• Journal of The Korean Association For Science Education
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• v.16 no.4
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• pp.389-400
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• 1996

The purposes of this study were to analyze chemistry problem solving processes of middle school students and to compare their problem solving behaviors in the aspects of the cognitive developmental level of student, the success in problem solving, and the context of problem. Their failures in solving problems were also analyzed in the aspects of problem solving stage and prior knowledge. Forty-two students individually solved four problems regarding density and solubility using a think-aloud method. Students' responses were analyzed after intercoder agreement for analyzing problem-solving processes had been established to be 0.94. The results were as follows: 1. Most students solved chemistry problems following the stages of understanding, planning, and solving, while few exhibited the behaviors of the reviewing stage. There was also individual difference in the number of the stages repeated and their behaviors at each stage. 2. Most students were successful in understanding problems. However, unsuccessful and/or concrete-operational students had more difficulties in understanding problems than successful and/or formal-operational students, and students tended to have more difficulties in understanding problems in everyday contexts than in scientific contexts. 3. Successful and/or formal-operational students exhibited more behaviors of the planning stage than unsuccessful and/or concrete-operational students. Students showed more behaviors of the planning stage, but failed more at this stage, in everyday contexts than in scientific contexts. 4. Most students did not review their solutions. Successful and/or formal-operational students exhibited these behaviors more than unsuccessful and/or concrete-operational students. Students tended to exhibit the behaviors more in everyday contexts than in scientific contexts. 5. Many students failed to solve problems correctly due to the lack of prior knowledge and the inability to plan appropriately.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.429-459
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• 2009

The purpose of this study was to help the students deepen their mathematical understanding and practitioner improve her mathematics lessons. The teacher-researcher developed mathematical situation based problem solving instruction model which was modified from PBL(Problem Based Learning instruction model). Three lessons were performed in the cycle of reflection, plan, and action. As a result of performance, reflective knowledges were noted as followed points; students' mathematical understanding, mathematical situation based problem solving instruction model, improvement of mathematics teachers.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.247-268
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• 2009

The purpose of this study was to examine the mathematical components of word problems and the structure of the components, to examine the characteristics of the understanding of mathematics high achievers about word problems, and ultimately to devise a teaching method geared toward facilitating learner understanding of the word problems. Given the findings of the study, the following conclusion was reached: First, word problems could be categorized according to their mathematical components, namely the mathematical structure of multiple variables provided to learners for their problem solving. And learner's reaction might hinge on the type of word problems. Second, the mathematics high achievers relied on diverse strategies to understand the mathematical components of word problems to solve the problems. The use of diverse strategies made it possible for them to succeed in problem solving. Third, identifying the characteristics of the understanding of the mathematics high achievers about word problems made it possible to layout successful lesson plans that stressed understanding of the mathematical structure of word problems. And the teaching plans enabled the learners to get a better understanding of the given word problems.

• School Mathematics
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• v.11 no.2
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• pp.227-241
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• 2009

The isoperimetric problem has been known from the time of antiquity. But the problem was not rigorously solved until Steiner published several proofs in 1841. At the time it stood at the center of controversy between analytic and geometric methods. The geometric approach give us more productive thinking (insight, structural understanding) than the analytic method (using Calculus). The purpose of this paper is to analysis and then to construct the isoperimetric problem which can be applied to the mathematically gifted students in the elementary school. The theoretical backgrounds of our analysis about our problem are based on the Gestalt psychology and mathematical reasoning. Our active program about the isoperimetric problem constructed by the Gestalt's view will contribute to improving a mathematical reasoning and to serving structural (relational) understanding of geometric figures.

• 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.

• The Mathematical Education
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• v.26 no.2
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• pp.9-13
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• 1988

Mathematics education is generally to cultivate mathematical thought. Most meaningful thought is to solve a certain given situation, that is, a problem. The aim of mathematies education could be identified with the cultivation of mathematical problem-solving ability. To cultivate mathematical problem-solving ability, it is necessary to study the nature of mathematical ability and its aspects pertaining to problem-solving ability. The purpose of this study is to investigate the relation between problem-solving ability and classficational viewpoint of mathematical verbal problems, and bet ween the detailed abilities of problem-solving procedure and classificational viewpoint of mathematical verbal problems. With the intention of doing this work, two tests were given to the third-year students of middle school, one is problem-solving test and the other classificational viewpoint test. The results of these two tests are follow ing. 1. The detailed abilities of problem-solving procedure are correlated with each other: such as ability of understanding, execution and looking-back. 2. From the viewpoint of structure and context, students classified mathematical verbal problems. 3. The students who are proficient at problem-solving, understanding, execution, and looking-back have a tendency to classify mathematical verbal problems from a structural viewpoint, while the students who are not proficient at the above four abilities have a tendency to classify mathematical verbal problems from a contextual viewpoint. As the above results, following conclusions can be made. 1. The students have recognized at least two fundamental dimensions of structure and context when they classified mathematical verbal problems. 2. The abilities of understanding, execution, and looking- back effect problem-solving ability correlating with each other. 3. The instruction emphasizing the importance of the structure of mathematical problems could be one of the methods cultivating student's problem-solving ability.

• 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 The Korean Association For Science Education
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• v.15 no.4
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• pp.437-451
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• 1995

Middle and high school students' conceptual understanding about stoichiometry, gas laws, and diffusion was compared with essay type test and multiple choice test. Whereas achievement of high school students was higher in stoichiometry, that of middle school students who were expected to go to high schools was higher in gas laws and diffusion. When students' achievement was compared to that of American college students, Korean students' achievement was higher in stoichiometry and was similar in gas laws. These results indicate that algorithmic problem solving is more emphasized than conceptual understanding in high schools and that quantitative aspects focused in chemistry education are not helpful in concept understanding. Nevertheless relatively smaller difference between concept understanding and algorithmic problem solving for high school students in this study seems to be from concept learning in middle schools.

• The Mathematical Education
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• v.51 no.4
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• pp.351-375
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• 2012

This research is a case study of the changes of students's problem solving ability and affective characteristics when we apply to general students MG-CPS model which is creative problem solving model for gifted students. MG-CPS model which was developed by Kim and Lee(2008) is a problem solving model with 7-steps. For this study, we selected 7 first grade students from girl's high school in Seoul. They consisted of three high level students, two middle level students, and two low level students and then we applied MG-CPS model to these 7 students for 5 weeks. From the study results, we found that most students's describing ability in problem understanding and problem solving process were improved. Also we observed that high level students had improvements in overall problem solving ability, middle level students in problem understanding ability and guideline planning ability, and that low level students had improvements in the problem understanding ability. In affective characteristics, there were no significant changes in high and middle level classes but in low level class students showed some progress in all 6 factors of affective characteristics. In particular, we knew that the cause of such positive changes comes from the effects of information collection step and presenting step of MG-CPS model.

• 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.