• Title/Summary/Keyword: Structure of mathematics

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A study on the characteristics of the structure of mathematics textbooks of North Korean secondary school (북한 고등중학교 수학 교과서 구성 방식의 변화 고찰)

  • 임재훈;이경화;박경미
    • Journal of Educational Research in Mathematics
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    • v.13 no.1
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    • pp.95-106
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    • 2003
  • This study attempts to identify the characteristics of the structure of mathematics textbooks of North Korean high schools. The previous researches on the mathematics textbooks of North Korea show that North Korean mathematics textbooks have a linear structure, which is different from a spiral structure of South Korean textbooks. However, this study found that the textbooks of North Korea published after 1994 indicate that some sections reveal a spiral structure. In addition, most sections of North Korean mathematics textbooks are collectively composed, particularly so in the section of algebra.

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A Study on Influential Factors in Mathematics Modeling Academic Achievement

  • Li, Mingzhen;Pang, Kun;Yu, Ping
    • Research in Mathematical Education
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    • v.13 no.1
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    • pp.31-48
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    • 2009
  • Utilizing the path analysis method, the study explores the relationships among the influential factors in mathematics modeling academic achievement. The following conclusions are drawn: 1. Achievement motivation, creative inclination, cognitive style, the mathematical cognitive structure and mathematics modeling self-monitoring ability, those have significant correlation with mathematics modeling academic achievement; 2. Mathematical cognitive structure and mathematics modeling self-monitoring ability have significant and regressive effect on mathematics modeling academic achievement, and two factors can explain 55.8% variations of mathematics modeling academic achievement; 3. Achievement motivation, creative inclination, cognitive style, mathematical cognitive structure have significant and regressive effect on mathematics modeling self-monitoring ability, and four factors can explain 70.1% variations of mathematics modeling self-monitoring ability; 4. Achievement motivation, creative inclination, and cognitive style have significant and regressive effect on mathematical cognitive structure, and three factors can explain 40.9% variations of mathematical cognitive structure.

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Teachers' Knowledge Base and The Structure of Mathematical Knowledge for Effective Mathematics Teaching (효과적인 수학 교수를 위한 교사 지식 기반 영역과 수학적 지식 구조)

  • Kim, Young-Ok
    • Journal of the Korean School Mathematics Society
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    • v.11 no.4
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    • pp.595-608
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    • 2008
  • The purpose of this study is to address the teachers' knowledge bases for effective mathematics teaching and especially to provide the various definitions and the structures of mathematics knowledge which is the most important one of the knowledge bases. The conceptual understanding about teachers' knowledge bases for effective mathematics teaching and the structure of mathematics knowledge may be used in evaluating effective mathematics teaching and teachers as well as in developing a new conceptual framework for the structure of mathematical knowledge.

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Structuralist view of Knowledge and the Structure of Knowledge in Mathematics (지식에 대한 구조주의적 관점과 수학에서의 '지식의 구조')

  • 임재훈
    • Journal of Educational Research in Mathematics
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    • v.8 no.1
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    • pp.365-380
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    • 1998
  • Structualist view distinguishes structure(reality) from phenomenon(appearance). Phenomenon is the outside aspect of structure and structure is the inside aspect of phenomenon. From the structualist view, the knowledge could e divided into two parts, the appearance of knowledge(the outside aspect of knowledge)and the structure of knowledge(the inside aspect of knowledge). Structualist view advices teachers to understand knowledge more totally from the inside-outside viewpoint, and not to teach mere the one aspect of knowledge, especially the outside aspect of knowledge, that is, the written expressions in textbook, but to teach the inside and outside aspects fo knowledge totally. In the history of mathematics education, the attempts to teach the structure of knowledge were flourishing in the period of discipline-centered curriculum. 'New Math movement' represents the attempts. The advocators of New Math, however, did not succeed sufficiently to understand the inside-outside view which the term the structure of knowledge represents, and failed to make mathematics teachers to understand the view well. Their attention was put on to introduce the modern mathematics to school math rather than to understand the educational and epistemological perspective which the term the structure of knowledge represents. To teach the structure of knowledge, mathematics teacher should be able to understand mathematical knowledge more totally from the inside-outside viewpoint. Especially, s/he should not regard the outside aspect of mathematical knowledge written in textbook as the totality of knowledge, but inquire into the inside aspect of mathematical knowledge from the outside aspect of mathematical knowledge.

