• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.411-428
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• 2012

There is no single definition of mathematical creativity. But creativity is a key competency to adapt and live in the future. So, there are so many attentions to develop students' mathematical creativity in school mathematics. In special, mathematical problem posing activity is a good method in enhancing mathematical creativity. The purpose of this paper is to analyse on the students' mathematical creativity using problems which are made by students in problem posing activities. 16 children who consist of three groups(high, middle, low) are participated in this study. They are trained to make the problem by Brown & Walter's 'What if not' strategy. The results are as follows: Total creativity is proportional to general achievement levels. There is a difference total creativity between items contents. The number of problems differs little according to the general achievement levels. According to the qualitative analysis, students make the problems using the change of terms. And there is no problem to generalize. Based on this paper, I suggest comparing the creativity between problem posing activity and other creative fields. And we need the deeper qualitative analysis on the students' creative output.

• The Mathematical Education
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• v.55 no.2
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• pp.147-169
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• 2016

This study analyzes the mathematical creativity test as an illustrative example with scoring domains of fluency, flexibility and originality in order to make suggestions for obtaining maximum reliability based on a composite score depending on combinations of each scoring domain weights. This is done by performing a multivariate generalizability analysis on the test scores, which were allowed to access publicly, of 30 mathematically gifted elementary school students, and therefore error variances, generalizability coefficients, and effective weights have been calculated. The main results were as follows. First, the optimal weights should adjust to .5, .4, and .1 based on the maximum generalizability coefficient even though the original weights in the mathematical creativity test were equal for each scoring domain with fluency, flexibility and originality. Second, the mathematical creativity test using the three scoring domains of fluency, flexibility, and originality showed higher reliability than using one scoring domain such as fluency. These results are limited to the mathematical creativity test used in this study. However, the methodology applied in this study can help determine the optimal weights depending on each scoring domain when the tests constructed in various researchers or educational fields are composed of multiple scoring domains.

• Research in Mathematical Education
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• v.16 no.2
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• pp.125-135
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• 2012

Students not only learn mathematics knowledge, but also have the capability of mathematical creativity. The latter has been thought an important task in mathematics education by more and more mathematicians and mathematics educators. In this paper, mathematicians' methods of creating mathematics are presented. Then, the paper elaborates on how these methods can be utilized to enhance mathematical creativity in the schools.

• The Mathematical Education
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• v.46 no.4
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• pp.503-519
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• 2007

In this study, the instrument of mathematical problem posing ability and mathematical creativity ability tests were considered, and the differences between gifted and regular students in the ability were investigated by the test. The instrument consists of each 10 items and 5 items, and verified its quality due to reliability, validity and discrimination. Participants were 218 regular and 100 gifted students from seventh grade. As a result, not only problem solving but also mathematical creativity and problem posing could be the characteristics of the giftedness.

• East Asian mathematical journal
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• v.34 no.4
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• pp.429-449
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• 2018

The purpose of this study is to investigate how the mathematical creativity of middle school mathematical gifted students is represented through the process of problem posing activities. For this goal, they were asked to pose real-world problems similar to the tasks which had been solved together in advance. This study demonstrated that just 2 of 15 pupils showed mathematical giftedness as well as mathematical creativity. And selecting mathematically creative and gifted pupils through creative problem-solving test consisting of problem solving tasks should be conducted very carefully to prevent missing excellent candidates. A couple of pupils who have been exerting their efforts in getting private tutoring seemed not overcoming algorithmic fixation and showed negative attitude in finding new problems and divergent approaches or solutions, though they showed excellence in solving typical mathematics problems. Thus, we conclude that it is necessary to incorporate problem posing tasks as well as multiple solution tasks into both screening process of gifted pupils and mathematics gifted classes for effective assessing and fostering mathematical creativity.

