• 한국수학교육학회지시리즈E:수학교육논문집
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• 제32권2호
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• pp.131-146
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• 2018

미분학은 적분학과 더불어 수학, 자연과학, 공학 등에서 널리 응용되는 중요한 분야이다. 도함수는 미분학의 중요 개념인데, 학생들은 이것의 개념을 제대로 파악하지 않은 채 정형화된 계산 문제를 푸는 기능 습득에만 치중하고 있어 미분에 대한 개념적 이해는 매우 빈약한 상태이다. 이에 본 연구에서는 학부 학생들을 대상으로 미분에 대한 설문조사를 실시하여, 미분학 문제를 풀 때 나타난 오류를 분석하고 도함수에 내재한 극한과정의 수학화 과정과 도함수에 대한 역사적 발달과정을 살펴보고자 한다. 이 과정을 통해 미분의 이해도를 분석하고 이에 대한 결과를 제시하고자 한다.

• 한국수학사학회지
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• 제21권2호
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• pp.81-90
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• 2008

대학교육에서 다변수함수의 미분은 수리적 분석을 요하는 학문의 발전과 더불어 점차 그 중요성이 강조되고 있다. 그러나 현재 대학교양교육에서 학생들에게 도입되고 있는 다변수함수의 미분 정의는 처음 접하는 학생들에게 쉽지 않게 느껴지는 면이 있다. 이에 본 저자가 최근 몇 년간 교양수학을 가르치면서 학생들의 이해를 돕기 위해 고안한 방법이 있어 이를 소개하고자 한다. 본 저자의 경험을 토대로 한 이 방법은 다변수함수의 미분 정의에 대한 직관적이면서 기하학적인 설명법으로서 엄밀한 증명에 의한 접근 방법은 아니지만 다변수 미분의 의미를 빠르게 전달할 수 있다는 장점이 있다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제1권1호
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• pp.7-12
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• 1997

The curriculum differentiation is supposed to maximize individual strength and possibilities of the students, and to maximize educational efficiency by differentiating the instructions according to students' abilities, aptitudes, needs and interests. The Ministry of Education has suggested a stepwise model for school mathematics. This model is named "Stepwise Curriculum Differentiation"(段階別 敎育課程 差別化). In this paper, we would like to make a specific proposal for the 7th curriculum. Our proposal reflects fully the guidelines of the Ministry of Education. It is also based on the national curriculum history up to the present time. It could be used as a reference for the continuing work of curriculum reformation. We suggest dividing the contents of mathematics for 1-10th graders into about 15 steps, to use the step-based textbooks instead of the grade-based ones, and to prepare evaluation standards for each step. We also suggest that the classes for grades 11-12 be organized according to their optional courses and/or their steps.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.963-980
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• 2009

In this paper, spectral scheme based on Hermite interpolation for solving partial differential equations is presented. The idea of this Hermite spectral method comes from the spectral method on arbitrary grids of Carpenter and Gottlieb [J. Comput. Phys. 129(1996) 74-86] using the Lagrange interpolation.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권2호
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• pp.157-177
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• 2018

The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제26권3호
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• pp.167-202
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• 2023

A central problem of mathematics teaching worldwide is probably the insufficient adaptive handling of tasks-especially in computational practice phases and modeling tasks. All students in a classroom must often work on the same tasks. In the process, the high-achieving students are often underchallenged, and the low-achieving ones are overchallenged. This publication uses different modeling of the tennis serve as an example to show a possible solution to the problem and develops and discusses one adaptive task each for middle school, high school, and college using three mathematical models of the tennis serve each time. From model to model within the task, the complexity of the modeling increases, the mathematical or physical demands on the students increase, and the new modeling leads to more realistic results. The proposed models offer the possibility to address heterogeneous learning groups by their arrangement in the surface structure of the so-called parallel adaptive task and to stimulate adaptive mathematics teaching on the instructional topic of mathematical modeling. Models A through C are suitable for middle school instruction, models C through E for high school, and models E through G for college. The models are classified in the specific modeling cycle and its extension by a digital tool model, and individual modeling steps are explained. The advantages of the presented models regarding teaching and learning mathematical modeling are elaborated. In addition, we report our first teaching experiences with the developed parallel adaptive tasks.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권3호
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• pp.313-327
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• 2014

'Tangent' is one of the most important concepts in the middle and high school mathematics, especially in dealing with calculus. The concept of tangent in the current textbook consists of the ways which make use of discriminant or differentiation. These ways, however, do not present dynamic view points, that is, the concept of variation. In this paper, after applying 'Roberval's way of finding tangent using vectors in terms of kinematics to parabola, ellipse, circle, hyperbola, cycloid, hypocycloid and epicycloid, we will identify that this is the tangent of those curves. This trial is the educational link of mathematics and physics, and it will also suggest the appropriate example of applying vector. We will also help students to understand the tangent by connecting this method to the existing ones.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.523-538
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• 1999

A new preconditioning method is investigated to reduce the roundoff error in computing derivatives using Chebyshev col-location methods(CCM). Using this preconditioning causes ration of roundoff error of preconditioning method and CCm becomes small when N gets large. Also for accuracy enhancement of differentiation we use a domain decomposition approach. Error analysis shows that for this domain decomposition method error reduces proportional to the length of subintervals. Numerical results show that using domain decomposition and preconditioning simultaneously gives super accu-rate approximate values for first derivative of the function and good approximate values for moderately high derivatives.

• 한국학교수학회논문집
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• 제3권1호
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• pp.59-67
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• 2000

This study has been done to help teach mathematics on the spot of education by providing the history of mathematics and illustrations concerning mathematics, which were rearranged for the level of the second grade students in highschool and intented to interest students in mathematics classes. The contents of teaching, according to each unit (Matrix, Sequence, Limit, Differentiation, Integration, Probability, Statistics) include the life of the representative mathematician, the historical background centered on episodes, questions linked with reality, questions making sensations in history and something for maxim in mathematics. If such contents are properly used, they are expected to be able to stimulate students' curiosity, and to be effective in improving students' learning ability in mathematics by causing them to show their active attitudes toward learning mathematics.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권2호
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.