• The Mathematical Education
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• v.44 no.2 s.109
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• pp.307-323
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• 2005

The purpose of this study was to develop a program to cultivate mathematical creativity based on open-ended problem and to investigate its effect. The major features of this innovative program are (a) breaking up fixations, (b) multiple answers, (c) various strategies, (d) problem posing, (e) exploring strategies, (f) selecting and estimating, (g) active exploration through open-ended problems. 20 units for 7th grade mathematics were developed. This study hypothesizes that experimental students may develop more divergent thinking abilities than their traditional counterparts. The participants were 7th grade students attending middle schools in Seoul. Instruments were pre and post tests to measure mainly divergent thinking skills through open-ended problems. The results indicated that the experimental students achieved better than the comparison students on overall and each component of fluency, flexibility, and originality of divergent thinking skills, when deleting the effect of covariance of the pretest. The developed program can be a useful resource for teachers to use in enhancing their students' creative thinking skills. Further this open-ended approach can be served as a model to implement in classes. This study suggests that further investigations are needed in order to examine effects on affective domains such as motivation and task perseverance which are also considered as important factors of creativity.

• Journal of The Korean Association For Science Education
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• v.18 no.2
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• pp.149-160
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• 1998

The purpose of this study was to analyze the 6th national secondary science curriculum and classroom practices to collect the basic data for developing secondary science program focusing on creative problem-solving ability. The creative problem-solving ability was conceptualized as an active process of producing new solutions to problems and consisted of five components: general knowledge, domain-specific knowledge, motivation, divergent thinking and critical thinking. The research questions were generated as follows: (1) Whether creative problem-solving elements-domain specific knowledge(declarative knowledge and inquiry methods) were included or not in the 6th secondary science curriculum, textbooks and teacher's guide? If so, how are they represented? (2) Whether the teachers tried to enhance divergent and critical thinking of their students. Through content analyses, observations and interviews, these research questions were answered as follows: (1) Inquiry methods, which are important to develop creative problem-solving abilities in science, were underestimated in comparison with declarative knowledge. In other words. inquiry methods were regarded only as tools to understand the scientific concepts and principles. (2) It was hard to find the situations which teachers provided opportunities for divergent and critical thinking to their students. Based on these results, the followings were recommended: (1) Inquiry methods should be regarded as a goal not as a tool and be used to acquire inquiry methods themselves. (2) Teachers should not stick to the prescribed inquiry methods prescribed in the textbook, but to give opportunities for thinking various kinds of inquiry methods to improve divergent and critical thinking.

• The Journal of Industrial Distribution & Business
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• v.10 no.11
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• pp.71-80
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• 2019

Purpose: The purpose of this study is to design the curriculum of Basic College Software Programming to develop creative and logical-thinking. This course is guided by algorithmic thinking and logical thinking that can be solved by computing for problem-solving, and it helps to develop by software through basic programming education. Through the stage of problem analysis, abstraction, algorithm, data structure, and algorithm implementation, the curriculum is designed to help learners experience algorithm problem-solving in various areas to develop diffusion thinking. For Learners aim to achieve the balanced development of divergent and convergent-thinking needed in their creative problem-solving skills. Research design, data and methodology: This study is to design a basic software education for improving algorithm-thinking for non-major. The curriculum designed in this paper is necessary to non-majors students who have completed the 'Creative Thinking and Coding Course' Design Thinking based are targeted. For this, contents were extracted through advanced research analysis at home and abroad, and experts in computer education, computer engineering, SW education, and education were surveyed in the form of quasi-openness. Results: In this study, based on ADD Thinking's algorithm thinking, we divided the unit college majors into five groups so that students of each major could accomplish the goal of "the ability to internalize their own ideas into computing," and extracted and designed different content areas, content elements and sub-components from each group. Through three expert surveys, we established a strategy for characterization by demand analysis and major/textbook category and verified the appropriateness of the design direction to ensure that the subjects and contents of the curriculum are appropriate for each family in order to improve algorithm-thinking. Conclusions: This study helps develop software by enhancing the ability of students who practice various subjects and exercises to explore creative expressions in various areas, such as 'how to think like a computer' that can implement and execute their ideas in computing. And it helps increase the ability to think logical and algorithmic computing based on creative solutions, improving problem-solving ability based on computing thinking and fundamental understanding of computer coding and development of logical thinking ability through programming.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.2
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• pp.253-267
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• 2012

In this paper, we primarily focus on the perspectives about creative process, which is how mathematical creativity emerged, as one aspect of mathematical creativity and then present a desirable task characteristic to measure and program characteristics to develop mathematical creativity. At first, we describe domain-generality perspective and domain-specificity perspective on creativity. The former regard divergent thinking skill as a key cognitive process embedded in creativity of various discipline domain involving language, science, mathematics, art and so on. In contrast the researchers supporting later perspective insist that the mechanism of creativity is different in each discipline. We understand that the issue on this two perspective effect on task and program to foster and measure creativity in mathematics education beyond theoretical discussion. And then, based on previous theoretical review, we draw a desirable characteristic on instruction program and task to facilitate and test mathematical creativity, and present an applicable task and instruction cases based on Geneplor model at the mathematics class in elementary school. In conclusion, divergent thinking is necessary but sufficient to develop mathematical creativity and need to consider various mathematical reasoning such as generalization, ion and mathematical knowledge.

