• Title/Summary/Keyword: 미분개념

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다원환의 보편적 미분가군

  • Han, Jae-Yeong;Yeon, Yong-Ho
    • Communications of Mathematical Education
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    • v.6
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    • pp.383-407
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    • 1997
  • 가환다원환의 대수적 미분에 관한 성질들은 많은 연구의 대상이 되어 왔다. 본 논문은 가환 다원환에서 정의된 대수적 미분의 일반화로써 가환일 필요가 없는 일반다원환의 대수적 미분의 성질을 연구한 것이다. 비가환다원환의 미분정의를 바탕으로 하여 가환다원환에서 연구되어 온 보편적 미분가군의 성질을 일반다원환 의 미분가군에 적용하려고 노력하였다. 이 논문에서 사용한 정리의 증명과정이나 기본개념은 가환다원환의 미분개념에서 나타난 성질들을 바탕으로 하였다.

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Students' Understanding of the Derivative - Literature Review of English and Korean Publications - (학생들의 미분에 대한 이해에 관한 문헌 연구)

  • Park, Jung-Eun
    • Journal of the Korean School Mathematics Society
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    • v.15 no.2
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    • pp.331-348
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    • 2012
  • With a gradual increase in research on teaching and learning calculus, there have been various studies about students' thinking about the derivative. This paper reviews the results of the existing empirical studies published in Korean and English. These studies mainly have shown that how students think about the derivative is related to their understanding of the related concepts and the representations of the derivative. There are also recent studies that emphasize the importance of how students learn the derivative including different applications of the derivative in different disciplines. However, the current literature rarely addressed how students think about the derivative in terms of the language differences, e.g., in Korean and English. The different terms for the derivative at a point and the derivative of a function, which shows the relation between concepts, may be closely related to students' thinking of the derivative as a function. Future study on this topic may expand our understanding on the role language-specific terms play in students' learning of mathematical concepts.

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Students' Conceptual Metaphor of Differential Equations: A Sociocultural Perspective on the Duality of the Students' Conceptual Model (학생들의 미분방정식 개념에 대한 수학적 은유의 분석: 개념적 모델의 이중성에 대한 사회문화적 관점)

  • 주미경;권오남
    • School Mathematics
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    • v.5 no.1
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    • pp.135-149
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    • 2003
  • We present an understanding about students' conceptual model of differential equations, based on the discourse data that were collected in a differential equations course at a university in Korea. An interpretive approach is taken to analyze classroom discourse. This paper consists of three main parts. First, we completely analyze the students' use of conceptual metaphor in a university differential equations class. Secondly, we identify conceptual metaphors representing students' conceptual model of differential equations. Finally, we describe the mathematical characteristics of the conceptual metaphors identified in detail. Among other things, this paper reveals that there exists dual aspects of the students' conceptual model of differential equations. In other words, in the differential equations course observed we found that the students very often used two kinds of conceptual metaphor,“machine metaphor”and“fictive motion metaphor”, that have contrastingly different mathematical characteristics. In order to interpret the duality, we take a sociocultural perspective, and this perspective suggests and helps us to realize the significance of understanding of cognitive diversity in mathematics classroom.

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An Analysis on the Understanding of High School Students about the Concept of a Differential Coefficient Based on Integrated Understanding (통합적 이해의 관점에서 본 고등학교 학생들의 미분계수 개념 이해 분석)

  • Lee, Hyun Ju;Ryu, Jung Hyeon;Cho, Wan Young
    • Communications of Mathematical Education
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    • v.29 no.1
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    • pp.131-155
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    • 2015
  • The purpose of this study is to investigate if top-ranked high school students do integrated understanding about the concept of a differential coefficient. For here, the meaning of integrated understanding about the concept of a differential coefficient is whether students understand tangent and velocity problems, which are occurrence contexts of a differential coefficient, by connecting with the concept of a differential coefficient and organically understand the concept, algebraic and geometrical expression of a differential coefficient and applied situations about a differential coefficient. For this, 38 top-ranked high school students, who are attending S high school, located in Cheongju, were selected as subjects of this analysis. The test was developed with high-school math II textbooks and various other books and revised and supplemented by practising teachers and experts. It is composed of 11 questions. Question 1 and 2-(1) are about the connection between the concept of a differential coefficient and algebraic and geometrical expression, question 2-(2) and 4 are about the connection between occurrence context of the concept and the concept itself, question 3 and 10 are about the connection between the expression with algebra and geometry. Question 5 to 9 are about applied situations. Question 6 is about the connection between the concept and application of a differential coefficient, question 8 is about the connection between application of a differential coefficient and expression with algebra, question 5 and 7 are about the connection between application of a differential coefficient, used besides math, and expression with geometry and question 9 is about the connection between application of a differential coefficient, used within math, and expression with geometry. The research shows the high rate of students, who organizationally understand the concept of a differential coefficient and algebraic and geometrical expression. However, for other connections, the rates of students are nearly half of it or lower than half.

