• School Mathematics
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• v.4 no.2
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• pp.147-160
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• 2002

The purpose of this study is to examine the The correlation between information processing types and mathematical communication abilities / word problem solving abilities. The results obtained are as follows: 1 Simultaneous/continuous information process types showed statistically high correlation with mathematical communication abilities. However, the correlation between simultaneous information process and mathematical communication abilities is a little higher than the correlation between continuous information process and mathematical communication abilities. 2. There is a high correlation between mathematical communication abilities and word problem solving abilities. Especially, speaking ability is much more correlated with four factors of word problem solving than reading, writing and listening, Through this study, we can conclude that information process types should be consider ed in order to improve mathematical communication abilities and mathematical communication abilities is essential in word problem solving.

• The Mathematical Education
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• v.38 no.2
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• pp.159-164
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• 1999

The purpose of this paper is to find role of in and logic in creative problem solving process. Intuition and logic have played an important role in creative problem solving process. Nevertheless, Intuition has been treated less importantly than logic. Therefore, I intend to review the role of intuition, and then the relationship of intuition and logic, and the role of intuition and logic in creative problem solving process. Although intuition gives an important clue in problem solving process, it may sometimes cause an error. This fact gives an idea that intuition and logic have to be harmoniously cultivated. In fact, Intuition and logic have been playing a complementary role in creative problem solving process. A creative learner is regarded as a mathematician of his age. It must be through intuition and logic that he/she solves the problem creatively, just as a mathematician invents the new mathematical fact through unconscious and conscious process. In this respective, teachers also should make every effort to cultivate intuition and logic themselves.

• Korean Journal of Child Studies
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• v.28 no.4
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• pp.319-331
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• 2007

This review of literature establishes a contemporary meaning of mathematical problem solving including young children's mathematical problem solving processes/assessments and teaching strategies. The contemporary meaning of mathematical problem solving involves complicated higher thinking processes. Explanations of the mathematical problem solving processes of young children include the four steps suggested by $P{\acute{o}}lya$(1957) : understand the problem, devise a plan, carry out the plan, and review/extend the plan. Assessments of children's mathematical problem solving include both the process and the product of problem solving. Teaching strategies to support children's mathematical problem solving include mathematical problems built upon children's daily activities, interests, and questions and helping children to generate new approaches to solve problems.

• The Mathematical Education
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• v.48 no.2
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• pp.183-190
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• 2009

This is a following study of the preceding study, Flexibility of mind and divergent thinking in problem solving process that was performed by Choi & Do in 2005. In this paper, we discuss the relationship between ability to shift a viewpoint and insight into invariance, another major consideration in mathematical creativity, in the process of mathematical problem solving.

• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• Journal for History of Mathematics
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• v.32 no.6
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• pp.281-299
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• 2019

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

• The Mathematical Education
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• v.51 no.3
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• pp.265-280
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• 2012

This study aims to provide implications from mathematics education perspective by designing a process of 'validity review on the problem solving process', and then, by analyzing the results. In the result of analysis on the features of children's thinking in accordance with 4 stages of problem solving, children's thinking was equally observed in every stage rather than intensively observed in one stage, and reflective thinking related to important elements from each stage of problem solving process was observed. In the result of analysis of changes in description for problem solving process, there was a difference in the aspects of changes by children's knowledge level in mathematics, however, the activity of validity review on problem solving process in overall induced positive changes in children's description, especially the changes in problem solving process of children. Through the result of this study, we could see that the validity review on problem solving process promotes children's reflective thinking and enables meta-cognition thus has a positive influence on children's description of problem solving process.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.265-274
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• 2002

The purpose of the paper is to provide the importance of matacognition as a factor to correct the errors generated by the intuition. For this, first of all, we examine not only the role of metacognition in mathematics education but also the errors generated by the intuition in the mathematical problem solving process. Next, we research the possibility of using metacognition as a factor to correct the errors in the mathematical problem solving process via both the related theories about the metacognition and an example. In particular, we are able to acknowledge the importance of the role of metacognition throughout the example in the process of the problem solving It is not difficult to conclude from the study that emphasis on problem solving will enhance the development of problem solving ability via not only the activity of metacognition but also intuitive thinking. For this, it is essential to provide an environment that the students can experience intuitive thinking and metacognitive activity in mathematics education .

• The Mathematical Education
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• v.42 no.5
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• pp.623-636
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• 2003

Metacognition is defined to be 'thinking about thinking' and 'knowing what we know and what we don't know'. It was verified that the metacognitive abilities of high school students can be improved via instruction. The purpose of this article is to investigate a new method for activating the metacognitive abilities that play a key role in the Mathematical Problem Solving Process(MPSP). Hyunsung participated in the MPSP using Visual Basic Programming. He actively participated in the MPSP. There are sufficient evidences about activating the metacognitive abilities via the activity processes and interviews. In solving mathematical problems, he had basic metacognitive abilities in the stage of understanding mathematical problems; through the experiments, he further developed his metacognitive abilities and successfully transferred them to general mathematical problem solving.

• The Mathematical Education
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• v.48 no.4
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• pp.455-467
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• 2009

During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The test questions are formulated into several areas of questioning-types which can reveal rather different result. The lower level questions are to investigate individual ability to solve multiple mathematical problems while using "mathematical thought." During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The scope of this case study is to present a desirable model in solving mathematical problems and to improve teaching methods for math teachers.