• Journal of Engineering Education Research
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• v.23 no.2
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• pp.3-13
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• 2020

Key objective of cornerstone design is that students are able to experience developing creative design concepts through team activities, but the objective is hard to achieve. Based on a study of research materials, this paper asserts that the possibilities of creative problem solving can be promoted in question-centering ideation model if design artifacts are represented in some forms that could invoke design thinking and then the solution space is appropriately established. In particular, design problem on which divergent questions are asked should be explored and defined so that it can be a linguistic artifact represented by various visual aids. It is recommended that curriculum is modified so that students can experience creative conceptual design.

• Korean Journal of Cognitive Science
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• v.26 no.4
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• pp.393-433
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• 2015

Creativity refers to the ability to generate novel and useful ideas. Understanding the mechanism of creativity and its enhancement is important in order to solve major problems of the modern society and to improve the wellness of mankind. Creativity is a highly heterogeneous and complex ability which should not be conceptualized as a single entity. Thus, the current literature on creativity is based on a component process approach to creativity. The present study introduces cognitive neuroscience research studying the mechanism of divergent thinking, insight, relational thinking and artistic creativity which are the major components of creativity. Based on an expansive review, the early hypothesis of hemispheric asymmetry emphasizing the importance of the right as opposed to the left hemisphere is not supported by scientific evidence. In addition, there is no consensus or consistency on which specific brain region is related to a certain component of creativity. In fact, there is a mixture of studies reporting involvement of various brain regions across all four lobes of the brain. This inconsistency in the literature most likely reflects heterogeneity of the component processes of creativity and sensitivity of the neural response to differences across tasks and cognitive strategy. The present study introduces examples of representative studies reporting seminal findings on the neural basis and the enhancement of creativity based on innovative methodology. In addition, we discuss limitations of the current cognitive neuroscience approach to creativity and present directions for future research.

• East Asian mathematical journal
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• v.29 no.4
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• pp.425-447
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• 2013

Since the center of mass of mathematics curriculum in middle school is dealt with only on triangle and it is defined as just an intersection point of median lines without any physical experiments, students sometimes have misconception of the centroid as well as it is difficult to promote divergent thinking that enables students to think the centroids of various figures. To overcome these problems and to instruct effectively the centroid unit in middle school mathematics classroom, this study suggests a teaching and learning method for the unit which uses physical experiments, drawing, and calculation methods sequentially based on the investigation of students' understanding on the centroid of triangle and the analysis of the mathematics textbooks.

• Education of Primary School Mathematics
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• v.11 no.1
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• pp.59-74
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• 2008

Mathematical knowledge is not exact definition but the supposition. Considering the nature of mathematics, realization of mathematics teaching which pursues critical thinking and rationality would be our problems. Accordingly, I set the subject of this study whether learning of constructivist discussion, which induces reflective thinking through communicating with others by expression with language of mathematical thinking in discussion, is effective against attitude on Mathematics and Mathematics achievement and study themes are as follows; A. Is learning of constructivist discussion effective against attitude on Mathematics? A-1. Is there any difference of self-conception on the subject between experimental group applied to learning of constructivist discussion and comparative group? A-2. Is there any difference of attitude on the subject between experimental group applied to learning of constructivist discussion and comparative group? A-3. Is there any difference of learning habits on the subject between experimental group applied to learning of constructivist discussion and comparative group? B. Is learning of constructivist discussion effective against mathematics achievement? The objects of study are 30 children of one class in the third grade of elementary school in Seoul for experimental group, and another one class with 30 children is comparative group. Study results and conclusion based on those results are as follows; First, students make reflective thinking through communication each other, therefore, instructor should create discussion environment for communication to express and form their mathematical thinking. Next, adaptability in student's mathematics activities and mathematical ideas should be permissible, and those should become divergent thinking. However, this study analyzed comparative results from only two each class having enrollment of thirty in the third grade. Accordingly, results from students in various grades and environment that are required to get more significant conclusion statistically.

• Journal of Science Education
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• v.38 no.3
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• pp.599-611
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• 2014

The purpose of this research is to analyze creativity-personality activities given in the high school science textbooks, which developed according to 2009 Revised Science Curriculum, and to examine how goals of new science curriculum were reflected in sceince the textbooks. An analysis shows that the proportion of inquiry is the best high among the types of creativity-personality activities. Also it is organized for a various activities such as reading, writing and debate. As a result of analyzing creativity-personality activities regarding creative thinking and personality element, a variety of creative thinking and personality element was not composed. The creative thinking is primarily divergent thinking, convergent thinking and associative thinking appears in order. In addition, the caring of personality elements is the most, and then honesty, cooperation and responsibility appears in order. Thus, it is necessary to structure a variety of activities for edification of creativity-personality in high school science textbooks. As an analysis of creativity-personality activities regarding elements of the decision-making, the review process do not appear at all, and there are few decision points generally. Therefore, a rational decision making for the sake of edification should be provided with specific decision-making factors.