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On the instruction of concepts of groups in elementary school (초등학교에서의 군 개념 지도에 관한 연구)

  • 김용태;신봉숙
    • Education of Primary School Mathematics
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    • v.7 no.1
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    • pp.43-56
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    • 2003
  • In late 19C, German mathematician Felix Klein declaired "Erlangen program" to reform mathematics education in Germany. The main ideas of "Erlangen program" contain the importance of instructing the concepts of functions and groups in school mathematics. After one century from that time, the importance of concepts of groups revived by Bourbaki in the sense of the algebraic structure which is the most important structure among three structures of mathematics - algebraic structure. ordered structure and topological structure. Since then, many mathematicians and mathematics educators devoted to work with the concepts of group for school mathematics. This movement landed on Korea in 21C, and now, the concepts of groups appeared in element mathematics text as plane rigid motion. In this paper, we state the rigid motions centered the symmetry - an important notion in group theory, then summarize the results obtained from some classroom activities. After that, we discuss the responses of children to concepts of groups.of groups.

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The Main Problems of Internal Professional Structure of Mathematics Teachers in Middle Schools

  • Li Miao;Yu Ping
    • Research in Mathematical Education
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    • v.9 no.2 s.22
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    • pp.97-113
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    • 2005
  • Investigating mathematics teachers in middle schools by questionnaire and interview, we find some problems of internal professional structure of mathematics teachers in middle schools. These are reflected in five aspects: professional theory, professional knowledge, professional ability, professional morality, reflection and innovative consciousness.

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A Study on Improvement of MCPSS and Searching Structure of the Concept of Creative Products (수학 창의적 산출물 의미 척도의 개선 및 창의적 산출물의 구조 탐색)

  • Hong, Juyeun;Kim, Minsoo;Han, Inki
    • The Mathematical Education
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    • v.54 no.4
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    • pp.317-334
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    • 2015
  • In this article we study structure of the concept of creative products in mathematics using mathematical creative products. We develop MCPSS1 that improve reliability and validity of MCPSS(Creative Product Semantic Scale in Mathematics). And we search structure of the concept of creative products in mathematics using mathematical creative products focused on theoretical investigation. So we suggest structure model of the concept of creative products focused on theoretical investigation. We compare the result with preceding research using various mathematical creative products, find some difference between relations of sub-factors of structure of the concept of creative products. Our result will provide meaningful data to mathematics education researchers that want to know structure of the concept of creative products in mathematics.

A Cognitive Structure Theory and its Positive Researches in Mathematics Learning

  • Yu, Ping
    • Research in Mathematical Education
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    • v.12 no.1
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    • pp.1-26
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    • 2008
  • The concept field is defined as the schema of all equivalent definitions of a mathematics concept. Concept system is defined as the schema of a group concept network where there are mathematics relations. Proposition field is defined as the schema of all equivalent proposition sets. Proposition system is defined as a schema of proposition sets where one mathematics proposition at least is "derived" from the other proposition. CPFS structure that consists of concept field, concept system proposition field, proposition system describes more precisely mathematics cognitive structure, and reveals the unique psychological phenomena and laws in mathematics learning.

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How We Teach 'Structure' - Focusing on the Group Concept (어떻게 '구조'를 가르칠 것인가 - 군 개념을 중심으로)

  • 홍진곤
    • Journal of Educational Research in Mathematics
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    • v.10 no.1
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    • pp.73-84
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    • 2000
  • This study, after careful consideration on Piaget's structuralism, showed the relationship between Bourbaki's matrix structure of mathematics and Piaget's structure of mathematical thinking. This, studying the basic characters that structure of knowledge should have, pointed out that 'transformation' and to it, too. Also it revealed that group structure is a 'development' are essential typical one which has very important characters not only of mathematical structure but also general structure, and discussed the problem that learners construct the group structure as a mathematical concept.

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An Analysis of Geometrical Differentiated Teaching and Learning Materials Using Inner Structure of Mathematics Problems (수학 문제의 내적구조를 활용한 기하 영역의 수준별 교수-학습 자료의 분석 연구)

  • Han, In-Ki
    • Communications of Mathematical Education
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    • v.23 no.2
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    • pp.175-196
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    • 2009
  • In this paper we analyze Ziv's geometrical differentiated teaching and learning materials using inner structure of mathematics problems. In order to analyze inner structure of mathematics problems we in detail describe problem solving process, and extract main frame from problem solving process. We represent inner structure of mathematics problems as tree including induced relations. As a result, we characterize low-level problems and middle-level problems, and find some differences between low-level problems and middle-level problems.

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