• School Mathematics
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• v.15 no.2
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• pp.481-501
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• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• School Mathematics
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• v.14 no.4
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• pp.565-577
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• 2012

In this study, we investigated the process of constructing the geometrical solutions to quadratic equation, through proportions between lengths of similar triangles in a dynamic environment. To do this, we provided one task to 4 ninth grades students and observed the process of the students' activities and strategies. As a result of this pilot lesson study, our research shows the advantage and possibility of geometrical method in learning and teaching quadratic equation.

• School Mathematics
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• v.13 no.3
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• pp.447-468
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• 2011

For the instruction of units dealing with the conic section, the most important factor that we need to consider is the connections. In other words, the algebraic approach and the geometric approach should be instructed in parallel at the same time. In particular, for the students of low proficiency who are not good at algebraic operation, the geometric approach that employs visual representation, expressing the conic section's characteristic in a dynamic manner, is an important and effective method. For this, during this research, to suggest the importance of dynamic visual representation based on GeoGebra in teaching Quadratic Curve, we taught an experimental class that suggests the instruction method which maximizes the visual representation and analyzed changes in the representation of students by analyzing the part related to the unit of a parabola from units dealing with a conic section in the "Geometry and Vector" textbook and activity book.

• Communications of Mathematical Education
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• v.13 no.2
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• pp.515-525
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• 2002

중학교 기하영역 중 피타고라스의 정리를 논증적인 증명 대신에 역동적인 방법으로 이해할 수 있도록 GSP(Geometer's Skechpad)를 활용하여 구현했으며, 멀티미디어 환경에 익숙한 중학생들에게 시 ${\cdot}$ 공간을 초월하여 웹 상에서 개별학습, 반복학습을 할 수 있도록 JAVA 언어를 사용하여 웹으로 변환시켰다.

• Communications of Mathematical Education
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• v.3
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• pp.169-172
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• 1997

• School Mathematics
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• v.13 no.1
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• pp.107-125
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• 2011

In this paper, we investigated how the GSP environments impact students' conjecturing of geometric properties. And we wanted to draw some implication in teaching and learning geometry in dynamic geometric environments. As results, we conclude that when students were given the problem situations which almost has no condition, they were not successful, and rather when the problem situations had appropriate conditions students were able to generate many conditions which were not given in the original problem situations, and consequently they were more successful in conjecturing geometric properties. And the geometric properties conjectured in GSP environments are more complex and difficult to prove than those in paper and pencil environments. Also the function of moving screen with 'Alt' key is frequently used in conjecturing geometric properties with functions of measurement and calculation of GSP. And students felt happier when they discovered geometric properties than when they could prove geometric properties.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2004.11a
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• pp.92-97
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• 2004

This purpose of this study was about the analysis on the dynamic expression of geometric manipulation in interior composition elements. The paradigm of contemporary times became different from paradigm of modern times. The change of paradigm is caused by the side effect of paradigm of pre-times. In the contemporary architectural condition, architecture have a tendency to plural characteristics. This study investigates systemically ‘the DYNAMISM’ as a part of contemporary interior space's feature, based on geometric manipulation in interior composition elements. First of all, the dynamic characteristics of architectural space. The second, relationship between the architecture and geometric manipulation.

• 주택과사람들
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• s.192
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• pp.58-61
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• 2006

바르셀로나 몬주의 통신탑을 비롯해 기하학적인 형태의 다리나 건축물로 유명한 초현실주의 건축가 산티아고 칼라트라바. 공학자이자 건축가였던 그의 역동적인 작품 세계를 들여다본다.

• The Mathematical Education
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• v.34 no.2
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• pp.141-202
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• 1995

van Hiele의 사고수준 이론에는 기초수존, 제1수준, 제2수준, 제3수준, 제4수준 등 5가지가 있고, 이 중에서 국민학교에 해당되는 것은 기초수준 (1학년), 제1수준(2, 3학년), 제2주순 (4, 5, 6학년) 등 세 가지 뿐이다. 그리고 기하학적의 구조 인식론에는 관제, 구성, 정의, 공리, 정리, 증명, 척도, 자호, 응용 등 9가지 단계가 있고, 이 9가지 단계를 기초수준, 제 1수준, 제 2수준의 각 수준에 대응시켜서 거기에 해당되는 기하도형 학습을 연구·분석하였다. 기하도형에 관한 학습은 주로 경험성과 창의성을 바탕으로 하는 보기문제를 제시하여 그 흐름을 해결함으로써 각 수준의 각 단계들을 스스로 인식하도록 하였다. 특히 여기에서 처음으로 등장하는 기하학의 구조 인식론이라는 것은 위에서 언급한 9가지 단계를 차례로 거쳐 가야만 아동들은 도형을 올바르게 빠짐없이 인식할 수 있다는 이론이다. 이 이론의 특징을 예를 하나 들어서 설명해 보면, 흔히들 정의를 단순히 무정의어와 정의어로 구분하고 있는데 반하여, 이 이론에서는 서로 역동적인 관계를 갖고 있는 기초정의, 상황정의, 포괄정의, 기본정의, 부수정의, 특수정의 등으로 나누었다는 점이다.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.411-429
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• 2015

In this study we investigated the effects of using GSP in solving geometric problems. Especially we focused the effects of GSP in leveled students' connection of geometry and algebra. High leveled students prefer to use algebraic formula to solve geometric problems. But when they did not know the geometric meaning of their algebraic formula, they could recognize the meaning after using GSP. Middle and low leveled students usually used GSP to obtain hints to solve the problems. For the low leveled students GSP was usually used to understand the meaning of the problem, but it did not make them solve the problem.