• Title/Summary/Keyword: geometry education

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인간교육으로서 기하교육의 인식론적 기초에 관한 연구

  • Yu, Chung-Hyun
    • East Asian mathematical journal
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    • v.28 no.4
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    • pp.403-417
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    • 2012
  • We can understand in the context of kant's philosophy the intuitive geometry education arguing that geometry education should begin with intuition. Both Pestalozzi and Herbart advocate a connection between geometry and intuition as well as a close relationship between geometry and the world. Significance of the intuitive geometry education resizes in the fact that geometry becomes both an example of and a principle of general cognition. The intuitive geometry education uses figures as an educational foundation in the transcendental condition for the main agent of cognition. In this regard, the intuitive geometry education provides grounds for the human character development.

Development of Curricula on Geometry Related Courses for Training of Mathematics Teacher of Secondary Schools (중등 교사 양성을 위한 기하 영역의 교육과정 개발)

  • 박혜숙
    • The Mathematical Education
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    • v.42 no.4
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    • pp.503-521
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    • 2003
  • In this paper, we propose programs of geometry related courses for the department of mathematics education of teacher training universities. We suggest 4 courses, ‘Geometry I’, ‘Geometry II’, ‘Differential Geometry’, ‘Topology’ as geometry related courses in Shin et. al.(2003). Among those 4 courses, we state desirable direction of curricula on 3 courses, ‘Geometry I’, ‘Geometry II’, ‘Differential Geometry’ in this paper.

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Reflections on the Elementary School Geometry Curriculum in the Netherlands -Based on the Realistic Mathematics Education- (네덜란드의 초등학교 기하 교육과정에 대한 개관 -현실적 수학교육을 중심으로-)

  • Chong, Yeong-Ok
    • School Mathematics
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    • v.9 no.2
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    • pp.197-222
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    • 2007
  • The study aims to reflect the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands in the light of the results from recent researches in geometry education and the direction of geometry standards for school mathematics of the National Council of Teachers of Mathematics in order to induce implications for improving korean geometry curriculum and textbook series. In order to attain these purposes, the present paper reflects the history of elementary school geometry education in the Netherlands, sketches the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands by reflecting general goals of the mathematics education, the core goals for geometry strand of the Netherlands, and geometry and spatial orientation strand of Dutch Pluspunt textbook series for the elementary school more concretely. Under these reflections on the documents, it is analyzed what is the characteristics of geometry strand in the Netherlands as follows: emphasis on realistic spatial phenomenon, intuitive and informal approach, progressive approach from intuitive activity to spatial reasoning, intertwinement of mathematics strands and other disciplines, emphasis on interaction of the students, cyclical repetition of experiencing phase, explaining phases, and connecting phase. Finally, discussing points for improving our elementary school geometry curriculum and textbook series development are described as follows: introducing spatial orientation and emphasizing spatial visualization and spatial reasoning with respect to the instruction contents, considering balancing between approach stressing on grasping space and approach stressing on logical structure of geometry, intuitive approach, and integrating mathematics strands and other disciplines with respect to the instruction method.

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The Role of "Personal Knowledge" in Solid Geometry among Primary School Mathematics Teachers

  • Patkin, Dorit
    • Research in Mathematical Education
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    • v.14 no.3
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    • pp.263-279
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    • 2010
  • Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.

Developing Geometry Software for Exploration-Geometry Player

  • Yuan, Yuan;Lee, Chun-Yi;Huang, Jiung-Rong
    • Research in Mathematical Education
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    • v.11 no.3
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    • pp.209-218
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    • 2007
  • The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

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A Study on Application of Euclid's Geometry at Unit of Equation of Figures in High School 1st Grade (고등학교 도형의 방정식 단원에서 논증기하의 활용에 대한 연구)

  • Kwon, Young-In;Suh, Bo-Euk
    • Communications of Mathematical Education
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    • v.21 no.3
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    • pp.451-466
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    • 2007
  • Geometry in school mathematics is the field that has the possibility of diverse approach such as Synthetic Geometry and Analytic Geometry. Synthetic Geometry is handled in middle schools and Analytic Geometry in the first year of high schools. Therefore, this research show for the possibility of using Synthetic Geometry in high schools which was learned already in middle schools and the way of integrating both of them concretely. This is expected to help students understand the mathematical meaning of figures a lot.

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S/W Cinderella for Student's mental Representation about Non-Euclidean Geometry (비유클리드 기하의 정신적 표상을 위한 S/W Cinderella)

  • Kye Younghee;Shin Kyunghee
    • The Mathematical Education
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    • v.44 no.2 s.109
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    • pp.297-306
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    • 2005
  • In this paper, we propose a computer environment class for student's mental representations about non-Euclidean geometry. Through the software Cinderella, students construct knowledge about non-Euclidean geometry and recognize differentness between Euclidean and non-Euclidean geometry. Also they recognize an existence of non-Euclidean geometry newly and its mental representations with images represented in Cinderella. In geometry class, we make students can use many representations systematically and can figure a visual internal image by emphasizing a transform process. And then students can reason about non-Euclidean geometry.

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On the Contents and Curriculum for University geometry course focused on applications (대학수학교육에서 기하학의 응용과 교과내용의 구성방안)

  • Jeon, Myung-Jin;Cho, Min-Shik
    • Communications of Mathematical Education
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    • v.19 no.4 s.24
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    • pp.621-631
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    • 2005
  • The purpose of this study is to consider how to restructure the university geometry curriculum and contents in terms of applications to theoretical computer science. We analyzed various topics from computer graphics, CAGD(computer aided geometric design) and computational geometry suitable for geometry students interested in applications. Moreover we discussed about selections of topics for several cases.

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Revisiting Triangle : a Foundational Element of Plane Geometry (평면도형 탐구의 기본 요소로서 삼각형의 재조명)

  • Do, Jong-Hoon
    • The Mathematical Education
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    • v.46 no.4
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    • pp.493-502
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    • 2007
  • What is a foundational element of plane geometry? Isn't it possible to constitute the contents of plane geometry from that element? In this paper, we suggest a view point that triangle is a foundational element of plane geometry. And take some examples of reconstruction of usually given contents and mathematical activity centered on the triangle in plane geometry.

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Research on Pre-service Teacher Education Through Understanding of Conic Sections in Non-Endidean Geometry (비유클리드 기하학에서 이차곡선의 이해를 통한 예비교사교육)

  • Jieun Kang;Daehwan Kim
    • Journal of Science Education
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    • v.47 no.3
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    • pp.263-272
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    • 2023
  • We consider how a pre-service teacher can understand and utilize various concepts of Euclidean geometry by learning conic sections using mathematical definitions in non-Euclidean geometry. In a third-grade class of D University, we used mathematical definitions to demonstrate that learning conic sections in non-Euclidean space, such as taxicab geometry and Minkowski distance space, can aid pre-service teachers by enhancing their ability to acquire and accept new geometric concepts. As a result, learning conic sections using mathematical definitions in taxicab geometry and Minkowski distance space is expected to contribute to enhancing the education of pre-service teachers for Euclidean geometry expertise by fostering creative and flexible thinking.