• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.123-142
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• 2009

Dynamic context is considered as a source for intuitive understanding on the calculus. The relation between the area under time-velocity graph and distance is the base of the dynamic contexts which are treated in the integral calculus. The fundamental theorem of calculus has originated in dynamic contexts. This paper investigated the fundamental theorem of calculus via the relation between the area under time-velocity graph and distance. And we analyzed mathematics textbooks and the understanding of students. Finally we suggest some proposal for the teaching of the fundamental theorem of calculus.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.139-152
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• 2017

In this paper, we examine how secondary school mathematics textbooks on calculus introduce the history of calculus. In order to identify the problem, we consider the Babylonian integration by trapezoidal rule, which was made to calculate the location of Jupiter in 350-50 B.C., and the integration by the method of the rotating plate of ibn al-Haytham in Egypt, about 1000 years. In conclusion, our secondary school mathematics textbooks describe Newton and Leibniz as inventing calculus and place their roots in ancient Greece. The origin of the calculus is in Babylonia and the Faṭimah Dynasty (909-1171) (Egypt) and it is desirable that the calculus is developed in Europe after the development of the power series in India, and that the value of Asia Africa is introduced in the textbooks.

• Korean Architects
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• s.560
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• pp.82-87
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• 2015

지난 회에서는 형태와 형태이면에 있는 구현의 논리를 모두 다룰 수밖에 없는 파라메트릭 툴의 성격에 대하여 간략하게 이야기 해보았고 이를 반증할수 있는 곡면상의 패널링의 예를 살펴 보았습니다. 삼차원 곡면으로 인해 발생하는 패널들의 시각적 왜곡 및 구축상의 어려움을 해결하고자 왜곡이 발생하는 물리적인 이유를 이해하고 이를 미적분의 개념을 빌어 해결해 보았습니다. 오늘 살펴볼 예도 이와 비슷한 미적분의 개념을 빌리게 되지만 문제의 해결을 위함이 아닌 자연 현상을 시뮬레이션 하고 시뮬레이션의 결과로 얻어진 데이터를 설계에 반영하기 위함이라는데에 차이가 있다고 할 수 있겠습니다. 오늘 살펴볼 내용은 Harvard GSD에서 대학원 설계 수업의 일환으로 제가 진행하였던 파라메트릭 디자인 워크샵의 결과물이며 추후에 이를 실무에 이용하게 됩니다.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.157-185
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• 2013

This study was to investigate novice teachers' Specialized Content Knowledge for Teaching in High School Calculus Lessons. The lessons of two novice teachers in Kyunggi Do were observed from July, 2011 to Feb. 2012. All observed lessons were audeotaped and transcribed into word files. Their calculus lessons were analyzed into three kinds of knowledge consisting of SCKT. Their SCKT just copied the contents of the textbook and other additional SCKT were not found for teaching. Even though students asked a question that they did not understand, the teacher just repeated the previous contents that already he used. But this study included possible contents of SCKT within the areas these teachers covered so that teachers in school may use for teaching of Calculus. The novice teacher do not have sufficient experience, the program of the college of education and the contents of the teacher certificate-examination should include multi-dimensional approaches in SCKT to pre-service teachers in order to raise better specialized teachers in mathematics.

• The Journal of Korean Association of Computer Education
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• v.4 no.2
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• pp.105-114
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• 2001

This paper illustrates a calculus module which generates step-by-step solutions using J/Link that connects Java and Mathematica. Such a module provides intermediate and low level students with a practical environment where they can easily follow the solution paths on their own paces. The extra feature of this module depicts graphical images for a given function and its differentiated result to enhance the visual understandings of calculus concepts. Mathematica as a mathematical expert system that provides systematic mathematical knowledge to students with step-by-step solutions will be possibly extended to the tutorial or CMI development. The proposed module is implemented in a Java servlet that links to Mathematica FrontEnd. This approach results in adopting font systems to express two dimensional mathematical expressions in web documents as an alternative typesetting tool.

• The Mathematical Education
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• v.35 no.1
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• pp.15-23
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• 1996

• The Mathematical Education
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• v.32 no.3
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• pp.158-194
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• 1993

• School Mathematics
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• v.5 no.4
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• pp.521-540
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• 2003

The processes of mathematics development and the results of it are always those of making a conquest of the circumscription by historical inevitability within the historical circumscription. It is in this article that I try to show this processes through the history of calculus. This article develops on the basis of the dialectical materialism. It views the change and development as the facts that take place not by individual subjective judgments but by social-historical material conditions as the first conditions. The dialectical materialism is appropriate for explaining calculus treated in full-scale during the 17th century, passing over ahistorical vacuum after Archimedes about B.C. 4th century. It is also appropriate for explaining such facts as frequent simultaneous discoveries observed in the process of the development of calculus. 1 try to show that mathematics is social-historical products, neither the development of the logically formal symbols nor the invention by subjectivity. By this, I hope to furnish philosophical bases on the discussion that mathematics teaching-learning must start from the real world.

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.109-116
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• 2008

The variation of real phenomena and shape of nature in our world is so complicated that some mathematical tools using the traditional geometric methods based on the Euclidean geometry and analytical differential method may be irrelevant or insufficient in some problems. Recently, to deal with these circumstances, one can use the fractal geometric method. As another measures, in this paper we introduce the non-integral order derivative function for the analytical method and construct to facilitate their calculation.

• The Science & Technology
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• v.28 no.6 s.313
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• pp.24-25
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• 1995

근대 물리학의 아버지로 불리는 아이작 뉴턴은 「프린키피아」에 만유인력의 법칙을 발표 근대과학의 새로운 우주관을 완성했다. 또한 뉴턴은 스팩트럼,미적분의 발견 등 수학에도 큰 업적을 암긴 것으로 유명하다