• The Mathematical Education
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• v.55 no.1
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• pp.21-39
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• 2016

This research examined the Korean and American $6^{th}$ grade students' mathematical problem solving ability and methods via an intuitive thinking. For this, the survey research was used. The researcher developed the questionnaire which consists of problems with intuitive and algorithmic problem solving in number and operation, figure and measurement areas. 57 Korean $6^{th}$ grade students and 60 American $6^{th}$ grade students participated. The result of the analysis showed that Korean students revealed a higher percentage than American students in correct answers. But it was higher in the rate of Korean students attempted to use the algorithm. Two countries' students revealed higher rates in that they tried to solve the problems using intuitive thinking in geometry and measurement areas. Students in both countries showed the lower percentages of correct answer in problem solving to identify the impact of counterintuitive thinking. They were affected by potential infinity concept and the character of intuition in the problem solving process regardless of the educational environments and cultures.

• School Mathematics
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• v.16 no.4
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• pp.691-708
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• 2014

In general, the intuitive knowledge that can use in mathematics problem solving is one of the important knowledge to teachers as well as students. So, this study is aimed to analyze the elementary preservice teachers' intuitive knowledge in relation to intuitive and counter-intuitive problem solving. For this, I performed survey to use questionnaire consisting of problems that can solve in intuitive methods and cause the errors by counter-intuitive methods. 161 preservice teachers participated in this study. I got the conclusion as follows. preservice teachers' intuitive problem solving ability is very low. I special, many preservice teachers preferred algorithmic problem solving to intuitive problem solving. So, it's needed to try to improve preservice teachers' problem solving ability via ensuring both the quality and quantity of problem solving education during preservice training courses. Many preservice teachers showed errors with incomplete knowledges or intuitive judges in counter-intuitive problem solving process. For improving preservice teachers' intuitive problem solving ability, we have to develop the teacher education curriculum and materials for preservice teachers to go through intuitive mathematical problem solving. Add to this, we will strive to improve preservice teachers' interest about mathematics itself and value of mathematics.

• Journal of the Korean School Mathematics Society
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• v.18 no.3
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• pp.241-258
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• 2015

The purpose of this paper is to examine the students' mathematics problem solving process in the intuitive stages. For this, researcher developed the questionnaire which consisted of problems in relation to intuitive and algorithmic problem solving. 73 fifth grade and 66 sixth grade elementary students participated in this study. I got the conclusion as follows: Elementary students' intuitive problem solving ability is very low. The rate of algorithmic problem solving is higher than that of intuitive problem solving in number and operation areas. The rate of intuitive problem solving is higher in figure and measurement areas. Students inclined to solve the problem intuitively in that case there is no clue for algorithmic solution. So, I suggest the development of problems which can be solved in the intuitive stage and the preparation of the methods to experience the insight and intuition.

• Education of Primary School Mathematics
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• v.12 no.1
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• pp.1-20
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• 2009

The purposes of this study are to analyze elementary school student's intuitive thinking in the process of mathematical problem solving and to analyze elementary school student's errors of intuitive thinking in the process of mathematical problem solving. According to these purposes, the research questions can be set up as followings. (1) How is the state of illumination of the elementary school student's intuitive thinking in the process of mathematical problem solving? (2) What are origins of errors by elementary school student's intuitive thinking in the process of mathematical problem solving? In this study, Bogdan & Biklen's qualitative research method were used. The subjects in this study were 4 students who were attending the elementary school. The data in this study were 'Intuitine Thinking Test', records of observation and interview. In the interview, the discourses were recorded by sound and video recording. These were later transcribed and analyzed in detail. The findings of this study were as follows: First, If Elementary school student Knows the algorithm of problem, they rely on solving by algorithm rather than solving by intuitive thinking. Second, their problem solving ability by intuitive model are low. What is more they solve the problem by Intuitive model, their Self- Evidence is low. Third, in the process of solving the problem, intuitive thinking can complement logical thinking. Last, in the concept of probability and problem of probability, they are led into cognitive conflict cause of subjective interpretation.

• Journal for History of Mathematics
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• v.28 no.5
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• pp.263-278
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• 2015

As intuition is more unreliable than logic or reason, its studies in mathematics and mathematics education have not been done that much. But it has played an important role in the invention and development of mathematics with logic. So, it is necessary to recognize and explore the value of intuition in mathematics education. In this paper, I investigate the function and role of intuition in terms of mathematical learning and problem solving. Especially, I discuss the positive and negative aspects of intuition with its characters. The intuitive acceptance is decided by self-evidence and confidence. In relation to the intuitive acceptance, it is discussed about the pedagogical problems and the role of intuitive thinking in terms of creative problem solving perspectives. Intuition is recognized as an innate ability that all people have. So, we have to concentrate on the mathematics education via intuition and the complementary between intuition and logic. For further research, I suggest the studies for the mathematics education via intuition for students' mathematical development.

• 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.

• 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 .

• Journal of The Korean Association For Science Education
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• v.37 no.3
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• pp.523-537
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• 2017

The purpose of this study is to investigate the features of elementary students' intuitive thinking emerged during problem solving activities as it related to thermal phenomena, focusing on when intuitive thinking appears and how it is related to logical thinking. For this, we presented a problem related to thermal phenomena to nine 5th-grade students, and examined how students' thinking emerged in the activities. We conducted clinical interviews to investigate the thinking process of students. The results of this study are as follows. First, students made their own solutions and justified it later during the emergence process of intuitive thinking. It was also found that students connected concrete materials and abstract concepts intuitively. They solved the problem by making predictions even when information is insufficient. Second, it was shown that intuitive thinking can emerge through the intended strategies such as drawing a mental image, thinking from a different perspective, and integrating methods. These results, which are related to the students' intuitive thinking has received little attention and will be the basis for helping students in the context of discovery of their problem solving activities.

• Journal of Korea Society of Industrial Information Systems
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• v.14 no.4
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• pp.198-204
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• 2009

It is one of important and interesting topics in mathematics education to study the process of the logical thinking and the intuitive thinking in mathematical problem-solving abilities from the viewpoint of mathematical thinking. The main purpose of the present paper is to investigate on this problem with reference to secondary talented students (students aged 16~17 years). In particular, we focus on the relationship between the preference of mathematical thinking and their problem-solving abilities for logical-type problems by applying logistic regression analysis.

• School Mathematics
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• v.15 no.2
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• pp.389-404
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• 2013

Researchers have suggested that students should be experienced in progress of geometric thinking set out in naive and intuitive level and deduced throughout gradual formalization rather than completed mathematics are conveyed to students for students' understanding. This study examined naive and intuitive thinking of students by investigating students' geometric problem solving without diagrams. The students showed these naive thinking: lack of recognition of relation between problem and conditions, use of intuitive judgement depending on diagrams, lacking in understanding of role of specific case, and use of unjustified assumption. This study suggests implication for instruction in geometry.