• 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 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.

• 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 Educational Research in Mathematics
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• v.16 no.4
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• pp.345-366
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• 2006

In this study, we investigated the methods of using the Cabri3D program for education of problem solving in school mathematics. Cabri3D is the program that can represent 3-dimensional figures and explore these in dynamic method. By using this program, we can see mathematical relations in space or mathematical properties in 3-dimensional figures vidually. We conducted classroom activity exploring Cabri3D with 15 pre-service leachers in 2006. In this process, we collected practical examples that can assist four stages of problem solving. Through the analysis of these examples, we concluded that Cabri3D is useful instrument to enhance problem solving ability and suggested it's educational usage as follows. In the stage of understanding the problem, it can be used to serve visual understanding and intuitive belief on the meaning of the problem, mathematical relations or properties in 3-dimensional figures. In the stage of devising a plan, it can be used to extend students's 2-dimensional thinking to 3-dimensional thinking by analogy. In the stage of carrying out the plan, it can be used to help the process to lead deductive thinking. In the stage of looking back at the work, it can be used to assist the process applying present work's result or method to another problem, checking the work, new problem posing.

• School Mathematics
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• v.8 no.3
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• pp.265-290
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• 2006

The purpose of this study is to search an effective teaching & learning program by examining how much does Excel affect on problem solving of linear function. This study was based on qualitative case study. Teaching experiment was performed for seven periods with five students in 8th graders. Pre and posts tests were attempted to analyze the changes of student's ability on problem solving of linear function. The analysis of tests were performed in category with correct process-object perspective, near process-object perspective, incorrect process-object perspective. According to this study, the subjects showed an improvement on problem solving perspective of linear function. This meant that lessons using Excel had influenced on the problem solving of linear function. We noticed that exploring the learning environment with Excel could supplement paper-and-pencil environment. We believed that Excel with an intuitive dynamic and explorative skills can play a role in scaffolding to support problem solving of linear function.

• Journal of The Korean Association For Science Education
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• v.16 no.4
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• pp.340-350
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• 1996

Knowledge is composed through the interaction between the concept structure already held by students and their experience, and learning can be said to be the active process of solving the cognitive conflict caused by this interaction. Therefore, this study consists in showing the effective learning method and finding out the elements which the teacher has to own, through examining several forms of pre-conception or mis-conception of the inertia, the force-equilibrium, the action and reaction, the heat, and the electric current, and then finding out their solution and studying student's change in science concepts. For this study, the types of concept on the five above-mentioned materials which students have were examined through the concept-classifying question paper, and the classes to which the class mode for the change of concepts applied, were practised in each different classroom by each different instructor - a professor, a scientist, a teacher, and two students, respectively. And the effect of the teaching strategy based on these classes, and each different instructor' influence on the change of concept in students. were examined. The result of my study is as follows; 1. Students have various types of pre-conception which are different from science concept, and these types of pre-conception tend to last even after learning in class. 2. The thoughts on the correct science concept of the high school third-grade students who learned the physics in the traditional teaching method, and the second grade students who don't learn the physics yet, were nearly equal those of the second grade students by receiving the physics class through the cognitive conflict course were greatly changed especially that students showed the distinct change on mechanics and electric current. 3. Students didn't show the remarkable change of the science concept on the five materials in the four kinds of experimental classes by each different instructor but in the part of mechanics, there was the distinct change between the class by professor and those by the students. This was due to the difference of the authority and the attitude of the concept demonstrator. 1) The authority, the kind attitude, and the responsibility of the expert played an important role in the correct concept-formation of mechanics part - especially in the case of the mis-conception caused by the intuitive belief. 2) In the class by instructor with the democratic teaching method, the change of concept took place more easily, because in his class students could discuss the subject freely, so that they might experience the thought course to give them the confidence on the science concept.