• 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 for History of Mathematics
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• v.19 no.4
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• pp.31-62
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• 2006

In this article, the theoretical basis of applying mathematical his tory in lessons is inquired in various educational aspects. It also covers the psychological genetic principle, mainly concerning the childish development and states that it has to be compatible with the historico-genetic principle, which is suggested mainly concerning the development of data. In addition, it evolves the arguments about the meaning of mathematical history in math lessons based on the mentioned aspects besides that in ordinary math lessons. Next, the link between the apply of mathematical history and education for gifted children is examined. Last, cases of mathematic history applied to mathematic education is suggested mainly concerning the understanding of differential concepts.

• The Mathematical Education
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• v.55 no.2
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• pp.209-232
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• 2016

This study analyzed the process of steps in a program introducing Renzulli's enrichment triad model and various levels of posing open-ended problems of those who participated in the program for mathematics-gifted elementary students. As results, participants showed their abilities of problem posing related to real life in a program introducing Renzulli's enrichment triad model. From eighteen mathematical responses, gifted students were generally outstanding in terms of producing problems that demonstrated high quality completion, communication, and solvability. Amongst these responses from fifteen open-ended problems, all of which showed that the level of students' ability to devise questions was varied in terms of the problems' openness (varied possible outcomes), complexity, and relevance. Meanwhile, some of them didn't show their ability of composing problem with concepts, principle and rules in complex level. In addition, there are high or very high correlations among factors of mathematical problems themselves as well as open-ended problems themselves, and between mathematical problems and open-ended problems. In particular, factors of mathematical problems such as completion, communication, and solvability showed very high correlation with relevance of the problems' openness perspectives.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.19-30
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• 2008

Cavalieri is chiefly remembered for his work on the problem "indivisibles." Building on the work of Archimedes, he investigated the method of construction by which areas and volumes of curved figures could be found. Cavalieri regarded an area as made up of an indefinite number of parallel line segments and a volume of an indefinite number of parallel plane areas. He called these elements the indivisibles of area and volume. Cavalieri developed a method of the indivisibles which he used to determine areas and volumes. We call this Cavalieri's principle which states that there exists a plane such that any plane parallel to it intersects equal areas In both objects, then the volumes of the two objects are equal. Cavalieri's principle and method of the indivisibles are very important to understand of volume of a pyramid for gifted students.

• 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.

• Journal of The Korean Association For Science Education
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• v.30 no.2
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• pp.192-205
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• 2010

We have investigated the recognition for the gifted science education program of middle school students being educated at the local center for the gifted. We developed a questionnaire that includes items for contents of the program, learning environments, participation attitude, effects of the program and improvements, and consists of it5-point Likert items and related descriptive items. 161 students at the local centers for the gifted responded to the questionnaire. The total score was 3.70 on a 5-point Likert scale. The score of effects of the program was highest, learning environments was the lowest. Most of the students referred that the participation of the programs help their schoolwork because of schoolwork preparations & review, learning the process of the solving problem and principle. On the contrary, difficult contents and long lesson hours interrupted their schoolwork. Students recognized that the programs are mainly composed of students' self-activities and the role of teachers is subsidiary. The programs have a good effect on them to increase interest in science and creative thinking. It is necessary that the program be improved in lesson hours, contents of the program, school facilities, and full service.

• Journal of Korean Elementary Science Education
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• v.31 no.4
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• pp.513-531
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• 2012

This study was to analyze the characteristic of scientific argumentation in the classes for the gifted of elementary school. The participants of this study were 5 fifth graders and 9 sixth graders, 14 in total, from the basic unit schools for gifted students of J elementary school in Incheon city. And it constituted small scale groups made up of 2~3 students with similar or identical ability in scientific reasoning. It had set up hypothesis for each group before the experiment, and students had a group discussion as a whole after the experiment. Classes were conducted 4 times, all courses were recorded as a sound/video. The ability in scientific reasoning of the students was inspected, making use of SRT II by means of pre-survey, and their argumentation levels were analyzed, utilizing 'Rubric for scientific argumentation course assessment.' As a result, argumentations did not incurred in every class. Analysis in argumentations of the students resulted in low level argumentation. This means argumentation cannot incur based on that with the limit in understanding the principle of experiments over the threshold of textbook no matter that he is an gifted student or not. The student both in formal operational period and transition period (2B/3A), the ability of scientific thinking in upper level, was improved of his argumentative ability in an overall aspect. However, a student of concrete operational period, the ability of scientific thinking in lower level, had argumentation with still lower level even after the experiment at the moment of discussing with the students on the upper level of scientific thinking ability.

• Journal of The Korean Association For Science Education
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• v.34 no.7
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• pp.657-666
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• 2014

To identify the gifted, it is essential to perform overall evaluation on cognitive and affective aspects considering all the characteristics of the science gifted. Nowadays, not only cognitive factors but also affective factors are being emphasized. Among the affective factors of the gifted, the task commitment is an important factor to describe the gifted and their outstanding achievements. From this research, by measuring the characteristics of task commitment shown in the science gifted, this can offer good implications regarding the selection of the gifted and the education. We developed the rubric of the gifted students by analyzing the students' experience of showing task commitment. By applying the rubric, we measured the levels by areas of the characteristics of task commitment shown in the experiences which the science gifted had by deeply exploring the cause or the principle. To better understand the characteristics of the science gifted students' task commitment, each and every students' characteristics were specifically described. The students' task commitment can be measured objectively and effectively by using the measuring tool in the form of rubric based on the characteristics of the task commitment. Specifically describing the students' characteristics on the basis of their performance criteria is the grounds for the level judgment and enhances the understanding of the characteristics of students' task commitment.

• KIPS Transactions on Computer and Communication Systems
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• v.4 no.12
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• pp.391-398
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• 2015

This paper devises a performance improvement and evaluation process of circuit minimization algorithms for mentorship education of distinguished informatics gifted secondary students. In the process, students learn that there are several alternative equivalent circuits for a target function and recognize the necessity for formalized circuit minimization methods. Firstly, they come at the concept of circuit minimization principle from Karnaugh Map which is a manual methodology. Secondly, they explore Quine-McCluskey algorithm which is a computational methodology. Quine-McCluskey algorithm's time complexity is high because it uses set operations. To improve the performance of Quine-McCluskey algorithm, we encourage them to adopt a bit-wise data structure instead of integer array for sets. They will eventually see that the performance achievement is about 36%. The ultimate goal of the process is to enlarge gifted students' interest and integrated knowledge about computer science encompassing electronic switches, logic gates, logic circuits, programming languages, data structures and algorithms.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.145-158
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• 2010

In this paper we study tetrahedron's properties related with center of inscribed sphere using the center of mass. We show that the center of mass of four mass points (A,a), (B,b), (C,c), (D,d) coincide with center of tetrahedron's inscribed sphere, suggest equalities and inequalities related with center of inscribed sphere, and prove theses using the center of mass. Our results can be used in research and education programs, various types of gifted student education.