• Communications of Mathematical Education
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• v.31 no.2
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• pp.103-121
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• 2017

Taxicab geometry was a typical non-Euclid geometry for mathematically gifted. Most educational material related quadratic curves on taxicab geometry for mathematically gifted served them to inquire the graph of the curves defined by focis and constant. In this study, we provide a shape of quadratic curves on taxicab geometry by applying three definitions(geometric algebraic definition, eccentricity definition, conic section definition).

• Journal of Gifted/Talented Education
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• v.11 no.2
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• pp.107-126
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• 2001

This study is focused on the selection program of mathematical gifted children on the middle school. To fulfill this purpose, I consider the testing program using cyber system. If we use the cyber system, we can survey mathematical play(for example, puzzle) and several mathematical activity of gifted children. Cyber system will be help as a subsidiary selection tool.

• School Mathematics
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• v.11 no.2
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• pp.317-333
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• 2009

The purpose of this study was to examine the thinking characteristics of mathematically gifted elementary school students in the process of modified prize-sharing problem solving and each student's thinking changes in the middle of discussion. To determine the relevance of the research task, 19 sixth graders enrolled in a local joint gifted class received instruction, and then 49 students took lessons. Out of them, 19 students attended a gifted education institution affiliated to local educational authorities, and 15 were in their fourth to sixth grades at a beginner's class in a science gifted education center affiliated to a university. 15 were in their fifth and sixth grades at an enrichment class in the same center. Two or three students who seemed to be highly attentive and express themselves clearly were selected from each group. Their behavioral and teaming characteristics were checked, and then an intensive observational case study was conducted with the help of an assistant researcher by videotaping their classes and having an interview. As a result of analyzing their thinking in the course of solving the modified prize-sharing problem, there were common denominators and differences among the student groups investigated, and each student was very distinctive in terms of problem-solving process and thinking level as well.

• Journal of Gifted/Talented Education
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• v.15 no.1
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• pp.85-102
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• 2005

Some properties on the mathematical hyper-dimensional figures by 'the principle of the permanence of equivalent forms' was investigated. It was supposed that there are 2 conjectures on the making n-dimensional figures : simplex (a pyramid type) and a hypercube(prism type). The figures which were made by the 2 conjectures all satisfied the sufficient condition to show the general Euler's Theorem(the Euler's Characteristics). Especially, the patterns on the numbers of the components of the simplex and hypercube are fitted to Binomial Theorem and Pascal's Triangle. It was also found that the prism type is a good shape to expand the Hasse's Diagram. 5 mathematically gifted high school students were mentored on the investigation of the hyper-dimensional figure by 'the principle of the permanence of equivalent forms'. Research products and ideas students have produced are shown and the 'guided re-invention method' used for mentoring are explained.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.201-220
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• 2007

This research is designed to analyze the metacognitive thinking that mathematically gifted elementary students use to solve problems, study the effects of the metacognitive function on the problem-solving process, and finally, present how to activate their metacognitive thinking. Research conclusions can be summarized as follows: First, the students went through three main pathways such as ARE, RE, and AERE, in the metacognitive thinking process. Second, different metacognitive pathways were applied, depending on the degree of problem difficulty. Third, even though students who solved the problems through the same pathway applied the same metacognitive thinking, they produced different results, depending on their capability in metacognition. Fourth, students who were well aware of metacognitive knowledge and competent in metacognitive regulation and evaluation, more effectively controlled problem-solving processes. And we gave 3 suggestions to activate their metacognitive thinking.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.327-344
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• 2006

This study examined the proof levels and understanding of constituents of proving by three mathematically gifted 6th grade korean students, who belonged to the highest 1% in elementary school, through observation and interviews on the problem-solving process in relation to constructing a rectangle of which area equals the sum of two other rectangles. We assigned the students with Clairaut's geometric problems and analyzed their proof levels and their difficulties in thinking related to the understanding of constituents of proving. Analysis of data was made based on the proof level suggested by Waring (2000) and the constituents of proving presented by Galbraith(1981), Dreyfus & Hadas(1987), Seo(1999). As a result, we found out that the students recognized the meaning and necessity of proof, and they peformed some geometric proofs if only they had teacher's proper intervention.

