• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.565-581
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• 2016

Intuition in the mathematical problem solving has been stressed the importance with the logic because intuition is the cognition that give significant clue or idea to problem solving. Fischbein classified intuition by the origin; primary intuition and secondary intuition And he said the role of the personal experience and school education. Through these precedent research, we can understand the social influence. This study attempt to investigate social intuition model of Haidt, moral psychologist that has surfaced social property of intuition in terms of the mathematical problem solving. The major suggestions in problem solving and the education of intuition are followed. First, I can find the social property of intuition in the mathematical problem solving. Second, It is possible to make the mathematical problem solving model by transforming the social intuitionist model. Third, the role of teacher is important to give the meaningful experience for intuition to their students. Fourth, for reducing the errors caused by the coerciveness and globality of intuition, we need the education of checking their own intuition. In other words, we need intuition education emphasized on metacognition.

• 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 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.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2009.05a
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• pp.101-106
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• 2009

수학적 사고의 입장에서 중등학생들이 수학적 문제해결에 논리적 사고와 직관적 사고가 어떻게 작용하는지를 연구하는 것은 수학교육에서 중요하고도 흥미로운 과제의 하나이다. 본 연구의 주된 목적은 중등학교 영재학생을 대상으로 이러한 문제를 조사하는 것이다. 특히 이들 중등영재학생들의 논리적 사고와 직관적 사고에 대한 선호도와 논리적 문제의 문제해결능력 사이의 관계를 조사한다.

• 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.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.197-215
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• 2010

Intuition plays an important role in the mathematical education as well as the process of invention in mathematics. And many mathematics educators became interested in intuition in mathematics education. So we need to analyze the effect of the characters of intuition of elementary students. In this study, the questionnaire and the interview were used. The subjects were 6 grade-103 students in the questionnaire. They were asked to solve the problems in the questionnaire which was designed by the researcher and to describe the reasons why they answered like that. Students are effected directly by the characters of intuition, ie self-evidence, intrinsic certainty, implicitness, etc. And the effect come from intuitive and ordinary experiences and the results of previous learning. In conclusion, we have to be interested in teaching via intuition and to control the effect of the characters of 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.

• 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.

• 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.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.23-30
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• 2005

Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.