• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.225-241
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• 2010

Even though geometry is an important part basic to mathematics, studies on the program designs and teaching strategies of geometry are insufficient. The aims of this study are to propose the model of program design for autonomous learners taking their characteristics of the mathematically gifted into consideration. The core of teaching materials are analytic geometry and projective geometry. And the new teaching strategy will introduce three steps ; a draft strategies step(problem presentation, problem solving), a supportive strategies step(abstraction of a mathematical concept, mathematical induction, and extension), a transference strategies step to teaching strategy suitable for mathematically gifted. As a result, this study will suggest the effective methods of geometry teaching for the mathematically gifted.

• 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.

• School Mathematics
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• v.2 no.1
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• pp.111-144
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• 2000

The purpose of this study is to develop instruction sequence and teaching units for secondary school geometry using dynamic computer software like CabriII, GSP, Wingeom, Poly. For this purpose, literature was reviewed on various issues of geometry education and geometry curriculum using dynamic software. By the literature review, instructional sequence for teaching geometry in middle schools was designed. And, based on the newly developed instructional sequence, one sample teaching unit was developed. The basic principles for the development were to connect intuition geometry and formal geometry, and to emphasize students' investigative experience. Finally, experiment to check out teachers' response to the newly developed material was conducted by using questionnaire.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.215-227
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• 2000

This study is on the differences of the functions of definitions between in proof geometry and in intuitional geometry. There are the functions of definitions in intuitional geometry which may connect to those in proof geometry. We assert that when we teach them, we should be careful, for the teaching of the functions of definitions in proof.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.105-109
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• 1983

I shall not touch on everything that could be included under this heading. What I shall do is as follows: select three aspects of the teaching of geometry in Korea, and then report the present situations and future prospects of the teaching of geometry in Korea as regards these aspects alone.

• 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.

• The Mathematical Education
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• v.40 no.1
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• pp.93-102
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• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• Research in Mathematical Education
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• v.6 no.2
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• pp.107-116
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• 2002

Geometry is one of the important parts of Chinese school mathematics. There is a large difference in teaching and contents (standards, curriculum) between the US and China. Many mathematics educators in both countries are trying to reform the instruction of geometry and have made some progress. Close attention has been given to the Principles and Standards for School Mathematics (NCTM 2000), in which we have found many good ideas. In this paper, we introduce new developments of school geometry in China and have made some comparisons between the US and China. The new technology is becoming popular step by step in Chinese high schools. We believe we should learn from each other and exchange the ideas. In doing this mathematics teaching will be improved.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.69-96
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• 2008

The purpose of this paper is to perceive the problems of current geometry education in the middle school mathematics, to develop some learning materials fitted for the mathematising activities based on Freudenthal's learning theories and to analyze the mathematising process followed by teaching-learning activities. For this purpose, we design activity-oriented learning materials for geometry based on Freudenthal's learning theories, and appropriate teaching-learning models are established for the middle school geometry at the 8-NA stage level according to the theory of van Hiele's geometry learning steps. After applied to the practical lessons, the effects of mathematical activities are analyzed.

• Research in Mathematical Education
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• v.2 no.1
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• pp.21-39
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• 1998

The article examines four activities whereby the human face of geometry may be promoted in mathematical teaching at the upper secondary level. The activities deal with the historical, epistemological, structural and applicative issues of geometric knowledge.