• The Mathematical Education
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• v.50 no.4
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• pp.467-487
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• 2011

The purpose of this study is to analyze of gifted students' improvement on mathematical attitude and problem-solving ability through project-based materials in science high school. For this study, research questions are established as follows. 1. Does the project-based materials-used instruction have a positive effect on improving problem-solving ability? 2. Does the project-based materials-used instruction have a positive effect on improving mathematical attitude? To solve these research questions, this study employed a survey and interview type investigation for gifted students' mathematical attitude and problem-solving ability. A subject of classes were randomly selected among the 11th grader in D science high school and designated one class as the experimental group and the other class as the control group. Twelve hours of the project-based materials-used instruction and the traditional textbook-oriented instruction had been carried out in each class. Findings on this study are as follows: First, the project-based material-used instruction is shown to be more effective in enhancing problem-solving ability than the traditional textbook-oriented instruction. Second, the project-based material-used instruction is shown to be more effective in improving mathematical attitude than the traditional textbook-oriented instruction.

• The Mathematical Education
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• v.33 no.2
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• pp.147-154
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• 1994

• Education of Primary School Mathematics
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• v.18 no.1
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• pp.17-30
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• 2015

The purpose of this study is to identify how developed program influence students' creativity by analyzing creative thinking and creative attitude which is appeared when mathematically gifted students get the program expected to improve their creativity. For the study, the 'dimension based geometry exploring program' was developed that consist of twelve lessons. The main idea of it, is implication of the novel . Through a pre and post-test, students's creativity were measured and compared. The results show significant changes on the scores of creative thinking skills and creative attitudes. As the result, mathematically gifted students' creative thinking skills and creative attitudes were improved by applying the of dimension based geometry exploring program.

• Journal of Gifted/Talented Education
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• v.26 no.1
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• pp.211-230
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• 2016

The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.

• 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.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.45-61
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• 2009

The powerful role of analogical reasoning in discovering mathematics is well substantiated in the history of mathematics. Mathematically gifted students, thus, are encouraged to learn via in-depth exploration on their own based on analogical reasoning. In this study, 57 gifted students (31in the 7th and 26 8th grade) were asked to formulate or clarify analogy. Students produced fruitful constructs led by analogical reasoning. Participants in this study appeared to experience the deep thinking that is necessary to solve problems made with analogies, a process equivalent to the one that mathematicians undertake. The subjects had to reflect on prior knowledge and develop new concepts such as an orthogonal projection and a point of intersection of perpendicular lines based on analogical reasoning. All subjects were found adept at making meaningful analogues of a triangle since they all made use of meta-cognition when searching relations for analogies. In the future, methodologies including the development of tasks and teaching settings, measures to evaluate the depth of mathematic exploration through analogy, and research on how to promote education related to analogy for gifted students will enhance gifted student mathematics education.

• 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.23 no.5
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• pp.835-855
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• 2013

The purpose of this study was to investigate the predictive validity of behaviroal characteristics checklists that are widely used in Korea for identifying mathematically gifted students. Three most widely used checklists were selected and implemented to classroom teachers who could teach and observe gifted students in regular classes. The predictive validity of the tree checklists were explored by generating the correlations between their ratings using those three checklists and the performance levels of gifted students, which were measured by teachers in gifted classes. Findings of this study are the followings: First, all three checklists could statistically significantly predict the performance of gifted students in gifted programs, and the checklist B showed the highest predictability. Secondly, without the assistance by those checklists, teachers could not predict the performance level of gifted students. Lastly, teachers that were trained for educating gifted students could very effectively predict the performance of gifted students with the aid of those checklists while teachers without appropriate training could not at all even with the aid of those checklists.

• The Mathematical Education
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• v.46 no.4
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• pp.445-464
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• 2007

On considering the mathematical creativity of the gifted in mathematics, some points should be reflected such as the characteristics of leaners, the gifted and of domain-special facts in mathematics. And the clear view of mathematical creativity of the gifted in mathematics makes a way to define the meanings of creative-productive ability and of creative products. Therefore to explicate the concept of mathematical creativity of the gifted in mathematics, researcher reviewed literacies of the concept of creativity in general fields, classical mathematicians, and school mathematics. In conclusion, first, mathematical creativity of the gifted in mathematics should be considered on the aspects of subject-mathematics, object-the gifted, and performing-gifted education. Second, it contains advanced problem solving matters on the school mathematics curriculum but reflect the process of recovery and reinvent and it is suggested in [fig.1] and [fig.2].

• School Mathematics
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• v.11 no.2
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• pp.227-241
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• 2009

The isoperimetric problem has been known from the time of antiquity. But the problem was not rigorously solved until Steiner published several proofs in 1841. At the time it stood at the center of controversy between analytic and geometric methods. The geometric approach give us more productive thinking (insight, structural understanding) than the analytic method (using Calculus). The purpose of this paper is to analysis and then to construct the isoperimetric problem which can be applied to the mathematically gifted students in the elementary school. The theoretical backgrounds of our analysis about our problem are based on the Gestalt psychology and mathematical reasoning. Our active program about the isoperimetric problem constructed by the Gestalt's view will contribute to improving a mathematical reasoning and to serving structural (relational) understanding of geometric figures.