• Journal of Educational Research in Mathematics
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• v.17 no.1
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• pp.51-66
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• 2007

The purpose of this study is to analyse the cases of the posed problems while the mathematically gifted students are playing the NIM game. The findings of a qualitative case study have led to the conclusions as follows. Most of all mathematically gifted students in the elementary school are not intend to suggest the solutions of the posed problem unless the teacher or the 'problem is requested. But a higher level of promising children were changing each data components of a problem in a consistent way and restructuring the problems while controlling their cognitive process. This is compared to that a relatively lower level of promising children tends to modify one or two data components instantly without trying to look at the whole structure. And we gave 2 suggestions to teach the mathematically gifted students in the problem posing.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.539-560
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• 2013

The purpose of this study was to investigate characteristics of mathematically gifted high school students' thinking in design activities using GrafEq. Eight mathematically gifted high school students, who already learned graphs of functions and inequalities necessary for design activities, were selected to work in pairs in our experiment. Results indicate that logical thinking and mathematical abstraction, intuitive and structural insights, flexible thinking, divergent thinking and originality, generalization and inductive reasoning emerged in the design activities. Nonetheless, fine-grained analysis of their mathematical activities also implies that teachers for gifted students need to emphasize both geometric and algebraic aspects of mathematical subjects, especially, algebraic expressions, and the tasks for the students are to be rich enough to provide a variety of ways to simplify the expressions.

• The Mathematical Education
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• v.50 no.4
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• pp.441-466
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• 2011

In this article, we study on the teaching design, focused on the geometric methods, of 2-D isoperimetric problem for the elementary mathematically gifted students. For our teaching design, we discussed the ideals of Zenodorus's polygon proof, Steiner's four-hinge proof, Steiner's mean boundary proof, Steiner's snowball-packing proof, Edler's finite existence proof and Lawlor's dissection proof, and then the ideals achieved were modified with the theoretical backgrounds-the theory of Freudenthal's mathematisation, the method of analysis-synthesis. We expect that this article would contribute to the elementary mathematically gifted students to acquire and to improve spatial sense.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.1-20
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• 2013

The aim of this study was to develop a gifted educational program in math-gifted class in elementary school using recently developed 4D-frame. This study identified how this program impacted on spatial sense and mathematical creativity for mathematically gifted students. The investigation attempted to contribute to the developments for the gifted educational program. To achieve the aim, the study analysed the 5 and 6th graders' figure learning contents from a revised version of the 2007 national curriculum. According to this analysis, twelve learning sections were developed on the basis of 4D-frame in the math-gifted educational program. The results of the study is as follows. First, a learning program using 4D-frame for spatial sense from mathematically gifted elementary school students was statistically significant. A sub-factor of spatial visualization called mental rotation and sub-factors of spatial orientations such as sense of distance and sense of spatial perception were statistically significant. Second, the learning program that uses 4D-frame for mathematical creativity was statistically significant. The sub-factors of mathematical creativity such as fluency, flexibility and originality were all statistically significant. Third, the manipulation properties of 4D-frame helped to understand the characteristics of various solid figures. Through the math discussions in the class, participants' error correction was promoted. The advantage of 4D-frame including easier manipulation helped participants' originality for their own sculpture. In summary, this found that the learning program using 4D-frame attributed to improve the spatial sense and mathematical creativity for mathematically gifted students in elementary school. These results indicated that the writers' learning program will help to develop the programs for the gifted education program in the future.

• Journal of Gifted/Talented Education
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• v.20 no.3
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• pp.655-679
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• 2010

This study was created with the intent of improving the teaching quality of the teachers responsible for instructing higher level math programs. Additionally, this research study was designed to analyze the instruction of mathematically gifted students by using "The Flanders Category System" and "TIMSS video analysis". The results of this study will provide opportunities for a deeper understanding of ways to improve the quality of gifted instruction in mathematics and furthermore will increase the expertise of teachers in the realm of gifted education in mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.2
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• pp.205-230
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• 2015

The purpose of this study is, targeting 5th and 6th grades mathematically gifted elementary students, to analyze the effect of independent study project learning on self-directed learning ability and mathematical self-efficacy, and based on the results, examine the implications that independent study project learning has in special education for the gifted. In order to solve the study problems, 5th grade mathematically gifted elementary students(40) and 6th grade mathematically gifted elementary students(39) who had passed the selection criteria of D education institute for the gifted and had been receiving special education for the gifted were selected. The study results are as below. First, although self-directed learning ability had no significant difference at p<0.05, it statistically had some differences in averages between pre-test and post-test results. Second, although mathematical self-efficacy had no significant difference at p<0.05, it statistically had some differences in averages between pre-test and post-test results. Third, in the aspects of self-directed learning ability and mathematical self-efficacy, independent study project learning had a more positive effect on 5th grade mathematically gifted elementary students than 6th grade mathematically gifted elementary students. In addition, it had significant differences in 'the level of mathematical tasks', a sub-level of mathematical self-efficacy, and 'the openness of learning', 'the initiative of learning', and 'a sense of responsibility for learning', sub-levels of self-directed learning ability. These results imply that independent study project learning has a positive effect on self-directed learning ability and mathematical self-efficacy of mathematically gifted elementary students so that it could be meaningfully used as a teaching method for special education for the gifted at educational sites of independent study project learning.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.415-444
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• 2010

