• Journal for History of Mathematics
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• v.20 no.2
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• pp.73-88
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• 2007

In this paper, we study the symmetry of figures in elementary geometry. First, we investigate the historical and mathematical background of symmetry of figures and we explore the suitable teaching and learning methods for symmetry in elementary geometry. Also we study the major problem of geometry education that occurring in elementary school.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.459-474
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• 2014

The purpose of this study was to investigate the effects of mathematical instruction using GSP program on the symmetrical figures learning and self-directed learning attitude. According to the pretest result, the experiment group and the comparison group showed to be homogeneous groups. The experiment group has learned symmetrical figures for 9 hours using the GSP program and the comparison group has learned for 9 hours using the traditional method(paper and pen lesson). As the posttests, self-directed learning attitude test and symmetry figure understanding test were performed. The results obtained in this research are as follows; First, there was a significant difference in symmetry figure understanding test between the experiment group which learned through GSP program and the comparison group which learned through traditional method. Since there showed a very high achievement in the experiment group which learned using GSP, it can be inferred that GSP was very effective in the lessons of symmetrical movements. Second, there was a significant difference in self-directed learning attitude test between the experiment group and the comparison group. This seems to be because the length of the sides of the figures, size of the angles of the figures etc can be verified instantly and the students can correct by themselves and give feedbacks when they use GSP program. Students preferred drawing using the GSP over drawing using rulers and pencils, and they showed interest in the GSP program and they did not have burden in being wrong in their study and studied in various methods. And as they become familiar with the GSP program, they even studied other contents beyond the scope presented in the textbook.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.299-327
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• 2023

In this study, we tried to find out the level of inductive reasoning ability and the aspects of visualization components shown in students in the class using exploratory software for the 'congruence and symmetry' unit in the second semester of the 5th grade of elementary school. To this end, classes using GeoGebra, one of the exploratory software, were conducted for a total of 19 students in one class of fifth graders in elementary school, and the results of the students' activities were analyzed. As a result of this study, the level of inductive reasoning ability of students remained at a similar level or developed, and it was shown that students inferred new properties of shapes using various functions of software inductively. In addition, in terms of visualization, students were able to quickly and easily draw shapes that met the conditions, and unlike the paper-and-pencil environment, using the 'measurement' and 'symmetry' functions, they transformed and manipulated complex yet precisely congruent and symmetrical external representations. Based on these analysis results, implications for the use of exploratory software in the area of figures were derived.

• 한국정보교육학회:학술대회논문집
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• 2007.08a
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• pp.294-299
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• 2007

도형의 합동은 도형의 대칭이나 도형그리기를 배우는 데에 기본이 되며, 도형의 성질을 이해하고 모양을 그리는 능력을 기르게 할 수 있다. 도형의 합동을 공부해야 일상 생활에서 필요로 하는 디자인이나 아름다운 예술 작품에 대한 소양을 가질 수 있다. 하지만 합동 학습을 할 때에 개념을 형성하는데 드는 시간보다 종이를 자르고 도형의 본을 뜨는 행동과 같은 구체적 조작 시간이 많이 소요되기 때문에 학생들 간의 상호작용은 물론 교사와 학생들과의 상호작용 시간도 기대하기 어렵다. 따라서 본 연구에서는 초등학교 학생들에게 학습효과를 높일 수 있도록 상호작용 이론을 합동학습에 적용하여 학습자들이 합동의 개념을 쉽게 이해할 수 있도록 하였고 동시에 동시적 비동시적 의사소통이 가능한 웹상에서 실시하는 합동학습 코스웨어를 개발하고 적용하였다.

