• East Asian mathematical journal
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• v.40 no.2
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• pp.167-181
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• 2024

This study explored the characteristics of elementary gifted students' creative problem-solving skills combining creativity and problem-solving ability based on their work on Fermi estimation problems. The analysis revealed that gifted students exhibited strong logical validity and breadth but showed some weaknesses in divergent thinking abilities (fluency, flexibility, originality).

• Research in Mathematical Education
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• v.10 no.2 s.26
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• pp.89-102
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• 2006

The present article is dedicated to discussing the methods of teaching schoolchildren to solve creative problems. A few types of Olympiad problems were chosen as a didactic content of the article. The relevance of the choice receives proper grounding. Explanations are followed by examples from pedagogic practice. The article was written for the use of school teachers and educationalists that are researching the problem of improving creative thinking with schoolchildren.

• The Mathematical Education
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• v.50 no.4
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• pp.403-428
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• 2011

The direction of recent education literature points to the importance of creativity and creative practices, which also plays an important role in character education and has been recognized as being invaluable for the educational goals of the 21st century. As such, the goal of mathematics educators and researchers has also been on emphasizing the importance of building character and promoting creative practices. In this research, we study the pedagogical measures that can be easily implemented in classrooms to foster creative mathematical thinking and practices in students. In particular, the mathematical topic of interest is three-dimensional geometry, and especially polygons, and processes in which mathematical knowledge and creative practices play out in classrooms. For example, we explore how these creative lessons can be organized as the target internalization lessons, concepts definition lessons, regularity and relationship lessons, question posing lessons, and narrative story lessons. All of these lessons share three commonalities: 1) they require specific planning and execution challenges in order to achieve creative tasks, 2) they take advantage of open-ended problems, and 3) they are activity-oriented. Through this study, we hope to further our understanding on successful creative mathematical educational practices in the field of mathematics education, and help establish model lessons and materials for teachers and educators to use towards such goals.

• Research in Mathematical Education
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• v.10 no.1 s.25
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• pp.1-11
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• 2006

In today's world, it is not enough to be proficient at computation or at memorizing rote procedures to solve routine problems. These skills are important, but even more important are the abilities to recognize and define problems, generate multiple solutions or paths toward solution, reason, justify conclusions, and communicate results. These are not abilities that one is born with and they do not generally develop on their own. For students to become gifted, promising, and creative mathematicians, these talents must be cultivated and nurtured.

• The Mathematical Education
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• v.59 no.1
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• pp.81-99
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• 2020

This study examined the types of abduction and the thinking strategies by the mathematics problems posed by students. Four students who were 2nd graders in middle school participated in problem posing on four tasks that were given, and the problems that they posed were classified into equivalence problem, isomorphic problem, and similar problem. The type of abduction appeared were different depending on the type of problems that students posed. In case of equivalence problem, the given condition of the problems was recognized as object for posing problems and it was the manipulative abduction. In isomorphic problem and similar problem, manipulative abduction, theoretical abduction, and creative abduction were all manifested, and creative abduction was manifested more in similar problem than in isomorphic problem. Thinking strategies employed at abduction were examined in order to find out what rules were presumed by students across problem posing activity. Seven types of thinking strategies were identified as having been used on rule inference by manipulative selective abduction. Three types of knowledge were used on rule inference by theoretical selective abduction. Three types of thinking strategies were used on rule inference by creative abduction.

• Journal of Creative Information Culture
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• v.5 no.3
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• pp.295-306
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• 2019

Despite the popularity and convenient accessibility of puzzles, the variety of puzzles have led to a lack of research on the nature of the puzzle itself. In guiding certain skills, such as abstractness, creativity, and logic, a teacher should have the thinking skill and strategy that appear in solving puzzles. In this study, the mathematical thinking that appears in solving puzzles from the perspective of experts is identified, and the strategies and characteristics are described and classified accordingly. For this purpose, we analyzed 85 math puzzles including the well-know puzzles to the public, plus puzzles from a popular book for the gifted student. The research analysis shows that there are 6 types of mathematics puzzles in which require mathematical thinking.

• 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.

• Research in Mathematical Education
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• v.10 no.1 s.25
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• pp.55-70
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• 2006

The purpose of this study was to develop math creative problem solving test in order to identify the mathematically gifted on the basis of their math creative problem solving ability and evaluate the goodness of the test in terms of its reliability and validity of measuring creativity in math problem solving on the basis of fluency in producing valid solutions. Ten open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 open math test items were administered to 2,029 Grade 5 students who were recommended by their teachers as candidates for gifted education programs. Fluency, the number of valid solutions, in each problem was scored by math teachers. Their responses were analyzed by BIGSTEPTS based on Rasch's 1-parameter item-response model. The item analyses revealed that the problems were good in reliability, validity, difficulty, and discrimination power even when creativity was scored with the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creativity of the candidates for math gifted education programs. In addition, it discriminated applicants for two different gifted educational institutions and between male and female students as well.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.69-88
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• 2017

One of the most important activities in the process of mathematical modeling is to build models by conjecturing mathematical rules and principles in the real phenomena and to validate the models by considering its validity. Due to uncertainty and ambiguity inherent real-contexts, various strategies and solutions for mathematical modeling can be available. This characteristic of mathematical modeling can offer a proper environment in which creativity could intervene in the process and the product of modeling. In this study, first we analyze the process and the product of mathematical modeling, especially focusing on the students' models and validating way, to find evidences about whether modeling can facilitate students'creative thinking. The findings showed that the students' creative thinking related to fluency, flexibility, elaboration, and originality emerged through mathematical modeling.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.1-17
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• 2003

In this paper, we study the methods of improving an ability of a creative solving mathematical problem belonging to an educational system which every province office of education has adopted for the mathematically talented students. Especially, we give an attention on a preferential reaction in teaching styles according to student's LQ., the relationship between student's LQ. and an ability of creative solving mathematical problems, and seeking for an appropriative teaching methods of the improvement ability of a creative solving problem. As results, we have the followings; 1. The group having excellent students who have a higher intelligential ability prefers inquiry learning which is composed of several sub-groups to a teacher-centered instruction. 2. The correlation coefficient between student's LQ. and an ability creative solving of mathematical is not high. 3. Although the contents and the model of thematic inquiry learning don't have a great influence on the divergent thinking (ex. fluency, flexibility, originality), they affect greatly the convergent thinking - a creative mathematical - problem solving ability. Accordingly, our results show that we should use a variety of mathematical teaching materials apart from our regular textbooks used in schools to improve a creative mathematical problem solving ability in the process of thematic inquiry learning. Also we can see that an inquiry learning which stimulates student's participation and discussion can be a desirable model in the thematic mathematical classroom activities.