• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.171-188
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• 2009

This study was designed for the purpose of identifying the influences of improved teaching method which constructed at the base of results of survey for finding present teaching-learning method of incenter and circumcenter of triangle. For this, we surveyed the students' understanding and math teachers' teaching method of incenter and circumcenter of triangle. Then, we designed alternative teaching method which innovated the problems from the resultic approaches of Incenter and circumcenter of triangle. And then, we taught students through new method and analyzed the influences of it to students.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.355-375
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• 2011

This paper was designed for the purpose of helping the functional comprehension on the concept of a circumcenter and an incenter of triangle and offering the help for teaching-learning process on their definitions. We analysed the characteristic of the definition on a circumcenter and an incenter of triangle and studied the context, mean and purpose on the definition. The definition focusing on the construction is the definition stressed on the consistency of the concept through the fact that it is possible to draw figure of the concept. And this definition is the thing that consider the extend of the concept from triangle to polygon. Meanwhile this definition can be confused because the concept is not connected with the terminology. The definition focusing on the meaning is easy to memorize the concept because the concept is connected with the terminology but is difficult to search for the concept truth. And this definition is the thing that has the grounds on the occurrence but is taught in a made-knowledge. The definition focusing on both the construction and meaning is the definition that the starting point is vague in the logical proof process. We hope that the results are used to improve the understanding the concept of a circumcenter and an incenter of triangle in the field of mathematical education.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.37-45
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• 2008

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1059-1078
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• 2009

In this paper we study metric equalities related with distance between excenter and other points of triangle. Especially we find metric equalities between excenter and incenter, circumcenter, center of mass, orthocenter, vertex, prove these formulas, and transform these formulas into new formula containing another elements of triangle. We in detail describe proof process of these equalities, indicate references of some formulas that don't exist within secondary school curriculum.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.27-39
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• 2008

In this paper we study triangle's properties related with angle bisectors, perpendiculars, circumcenter using the principle of the lever. We analyze proof method using the principle of the lever, and describe how to investigate intersection of segments, how to prove equalities and inequalities using the principle of the lever in triangle.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.203-221
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• 2017

The purpose of this study is to suggest didactical principles for using mathematical teaching aids and to applicate didactical principles in a relation with curriculum. First, we meta-analyzed related literature to suggest didactical principles for using mathematical teaching aids. And we suggested didactical principles as follows: principle of activities, principle of instruments, principle of learning. Using mathematical teaching aids with didactical principles in mind would help avoiding situations in which mathematical teaching aids are only used as interesting tools. Second, we concretized the meaning to applicate didactical principles and use mathematical teaching aids in a relation with curriculum. We considered domain, key concept, function, achievement standard, which were presented in the curriculum of mathematics, and suggested concrete activities. Third, we produced two designs for lessons on incenter and circumcenter of triangle and linear function's graph using mathematical teaching aids.