• Title/Summary/Keyword: Mathematical analysis

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Learning and Teaching of Mathematical Analysis in Teachers College (교사 양성 대학에서의 해석학의 학습과 지도)

  • 이병수
    • The Mathematical Education
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    • v.42 no.4
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    • pp.541-559
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    • 2003
  • This paper considers learning and teaching of mathematical analysis in teachers college. It concentrates on showing a way how learning and teaching of mathematical analysis should be considered for mathematical teachers training. It is composed of five chapters including Chapter I as an introduction and Chapter Vasa concluding remarks. Chapter II deals with goal and contents of global mathematical analysis. The main Chapter, named Chapter III, demonstrates exhibition of contents, way of operations, and contents of teaching and learning of mathematical real analysis. Chapter IV shows an example of learning and teaching of mathematical real analysis concerning to fixed points and approximate solutions.

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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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A Study on the Educational Analysis of a Mathematical Problem and Systematization of Related Problems (한 가지 수학 문제의 교육적 분석 및 관련된 문제의 체계화에 대한 연구)

  • 한인기
    • The Mathematical Education
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    • v.42 no.1
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    • pp.57-67
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    • 2003
  • In this paper we analyze educational aspects of a mathematical problem. As a result of the analysis, we extract five meaningful mathematical knowledge and ideas. Corresponding with these we suggest some chains of mathematical problems that are expected to activate student's self-oriented mathematical investigation.

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An analysis of mathematical tasks in the middle school geometry (중학교 수학 교과서에 제시된 기하영역의 수학 과제 분석)

  • Kwon, JiHyun;Kim, Gooyeon
    • The Mathematical Education
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    • v.52 no.1
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    • pp.111-128
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    • 2013
  • The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the strand of geometry in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith(1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at high level and the rest at low level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.

A research on Mathematical Invention via Real Analysis Course in University (대학교의 해석학 강좌에서 학생들의 수학적 발명에 관한 연구)

  • Lee, Byung-Soo
    • Communications of Mathematical Education
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    • v.22 no.4
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    • pp.471-487
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    • 2008
  • Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

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Pre-service mathematics teachers' perceptions on mathematical modeling and its educational use (예비 수학 교사들의 수학적 모델링 및 그 교육적 활용에 대한 인식)

  • Han, Sunyoung
    • The Mathematical Education
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    • v.58 no.3
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    • pp.443-458
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    • 2019
  • Mathematical modeling has been a crucial topic in mathematics education as students' problem solving competency are regarded as a core skill for future society. Despite of the importance of mathematical modeling in school mathematics, there have been very limited studies relating pre-service teachers' knowledge and perceptions on mathematical modeling. In this vein, this study aimed to investigate pe-service mathematics teachers' perceptions on mathematical model, mathematical modeling and educational use of mathematical modeling, and their relationships. The current study utilized a survey consisted of 18 items. The responses of 210 pre-service mathematics teachers to the survey items were quantitatively analyzed using descriptive statistics, analysis of variance, exploratory and confirmatory factor analysis, the structural equation model, and multi group analysis. The results of analysis of variance revealed that pre-service teachers in difference groups (majors, grades, and experiences with mathematical modeling) showed statistically significant differences in mean values. Moreover, according to the results from the structural equation modeling analysis, pre-service mathematics teachers' perceptions on mathematical model and modeling affected their perceptions on educational use of mathematical modeling. In addition, depending on their pre-experiences with mathematical modeling, pre-service teachers represented a different relationship between perceptions on mathematical modeling and educational use of mathematical modeling. Implications for future studies and mathematics classrooms were discussed.

A Design and Implementation of a Web-based DSS for Mathematical Analysis (수리적 분석을 위한 웹 기반 의사결정지원시스템의 설계와 구현)

  • Kim, Sheung-Kown;Kim, Tae-Hyung
    • IE interfaces
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    • v.13 no.3
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    • pp.539-547
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    • 2000
  • An architecture of a Web-based Decision Support system for mathematical analysis is presented. Front-end modules provide web-client GUI environment for mathematical analysis. The networking architecture is built upon client/server system by Java socket and accesses database by JDBC in WWW. Back-end modules provide decision supporting service and data management for mathematical programming analysis. In the back-end any analysis tools, such as mathematical optimizer, simulation package, or statistics package can be used. As an application example for this implementation, optimal facility replacement decision problem is selected. In the implementation the optimal facility replacement decision problem is formulated as a shortest path problem. It uses Oracle DB and CPLEX package as the mathematical optimizer. While ORAWeb is designed and implemented on the optimal facility replacement problem, it can easily be extended to any decision supporting problems that would require mathematical optimization process.

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Exploration of Teaching Method through Analysis of Cases of Mathematical Modeling in Elementary Mathematics (수학적 모델링 사례 분석을 통한 초등 수학에서의 지도 방안 연구)

  • Kim, Min-Kyeong;Hong, Jee-Yun;Kim, Eun-Kyung
    • The Mathematical Education
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    • v.48 no.4
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    • pp.365-385
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    • 2009
  • Recently, mathematical modeling has been attractive in that it could be one of many efforts to improve students' thinking and problem solving in mathematics education. Mathematical modeling is a non-linear process that involves elements of both a treated-as-real world and a mathematics world and also requires the application of mathematics to unstructured problem situations in real-life situation. This study provides analysis of literature review about modeling perspectives, case studies about mathematical modeling, and textbooks from the United States and Korea with perspective which mathematical modeling could be potential and meaningful to students even in elementary school. Further, teaching method with mathematical modeling was investigated to see the possibility of application to elementary mathematics classroom.

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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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