• The Mathematical Education
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• v.55 no.1
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• pp.73-89
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• 2016

The purpose of this study was to analyze middle school students' problem posing types and strategies. we analyzed problems posed by 120 middle school students during mathematics class focused on problem posing activities in various aspects. Students' posed problems were classified into five types: not a problem(NP), non-math(NM), impossible(IM), insufficient(IN), sufficient(SU) and each of the posed problems. Students used three kinds of problem posing strategies such as goal manipulation(GM), assumption manipulation(AM), and condition manipulation(CM), and in posing one problem, one or more than two strategies were used. According to the prior studies, problem posing can contributes to the development of students' problem solving ability, creativity, mathematical aptitude, and a broader understanding of mathematical concepts. However, we found that some students had difficulties in posing problems or limited understandings of that. We hope the results of the study contribute to encouraging problem posing activities in mathematics instruction.

• The Mathematical Education
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• v.43 no.2
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• pp.139-149
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• 2004

This study was initiated by the idea to help students to be more ideally educated following the 7th curriculum that seeks the proactive students along with creativity for the 21st century. Mind-map was the main tool throughout the study and this was performed to find answers for the following questions : 1) to examine how students' drawing a mind-map affects their mathematical tendency or emotional aspects (motivation for study, interest, etc); 2) to investigate the types and characteristics of mind-maps that students draw; 3) to analyze advantages and obstacles that they experience during the process of drawing a mind-map and provide some suggestions for overcoming them. The research shows that students were highly motivated by the drawing a mind-map. There are types of mind-maps: tree shape and radial shape, and each shape has its own advantages. But the more important factor for being a good mind-map is where and how each concept is located and connected. Although it is true that drawing a mind-map helped students to see the bigger structure of what they learned, but there are several hardships taken care of. The study suggests to extend the experiment to various levels of students and diverse contents.

• The Mathematical Education
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• v.59 no.2
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• pp.147-166
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• 2020

Textbooks are important resources in support of teaching and learning mathematics competencies which are emphasized in the most recently revised mathematics curriculum. This study analyzed how six mathematics competencies and their sub-elements are implemented in the mathematics textbooks for the fifth and sixth grades. A total of 465 activities or items in the targeted textbooks were analyzed. The findings of this study showed that both the communication competence and the reasoning competence were the most frequent competencies, followed by the problem solving competence. In contrast, the other three competences (i.e., creativity and integration, attitude and practice, and information processing) were less popular. Detailed analyses of sub-elements according to each competence revealed that one or two specific sub-elements were emphasized within a competence. Whereas "expressing one's idea" was the most prevalent sub-element in the communication competence, both "analyzing mathematical facts" and "observation and conjecture" were the most frequent in the reasoning practice. Specific sub-elements were jointly implemented within or across competences. "External connections of mathematics and integration" in the creativity and integration competence was carried out in relation to "recognition of values" in the attitude and practice competence. This paper also included some examples of activities or items showing how specific sub-elements of each competence were reflected on. This study is expected to provide implications on how to implement mathematics competencies throughout the textbooks.

• Communications of Mathematical Education
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• v.31 no.4
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• pp.389-407
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• 2017

Many researches related to STEAM education have been actively conducted for developing elementary and secondary school students' comprehensive and logical thinking ability in relation to creativity education in Korea. Each sub factor of STEAM education requires creative thinking with the ability to be merged together to solve problems as integrated or combined forms in the fields of Science, Technology, Engineering, Arts, and Mathematics. Also, these STEAM activities and experiences should be carried out at various places outside the classroom in school. Although various educational programs to enhance mathematical creativity have been emphasized for elementary and secondary school students, recent tendency to focus on classroom learning in the school makes it difficult to develop creative thinking ability of students. This research is mainly based on the result of the project "Development and Administration of STEAM Outreach Program in 2016" supported by KOFAC(Korea Foundation for the Achievement of Science & Creativity). The purpose of this research is to develop a STEAM outreach program including students' activity books, teachers' manuals and administration manual that can maximize STEAM-related interest of students, and to provide a chance for elementary and secondary school students to experience creative thinking based on sub factors of STEAM. The STEAM competency total score and the perception of convergence education were significantly increased for all students participating this program, but some sub factors showed different result by school levels. The STEAM outreach program developed by this study is designed to emphasize STEAM education especially 'based on' mathematics in order to provide students with the opportunity to experience more interest in the field of mathematics and will be able to provide an interesting creative STEAM outreach program that utilizes a variety of activities which, we expect, would help students to consider their career in the future.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.257-277
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• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• East Asian mathematical journal
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• v.30 no.2
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• pp.197-222
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• 2014

