• School Mathematics
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• v.18 no.3
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• pp.527-539
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• 2016

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.

• Research in Mathematical Education
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• v.11 no.3
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• pp.209-218
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• 2007

The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

• Journal of Korea Game Society
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• v.6 no.3
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• pp.33-42
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• 2006

This study is aimed to develop adventure-game style learning program for offering different levels curriculum in mathematics and figure areas in elementary schools. The 7th mathematics curriculum introduced different levels curriculum considering learners' ability, aptitude, requirement, interest so that it could improve learners' growth potential and educational efficiency. But in reality, it is quite difficult to increase educational efficiency by conducting individual learning classes according to students' ability due to the big differences among students' levels in addition to high population in each classroom. The purpose of this study is to offer different levels curriculum based on van Hiele theory and develop adventure-game style learning program to increase interests of the learners. This program can improve students' academic achievement by offering differentiated curriculums to learners who need advanced or supplementary learning materials. And it also enhances leaners' spatial-perceptual ability by offering various operating activities in figures learning.

• Research in Mathematical Education
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• v.16 no.1
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• pp.31-50
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• 2012

The present study explored whether the implementation of focused activities (intervention programme) can enhance 22 pre-service mathematics teachers' proficiency in solid geometry thinking level as well as change for the better their feelings in this discipline. Over a period of 6 weeks the pre-service teachers participated in activities and diversified experiences with 3D shapes, using illustration aids and actual experience of building 3D shapes in relation to the various spatial thinking levels. The research objectives were to investigate whether the intervention programme, comprising task-oriented activities of solid geometry, enhance mathematics pre-service teachers' mastery of their geometric thinking levels as well as examine their feelings towards this discipline before and after the intervention programme. The findings illustrate that learners' levels of geometric thinking can be promoted, entailing control on higher thinking levels as well as a more positive attitude towards this field.

• School Mathematics
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• v.2 no.1
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• pp.165-181
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• 2000

The teaching-learning methods of figures using computers make loose the difficulties of geometry education from the viewpoint that the abstract figures can be visualized and that by means of this visualization the learning can be accomplished through the direct experience or control. In this thesis, we present a teaching-learning method of figures using Cabri II so that the learners establish their knowledge obtained through their search, investigation, supposition and they accomplish the positive transition to advanced 1earning. So the learners extend their ability of sensuous intuition to their ability of logical reasoning through their logical intuition.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Journal of The Korean Association of Information Education
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• v.14 no.3
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• pp.449-459
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• 2010

Using a geometric computer program achieve learning effects as handling various function and has advantage to overcome the environment of classroom through providing an inquiring surroundings in the figure learning at an elementary school. There are many software for drawing the geometric. But currently most is focus on how to use the softwares without contents. So, It is necessary to develope a geometric software adapted cognitive development of primary schoolchildren. This study is aim to analyze elementary mathematic curriculum based on Van Heiles theory, to develope the software(Geometry for Kids : GeoKids) considering cognitive level of the primary schoolchildren. This software is developed to substitute a ruler and a compass considering cognitive level of the primary schoolchildren. Using mouse, GeoKids software help a child to draw easily lines and circles and this software notice another lines and circle automatically for a more accurate drawing figures. Children can use practically this software in connection with subjects of elementary mathematic curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.165-184
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• 2013

In order to utilize Sphinx Puzzle in shape education or deductive reasoning, a lesson employing Dienes' six-stage theory of learning mathematics was structured to be applied to students of 6th grade of elementary school. 4 students of 6th grade of elementary school, the researcher's current workplace, were selected as subjects. The academic achievement level of 4 subjects range across top to medium, who are generally enthusiastic and hardworking in learning activities. During the 3 lessons, the researcher played role as the guide and observer, recorded observation, collected activity sheet written by subjects, presentation materials, essays on the experience, interview data, and analyzed them to the detail. A task of finding every possible triangle out of pieces of Sphinx Puzzle was given, and until 6 steps of formalization was set, students' attitude to find a better way of mathematical deduction, especially that of operational thinking and deductive thinking, was carefully observed and analyzed.