solving ability.

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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.

삼각함수 학습지도에서 테크놀로지의 활용

  • Choe, Jong-Sul;Kim, Hyang-Suk;Kim, Bu-Yun
    • Communications of Mathematical Education
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    • v.16
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    • pp.123-137
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    • 2003
  • 본 논문의 목적은 삼각함수의 학습에 테크놀로지가 기여할 수 있는 방법적인 측면과 인지적인 효과를 명시하는 것이다. 테크놀로지가 삼각함수의 학습에 기여할 수 있는 네 가지 방법론적인 면을 '수학과 학생들의 실제 경험의 연결', '수학적 대상과 수학적 관계의 구체화', '수학의 다양한 표현 체계의 연결', '사고력 중심의 수학교육 추구'의 관점에서 논한다. 이 네 가지 방법론적인 측면 중 '수학적 대상과 수학적관계의 구체화'와 '수학의 다양한 표현 체계의 연결'을 중심으로 삼각함수의 학습법을 예시하면서 이 두 가지 방법이 어떻게 인지적으로 기여하는지를 보여준다.

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Mathematical Exploration of Counterweight Activities (분동을 활용한 문제의 수학적 탐구)

  • Kim, Sang-Lyong
    • Journal of Elementary Mathematics Education in Korea
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    • v.14 no.1
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    • pp.123-134
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    • 2010
  • Recently, mathematics education have been emphasized on developing students' mathematical thinking and problem solving abilities. Accordance with this emphasis, dramatical changes are needed in learning mathematics not merely let alone students solve real-made mathematics problems. The project learning to explore a counterweight activity will have an effects on positive mathematical attitude(to pose problem, to have curiosity) and mathematical thinking(power 10-digit representation, 2-digit number, two representation of 3-digit number, connect exponential number and log situation) which could develop understanding problems and critical thinking.

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