• Journal for History of Mathematics
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• v.18 no.2
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• pp.75-94
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• 2005

This study is intended to develop the criterion for evaluating the creative products that mathematically gifted students produce in their education program to enhance the development of creative productive ability. 1 distinguish the mathematical creativity with the creativity in the general domain, and make the production model of the creative mathematical product grounded on the mathematicians' work through the mathematical history. The model has the following components; the mathematical knowledge, the mathematical thinking and the mathematical inquiry skill, surrounding the resultive creative product. The students products are focused on one component of the model. Thus the criterion for the creative products is grounded on the each component of the model. According to it, teachers could evaluate the students'work, which got the validity and the reliability.

• Communications of Mathematical Education
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• v.19 no.3 s.23
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• pp.557-569
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• 2005

수학 영재교육이 일반 학교수학교육과 차별화 되어야 한다는 점은 수학적 지식의 습득이 아니라 수학적 지식의 창출에 있다. 수학적 지식의 창출에 적절한 교육프로그램은 산출물을 중시하는 연구과정인데 본 연구는 이것을 성공적으로 수행할 수 있는 프로그램을 소개하며 그 기반으로서 창의적 문제해결과정을 제안한다.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.185-205
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• 2011

In this paper, we investigated the mathematical output of a gifted student's independent study. We chose one student who was taking a mentorship course in mathematics at the Gifted Education Center in Chonnam National University, and analyzed the characters of the result which a student showed through the output of independent study and studied the psychological change of a student while he was making a presentation of the results of his study. We found following facts. First, a mentor-independent study improves a mathematical gifted student's inductive thinking and ability to generalize and apply to other cases. Second, presenting a mathematical gifted student's output for mentor-independent study improves his ability of mathematical communication in the abilities of creative problem solving. Finally, there is an increased change in his perception and self-efficacy of mathematics after the presentation.

• Communications of Mathematical Education
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• v.21 no.1 s.29
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• pp.65-79
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• 2007

In this paper we study various aspects of Catalan number with its focus on creative output. As a result we we develop teaching and learning materials for the gifted students which can lead to creative output at the middle school level.

• School Mathematics
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• v.12 no.3
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• pp.301-322
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• 2010

In this study, researchers developed the criteria evaluating mathematically gifted students' creative products, which contain such evaluation headings as cognitive abilities(; creativity, analytic thinking, expert skill and knowledge), performing ability of the Mathematically Gifted-Creative Problem Solving process. And then a case study is carried out to apply the criteria to an actual condition of mathematically gifted education. This case study shows that how teachers can apply those of model and criteria in actual condition of the mathematically gifted education. Through the criteria above mentioned, the characteristics of creative productivity can be grasped clearly and evaluated in detail.

• The Mathematical Education
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• v.54 no.4
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• pp.317-334
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• 2015

In this article we study structure of the concept of creative products in mathematics using mathematical creative products. We develop MCPSS1 that improve reliability and validity of MCPSS(Creative Product Semantic Scale in Mathematics). And we search structure of the concept of creative products in mathematics using mathematical creative products focused on theoretical investigation. So we suggest structure model of the concept of creative products focused on theoretical investigation. We compare the result with preceding research using various mathematical creative products, find some difference between relations of sub-factors of structure of the concept of creative products. Our result will provide meaningful data to mathematics education researchers that want to know structure of the concept of creative products in mathematics.

• The Mathematical Education
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• v.53 no.2
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• pp.291-312
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• 2014

This study has to do with creative product in mathematics. We analyze Taylor's creative product according to a different developmental level of creativity, Taylor's creative product inventory, Besemer & Treffinger's creative products analysis matrix, O'Quin & Besemer's creative products semantic scale(CPSS) etc. The purpose of this study is to make creative products semantic scale in mathematics. O'Quin & Besemer's CPSS consists of 55 items, bipolar adjective checklist. We confirm that O'Quin & Besemer's CPSS is not fit to use for mathematics creative products. So we develop Creative Product Semantic Scale in Mathematics(MCPSS) which consists of 33 items, bipolar adjective checklist. Our result will provide convenience to mathematics teacher who guides a student make a creative product.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.171-194
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• 2006

As it is not long since the gifted education was implemented in elementary school, it is necessary to accumulate the practical studies on the mathematically gifted education. This paper focused on enhancing creativity by providing the various and divergent thinking activities for mathematically gifted students. For this purpose, I prepared two mathematics problems, and , and let the mathematically gifted 5th grade students solve them. After that, I investigated to analyse their reactions in detail and tried to find the methods for assessing their divergent products. Finally, I found that they could pose various and meaningful calculating equations and also identify the various relations between two numbers. I expect that accumulating these kinds of practical studies will contribute to the developments of gifted education, in particular, instructions, assessments, and curriculum developments for the mathematically gifted students in elementary schools.

• 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.

• Communications of Mathematical Education
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• v.18 no.3 s.20
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• pp.45-56
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• 2004

본고는 수학적 창의성과 관련한 논문으로 이를 창의적인 사람, 창의적인 산출물, 창의적인 과정이란 일반 창의성 연구자들이 연구하고 있는 분야로부터 유추적으로 논의를 시도하였다. 이런 접근으로부터, 얻을 수 있는 몇 가지 가정들은 다음과 같은 것이 있다. 첫 번째, 일반 보통아들을 대상으로 하는 공교육에서도 창의성 교육을 할 수 있으며, 이는 수학교과에도 적합한 진술이다. 두 번째, 현상학적 입장으로 부터 학교에서 교수${\cdot}$ 학습되고 있는 학교수학이 학생들 입장에서 보면 학습해야 할 필요가 있는 적절하고 새로운 지식이란 점을 공고히 해 주었다. 또한, 여기서 강조한 것은 새롭고 적절한 지식이 완성된 지식뿐만 아니라 발생상태 그대로의 지식 즉, 과정으로서의 지식도 포함하고 있음을 제안하였다. 세 번째, 수학자가 수학을 탐구하는 과정을 창의성 연구자들이 보듯이 인지과정으로 보는 대신에 한 수학적 아이디어를 이로부터 하나의 완성된 수학적 지식을 완성하기까지의 수학적 사고과정으로 보는 것이 수학교육적 의미에서 교수${\cdot}$ 학습에 의미가 있음을 살펴보았다.