• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.1-23
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• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.117-130
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• 2017

Euclid's elements have been recognized as a significant textbook in mathematics and mathematics education because of importance of its contents and methodology. This study discussed how the elements is connected with understanding of math textbooks in elementary school, trying to reveal the value for teacher training. First, when details in elementary textbooks were considered in aspect of elements, the importance of elements was illustrated with the purpose of understanding contents of elementary school by examining educational implications. In addition, the study discussed the value of the elements as the place for teachers and would-be teachers to experience math system.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.367-379
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• 2015

The existence of mathematical objects was considered through diorism which was used in ancient Greece as conditions for the existence of the solution of the problem. Proposition I-22 of Euclid Elements has diorism for the existence of triangle. By discussing the diorism in Elements, ancient Greek mathematician proved the existence of defined object by postulates or theorems. Therefore, the existence of mathematical object is verifiability in the axiom system. From this perspective, construction is the main method to guarantee the existence in the Elements. Furthermore, we suggest some implications about the existence of mathematical objects in school mathematics.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.351-364
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• 2003

by A.C. Clairaut is the first geometry textbook based on the historico-genetic principle against the logico-deduction method of Euclid's This paper aims to recognize Clairaut's historico-genetic principle by inquiring into this book and to search for its applications to school mathematics. For this purpose, we induce the following five characteristics that result from his principle and give some suggestions for school geometry in relation to these characteristics respectively : 1. The appearance of geometry is due to the necessity. 2. He approaches to the geometry through solving real-world problems.- the application of mathematics 3. He adopts natural methods for beginners.-the harmony of intuition and logic 4. He makes beginners to grasp the principles. 5. The activity principle is embodied. In addition, we analyze the two useful propositions that may prove these characteristics properly.

• Journal for History of Mathematics
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• v.34 no.1
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• pp.1-20
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• 2021

Logic and intuition are considered as the opposite extremes of teaching geometry, and any teaching method of geometry is to be placed between these extremes. The purpose of this study is to identify the characteristics of logical and intuitive approaches for teaching geometry and to derive didactical implications by taking Euclid's Elements and Clairaut's Elements respectively representing the extremes. To this end, comparing the composition and contents of each book, we analyze which propositions Clairaut chose from Euclid's Elements, how their approaches differ in definitions, proofs, and geometrical constructions, and what unique approaches Clairaut took. The results reveal that Clairaut mainly chose propositions from Euclid's books 1, 3, 6, 11, and 12 to provide the contexts that show why such ideas were needed, rather than the sudden appearance of abstract and formal propositions, and omitted or modified the process of justification according to learners' levels. These propose a variety of intuitive strategies in line with trends of teaching geometry towards emphasis on conceptual understanding and different levels of justification. Specifically, such as the general principle of similarity and the infinite geometric approach shown in Clairaut's Elements, we could confirm that intuition-based geometry does not necessarily aim for tasks with low cognitive demand, but must be taught in a way that learners can understand.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.119-139
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• 2017

The construction in the ancient Greek era had more meanings than a construction in the present education. Based on this fact, this study examines the meaning of the current textbook. In contrast, we have extracted the meaning of the constructions in Euclid Elements. In addition, we have been thinking about what benefits can come up if the meaning of the construction in Euclid Elements was reflected in current education, and suggested a way to exploit that advantage. As results, it was confirmed that the construction in the current textbook was merely a means for introducing and understanding the congruent conditions of the triangle. On the other hand, the construction had four meanings in Euclid Elements; Abstract activities that have been validated by the postulates, a mean of demonstrating the existence of figures and obtaining validity for the introduction of auxiliary lines, refraining from intervening in the argument except for the introduction of auxiliary lines, a mean of dealing with numbers and algebra. Finally we discussed the advantages of using the constructions as a means of ensuring the validity of the introduction of the auxiliary line to the argument. And we proposed a viewpoint of construction by intervention of virtual tools for auxiliary lines which can not be constructed with Euclid tool.

• Proceedings of the Korea Contents Association Conference
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• 2012.05a
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• pp.141-142
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• 2012

점과 선은 도형의 기초이며 수학과 물리학에서 중요한 요소라고 할 수 있다. 도형의 발달은 고대 이집트에서 이루어졌으며 이러한 도형의 발달은 그리스에서 체계화 되었으며 대표적으로 유클리드의 '기하학 원론'에서 점과 선에 대한 정의와 공리 등에 인하여 기하학은 발전하였다. 이러한 점에 관한 정의는 시대에 따라 재해석되고 논쟁과 토론의 과정을 거쳐왔으며. 즉 '점이 부분이 없는 것'이라는 기하학 원론'의 정의는 점의 존재성에 대한 다양한 철학적 사유를 이끌었으며 19세기 수학 기초의 위기 속에서 다양한 수학적 접근법이 나타나게 되었다. 본 논문에서는 점의 기존의 정의와 다양한 접근 방법에 대해서 살펴보고자 한다.

• The Korean Publising Journal, Monthly
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• s.58
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• pp.18-18
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• 1990