• Journal of Gifted/Talented Education
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• v.23 no.6
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• pp.947-963
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• 2013

This study investigated the difference of mathematical beliefs between common children and the gifted children, and then the effect of current mathematics gifted education on gifted children's mathematical belief. Gifted children from institution for gifted education and school based gifted classroom, and common children from regular classroom from S-city office of education in Gyenggi province were studied for this study. The results of this study was as follows. First, there was positive correlation between mathematics performance and mathematical belief. Second, common children and gifted children had significant difference in the degree of mathematical belief. And also, mathematically gifted students had much stronger and positive mathematical belief than common students before starting gifted education program. Third, there was no significant difference in common children and gifted children on the mathematical belief after they receive gifted education, but there were negative changes in gifted children from institution for gifted education on the mathematical belief after receiving gifted education.

• Journal of Gifted/Talented Education
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• v.20 no.3
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• pp.831-846
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• 2010

The Purposes of this study were to compare the level of study habits and test anxiety between gifted middle-school students and non-gifted and to find out the correlation between study habits and test anxiety in two groups. The total participants of this study were 437 middle school students. One hundred eighty three students (127 boys, 56 girls) belonged to gifted group who were enrolled in Cyber Education Center for Math & Science Gifted Students of KAIST in Daejeon. And two hundred fifty four (128 boys, 126 girls) were non-gifted group who were from the middle school in Seoul City and Gyeonggi province. The results revealed that the level of study habits of gifted middle school students was higher than that of non-gifted. And gifted group felt lower level of test anxiety than non-gifted group. Additionally gifted boys showed significantly higher level of study skills application behavior than gifted girls.

• School Mathematics
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• v.9 no.2
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• pp.277-289
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• 2007

This research aims to look into the mathematically gifted 6th and 7th graders spatial visualization ability of solid figures. The subjects of the research was six male elementary school students in the 6th grade and one male middle school student in the 1th grade receiving special education for the mathematically gifted students supported by the government. The task used in this research was the problems that compares the side lengths and the angle sizes in 4 pictures of its two dimensional representation of a regular icosahedron. The data collected included the activity sheets of the students and in-depth interviews on the problem solving. Data analysis was made based on McGee's theory about spatial visualization ability with referring to Duval's and Del Grande's. According to the results of analysis of subjects' spatial visualization ability, the spatial visualization abilities mainly found in the students' problem-solving process were the ability to visualize a partial configuration of the whole object, the ability to manipulate an object in imagination, the ability to imagine the rotation of a depicted object and the ability to transform a depicted object into a different form. Though most subjects displayed excellent spatial visualization abilities carrying out the tasks in this research, but some of them had a little difficulty in mentally imagining three dimensional objects from its two dimensional representation of a solid figure.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.351-370
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• 2013

The purpose of this study is to analyze the modes of visualization which appears in the process of thinking that mathematically gifted 6th grade students get to understand components of the three-dimensional shapes on the duality of regular polyhedrons, find the duality relation between the relations of such components, and further explore on whether such duality relation comes into existence in other regular polyhedrons. The results identified in this study are as follows: First, as components required for the process of exploring the duality relation of polyhedrons, there exist primary elements such as the number of faces, the number of vertexes, and the number of edges, and secondary elements such as the number of vertexes gathered at the same face and the number of faces gathered at the same vertex. Second, when exploring the duality relation of regular polyhedrons, mathematically gifted students solved the problems by using various modes of spatial visualization. They tried mainly to use visual distinction, dimension conversion, figure-background perception, position perception, ability to create a new thing, pattern transformation, and rearrangement. In this study, by investigating students' reactions which can appear in the process of exploring geometry problems and analyzing such reactions in conjunction with modes of visualization, modes of spatial visualization which are frequently used by a majority of students have been investigated and reactions relating to spatial visualization that a few students creatively used have been examined. Through such various reactions, the students' thinking in exploring three dimensional shapes could be understood.