The purpose of this research is to find out if it is possible to apply the Waldorf School's mathematics education method to Korean alternative schools which are run under the national curriculum. To achieve this, the researcher conducted class on geometry for three weeks with ten 7th graders(four girls and six boys) from Apple Tree Waldorf alternative school in Busan, which has adopted Valdorf education courses. For the first two weeks, the class was about 'fundamental geometrical construction', and then it was evaluated. On the third week, the lesson was on plane figures, followed by a test with 9 plane figure questions that are based on general middle school mathematics curriculum. The result shows that most of the students understood 'fundamental geometrical construction'. When it comes to the test on 'plane figures', seven students got 8 out of 9 right, two students got 6 out of 9 right, and one of them had difficulty solving the questions. According to the results of this research, it is thought that there will be no problem for students to understand mathematical concept even if the Waldorf School's mathematics education method is applied to Korean alternative schools. Also, the Waldorf School's mathematics education method is considered to be a good teaching model for the Korean mathematics curriculum which places emphasis on 'mathematical creativity' in regard to the curriculum and contents.

• Communications of Mathematical Education
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• v.21 no.1 s.29
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• pp.33-50
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• 2007

In this study, we made a survey for gifted students of science education center for gifted youth in a university to find their viewpoints about giftedness, need of gifted education, attribution. Using the results of the survey, we interviewed mathematical gifted student, parents, teachers to find their viewpoints about giftedness, need of gifted education, attribution. From this, we found the followings: First, Parents and teachers selected intellectual ability as a most important factor of giftedness. On the other hand, gifted students selected creativity as it. Second, gifted students show different communication ability depending on the education place. Third, mathematical gifted students attributed their problem solving ability to interior cause. On the other hand, parents and teachers of gifted students attributed students' problem solving ability to exterior cause.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.21-43
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• 2010

In this article three types of neuro-biological epistemology have been studied and applied to mathematics. Nativism or innatism is favored by many evolutionary psychologists and some mathematicians. They believe domain specific brain functions or modules, particularly language faculty and number instinct in infants. Number/mathematical cognition is a new research area and scientists try to localize areas related with mathematics. Selectionism has adopted Darwinism to synapse growth and supports neuronal regression. Mathematical creativity can be explained using selectionism. Neural constructivism has originated from J. Piaget and supports neuronal/synapse growth in children or adults if adequate exercise and practise is given. Unlike Piaget, neural constructivists accepts the importance of structured experience for the reorganization of brain. Authors opinion is all these theories of epistemology is equally important and they all give insights on how the brain and self is made.

• Research in Mathematical Education
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• v.7 no.3
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• pp.163-189
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• 2003

The purpose of this study is to develop a test, which can be used in creative problem solving ability in mathematics of the mathematically gifted and the regular students. This test tool is composed of three categories; fluency (number of responses), flexibility (number of different kinds of responses), and originality (degree of uniqueness of responses) which are the factors of the creativity. After applying to 462 middle school students, this test was analyzed into item analysis. As a results of item analysis, it turned out to be meaningful (reliability: 0.80, validity: item 1(1.05), item 2(1.10), item 3(0.85), item 4(0.90), item 5(1.08), item difficulty: item 1(-0.22), item 2(-0.41), item 3(0.23), item 4(0.40), item 5(-0.01), item discriminating power: item 1(0.73), item 2(0.73), item 3(0.67), item 4(0.51), item 5(0.56), over the level of a standard basis. This means that the test tool was useful in the test process of creative problem solving ability in mathematics

• The Mathematical Education
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• v.61 no.4
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• pp.631-651
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• 2022

It has been alerted that Korean students' mathematical affective achievement is very low. In order to solve this problem, various policies related to mathematical affective domains have been promoted, but it is necessary to examine various existing policies and explore the direction for improving them in more essential aspects. Based on previous studies that the growth mindset helps to increase students' affective achievement, this study focused on improving students' math-related growth mindset and ultimately exploring policies that can increase mathematical affective achievement. Therefore, the current status of mathematical affective achievement of Korean students was examined, and the policies and related cases in the mathematical affective domain were investigated. Based on the results, some keywords were derived and then the directions of policy for improving the math-related growth mindset and the affective achievement of students were suggested.