• 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.

• 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.

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2005.11a
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• pp.1.1-2.1
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• 2005

• Journal for History of Mathematics
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• v.19 no.4
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• pp.117-132
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• 2006

For a meaningful learning of the Construction Unit in 7-B Grade, this study aims to develop teaming materials on the basis of Clairaut's $El{\`{e}}ments$ de $G{\`{e}}om{\`{e}}trie$, which is grounded on a natural generation derived from the history of mathematics and emphasizes students' inquiry activity and reflective thinking activity, and to analyze the characteristics of learning process shown in classes which use the application of teaming materials. Six students were sampled by gender and performance and an interpretive case study was conducted. Construction was specified so as to be consciously executed with emphasis on an analysis to enable one to discover construction techniques for oneself from a standpoint of problem solving, a justification to reveal the validity of construction, and a step of reflection to generalize the results of construction.

• 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.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• 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.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• 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.