• Title/Summary/Keyword: mathematical structure

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Mathematical Thinking and Developing Mathematical Structure

  • Cheng, Chun Chor Litwin
    • Research in Mathematical Education
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    • v.14 no.1
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    • pp.33-50
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    • 2010
  • The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

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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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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From Counting to Mathematical Structure

  • Cheng, Chun Chor Litwin
    • Research in Mathematical Education
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    • v.12 no.2
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    • pp.127-142
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    • 2008
  • The most important aim of mathematics education is to promote mathematical thinking. In the Hong Kong primary school, mathematical thinking is usually conducted through the use of formula and working on "application problem" or "word problems". However, there are many other ways that can promote mathematical thinking, and investigation on mathematical structure by using counting is one important source for promoting mathematical thinking for primary school children, as every children can count and hence a well designed question that can be solved by counting can enable children of different abilities to work together and obtain different results.

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On the students' thinking of the properties of derivatives (도함수의 성질에 관련한 학생들의 사고에 대하여)

  • Choi, Young Ju;Hong, Jin Kon
    • The Mathematical Education
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    • v.53 no.1
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    • pp.25-40
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    • 2014
  • Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in 'Mathematics II' and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of 'function-derivatives', the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.

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.

SOME STRUCTURES ON A COMPLETE LATTICE

  • Lee, Seung On;Yon, Yong Ho
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.3
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    • pp.211-221
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    • 2007
  • In this paper, we define ${\bigwedge}$-structure, ${\bigvee}$-structure to generalize some lattices, and study the conditions that a lattice which has ${\bigwedge}$-structure or ${\bigvee}$-structure to be continuous or algebraic.

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A Case Studies for the Recovery of Mathematics Education: Focusing on the Utilization of Teachers' Mathematical Metaphors and the Structure of Teacher Discourse (수학 교육회복을 위한 사례 연구: 교사의 수학적 은유 활용과 교사 담론의 구조를 중심으로)

  • Choi, Sang-Ho
    • Communications of Mathematical Education
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    • v.36 no.3
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    • pp.397-415
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    • 2022
  • The purpose of this study is to analyze the discourse structure of teachers that can help students participate in class by using mathematical metaphors that can arouse students' interest and motivation. In order to achieve this goal, we observed a semester class of a career teacher who practiced pedagogy that connects students' experiences with mathematical concepts to motivate students to learn and promote participation. Among the metaphors that the study target teachers used in a variety of mathematical concepts and problem-solving processes during the semester, we extracted the two class examples that can help develop teaching methods using metaphors. Representatively selected two classes are one class example using metaphors and, the other class example using metaphors and expanding and applying problems. As a result of analysis, the structure of teacher discourse that uses metaphors and expands and applies problems by linking students' experiences with mathematical content was found to help solve a given problem and elaborate mathematical concepts. As a result of the analysis, the discourse structure of teachers using mathematical metaphors based on communication with students could provide implications for the development of teaching methods for the recovery of mathematics education.

Meaning and Structure of Understanding in Mathematics Education (수학 교육에서 '이해'의 의미와 구조에 대한 고찰)

  • 정인철
    • The Mathematical Education
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    • v.42 no.1
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    • pp.11-18
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    • 2003
  • One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

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