• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.67-86
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• 2013

The purpose of this study is to analyze selection of factors of Schoenfeld's problem solving behavior shown in problem solving process of mathematically gifted students based on brain preference of the students and to present suggestions related to hemispheric lateralization that should be considered in teaching such students. The conclusions based on the research questions are as follows. First, as for problem solving methods of the students in the Gifted Education Center based on brain preference, the students of left brain preference showed more characteristics of the left brain such as preferring general, logical decision, while the students of right brain preference showed more characteristics of the right brain such as preferring subjective, intuitive decision, indicating that there were differences based on brain preference. Second, in the factors of Schoenfeld's problem solving behavior, the students of left brain preference mainly showed factors including standardized procedures such as algorithm, logical and systematical process, and deliberation, while the students of right brain preference mainly showed factors including informal and intuitive knowledge, drawing for understanding problem situation, and overall examination of problem-solving process. Thus, the two types of students were different in selecting the factors of Schoenfeld's problem solving behavior based on the characteristics of their brain preference. Finally, based on the results showing that the factors of Schoenfeld's problem solving behavior were differently selected by brain preference, it may be suggested that teaching problem solving and feedback can be improved when presenting the factors of Schoenfeld's problem solving behavior selected more by students of left brain preference to students of right brain preference and vice versa.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.285-299
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• 2013

Problem posing activity of which a learner reinterprets an original problem via a new problem suggested, is a learning method which encourages an active participation and approves self-directed learning ability of the learner. Especially gifted students need to get used to a creative attitude to modify or reinterpret various mathematical materials found in everyday usual lives creatively in steady manner via such empirical experience beyond the question making level of the textbook. This paper verifies the possibility of lesson on question making strategy utilization for creativity development of gifted class, and analyzes various cases of students' trials to modify the rules of a board game called Rummikub in application of their own mathematics after learning What-If-Not strategy.

• 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 School Mathematics Society
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• v.15 no.3
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• pp.565-584
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• 2012

This study investigates how the GSP helps gifted and talented students understand geometric principles and concepts during the inquiry process in the generalization of the internal triangle, and how the students logically proceeded to visualize the content during the process of generalization. Four mathematically gifted students were chosen for the study. They investigated the pattern between the area of the original triangle and the area of the internal triangle with the ratio of each sides on m:n respectively. Digital audio, video and written data were collected and analyzed. From the analysis the researcher found four results. First, the visualization used the GSP helps the students to understand the geometric principles and concepts intuitively. Second, the GSP helps the students to develop their inductive reasoning skills by proving the various cases. Third, the lessons used GSP increases interest in apathetic students and improves their mathematical communication and self-efficiency.

• 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 Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.415-441
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• 2017

The purpose of this study is to develop elementary school math classes for the gifted and talented with a focus on social issues to investigate the possibility of character education through specialized subject classes. As suggested in the goals of the math education for social justice, which provide the fundamental theoretical basis, through mathematics activities with a theme of social issues, mathematically gifted and talented young students can critically perceive social issues, express a sense of mathematical and critical agency throughout the course and develop a willingness and mindset to contribute to social progress. In particular, the concept of Figured Worlds and agency is applied to this study to explain the concept of elementary math classes for the gifted and talented with a focus on social issues. The concept is also used as the theoretical framework for the design and analysis of the curriculum. Figured Worlds is defined as the actual world composed of social and cultural elements (Holland et al., 1998) and can be described as the framework used by the individual or the social structure to perceive and interpret their surroundings. Agency refers to the power of practice that allows one to perceive the potential for change within the Figured Worlds that he is a part of and to change the existing Figured Worlds. This study sees as its purpose the fostering of young talent that has the agency to critically perceive the social structure or Figured Worlds through math classes with a theme of social issues, and thus become a social capital that can contribute to social progress.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• School Mathematics
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• v.7 no.2
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• pp.169-192
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• 2005

The purpose of this study is to provide the conformity for developing project-based teaching$\cdot$learning materials for the mathematically gifted students. And this study presents development procedural model in order to improve the effectiveness, analyze its practical usage and examine the verification of the developed materials. It made the following results regarding the development of project-based teaching$\cdot$learning materials for gifted children in mathematics. First, it is necessary to provide appropriate teaching$\cdot$learning model to develop the materials, and the materials should be restructured to be available to other level students. Second, it is suggested to develop a prototype in order to develop teaching$\cdot$learning materials for gifted children in mathematics, further the prototype needs to be restructured until it satisfies theoretical frame. Third, an introduction should be made before the activity to perform the projects effectively. Fourth, a teacher's guidance should introduce children's examples corresponding to the objectives of learning, the examples of topics examined by students, and teacher's manual and attention for teaching. This study has a point of presenting the detailed guidelines with regards to development of teaching$\cdot$learning materials for gifted students in mathematics. This study has a point of presenting the detailed guidees with regards to development of teaching$\cdot$learning materials for gifted students in mathematics.

• 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.

• School Mathematics
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• v.12 no.3
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• pp.353-370
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• 2010

The purpose of this study was threefold: (1) to select the components of spatial ability that could be associated with the implementation of a polycube task, embody the selected components of spatial ability as learning elements and develop the prototype of polycube teaching-learning materials applicable to gifted education, (2) to make a close analysis of the development process of the teaching-learning materials to ensure the applicability of the prototype, (3) to give some suggestions on the development of teaching-learning materials geared toward mathematically gifted classes. The findings of the study were as follows: As for the first purpose of the study, relevant literature was reviewed to make an accurate definition of spatial ability, on which there wasn't yet any clear-cut explanation, and to find out what made up spatial ability. After 13 components of spatial ability that were linked to a polycube task were selected, the prototype of teaching-learning materials for gifted education in mathematics was developed by including nine components in consideration of children's grade and level. Concerning the second purpose of the study, materials for teachers and students were separately developed based on the prototype, and the materials were modified and finalized in light of when selected students exerted their spatial ability well or didn't in case of utilizing the developed materials in class. And then the materials were finalized after being finetuned two times by regulating the learning type, sequence and degree of learning difficulty. Regarding the third purpose of the study, the polycube task performed in this study might not be generalizable, but there are seven suggestions on the development process of teaching-learning materials.