• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.47-62
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• 2016

Cultivating mathematical creativity is one of the aims in the recently revised mathematics curricular. However, there have been lack of researches on how to nurture mathematical creativity for ordinary students. Perspective of Realistic Mathematics Education(RME), which pursues education of creative person as the ultimate goal of mathematics education, could be useful for developing principles and methods for cultivating mathematical creativity. This study reanalyzes RME from the points of view in mathematical creativity education. Major findings are followed. First, students should have opportunities for mathematical creation through mathematization, while seeking and creating certainty. Second, it is vital to begin with realistic contexts to guarantee mathematical creation by students, in which students can imagine or think. Third, students can create mathematics in realistic contexts by modelling. Fourth, students create the meaning of 'model of(MO)', which models the given context, the meaning of 'model for(MF)', which models formal mathematics. Then, students create MOs and MFs that are equivalent to the intial MO and MF given by textbook or teacher. Flexibility, fluency, and novelty could be employed to evaluate the MOs and the MFs created by students. Fifth, cultivation of mathematical creativity can be supported from development of local instructional theories by thought experiment, its application, and reflection. In conclusion, to employ the education model of cultivating mathematical creativity by RME drawn in this study could be reasonable when design mathematics lessons as well as mathematics curriculum to include mathematical creativity as one of goals.

• The Mathematical Education
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• v.52 no.2
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• pp.247-270
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• 2013

The purpose of this research was to analyze the convergent approaches for creativity in elementary mathematics textbooks in Korean and the united States. Convergent approaches have emphasized since NCTM(2000) consistently includes 'connections' as an important factor in mathematics curriculum and KOFAC(Korea Foundation for the Advancement of Science & Creativity) initiated the STEAM(Science, Technology, Engineering, Arts, and Mathematics) in mathematics and science education. For this research, two elementary mathematics textbooks were analyzed focused on their contexts and contents: Korean National Elementary Mathematics Textbooks and Navigations in Numbers, Data, and Space. In both textbooks, it was not easy to find so called the convergent approach in a real sense, but they use some contexts for connections between mathematical concepts and real world phenomena. For the enhancement of convergent approaches in mathematics education, we need to have a broader sense in the convergent approaches and develop various meaningful materials.

• 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.

• Education of Primary School Mathematics
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• v.7 no.1
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• pp.15-29
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• 2003

The present study examined the 7th national elementary school mathematics curriculum from a perspective of mathematical creativity. The study investigated to what extent the activities in the Pattern and Function lessons in the national elementary school mathematics textbooks promoted the development of mathematical creativity. The results indicated that the current elementary school mathematics curriculum was limited in many ways to promote the development of mathematical creativity. Regarding the activities in Pattern lessons, for example, most activities presented closed tasks involving finding and extending patterns. The lesson provided little opportunities to explore the relationships among various patterns, apply patterns to different situations, or create ones own patterns. In regard to the Function lessons, the majority of activities were about computing the rate. This showed that the function was taught from an operational perspective, not a relational perspective. It was unlikely that students would develop the basic understanding of function through the activities involving the computing the rate. Further, the lessons had students use exclusively the numbers in representing the function. Students were provided little opportunities to use various representation methods involving pictures or graphs, explore the strengths and limitations of various representation methods, or to choose more effective representation methods in particular contexts. In conclusion, the lesson activities in the current elementary school mathematics textbooks were unlikely to promote the development of mathematical creativity.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.77-95
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• 2012

The purpose of this study is to draw implication for the teacher education program in association with creativity through analysing teaching behavior for fostering creativity of the mathematics teachers at the primary and secondary schools. In order to do so, a survey was performed by sampling primary, middle, and high school teachers. According to the results, there is significant difference in teachers' behavior for fostering creativity in the perspective of school classification (primary and secondary school), but not gender, region, and career of teachers. In other words, there is significant difference in teaching behaviors for fostering creativity between primary and secondary school teachers, herein the score of teaching behavior of former is higher than latter. Furthermore, the result of teachers' recognition survey on the possibility of fostering students' creativity via education shows that the teachers of primary schools are more relatively positive than those of secondary schools on the matter.