• 한국정보교육학회:학술대회논문집
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• 2007.01a
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• pp.325-334
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• 2007

수학 교육이 해결해야하는 과제 중 하나는 학습 부진아 문제이다. 수학 학습 부진아 발생 원인은 학생의 수준에 맞지 않는 교재의 사용으로 인해 수학에 대한 흥미 부족, 이를 개선할 수 있는 교재의 미비, 부진아 지도를 위한 교사의 시간 부족 등이 있다. 본 연구에서는 이러한 문제점을 개선하기 위해 '도형아 놀자'라는 수학 학습 부진아 지도를 위한 교수 학습 시스템을 설계하였다. 학습 부진아의 수준에 부합된 맞춤식 교육을 목표로 7차 수학교과서의 도형 영역에 제시된 필수 학습 요소를 중심으로 교재를 재구성하였고, 수학과에 대한 흥미 및 자기 주도적 학습 능력을 길러주기 위해 교수 학습 방법으로 게임을 활용하였으며, 상호작용부분을 강화하여 가정과 연계된 교육이 가능하도록 시스템을 구성하였다. 이 시스템의 학습단계는 여러 가지 모양, 점, 선, 각, 평면도형, 합동과 대칭, 입체도형이라는 5단계로 각 단계의 시작과 끝에 평가를 실시하여 학습부진아의 수준을 정확하게 파악할 수 있도록 설계한다.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.361-379
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• 2002

본 논문은 재미있고 활동적인 기하 수업을 위한 학습자료를 제시한 것으로써 Amazing Triangle (NCTM, 1993)를 GSP를 활용하여 학교수업에서 사용할 수 있는 방안과 테셀레이션으로 확장시켜 도형의 각의 크기, 대칭과 변화, 합동 등의 학습을 통해 자연스럽게 기하에 관한 수학적 개념과 의미를 익히고 수학적 사고력과 창의력을 키우고자 하였다. 수학에 대한 정의적 측면에서의 향상과 동시에 타교과인 미술 분야에 수학이 어떻게 사용될 수 있는 가도 알 수 있다.

• Journal of The Korean Association of Information Education
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• v.12 no.2
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• pp.141-149
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• 2008

Congruence of figure is a basic to learn a symmetrical figure and helps to understand the characteristics of figure and know the way of drawing figures. The knowledge of congruence provides us art attainments to understand design and fine pieces of art. However, it is difficult to expect the interaction between students or between teachers and students, because of spending too much time for cutting papers and making the shapes of figure during the class for establishing the concepts. This study utilized a question-based interaction model which would foster elementary school student's learning effectiveness and make them understood the concept of congruence, also developed a congruence learning system which could communicate in both synchronous and asynchronous situation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.5
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• pp.1052-1060
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• 1989

Using a vortex stretching invariant term, the two-layer k-.epsilon. model has been modified to account for the extra staining of turbulence due to the mean-flow convergence and divergence. The calculations of turbulent boundary layers in a plane of symmetry are compared for experimental cases which are an axisymmetric body at an incidence of 15.deg.. The comparisons between the calculations and experimental data show that additional modifications to the dissipation rate equation have brought the significant improvement to the prediction of plane of symmetry boundary layers in the strong mean-flow convergence and divergence.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.517-538
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• 2018

The purpose of this study is to lay the groundwork for effectively supporting mathematics learning for multi-cultural students by enhancing understanding of the cultural background regarding mathematics. In order to attain these purposes, this study compared to learning contents, deployment of contents, teaching method of the Korean and Vietnamese elementary mathematics textbooks. According to analysis, Vietnamese textbooks emphasize mathematical rigor and logic over Korean textbooks, and it integrate learning contents from various areas according to mathematical relevance. But Vietnamese textbooks do not present the connection between mathematical content, such as the combination, symmetry, and coverage of shapes. While Korean textbooks use teaching method that students find and define the concept of shapes themselves, Vietnamese textbooks present concepts of shapes and let students to learn about them. From this result, this study presented suggestions for supporting mathematics learning for multi-cultural students.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.463-468
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• 2010

The mobile robot which accomplishes a work in explored region does not know location information of surroundings. Traditionally, simultaneous localization and mapping(SLAM) algorithms solve the localization and mapping problem in explored regions. Among the several SLAM algorithms, the EKF (Extended Kalman Filter) based SLAM is the scheme most widely used. The EKF is the optimal sensor fusion method which has been used for a long time. The odometeric error caused by an encoder can be compensated by an EKF, which fuses different types of sensor data with weights proportional to the uncertainty of each sensor. In many cases the EKF based SLAM requires artificially installed features, which causes difficulty in actual implementation. Moreover, the computational complexity involved in an EKF increases as the number of features increases. And SLAM is a weak point of long operation time. Therefore, this paper presents a symmetrical model based SLAM algorithm(called M-SLAM).