• 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.

• Korean Institute of Interior Design Journal
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• v.20 no.6
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• pp.145-152
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• 2011

Salvador Dali put a title of his work as 'A Propos of the Treatise on Cubic Form by Juan de Herrera' at 1960. Through this work which is consisted in cube frame surrounding black and white letter squares and nails in the sky, he directly referred about the cube which were showed in his pictures. To understand the meaning of this work, Dali's paintings and Juan de Herrera's design and architectural ideas are analysed by building. His concerning about absolute existence like god and nuclear takes the cubic form by Juan de Herrera instead of pictorial tendencies of Cubism, however pictorial elements such as sky and nails were still used in the work. He use alphabet letter as pattern consisting wall and symbol representing 'Juan de Herrera', moreover number '2' is taken to show up line attribute. Dali had several design develop process, and finally he reached an new stage called 'Hypercube'. Hypercube can distinguish from Cubism and Herrera's architectural idea, and it will be free from objective world based in Euclid geometry. Although cubic is the simplest shape. It can contain the variety of developments in these fields - philosophy, architecture, painting and etc.- from Platon to nuclear physics and coexists in a picture of Salvador Dali.

• 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 of the Korean School Mathematics Society
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• v.10 no.3
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• pp.341-351
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• 2007

The primary purpose of this treatise is to suggest the solutions as follows for the errors concerning the triangle determination and congruence in every Korean mathematics textbook for 7th graders: showing that SsA, along with SSS, SAS, ASA, should also be included as the condition for triangle determination, congruence and similarity; proving that contrary to what has been believed, minimality applies only to congruence and similarity but not to determination; examining related Euclidean propositions; discussing the confusion about the characteristics of determination and congruence; and considering the negative effects of giving definite figures in construction education. The secondary purpose is to analyze the significance of triangle determinant that is not dealt with in either Euclid's Elements or the text books in the U.S. or Japan, and suggest a way to effectively deal with triangle determination and congruence in education.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.263-277
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• 2000

mathematics holds a key position among the subject-matters of school education. Nevertheless, beyond Its Instrumental one, humanity-educational value of mathematics for the general public has been under estimated. For the past fifty years, in the our country there has not been enough systematic and profound examination and discussion concerning the goals of mathematics education in order to establish the philosophy of mathematics education. Thus, in this thesis we argue how mathematics education could contribute to the humanity education. For this, we examine how western educational theorists have emphasized the value of mathematics as humanity education and how their theories have been reflected in the goals of the modern mathematics education. First of all, we discuss Platonism as a philosophical basis of the traditional mathematics teaching mainly with Euclid's "Elements" since the ancient Greece and the relationship between mathematics education and humanity education in the light of this traditional thought. Next, we examine the thoughts of Pestalozzi, Harbert, Froebel who provided the theoretical basis for the public education since 19th century, and discuss the value of mathematics teaching in their humanistic educational thoughts. Also we examine the humanistic value of mathematics education in Dewey's educational philosophy, which criticized the traditional western ethics and epistemology, and established instrumen talism. Further, we analyze how such a philosophy of mathematics teaching is reflected mathematics education of 20th century, and confirm that the formation of Dewey's rational intelligence is one of the central aims of mathematics education of late 20th century. Finally, we discuss the ideals of humanistic mathematics education ; develop ment of the rational intelligence via 'doing knowledge'and change of mind via 'looking knowledge'. In this paper identify the humanistic values of mathematics education through the historical examination of the philosophies of mathematics education, and we could find significance as a fundamental study for one of the most important problems which Korean mathematics educational society confronts, that is establishing the philosophy of mathematics education.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.103-116
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• 2011

'The nine chapters on the mathematical art' has dominated the history of Chinese mathematics. It contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. But it has been greatly by improved by the commentary given Liu Hui and it was transformed from arithmetic text to mathematics. The improved book served as important textbook in China but also the East Asian countries for the past 2000 years. Also It is comparable in significance to Euclid's Elements in the West. In the middle of 19th century, Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) studied mathematical structures developed in Song(宋) and Yuan(元) eras on top of their early on 'The nine chapters' and 'ShuLiJingYun(數理精蘊)'. Their studies gave rise to a momentum for a prominent development of Choson mathematics in the century. Nam Byung Gil is also commentator on 'The Nine Chapters'. His commentary is 'GuJangSulHae(九章術解)'. This book provides figures and explanations of how the algorithms work. These are very helpful for prospective elementary teachers. We try to plan programs of elementary teacher education on the basis of 'The Nine Chapters' and 'GuJangSulHae'.