Students' Reinvention of Derivative Concept through Construction of Tangent Lines in the Context of Mathematical Modeling (수학적 모델링 과정에서 접선 개념의 재구성을 통한 미분계수의 재발명과 수학적 개념 변화)

  • Kang, Hyang Im
    • School Mathematics
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    • v.14 no.4
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    • pp.409-429
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    • 2012
  • This paper reports the process two 11th grade students went through in reinventing derivatives on their own via a context problem involving the concept of velocity. In the reinvention process, one of the students conceived a tangent line as the limit of a secant line, and then the other student explained to a peer that the slope of a tangent line was the geometric mean of derivative. The students also used technology to concentrate on essential thinking to search for mathematical concepts and help visually understand them. The purpose of this study was to provide meaningful implications to school practices by describing students' process of reinvention of derivatives. This study revealed certain characteristics of the students' reinvention process of derivatives and changes in the students' thinking process.

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A study on understanding of differentiation (미분의 이해에 대한 연구)

  • Oh, Hye-Young
    • Communications of Mathematical Education
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    • v.32 no.2
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    • pp.131-146
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    • 2018
  • Differentiation with integration is an important subject which is widely applied in mathematics, natural science, and engineering. Derivative is an important concept of differentiation. But students don't understand its concept well and concentrate on acquiring only the skill to solve the standardized calculus problem. So they are poor at understanding of the concept of differentiation. In this study, after making a survey of differentiation on college students, we try to analyze errors which appeared in solving differentiation problem and investigate mathematics process of limiting process inherent in the derivative and historical development about derivative. Thus, we try to analyze the understanding of differentiation and present the results about this.

Social Transformation of Students' Conceptual Model in an RME-based Differential Equations Course: An Analysis of Students' Use of Conceptual Metaphor (RME 기반 수학 교실에서의 개념적 모델의 사회적 변환: 미분방정식에 대한 개념적 은유 사용 패턴 분석)

  • 주미경;권오남
    • Journal of Educational Research in Mathematics
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    • v.14 no.3
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    • pp.221-237
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    • 2004
  • This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

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An Investigation on the Historical Development of the Derivative Concept (미분계수의 역사적 발달 과정에 대한 고찰)

  • Joung, Youn-Joon
    • School Mathematics
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    • v.12 no.2
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    • pp.239-257
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    • 2010
  • In school mathematics the derivative concept is intuitively taught with the tangents and the concept of instantaneous velocity. In this paper, I investigated the long historical developments of the derivative concepts and analysed the relationships between the definition of derivative and the related elements. Finally I proposed some educational implications based on the analysis.

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대학수학에 필요한 기초 개념 이해도 측정

  • Kim, Byeong-Mu
    • Communications of Mathematical Education
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    • v.19 no.1 s.21
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    • pp.57-68
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    • 2005
  • 무한, 극한, 연속, 미분가능과 같은 중요한 수학적 개념을 이해하는 것은 대학수학 교양과정의 미분적분학 수강생들에게 필수적이다. 이들 개념의 이해 수준을 부록1, 2, 3을 통해 알아보고 평가를 분석한다. 평가결과는 이해도가 낮은 학생들을 위한 새로운 교수법이 필요성을 알게 하고 수학적 기본개념의 이해를 증진시키는데 정의의 정확한 이해를 돕고 구체적인 예제를 제시하는 교수법 개발에 수학교수의 노력을 필요로 한다.

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A Study on Mathematizing Teaching and Learning in Highschool Calculus (고등학교 미적분에서의 수학화 교수.학습에 관한 연구)

  • Cho, Wan-Young
    • School Mathematics
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    • v.8 no.4
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    • pp.417-439
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    • 2006
  • Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.

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