• Title/Summary/Keyword: Mathematical concept

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Analysis of the Equality Sign as a Mathematical Concept (수학적 개념으로서의 등호 분석)

  • 도종훈;최영기
    • The Mathematical Education
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    • v.42 no.5
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    • pp.697-706
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    • 2003
  • In this paper we consider the equality sign as a mathematical concept and investigate its meaning, errors made by students, and subject matter knowledge of mathematics teacher in view of The Model of Mathematic al Concept Analysis, arithmetic-algebraic thinking, and some examples. The equality sign = is a symbol most frequently used in school mathematics. But its meanings vary accor ding to situations where it is used, say, objects placed on both sides, and involve not only ordinary meanings but also mathematical ideas. The Model of Mathematical Concept Analysis in school mathematics consists of Ordinary meaning, Mathematical idea, Representation, and their relationships. To understand a mathematical concept means to understand its ordinary meanings, mathematical ideas immanent in it, its various representations, and their relationships. Like other concepts in school mathematics, the equality sign should be also understood and analysed in vie w of a mathematical concept.

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Analysis Study of Mathematical Problem Structure through Concept Map (Concept Map을 통한 수학 문제의 구조 분석 연구)

  • Suh, Bo Euk
    • Communications of Mathematical Education
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    • v.32 no.1
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    • pp.37-57
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    • 2018
  • In the early days, the use of concept maps in mathematics education focused on how to represent mathematical ideas in the concept map. In recent years, however, concept maps have proved beneficial for improving problem solving ability. Conceptual diagrams can be used for collaboration among students, tools for exploring problems, tools for introducing problem structures, tools for developing and systematizing knowledge systems. In this study, we focused on the structure analysis of mathematical problems using Concept Map based on the analysis of previous research. In addition, we have devised a method of using concept maps for problem analysis and a method of analysis of systematic mathematical problem structure. The method developed in this study was found to have significant value by applying to the university scholastic ability test.

Error analysis related to a learner's geometrical concept image in mathematical problem solving (학생이 지닌 기하적 심상과 문제해결과정에서의 오류)

  • Do, Jong-Hoon
    • Journal of the Korean School Mathematics Society
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    • v.9 no.2
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    • pp.195-208
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    • 2006
  • Among different geometrical representations of a mathematical concept, learners are likely to form their geometrical concept image of the given concept based on a specific one. A learner's image is not always in accord with the definition of a concept. This can induce his or her errors in mathematical problem solving. We need to analyse types of such errors and the cause of the errors. In this study, we analyse learners' geometrical concept images for geometrical concepts and errors related to such images. Furthermore we propose a theoretical framework for error analysis related to a learner's concept image for a general mathematical concept in mathematical problem solving.

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An Analysis Study of Changes in Middle School Students' Mathematical Conceptual Structure Using a Learning Platform (수학 학습 플랫폼을 활용한 중학생의 문자와 식에 대한 개념 구조 변화 분석 연구)

  • Huh, Nan
    • East Asian mathematical journal
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    • v.39 no.2
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    • pp.167-181
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    • 2023
  • The purpose of this study is to confirm the possibility of whether learning using a math learning platform can be used to expand students' conceptual structure and to consider how to use it. To this end, first-year middle school students studied using a math learning platform. Then, the concept map created was compared and analyzed with the concept map created before learning to examine the change in the concept structure. The results of analyzing the concept map are as follows. First, the change in the hierarchical structure of the concept appeared as the division of the upper concept was subdivided. However, it has also been changed to comprehensively integrate and simplify higher concepts. The term-centered concept structure has changed to content-centered superordinate and subordinate concepts. In the concept structure, subordinate concepts linked to one higher concept were expanded and differentiated. Second, changes in the integrated structure did not form a linkage structure. The expansion of the integrated structure of concepts through learning using the learning platform was influenced by the composition of the learning contents designed in the learning platform.

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.

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.

Mathematical and Pedagogical Discussions of the Function Concept

  • Cha, In-Sook
    • Research in Mathematical Education
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    • v.3 no.1
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    • pp.35-56
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    • 1999
  • The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

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Instrument Development and Analysis of Secondary Students' Mathematical Beliefs (우리나라 중.고등학생의 수학적 신념 측정 및 특성 분석)

  • Kim, Bu-Mi
    • Journal of Educational Research in Mathematics
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    • v.22 no.2
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    • pp.229-259
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    • 2012
  • The purpose of the present study is to develop instrument of mathematical belief of middle school and high school students and to analysis results of test using the instrument. Based on the results of literature review, mathematical belief is the cumulative effects of self-assessment and self-concept in mathematical learning and achievement experience. Four sub-components of mathematical belief is identified belief of school mathematics, belief of mathematical problem solving, mathematical self-concept, belief of mathematical teaching and learning. The instrument was developed to investigate mathematical belief by reflecting Korean middle school and high school students' psychological characters. To develop the appropriate items for the mathematical belief, after reviewing literature thoroughly, first version of the instrument was developed and exploratory factor analysis and confirmatory factor analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Correlation Analysis and 1-way ANOVA was performed. Also, using multiple group confirmatory factor analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for middle school students is consisted 7 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 10 items of belief of mathematical teaching and learning. Instrument of mathematical belief for high school students is consisted 9 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 11 items of belief of mathematical teaching and learning. This study examined the differences about mathematical belief's sub-factors shown by three groups of mathematics achievement level. Students of higher achievement level showed that the degree of most factors ware the highest excepting stereotype of belief of school mathematics. Also, Male students preferred more positive in mathematics belief than female students.

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Mathematical Cognition as the Construction of Concepts in Kant's Critique of Pure Reason ("순수이성비판"에 나타난 수학적 인식의 특성: 개념의 구성)

  • Yim, Jae-Hoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.16 no.1
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    • pp.1-19
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    • 2012
  • Kant defines mathematical cognition as the cognition by reason from the construction of concepts. In this paper, I inquire the meaning and the characteristics of the construction of concepts based on Kant's theory on the sensibility and the understanding. To construct a concept is to exhibit or represent the object which corresponds to the concept in pure intuition apriori. The construction of a mathematical concept includes a dynamic synthesis of the pure imagination to produce a schema of a concept rather than its image. Kant's transcendental explanation on the sensibility and the understanding can be regarded as an epistemological theory that supports the necessity of arithmetic and geometry as common core in human education. And his views on mathematical cognition implies that we should pay more attention to how to have students get deeper understanding of a mathematical concept through the construction of it beyond mere abstraction from sensible experience and how to guide students to cultivate the habit of mind to refer to given figures or symbols as schemata of mathematical concepts rather than mere images of them.

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