The purpose of this study is to provide information that will help understand unique characteristics of mathematically gifted students and that can be utilized for special programs for mathematically gifted students, by investigating difference and relationship between attribution styles and attitude toward mathematics of mathematically gifted students and those of regular students. For that purpose, 202 mathematically gifted students and 415 regular students in 5th and 6th grades at elementary schools were surveyed in terms of attribution styles and attitude toward mathematics, and the result of the study is as follows. First, as for attribution styles, there was no difference between gifted students and regular students in terms of grade and gender, but there was significant difference in sub factors because of giftedness. Second, there was not significant difference between grades. but there was significant difference in sub factors between genders. Mathematically gifted students were more positive than regular students in every sub factor excepting gender role conformity, and especially they showed higher confidence and motivation. Third, according to the result of correlation analysis, there was significant static correlation between inner tendencies and attitude toward mathematics with both groups. The gifted group showed higher correlation between attribution of effort and attitude toward mathematics and inner tendencies and confidence than the regular group. The gifted group showed higher correlation in sub factors, and especially there was high static correlation between attribution of talent and confidence, and attribution of effort and motivation. Fourth, according to the result of multiple regression analysis, inner tendencies showed significant relation to attitude toward mathematics with both groups, and especially the influence of attribution of effort was high. Both attribution of effort and attribution of talent were higher in the gifted group than the regular group, and attribution of effort had a major influence on practicality and attribution of talent had a major influence on confidence.

• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.153-176
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• 2007

The purpose of this paper is to analyze teaching-learning program which can be applied to mathematically gifted students in primary school, Our program is based on constructivist views on teaching and learning of mathematics. Mainly, we study the algorithmic thinking of mathematically gifted students in primary school in connection with the network problems; Eulerian graph problem, the minimum connector problem, and the shortest path problem, The above 3-subjects are not familiar with primary school mathematics, so that we adapt teaching-learning model based on the social constructivism. To achieve the purpose of this study, seventeen students in primary school participated in the study, and video type(observation) and student's mathematical note were used for collecting data while the students studied. The results of our study were summarized as follows: First, network problems based on teaching-learning model of constructivist views help students learn the algorithmic thinking. Second, the teaching-learning model based on constructivist views gives an opportunity of various mathematical thinking experience. Finally, the teaching-learning model based on constructivist views needs more the ability of teacher's research and the time of teaching for students than an ordinary teaching-learning model.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.79-94
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• 2006

The purpose of this study is to find out the characteristics of the types(levels) of justification which are appeared by elementary mathematically gifted students in solving the tasks of plane division and spatial division. Selecting 10 fifth or sixth graders from 3 different groups in terms of mathematical capability and letting them generalize and justify some patterns. This study analyzed their responses and identified their differences in justification strategy. This study shows that mathematically gifted students apply different types of justification, such as inductive, generic or formal justification. Upper and lower groups lie in the different justification types(levels). And mathematically gifted children, especially in the upper group, have the strong desire to justify the rules which they discover, requiring a deductive thinking by themselves. They try to think both deductively and logically, and consider this kind of thought very significant.

• School Mathematics
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• v.9 no.2
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• pp.241-257
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• 2007

The study aims to figure out how to improve existing examination tools to distinguish mathematically gifted children and to clarify procedures and criteria for selecting candidates. Toward this end, it examined correlations between grades of gifted children selected through evaluation by pen-and-pencil tests and their creative problem-solving capability and performance assessment, and analyzed learning activities of the gifted children. According to the analysis, results of pen-and-pencil tests turned out to have low correlations with their creative problem-solving capability and performance assessment, but it was found that their creative problem-solving capability has high correlations with results of performance assessment. The analysis also found that there were some students who participated in a program for gifted children with high marks but had difficulties in adapting themselves to it. It found that there were children who joined the program with low marks but emerged as successive performers later on. In this regard, the existing examination tools to tell the gifted students apart need to be used to the fullest extent, and other diversified tools to evaluate mathematical capabilities that include mathematical creativity need to be further studied and developed. Qualitative studies on affective development of the gifted students and their creative problem-solving processes need to be conducted.