• 한국학교수학회논문집
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• 제2권1호
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• pp.121-131
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• 1999

Recently our educational methodologies have been changed to an open, student-centered structure. Mathematics is now learned through experiential interaction and less emphasis is placed on abstract theories. For example, the axioms of the geometry in the middle school curriculum have been expressed by using symbolic letters. Students find these abstractions very difficult and it hinders their ability to grasp the significance of geometrical concepts. In an effort to simplify these abstract concepts and enhance the students interest and ability to learn, the GSP (Geometry Sketchpad) is proving to be a useful and effective tool. First, Second and third grade students have found the GSP to be extremely useful. While the pad has no sound function it still enables the students to freely change diagrams without disrupting the integrity of the program. There is also a running order of instructions at the bottom of the screen to facilitate the step by step understanding of mathematical procedures. This function makes the program ideal for use by teachers, students and even beginners. Anyone experiencing difficulty can get immediate assistance from the guidebook which is located at the back of each program. Allowing individuals to manipulate and actually see the changing deductions and axiom proofs on the computer screen provides them with immediate feedback and reinforcement. It also enhances their overall interest in learning geometry. The use of the GSP is proving to be an innovative and effective tool in facilitating the transition of mathematics into an open, student-centered educational forum.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제30권4호
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• pp.453-468
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• 2016

본 연구자는 만다라를 유아미술교육에 활용하였을 때 유아의 공간과 도형의 개념이 현저하게 향상된 결과를 얻었다. 본 논문은 그 후속연구로 부산광역시 H어린이집의 만3세 유아 44명, 만5세 유아 34명을 대상으로, 만다라와 유사한 구조를 가지는 프랙털 조형 활동이 유아의 공간과 도형의 수학적 개념에 미치는 영향을 연구하였다. 연구결과 만3세 유아는 4개 영역에서, 만5세 유아는 3개 영역에서 유의미함을 보였다. 만3세 유아는 조형 활동에서 과거의 기억을 표현하기 시작했으며, 만5세 유아는 스토리를 만들며 실물과 유사하게 재현하기도 했다. 또한 만5세의 경우 그림과 지점토의 표현에서 성별의 차이가 뚜렷하게 드러났으며, 만다라보다 프랙털이 더욱 효과적임을 보였다.

• 대한수학교육학회지:학교수학
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• 제8권1호
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• pp.45-68
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• 2006

본 연구는 싱가포르 수학 교육과정 및 교과서에 대해 최근 고조된 국제적 관심을 바탕으로, 도형과 측정 영역을 중심으로 한국과 싱가포르의 초등학교 수학교과서를 비교분석하였다. 우선 단원의 전반적인 전개방식 및 각 학년별 학습 내용과 주요 학습 주제 도입 시기를 면밀히 분석하여 교과서 개발에 관한 구체적인 시사점을 얻는 데 초점을 두었다. 또한, 구체적인 교과서 사례를 바탕으로 학습 내용 구성의 특징을 비교 분석하였다. 우리나라는 블럭 학습형태인 반면에, 싱가포르는 반복 학습형태를 취하고 있었다. 또한 싱가포르는 다각적인 분류 활동을 강조하여 도형의 핵심적인 속성을 파악하도록 교과서를 구성한 점이 돋보였다. 우리나라는 전형적인 모델을 주로 사용하는 반면에, 싱가포르는 다양한 모델을 제공하여 개념 형성에 폭넓은 기회를 주고 있었다.

• Smart Structures and Systems
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• 제14권2호
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• pp.159-189
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• 2014

One of the most important requirements in the evaluation of existing structural systems and ensuring a safe performance during their service life is damage assessment. Damage can be defined as a weakening of the structure that adversely affects its current or future performance which may cause undesirable displacements, stresses or vibrations to the structure. The mass and stiffness of a structure will change due to the damage, which in turn changes the measured dynamic response of the system. Damage detection can increase safety, reduce maintenance costs and increase serviceability of the structures. Artificial Neural Networks (ANNs) are simplified models of the human brain and evolved as one of the most useful mathematical concepts used in almost all branches of science and engineering. ANNs have been applied increasingly due to its powerful computational and excellent pattern recognition ability for detecting damage in structural engineering. This paper presents and reviews the technical literature for past two decades on structural damage detection using ANNs with modal parameters such as natural frequencies and mode shapes as inputs.

• 대한수학회지
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• 제50권5호
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• pp.1083-1103
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• 2013

The concepts of reversible, right duo, and Armendariz rings are known to play important roles in ring theory and they are independent of one another. In this note we focus on a concept that can unify them, calling it a right Armendarizlike ring in the process. We first find a simple way to construct a right Armendarizlike ring but not Armendariz (reversible, or right duo). We show the difference between right Armendarizlike rings and strongly right McCoy rings by examining the structure of right annihilators. For a regular ring R, it is proved that R is right Armendarizlike if and only if R is strongly right McCoy if and only if R is Abelian (entailing that right Armendarizlike, Armendariz, reversible, right duo, and IFP properties are equivalent for regular rings). It is shown that a ring R is right Armendarizlike, if and only if so is the polynomial ring over R, if and only if so is the classical right quotient ring (if any). In the process necessary (counter)examples are found or constructed.