• East Asian mathematical journal
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• v.38 no.4
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• pp.463-496
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• 2022

The purpose of this study is to analyze the mathematical creativity and computational thinking of mathematically gifted elementary students through a convergence class using programming and to identify what it means to provide the convergence class using Python for the mathematical creativity and computational thinking of mathematically gifted elementary students. To this end, the content of the nine sessions of the Python-applied convergence programs were developed, exploratory and heuristic case study was conducted to observe and analyze the mathematical creativity and computational thinking of mathematically gifted elementary students. The subject of this study was a single group of sixteen students from the mathematics and science gifted class, and the content of the nine sessions of the Python convergence class was recorded on their tablets. Additional data was collected through audio recording, observation. In fact, in order to solve a given problem creatively, students not only naturally organized and formalized existing mathematical concepts, mathematical symbols, and programming instructions, but also showed divergent thinking to solve problems flexibly from various perspectives. In addition, students experienced abstraction, iterative thinking, and critical thinking through activities to remove unnecessary elements, extract key elements, analyze mathematical concepts, and decompose problems into small components, and math gifted students showed a sense of achievement and challenge.

• Research in Mathematical Education
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• v.8 no.3
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• pp.145-155
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• 2004

Mathematics, by its nature, is a creative activity. Creativity can be developed either through considering its intrinsic beauty or by examining the role that it plays in applications to real world problems. Many of the great mathematicians have been vitally interested in applications and gained inspiration in developing new mathematics from the mathematical descriptions of physical phenomena. In this paper we will examine the processes of applying mathematics by looking at how mathematical models are formed and used. Applications from sport, the environment and populations are used as illustrations.

• Research in Mathematical Education
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• v.9 no.2 s.22
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• pp.175-182
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• 2005

This paper will present two activity cases for developing mathematical creativity at The Center for Science Gifted Education (CSGE) of Chongju National University of Education of Korea. One is 'the magic card mystery'; the other is 'mathematicians' efforts to solve equations'.

• Journal of Gifted/Talented Education
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• v.24 no.6
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• pp.1053-1071
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• 2014

Problem posing is used to develop the creativity program and adaption for the gifted, and to screen the gifted students in the selection process. However existing creativity assessment factors(fluence, flexibility, originality) has been recognized to have it's limitation to assess the mathematical creativity. To improve the creativity assessment, we propose new set of assessment factors for mathematical creativity test through problem posing. For this study, we let 19 mathematically gifted students to pose two good mathematical problems for a limited time after solving a certain problem so called a reference problem. A week late, we let the subjects, pre-service teachers, and experts to evaluate the problems posed by the subjects, and leave the reasons for evaluating highest mark and lowest mark. With this date, we propose fluence, flexibility, originality, anti-similarity, complexity, elaboration as the set of mathematics creativity assessment factors.

• Education of Primary School Mathematics
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• v.24 no.4
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• pp.175-187
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• 2021

The purpose of this study is to investigate the effects of solving multi-strategic mathematics problems on mathematical creativity and attitudes of the 6th grade students. For this study, the researchers conducted a survey of forty nine (26 students in experimental group and 23 students in comparative group) 6th graders of S elementary school in Seoul with 19 lessons. The experimental group solved the multi-strategic mathematics problems after learning mathematics through mathematical strategies, whereas the group of comparative students were taught general mathematics problem solving. The researchers conducted pre- and post- isomorphic mathematical creativity and mathematical attitudes of students. They examined the t-test between the pre- and post- scores of sub-elements of fluency, flexibility and creativity and attitudes of the students by the i-STATistics. The researchers obtained the following conclusions. First, solving multi-strategic mathematics problems has a positive impact on mathematical creativity of the students. After learning solving the multi-strategic mathematics problems, the scores of mathematical creativity of the 6th grade elementary students were increased. Second, learning solving the multi-strategy mathematics problems impact the interest, value, will and efficacy factors in the mathematical attitudes of the students. However, no significant effect was found in the areas of desire for recognition and motivation. The researchers suggested that, by expanding the academic year and the number of people in the study, it is necessary to verify how mathematics learning through multi-strategic mathematics problem-solving affects mathematical creativity and mathematical attitudes, and to verify the effectiveness through long-term research, including qualitative research methods such as in-depth interviews and observations of students' solving problems.