• Journal of Gifted/Talented Education
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• v.21 no.4
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• pp.847-860
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• 2011

In this study, the instrument of mathematical thinking ability tests were considered, and the differences between gifted and regular high school students in the ability were investigated by the test. The instrument consists of 9 items, and verified its quality due to reliability. Participants were 353 regular and 252 gifted high school students from tenth grade. As a result, not only organizing ability of information but also ability of space perception and visualization and intuitive insight ability could be the characteristics of the mathematical giftedness.

• Journal of Gifted/Talented Education
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• v.17 no.1
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• pp.1-26
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• 2007

The purpose of this study was to develop a math test for identification of the mathematically gifted on the basis of their math creative problem solving ability and to evaluate the goodness of the test. Especially, testing reliability and validity of scoring method on the basis of fluency only for evaluation of math creative problem solving ability was one of the main purposes. Ten closed math problems and 5 open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 closed math test items of Type I and the 5 open math test items of Type II were administered to 1,032 Grade 7 students who were recommended by their teachers as candidates for gifted education programs. Students' responses were scored by math teachers. Their responses were analyzed by BIGSTEPS and 1 parameter model of item analyses technique. The item analyses revealed that the problems were good in reliability, validity, item difficulty and item discriminating power even when creativity was scored based on the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creative problem solving ability of the candidates for math gifted education programs. In addition, it was found that the math creative problem solving tests discriminated applicants for the two different gifted educational institutions.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.81-102
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• 2010

The purpose of this study was to analyze the content and design of the seven math camp programs for students of the education centers for the elementary gifted students. The analysis focused on the goals, content, and evaluations utilized in the math camp programs. The results of the study were as follows. First, there was no big difference between the goals set for each camp, and they mainly focused on the goals in affective domain. Second, the content of math camp programs was focused on enrichment rather than acceleration. Most of the programs were focused on geometry, whereas fewer programs were focused on measurement, probability and statistics. Based on the Analysis, we found that only nine out of 27 programs applied level-wised or individual exercise programs. Third, all centers for the mathematically gifted carried out evaluations of their math camp programs. However, a specific evaluation plan was not established for the math camp program plans. We suggested the direction of math camp programs as follows. First, the goals should reflect on the intended outcomes of the math camp programs. Also, the goals of math camp programs need to be distinctive from general education goals. Second, the programs should contain harmonious contents with enrichment and acceleration and must include various reactions and task commitment. The math camp programs need to include references and an appropriate information for the gifted students to encourage self-directed learning. Third, a more specific evaluation plan for math camp programs needs to be developed for effective education for the gifted students.

• Journal of Gifted/Talented Education
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• v.21 no.4
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• pp.829-845
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• 2011

The purpose of this study was to examine mathematical performance predictions with gifted behavior ratings by teachers and parents. The participants of this study were 787 elementary 5th and 6th grade gifted students who took the mathematical performance test. This study asked gifted teachers and parents to rate gifted behaviors of these gifted students with using SRBCSS-R (Renzulli et al., 2002, 2009). The results indicated that gifted teachers rated gifted behaviors of the 5th grade gifted students higher than the 6th grade gifted students, except in 'mathematical characteristics.' Gifted teachers rated 'learning' gifted behaviors of male gifted students higher than those of female gifted students. In the meanwhile, parents of the 5th grade gifted students rated gifted behaviors higher than parents of the 6th grade gifted students in 'learning' and 'motivation.' In comparing the gifted behavior ratings by gifted teachers and parents, there were significant differences in 'learning' and 'motivation' ratings. That is, gifted teachers rated significantly higher 'learning' and 'motivation' of gifted students than parents. When this study explored the prediction of gifted behavior ratings by gifted teachers and parents on mathematical performances of gifted students, 'learning' and 'mathematical characteristics' ratings by gifted teachers predicted the mathematical performances of gifted students.

• Research in Mathematical Education
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• v.1 no.1
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• pp.95-106
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• 1997

Even though there are extracurricular mathematics classes for gifted students in all levels of schools in Korea, teachers cannot conduct the classes properly because the contents of the textbook are not adequate for the purpose of the classes. So, what they tend to do in the classes is just drilling with many problems which have already shown up at university entrance examinations and various mathematics competitions. The purpose of this paper is to give an example of what the content should be in "Mathematics III" (an elective subject for the science high school students according to the fifth and sixth amendment of national curriculum) and to suggest how to design the extracurricular classes for gifted students. Extracurricular classes of the ordinary secondary school as well as the elective course for the science high school can be suitably designed with choices of topics in the contents of Mathematics III.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.87-101
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• 2006

Gifted students in elementary, middle and high schools require a specialized curriculum to foster their mathematically gifted natures. Questions that stimulate the teacher's intellectual curiosity, student reactions and methods pertaining to content organization and problem formation are the main foci.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.53-74
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• 2013

The purpose of this paper is to analyze how mathematically gifted middle school students find out the necessary and sufficient condition for a certain hyperbolic line to be parallel to a given hyperbolic line in Non-Euclidean disc model (Poincar$\acute{e}$ disc model) using the Geometer's Sketchpad. We also investigated their characteristic of mathematical thinking and analyze how they express what they had observed while they did mental experiments in the Poincar$\acute{e}$ disc using computer-aided construction tools, measurement tools and inductive reasoning.

• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• School Mathematics
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• v.12 no.4
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• pp.563-584
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• 2010

This study is aimed at analysing the mathematical thinking processes based on image by the mathematically gifted. For this, the 'Splitting a Tetrahedron' Task was used and mathematical thinking of the two middle school students were investigated. One of them deduced how many tetrahedral and octahedral were there when a tetrahedra was splitted by the surfaces which were parallel to each face of the tetrahedra without using any physical material. The other one solved the task using physical material and invented new images. A concrete image, indexical image and symbolic image were founded and the various roles of images could be confirmed.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.103-115
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• 2006

We integrated and utilized the currently existing international AP(Advanced Placement) program in mathematics. In 2005, the KMEHRD(Korean Ministry of Education and Human Resources Development) began the mathematics AP program; we attempt to maximize its effectiveness through continuous development. In boosting educational excellence, our AP program will affect the intellectual desire and enhance the performance of mathematically gifted leaners. This program assists high school students to achieve their fullest potential.