• 대한수학회지
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• 제59권6호
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• pp.1229-1254
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• 2022

In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for ℤ^d₊-actions, explore the connections of levels of the topological structure the orbits of (quasi-)weakly almost periodic points and discuss the relations between (quasi-)weakly almost periodic point and minimal center of attraction. Especially, we investigate the chaotic dynamics near or inside the minimal center of attraction of a point in the cases of S-generic setting and non S-generic setting, respectively. Actually, we show that weakly almost periodic points and quasi-weakly almost periodic points have distinct topological structures of the orbits and we prove that if the minimal center of attraction of a point is non S-generic, then there exist certain Li-Yorke chaotic properties inside the involved minimal center of attraction and sensitivity near the involved minimal center of attraction; if the minimal center of attraction of a point is S-generic, then there exist stronger Li-Yorke chaotic (Auslander-Yorke chaotic) dynamics and sensitivity (ℵ₀-sensitivity) in the involved minimal center of attraction.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권4호
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• pp.407-438
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• 2006

This study investigated school mathematics curriculum of England, newly revised in 1998, focused on the 'shape, space, and measures' domain among three major domains of the English curriculum. On the basis of its understanding, this domain was compared and analyzed with school mathematics curriculum of Korea. In doing so, this study explored its plans and procedures and established a frame of comparison for the curriculums between the two countries. The structure of the National Curriculum in England is composed of programmes of study and attainment targets. The former sets out what should be taught in mathematics at key stages 1, 2, 3, and 4 and provides the basis for planning schemes of work, and the latter sets out the knowledge, skills, and understanding that pupils of different abilities and matures are expected to have by the end of each key stage. Attainment targets are composed of eight levels and an additional level of increasing difficulty. According to the results of the present study, Korea focuses on the formal and systematic mathematical knowledge on the basis of sound understanding of certain mathematical terms or concepts. On the other hand, England curriculum tends to deal with the content which can be understood more intuitively, flexibly, and naturally through the experience and aquisition based on the concrete manipulation. Particularly, it emphasizes that mathematics be realistic and useful in solving a diverse problems confronted in everyday life.

• 대한수학교육학회지:학교수학
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• 제9권4호
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• pp.487-506
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• 2007

본 연구는 14명의 중학교 2학년 수학영재들이 아르키메데스 다면체를 소재로 한 공간기하과제를 해결하면서 보여주는 정당화 유형과 수학적 표현에 대한 연구이다. 문헌 연구를 통해 정당화 유형과 수학적 표현 분석을 위한 분석틀을 마련하고 이들의 다양한 반응들을 분석하였다. 정당화 유형에서는 부분적인 분석을 통해 형식화를 추구하는 학생과 비형식적이며 경험적인 정당화이지만 모든 구성요소를 고려하여 전체적 정당화를 시도하는 두 반응간의 비교를 통해 비형식적 정당화의 유용성에 분명한 주의를 기울일 필요가 있었다. 수학적 표현에서 시각적 표현은 문제해결을 위한 아이디어를 찾고, 구조를 파악하는데 유용한 역할을 하고 있었으며, 기호적 표현을 점진적으로 발전시키는 과정에서 수학적 개념을 표현 속에 함축시키고 정제시켜 정교한 기호(Harel & Paput. 1994)를 창출하려는 욕구를 발견할 수 있었다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 추계학술대회 논문집 학회본부 D
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• pp.791-793
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• 2000

The fuzzy inference system is a popular computing framework based on the concepts of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. The advantage of fuzzy approach over traditional ones lies on the fact that fuzzy system does not require a detail mathematical description of the system while modeling. As modeling method. the Group Method of Data Handling(GMDH) is introduced by A.G. Ivakhnenko GMDH is an analysis technique for identifying nonlinear relationships between system's inputs and output. We study a Novel Neuro-Fuzzy Network (NNFN) in this paper. NNFN is a network resulting from the combination of a fuzzy inference system and polynomial neural network(PNN) (7) which is advanced structure of GMDH. Simulation involve a series of synthetic as well as experimental data used across various neurofuzzy systems.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1989년도 가을 학술발표회 논문집
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• pp.34-39
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• 1989

Recent trends in design standards development have encouraged the use of probabilistic limit sate design concepts. Reliability analysis adopted in those advanced countries have the potentials that they afford for symplifying the design Process arid placing it on a consistent reliability based for various construction materials. This study is proposed in the reliability analysis of plane frame structures using second-order moment method(Level-II they). Lind-Hasofer's minimum distance method is use in the derivation of an mathematical algorithm as well as an determination of Correlation cofficients, reliability index and total reliability index depending on the multiple failure modes. In addition. This study is employed as a practical tool for the approximate reliability analysis. Results of the numerincal analysis showed that the difference between the reliability index of the failure probability of the multiple failure modes and the total reliability index of the failure probability with the simultaneous failure modes deviated nearly 3∼10% depending on tile performance functions.