• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.399-420
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• 2008

In this paper we solve various triangle construction problems related with radius of escribed circle using algebraic method. We describe essentials and meaning of algebraic method solving construction problems. And we search relation between triangle construction problems, draw out 3 base problems, and make hierarchy of solved triangle construction problems. These construction problems will be used for creative mathematical investigation in gifted education.

• School Mathematics
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• v.13 no.1
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• pp.19-36
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• 2011

This study provides middle school students with an opportunity to construct elementary functions with dynamic geometry based on the proportion between lengths of triangle to activate students' intuition in handling elementary algebraic functions and their geometric properties. In addition, this study emphasizes the process of justification about the choice of students' construction method to improve students' deductive reasoning ability. As a result of the pilot lesson study, this paper shows the characteristics of the students' construction process of elementary functions and the roles the teacher plays in the process.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.247-282
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• 2011

In the elementary school mathematics textbooks of the 7th national curriculum, just simple construction education is provided by having students draw a circle and triangle with compasses and drawing vertical and parallel lines with a set square. The purpose of this study was to examine the mathematical thinking of sixth-grade elementary school students in the construction process in a bid to give some suggestions on elementary construction guidance. As a result of teaching the sixth graders in gifted and nongifted classes about the equal division of line segments and evaluating their mathematical thinking, the following conclusion was reached, and there are some suggestions about that education: First, the sixth graders in the gifted classes were excellent enough to do mathematical thinking such as analogical thinking, deductive thinking, developmental thinking, generalizing thinking and symbolizing thinking when they learned to divide line segments equally and were given proper advice from their teacher. Second, the students who solved the problems without any advice or hint from the teacher didn't necessarily do lots of mathematical thinking. Third, tough construction such as the equal division of line segments was elusive for the students in the nongifted class, but it's possible for them to learn how to draw a perpendicular at midpoint, quadrangle or rhombus and extend a line by using compasses, which are more enriched construction that what's required by the current curriculum. Fourth, the students in the gifted and nongifted classes schematized the problems and symbolized the components and problem-solving process of the problems when they received process of the proble. Since they the urally got to use signs to explain their construction process, construction education could provide a good opportunity for sixth-grade students to make use of signs.

• Communications of Mathematical Education
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• v.10
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• pp.189-199
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• 2000

수학 교수-학습을 동해 개발 ${\cdot}$ 육성할 가치가 있는 중요한 인지 활동들 중의 하나가 분석적 활동이다. 분석적 활동의 중요성은 이미 오래 전부터 강조되어 왔으며, 저자는 이미 수학 교수-학습과 직접적으로 관련된 몇 가지 분석적 활동의 유형들을 제시한 바 있다. 본 논문에서는 수학 교수-학습 과정에서 분석적 활동을 활성화시키기 위한 한 방법으로, 다양한 작도 문제를 활용하는 방법과 다양한 학습 자료들을 제시할 것이다.

• The Mathematical Education
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• v.46 no.3
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• pp.303-314
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• 2007

In this paper we try to study a method of constructing plane sections of regular tetrahedron and regular hexahedron. In order to construct plane sections of regular tetrahedron and regular hexahedron first of all, we extract some base problems that are used for construction. And we describe construction process using base problems in detail.

• The Mathematical Education
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• v.31 no.3
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• pp.83-92
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• 1992

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.319-320
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• 2005

• Journal of Wetlands Research
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• v.14 no.4
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• pp.675-685
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• 2012

The purpose of this study was to propose a measure for eco-cultural regeneration by a detailed examination of closed down schools, old defective residences, deteriorated industrial facilities and space no long in use located throughout Ijak-do. The reserch method utilized a selection of the major elements from the eco-cultural regeneration element of island regions and a measure for application and regeneration on the deteriorated facilities of Ijak-do was proposed.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.69-75
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• 2010

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.