• Communications of Mathematical Education
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• v.23 no.1
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• pp.53-72
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• 2009

The purpose of the study was to develop a program based on PCM(Parallel Curriculum Model) model for the gifted students, and investigate the effectiveness of the program with qualitative research methods. This program was designed to encourage the gifted students to explore mathematics that is closely related to the real world. The results of the study revealed that the program based on the PCM model had positive effect on the gifted students emotionally and cognitively. In conclusion, PCM program is considered an appropriate program for the gifted students of elementary school.

• 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.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.265-276
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• 2004

In this study we in detail analyze Kolmogorov's viewpoint of mathematical abilities, and conclude that school geometry plays important role in developing and upbringing mathematical abilities. We discuss meanings of school geometry in gifted students education, and draw didactical principles concerned with gifted students education. We suggest some geometrical materials which aim for developing and upbringing mathematical abilities.

• The Mathematical Education
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• v.48 no.4
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• pp.387-398
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• 2009

In this paper, we investigated the influence of technology, which gave an impact on students through the process of teaching & learning for the proof of an additive law of sine function in the mathematics education for the gifted. We chose students who were taking a course in enrichment mathematics at Science Education Institute for the Gifted in Mokpo National University, and analyzed their processes of a mathematical inference or conjecture, an algebraic description and a proof by visualization using technology. We found the following facts. That is, the visualization using technology is helpful to the gifted students in understanding principles and concepts of mathematics by intuition. Also, it is helpful to ones verifying various cases and generalizing principles. But, using technology can be a factor that disturbs learning of students who are clumsy with operating technology.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.335-351
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• 2016

The purpose of this study is to develop Project-Based Teaching-Learning materials for mathematically gifted students using a Fermat Point and apply the developed educational materials to practical classes, analyze, revise and correct them in order to make the materials be used in the field. I reached the conclusions as follows. First, Fermat Point is a good learning materials for mathematically gifted students. Second, when the students first meet the challenge of solving a problem, they observed, analyzed and speculated it with their prior knowledge. Third, students thought deductively and analogically in the process of drawing a conclusion based on observation. Fourth, students thought critically in the process of refuting the speculation. From the result of this study, the following suggestions can be supported. First, it is necessary to develop Teaching-Learning materials sustainedly for mathematically gifted students. Second, there needs a valuation criteria to analyze how learning materials were contributed to increase the mathematical ability. Third, there needs a follow up study about what characteristics of gifted students appeared.

• Journal of Gifted/Talented Education
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• v.24 no.6
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• pp.1039-1051
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• 2014

This study aims to measure intelligence (cognitive characteristics), self-esteem, mathematical attitudes, and scientific attitudes (affective characteristics) of gifted students from low-income families, and to identify the relationship among these variables. 147 students in the lower grades of elementary schools who were enrolled to university-based gifted education centers were participants of the study. The results showed that the percentile scores of each variable were 85% for intelligence, 75.6% for self-esteem, 73.3% for mathematical attitudes, and 71.3% for mathematical attitudes. There was no statistically significant relationship between intelligence and the affective characteristics (i.e., self-esteem, mathematical attitudes, and scientific attitudes), while statistically significant relationships were shown between self-esteem and mathematical attitudes (r=.448, p=.000), between self-esteem and scientific attitudes (r=.522, p=.000), and between mathematical attitudes and scientific attitudes (r=.448, p=.000). The results suggest that although the gifted students from low-income families show lower levels compared to other gifted student groups, their potential level of giftedness is considerably high, which calls for appropriate educational support systems designed for this population.

• Journal of Gifted/Talented Education
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• v.11 no.3
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• pp.175-202
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• 2001

The purpose of this work is to analyze various mathematics programs and related studies for gifted students of secondary school, to extract meaningful suggestions, and to develop some mathematics materials to realize our suggestions. We analyzed mathematics curriculum drafts for gifted students(by KEDI), mathematics program for the gifted students of Russia, and mathematics programs of some specialist of gifted education. We were able to extract some important aspects for developing teaching & teaming materials. Especially in this study we took notice of systematization of mathematical problems, and suggested a model of systematization of mathematical problems.