• The Mathematical Education
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• v.44 no.1 s.108
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• pp.103-112
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• 2005

This paper is designed to characterize the concept of flexibility of mind and analyze relationship between flexibility of mind and divergent thinking in view of mathematical problem solving. This study shows that flexibility of mind is characterized by two constructs, ability to overcome fixed mind in stage of problem understanding and ability to shift a viewpoint in stage of problem solving process, Through the analysis of writing test, we come to the conclusion that students who overcome fixed mind surpass others in divergent thinking and so do students who are able to shift a viewpoint.

• 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.

• The Mathematical Education
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• v.57 no.2
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• pp.111-136
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• 2018

This study suggests a framework for analyzing items based on the characteristics, and shows the relationship among the characteristics, difficulty, percentage of correct answers, academic achievement and the actual mathematical problem solving competency. Three mathematics educators' classification of 30 items of Mathematics 'Ga' type, on 2017 College Scholastic Ability Test, and the responses given by 148 high school students on the survey examining mathematical problem solving competency were statistically analyzed. The results show that there are only few items satisfying the characteristics for mathematical problem solving competency, and students feel ill-defined and non-routine items difficult, but in actual percentage of correct answers, routineness alone has an effect. For the items satisfying the characteristics, low-achieving group has difficulty in understanding problem, and low and intermediate-achieving group have difficulty in mathematical modelling. The findings can suggest criteria for mathematics teachers to use when developing mathematics questions evaluating problem solving competency.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.125-147
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• 2017

The purpose of this study was to investigate the effects of mathematics-centered STEAM program which was operated in free semester system classes on middle school students' interest in science, technology/engineering, and mathematics(STEM) career and integrated problem solving ability. The study was conducted with 40 first graders in a middle school for 12 weeks using mathematics-centered STEAM program developed for the use of free semester system classes by the support of the Ministry of Education/KOFAC in 2016. According to the results of STEM career interest survey, mathematics-centered STEAM program was effective for improving middle school students' interest in STEM career. And it was also effective in the development of students' integrated problem solving ability.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.135-142
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• 2001

The selected questions for this study was their conversation in problem solving way of working together. To achieve its purpose researcher I chose more detail questions for this study as follows. $\circled1$ What is the difference of strategy according to its level \ulcorner $\circled2$ What is the mathematical ability difference in problem solving process concerning its level \ulcorner This is the result of the study $\circled1$ Difference in the strategy of each class of students. High class-high class students found rules with trial and error strategy, simplified them and restated them in uncertain framed problems, and write a formula with recalling their theorem and definition and solved them. High class-middle class students' knowledge and understanding of the problem, yet middle class students tended to rely on high class students' problem solving ability, using trial and error strategy. However, middle class-middle class students had difficulties in finding rules to solve the problem and relied upon guessing the answers through illogical way instead of using the strategy of writing a formula. $\circled2$ Mathematical ability difference in problem solving process of each class. There was not much difference between high class-high class and high class-middle class, but with middle class-middle class was very distinctive. High class-high class students were quick in understanding and they chose the right strategy to solve the problem High class-middle class students tried to solve the problem based upon the high class students' ideas and were better than middle class-middle class students in calculating ability to solve the problem. High class-high class students took the process of resection to make the answer, but high class-middle class students relied on high class students' guessing to reconsider other ways of problem-solving. Middle class-middle class students made variables, without knowing how to use them, and solved the problem illogically. Also the accuracy was relatively low and they had difficulties in understanding the definition.

• Education of Primary School Mathematics
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• v.2 no.2
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• pp.133-144
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• 1998

We examined two kinds of problem posing, 'problem making' and 'problem modifying' to find which one is more effective for improving mathematical problem solving ability according to the student's learning-levels and sexes. The results showed that 'problem making' is more effective for high and middle-level groups than 'problem modifying'. There was no big difference according to the sexes. These facts implies that making a problem when a situation was presented is more effective to develop problem solving ability than modifying a problem ： modifying some conditions and contents of given problem.

• School Mathematics
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• v.1 no.2
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• pp.617-636
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• 1999

This study was executed with the intention of guiding ‘open education’ toward a desirable school innovation. The basic two directions of curriculum reconstruction essential for implementing ‘open education’ are one toward intra-subject (within a subject) and inter-subject (among subjects). This study showed an example of intra-subject curriculum reconstruction with a problem solving area included in elementary mathematics curriculum. In the curriculum, diverse strategies to enhance ability to solve problems are included at each grade level. In every elementary math textbook, those strategies are suggested in two chapters called ‘diverse problem solving’, in which problems only dealing with several strategies are introduced. Through this method, students begin to learn problem solving strategies not as something related to mathematical knowledge or contents but only as a skill or method for solving problems. Therefore, problems of ‘diverse problem solving’ chapter should not be dealt with separatedly but while students are learning the mathematical contents connected to those problems. Namely, students must have a chance to solve those problems while learning the contents related to the problem content(subject). By this reasoning, in the name of curriculum reconstruction toward intra-subject, this study showed such case with two ‘diverse problem solving’ chapters of the 4th grade second semester's math textbook.

• The Journal of the Korea Contents Association
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• v.16 no.5
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• pp.746-759
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• 2016

The purpose of this study was examine the effects of STEAM(Science-Technology-Engineering-Art-mathematics) activities on young children's scientific process skill ability and problem solving ability. Subjects were 34 five-year-old young children from S and H child care centers located in G city. Subjects were divided into an experimental(n=17) and a control group(n=17). The experimental group took part in the STEAM activities during 8 weeks, while the control group took part in the traditional science activities. The procedure for this study consisted of a pre-study, a pre-test, the treatment, and a post-test schedule. The results of this study were as follows: First, the experimental group showed significantly higher score than the control group in total scientific process skill ability. Second, the experimental group showed significantly higher score than the control group in total problem solving ability. These findings suggest that the experience of STEAM activities for young children can be effective teaching-learning methods for young children's scientific process skill ability and problem solving ability.

• 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.

• Research in Mathematical Education
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• v.9 no.1 s.21
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.