• Journal of Gifted/Talented Education
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• v.26 no.4
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• pp.747-761
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• 2016

The purpose of this research is to study the perception of mathematical creativity through gifted elementary mathematics students. The analysis on perception for mathematical creativity was done by testing 200 elementary school students in grades 4, 5, and 6 who are receiving gifted education in elementary mathematics gifted class operated by ${\bigcirc}{\bigcirc}$ City Dept of Education through the questionnaire that was developed based on Rhodes' 4P theory. This survey asked them to name what they think is the most creative from educational programs they have as far received. Then we analyzed the reason for the students' choice of the creativity program and interviewed the teachers who had conducted chosen program. As a result of analyzing the data, these students chose as mathematical creativity primarily creative problem solving, task commitment, and interest in mathematics in such order. This result is explained through analyzing the questionnaire that was based on Rhodes' 4P theory on areas of process, product and press. The perception of mathematical creativity by the gifted mathematical students not only helps to clarify the concept of mathematical creativity but also has implication for future development for gifted education program.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.117-134
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• 2011

The purpose of this research was to analyze mathematical task types to enhance creativity. Creativity is increasingly important in every field of disciplines and industries. To be excel in the 21st century, students need to have habits to think creatively in mathematics learning. The method of the research was to collect the previous research and papers concerning creativity and mathematics. To search the materials, the researcher used the search engines such as the GIL and the KISTI. The mathematical task types to enhance creativity were categorized 16 different types according to their forms and characteristics. The types of tasks include (1) requiring various strategies, (2) requiring preferences on strategies, (3) making word problems, (4) making parallel problems, (5) requiring transforming problems, (6) finding patterns and making generalization, (7) using open-ended problems, (8) asking intuition for final answers, (9) asking patterns and generalization (10) requiring role plays, (11) using literature, (12) using mathematical puzzles and games, (13) using various materials, (14) breaking patterned thinking, (15) integrating among disciplines, and (16) encouraging to change our lives. To enhance students' creativity in mathematics teaching and learning, the researcher recommended the followings: reshaping perspectives toward teaching and learning, developing and providing creativity-rich tasks, applying every day life, using open-ended tasks, using various types of tasks, having assessment ability, changing assessment system, and showing and doing creative thinking and behaviors of teachers and parents.

• 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.

• Education of Primary School Mathematics
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• v.13 no.1
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• pp.25-35
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• 2010

The purpose of this research was to analyze questioning types of the Korean Elementary Mathematics Textbook in grade 3 and suggest the direction of questioning strategies for enhancing creativity in mathematics lessons. For the research, the researcher analyzed questioning types of the 3rd grade mathematics textbook and the changes of the questions compared with the questions in the previous textbooks. The author suggested the following recommendations. First, the questioning strategies of the revised mathematics textbook tends more to enhance students' creativity than the previous ones did. Second, teachers need to know the students' level of mathematics before starting their mathematics lessons because teachers can provide more effective differentiated questioning to the students. Third, students can response tuned to their level of mathematics if they meet with open-ended questions. It is desirable to develop good open-ended questions to fit students' abilities. Last, teachers should provide opportunities for students to share their own mathematical thinking. In risk-free environment, students can willingly participate at debating over mathematics proofs and refutation. Teachers should make efforts to make the classroom norm or culture free to debate among students, which leads to enhancement of students' creativity or mathematical creativity.

• Journal of the Korean School Mathematics Society
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• v.25 no.2
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• pp.195-224
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• 2022

In this study, pre-service mathematics teachers cultivated technology content teaching knowledge (TPACK) in the regular curriculum of the College of Education. The course was designed to enhance pre-service teachers' mathematical communication skills by using an application, which is a mobile mathematics learning content for the development of group creativity of high school students. The educational program to improve mathematics teaching expertise using the application for group creativity expression consists of pre-education, goal setting, planning, teaching at school, and evaluation. In this process, pre-service teachers evaluated technology tools. They also wrote a task dialogue, lesson play, reflective journal, and lesson plan to guide high school students to develop group creativity in both app activities. As a result of the educational program, pre-service mathematics teachers cultivated TPACK and enhanced their mathematical communication skills with high school students to develop group creativity.