• Research in Mathematical Education
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• v.12 no.3
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• pp.179-191
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• 2008

Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

• Journal of Engineering Education Research
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• v.24 no.2
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• pp.61-67
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• 2021

The creative problem-solving becomes one of the most important cognitive skills in the engineering education. As AI and automation technology(of 4th Industrial Revolution) penetrate our everyday life, its role as a human ability is highlighted. In this paper, we examine the relation between the creative problem-solving and the critical thinking, and the usefulness of the latter in the engineering education. To sum up, the critical thinking is the pre-conditon of the creative problem-solving.

• Educational Technology International
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• v.12 no.1
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• pp.125-145
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• 2011

Facilitating critical thinking is important for students' cognitive growth and knowledge acquisition. This study examines the dimensions of tutors' roles in facilitating the critical thinking required for problem solving in online discussions. The research procedures include identifying the research problems related to critical thinking skills; synthesizing theories and perspectives on critical thinking skills; and analyzing, validating, and determining tutors' roles. Using the results of this study, problem solving processes are divided into four phases: analyzing, judging, inferencing, and meta-cognitively evaluating. Tutors' roles in online problem solving can be categorized into four domains: cognitive, social, managerial, and technical. Tutors' roles in each domain are specifically analyzed, and the strengths, weaknesses, and improvements in tutors' facilitation of critical thinking for online problem solving are evaluated.

• Journal of the Korea Society of Computer and Information
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• v.17 no.8
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• pp.181-188
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• 2012

In this paper, we propose an a strategy using writing based on STEAM Instruction for information gifted students' creative problem-solving. It is needed a complex and dynamic interaction of variety elements for creative problem solving. And it should be provided experience encompassing various disciplines thorough convergence education for leading to the these interactions and developing the ability to solve complex problems. Writing has already been verified educational effects in a variety subjects. And writing gives a positive impact on creative problem solving by helping awareness of the problem and encouraging critical thinking. In addition, writing can be used as an effective tool for improving problem solving based on similarities between problem-solving process. Learners will find algorithm thorough the process analyzing and writing experience with high-tech products like vending machines, mobile phones and can learn naturally the principles of various disciplines used in real life. Furthermore, learners will experience interaction, convergence of various thinking and cultivate creative problem- solving skills.

• The Journal of Korean Association of Computer Education
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• v.18 no.4
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• pp.1-9
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• 2015

Problem solving is essential skill for all students in the $21^{st}$ century. In particular, as the computing system ensures the effectiveness of problem solving in the various disciplines and real life, interest in learning algorithms to design a problem solving process is increasing. In order to improve problem solving skill, students should not only understand algorithm design skills but also apply appropriate skills to solve faced problem. In terms of these the puzzle can be considered a preferred learning tools to improve problem solving skill. Therefore, in this study we designed puzzled based algorithm learning and analyzed the impact of puzzle based algorithm learning on problem solving skills of leaners. As the results of research, we confirmed that the puzzled based algorithm learning took positive effect on enhancing problem solving skills of the learners.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.583-605
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• 2016

Problem solving has been consistently emphasized in national mathematics curricula, whereas the foci of such an emphasis have been changed. Given this background, this study traced down major changes in emphasizing problem solving from the first national mathematics curriculum to the most recent 2015 curriculum. In particular, both the 2009 and the 2015 revised curricula were analyzed in detail to figure out the latest emphasis and trends. This paper then investigated whether a series of mathematics textbooks were aligned to the emphases of recent curricula. It finally discussed some issues that we need to reconsider with regards to problems, problem solving strategies, and the process of problem solving. As such, this study is expected to provide textbook developers with detailed implications on how to employ problem solving in new series of textbooks.

• The Mathematical Education
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• v.43 no.3
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• pp.233-255
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• 2004

Problem solving in math education is of great importance. The interest on problem solving in math education is growing all over the world. Problem solving ability is important throughout the fourth-sixth national curriculum in Korea and this is also necessary in the seventh national curriculum. The writer has implemented a proper model for problem posing and this is also necessary in the seventh national curriculum that emphasizes self-leading for improvement in the classroom. This model has advantages to cultivate a good habit of students who tries to solve the problems with concrete strategies, to take part in the problem solving activity and to change their mathematical attitude.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.123-132
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• 2004

In this paper, we reviewed the history of mathematical problem solving since 1900 and investigated problem solving in modeling perspective which is focused on the 21th century. In modeling perspective, problem solvers solve the realistic problem which includes contextualized situations in which mathematics is useful. In this case, the problem is different from the traditional problems which are routine, close, and words problem, etc. Problem solving in modeling perspective emphasizes mathematizing. Most of all, what is important enables students to use mathematics in everyday problem solving situation.

• Journal of The Korean Association For Science Education
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• v.22 no.5
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• pp.1030-1043
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• 2002

The development of cognitive psychology provides us a theoretical base from which we can obtain information about human problem solving. One purpose of this study was to investigate the effects of cognitive psychological factors on the problem solving of the two kinds of tasks (content free, content specific). And the other purpose was to find out the existence of critical situation in problem solving process. Even the items of tasks with the same logical structure and content knowledge could have different sizes of mental demand. The results were as follows. The mental demand of the problem, and the problem solver's mental capacity, might be the main factors in problem solving. Critical situation of both a group and an individual existed in the tasks that need content free knowledge (FIT 752 task). But the critical situation of a group was completely different from that of the individual in the tasks that need content specific knowledge (electric circuit task). According to the analysis of achievement for each individual in the task that need content specific knowledge, the critical situation of an individual existed in problem solving, but the critical situation of a group was not existed by were summed up the individual results.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.653-674
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• 2023

The development of mathematical problem solving ability and the making(transforming) mathematical problems are consistently emphasized in the mathematics curriculum. However, research on the problem making methods or the analysis of the characteristics of problem making methods itself is not yet active in mathematics education in Korea. In this study, we concretize the method of deductive problem making(DPM) in a different direction from the what-if-not method proposed by Brown & Walter, and present the characteristics and phases of this method. Since in DPM the components of the problem solving process of the initial problem are changed and problems are made by going backwards from the phases of problem solving procedure, so the problem solving process precedes the formulating problem. The DPM is related to the verifying and expanding the results of problem solving in the reflection phase of problem solving. And when a teacher wants to transform or expand an initial problem for practice problems or tests, etc., DPM can be used.