• Title/Summary/Keyword: turtle representation system

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Educational Application of Turtle Representation System for Linking Cube Mathematics Class (연결큐브 수업을 위한 거북표현체계의 활용)

  • Jeong, Hye Rim;Lee, Seung Joo;Cho, Han Hyuk
    • School Mathematics
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    • v.18 no.2
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    • pp.323-348
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    • 2016
  • The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.

Representation Systems of Building Blocks in Logo-based Microworld

  • Lee, Ji-Yoon;Cho, Han-Hyuk;Song, Min-Ho;Kim, Hwa-Kyung
    • Research in Mathematical Education
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    • v.15 no.1
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    • pp.1-14
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    • 2011
  • Logo has influenced many researchers and learners for the past decades as a 20 turtle geometry environment in the perspective of constructionism. Logo uses the metaphor of 'playing turtle' that is intrinsic, local and procedural. We, then, design an environment in which the metaphor of 'playing turtle' is applied to construct 3D objects, and we figure out ways to represent 3D objects in terms action symbols and 3D building blocks. For this purpose, design three kinds of representation systems, and asked students make various 3D artifacts using various representation systems. We briefly introduce the results of our investigation into students' cognitive burden when they use those representation systems, and discuss the future application measures and the design principles of Logo-based 3D microworld.

On the Design of Logo-based Educational Microworld Environment

  • Cho, Han-Hyuk;Song, Min-Ho;Lee, Ji-Yoon;Kim, Hwa-Kyung
    • Research in Mathematical Education
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    • v.15 no.1
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    • pp.15-30
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    • 2011
  • We study to design educational Logo-based microworld environment equipped with 3D construction capability, 3D manipulation, and web-based communication. Extending the turtle metaphor of 2D Logo, we design simple and intuitive symbolic representation system that can create several turtle objects and operations. We also present various mathematization activities applying the turtle objects and suggest the way to make good use of them in mathematics education. In our microworld environment, the symbolic representations constructing the turtle objects can be used for web-based collaborative learning, communication, and assessments.

Computational Thinking based Mathematical Program for Free Semester System

  • Lee, Ji Yoon;Cho, Han Hyuk
    • Research in Mathematical Education
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    • v.18 no.4
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    • pp.273-288
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    • 2014
  • In recent years, coding education has been globally emphasized and the Free Semester System will be executed to the public schools in Korea from 2016. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this research aims to design 'learning environment' in which learners can design and construct mathematical objects through computers and print them out through 3D printers. Furthermore, it will design learning mathematics by constructing the figurate number patterns from 'soma cubes' in the playing context and connecting those to algebraic and combinatorial patterns, which will allow students to experience mathematical connectivity. It is expected that the activities of designing figurate number patterns suggested in this research will not only strengthen CT capacity in relation to mathematical thinking but also serve as a meaningful program for the Free Semester System in terms of career experience as 3D printers can be widely used.

A Study on Learning and Teaching Environments for Computers and Mathematics Education ('컴퓨터와 수학교육' 학습-지도 환경에 관한 연구)

  • Kim, Hwa-Kyung
    • Journal of Educational Research in Mathematics
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    • v.16 no.4
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    • pp.367-386
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    • 2006
  • There are two strands for considering tile relationships between education and technology. One is the viewpoint of 'learning from computers' and the other is that of 'learning with computers'. In this paper, we call mathematics education with computers as 'computers and mathematics education' and this computer environments as microworlds. In this paper, we first suggest theoretical backgrounds ai constructionism, mathematization, and computer interaction. These theoretical backgrounds are related to students, school mathematics and computers, relatively As specific strategies to design a microworld, we consider a physical construction, fuctiionization, and internet interaction. Next we survey the different microworlds such as Logo and Dynamic Geometry System(DGS), and reform each microworlds for mathematical level-up of representation. First, we introduce the concept of action letters and its manipulation for representing turtle actions and recursive patterns in turtle microworld. Also we introduce another algebraic representation for representing DGS relation and consider educational moaning in dynamic geometry microworld. We design an integrating microworld between Logo and DGS. First, we design a same command system and we get together in a microworld. Second, these microworlds interact each other and collaborate to construct and manipulate new objects such as tiles and folding nets.

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A Study on Lyricism Expression of Color & Realistic Expression reflected in Oriental Painting of flower & birds (전통화조화의 사실적(寫實的) 표현과 시정적(詩情的) 색채표현)

  • Ha, Yeon-Su
    • Journal of Science of Art and Design
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    • v.10
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    • pp.183-218
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    • 2006
  • Colors change in time corresponding with the value system and aesthetic consciousness of the time. The roles that colors play in painting can be divided into the formative role based on the contrast and harmony of color planes and the aesthetic role expressed by colors to represent the objects. The aesthetic consciousness of the orient starts with the Civility(禮) and Pleasure(樂), which is closely related with restrained or tempered human feelings. In the art world of the orient including poem, painting, and music, what are seen and felt from the objects are not represented in all. Added by the sentiment laid background, the beauty of the orient emphasizes the beauty of restraint and temperance, which has long been the essential aesthetic emotion of the orient. From the very inception of oriental painting, colors had become a symbolic system in which the five colors associated with the philosophy of Yin and Yang and Five Forces were symbolically connected with the four sacred animals of Red Peacock, Black Turtle, Blue Dragon, and White Tiger. In this color system the use of colors was not free from ideological matters, and was further constrained by the limited color production and distribution. Therefore, development in color expression seemed to have been very much limited because of the unavailability and unreadiness of various colors. Studies into the flow in oriental painting show that color expression in oriental painting have changed from symbolic color expression to poetic expression, and then to emotional color expression as the mode of painting changes in time. As oriental painting transformed from the art of religious or ceremonial purpose to one of appreciation, the mast visible change in color expression is the one of realism(simulation). Rooted on the naturalistic color expression of the orient where the fundamental properties of objects were considered mast critical, this realistic color expression depicts the genuine color properties that the objects posses, with many examples in the Flower & Bird Painting prior to the North Sung dynasty. This realistic expression of colors changed as poetic sentiments were fused with painting in later years of the North Sung dynasty, in which a conversion to light ink and light coloring in the use of ink and colors was witnessed, and subjective emotion was intervened and represented. This mode of color expression had established as free and creative coloring with vivid expression of individuality. The fusion of coloring and lyricism was borrowed from the trend in painting after the North Sung dynasty which was mentioned earlier, and from the trend in which painting was fused with poetic sentiments to express the emotion of artists, accompanied with such features as light coloring and compositional change. Here, the lyricism refers to the artist's subjective perspective of the world and expression of it in refined words with certain rhythm, the essence of which is the integration of the artist's ego and the world. The poetic ego projects the emotion and sentiment toward the external objects or assimilates them in order to express the emotion and sentiment of one's own ego in depth and most efficiently. This is closely related with the rationale behind the long-standing tradition of continuous representation of same objects in oriental painting from ancient times to contemporary days. According to the thoughts of the orient, nature was not just an object of expression, but recognized as a personified body, to which the artist projects his or her emotions. The result is the rebirth of meaning in painting, completely different from what the same objects previously represented. This process helps achieve the integration and unity between the objects and the ego. Therefore, this paper discussed the lyrical expression of colors in the works of the author, drawing upon the poetic expression method reflected in the traditional Flower and Bird Painting, one of the painting modes mainly depending on color expression. Based on the related discussion and analysis, it was possible to identify the deep thoughts and the distinctive expression methods of the orient and to address the significance to prioritize the issue of transmission and development of these precious traditions, which will constitute the main identity of the author's future work.

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