• 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.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.1-24
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• 2009

The applications of ratio and similarity have been in need of everyday life from ancient times. Euclid's elements Ⅴand Ⅵ cover ratio and similarity respectively. In this note, we have done a comparative analysis to button down the contents of ratio and similarity covered by the math text books used in Korea, Euclid's elements and the math text books used in Japan and America. As results, we can observe some differences between them. When math text books used in Korea introduce ratio, they presented it by showing examples unlike math text books used in America and Japan which present ratio by explaining the definition of it. In addition, in the text books used in Korea and Japan, the order of dealing with condition of similarity of triangles and the triangle proportionality is different from that of the text books used in America. Also, condition of similarity of triangles is used intuitively as postulate without any definition in text books used in Korea and Japan which is different from America's. The manner of teaching depending on the way of introducing learning contents and the order of presenting them can have great influence on student's understanding and application of the learning contents. For more desirable teaching in math it is better to provide text books dealing with various learning contents which consider student's diverse abilities rather than using current text books offering learning contents which are applied uniformly.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.27-41
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• 2011

This study is the consideration to 'The Data' and 'On Divisions' of Euclid which is the historical start of analysis and synthesis. 'The Data' and 'On Divisions' compared to Euclid's Elements is not interested. In this study, analysis and synthesis were examined for significance. In this study, means for 'analysis' and 'synthesis' were examined through an analysis of 'The Data' and 'On Divisions'. First, the various terms including analysis and synthesis were examined and the concepts of the terms were analyzed. Then, analysis was divided into 'external analysis' and 'internal analysis'. And synthesis was divided into 'theoretical synthesis' and 'empirical synthesis'. On the basis of this classification problem presented in elementary textbooks and the practical applications were explored.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.43-54
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• 2006

The purpose of this paper, followed by 'Nature$\cdot$Human, and Golden Section I ', is to study aesthetic consciousness, mentality model and body proportion of human, and the golden section applied to architecture and hand axe of stone age. In particular, handaxes of one million years ago have shown that they had critical competency to the basis of art and mathematics in the future. Furthermore, without pen, paper and ruler, the existence of mentality model made fundamental conversion of mathematics possible. Different sizes of handaxes were made by maintaining the equal golden section. This was the first example in relation to the principle mentioned in 'Stoicheia' by Euclid which was published hundred thousands of years later.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.581-598
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• 2017

The early Renaissance artist Albrecht $D{\ddot{u}}rer$ is an amateur mathematician. He published a book on geometry. In the second part of that book, $D{\ddot{u}}rer$ gave compass and straight edge constructions for the regular polygons from the triangle to the 16-gon. For mathematics education, I extracted base constructions of polygon constructions. And I also showed how to use $D{\ddot{u}}rer^{\prime}s$ idea in constructing divergent forms with compass and ruler. The contents of this paper can be expected to be the baseline data for mathematics education.

• Education of Primary School Mathematics
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• v.18 no.1
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• pp.45-59
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• 2015

This study focused on the classification of triangles by angles in elementary school mathematics. We examined Korean national mathematics curriculum from the past to the present. We also examined foreign textbooks and the Euclid's . As a result, it showed that the classification is not indispensable from the mathematical and the perceptual viewpoint. It is rather useful for students to know the names of triangles when studying upper level mathematics in middle and high schools. This study also suggested that the classification be introduced in elementary school mathematics in the context of reasoning and inquiring as shown foreign textbooks, and example topics for the reasoning and inquiring.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.221-234
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• 2010

So far, around 370 various verification of Pythagorean Theorem have been introduced and many studies for the analysis of the method of verification are being conducted based on these now. However, we are in short of the research for the study of the generalization for Pythagorean Theorem. Therefore, by abstracting mathematical materials that is, data(lengths of sides, areas, degree of an angle, etc) which is based on Euclid's elements Vol 1 proposition 47, various methods for the generalization for Pythagorean Theorem have been found in this study through scrutinizing the school mathematics and documentations previously studied.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.171-186
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• 2009

$Poincar\acute{e}$ is mathematician and the episodes in his mathematical invention process give suggestions to scholars who have interest in how mathematical invention happens. He emphasizes the value of unconscious activity. Furthermore, $Poincar\acute{e}$ points the complementary relation between unconscious activity and conscious activity. Also, $Poincar\acute{e}$ emphasizes the value of intuition and logic. In general, intuition is tool of invention and gives the clue of mathematical problem solving. But logic gives the certainty. $Poincar\acute{e}$ points the complementary relation between intuition and logic at the same reasons. In spite of the importance of relation between intuition and logic, school mathematics emphasized the logic. So students don't reveal and use the intuitive thinking in mathematical problem solving. So, we have to search the methods to use the complementary relation between intuition and logic in mathematics education.