• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.277-293
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• 2011

The purpose of mathematics education is to develop the ability of transforming various problems in general situations into mathematics problems and then solving the problem mathematically. Various teaching-learning methods for improving the ability of the mathematics problem-solving can be tried. However, it is necessary to choose an appropriate teaching-learning method after figuring out students' level of understanding the mathematics learning or their problem-solving strategies. The error analysis is helpful for mathematics learning by providing teachers more efficient teaching strategies and by letting students know the cause of failure and then find a correct way. The following subjects were set up and analyzed. First, the error classification pattern was set up. Second, the errors in the solving process of the function problems were analyzed according to the error classification pattern. For this study, the survey was conducted to 90 first grade students of ${\bigcirc}{\bigcirc}$high school in Chung-nam. They were asked to solve 8 problems in the function part. The following error classification patterns were set up by referring to the preceding studies about the error and the error patterns shown in the survey. (1)Misused Data, (2)Misinterpreted Language, (3)Logically Invalid Inference, (4)Distorted Theorem or Definition, (5)Unverified Solution, (6)Technical Errors, (7)Discontinuance of solving process The results of the analysis of errors due to the above error classification pattern were given below First, students don't understand the concept of the function completely. Even if they do, they lack in the application ability. Second, students make many mistakes when they interpret the mathematics problem into different types of languages such as equations, signals, graphs, and figures. Third, students misuse or ignore the data given in the problem. Fourth, students often give up or never try the solving process. The research on the error analysis should be done further because it provides the useful information for the teaching-learning process.

• The Mathematical Education
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• v.42 no.5
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• pp.623-636
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• 2003

Metacognition is defined to be 'thinking about thinking' and 'knowing what we know and what we don't know'. It was verified that the metacognitive abilities of high school students can be improved via instruction. The purpose of this article is to investigate a new method for activating the metacognitive abilities that play a key role in the Mathematical Problem Solving Process(MPSP). Hyunsung participated in the MPSP using Visual Basic Programming. He actively participated in the MPSP. There are sufficient evidences about activating the metacognitive abilities via the activity processes and interviews. In solving mathematical problems, he had basic metacognitive abilities in the stage of understanding mathematical problems; through the experiments, he further developed his metacognitive abilities and successfully transferred them to general mathematical problem solving.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.455-469
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• 2007

In this study, we want to being helpful to improvement of ability to solve mathematical problem, that is grafted on the subjects being able to occur in real life, of students in teaching materials and results studied and developed in the university. For increasing ability to solve ingenious problem and growing in the learning ability of oneself leading of students. The goal of this study is to make possible open research as a result of that students look for problem around real life by one's own efforts and take interest in them through learning mathematics of parents of students, they are the most important fact of educational environment in the mathematics education - earlier than students. In particular, the goal of this study is that students have an positive attitude of mind for mathematics and maximize ability of practical application by the analytic thinking learned through experience of their parents, they survey, analyze and solve problems taken from real life in the method transmitting one's knowledge to others. This study is divided into 2 categories: education of students and education of their parents. By these, we want to disseminate advanced knowledge and theory through students improve the powers of thought, logic and inference, develop ability to solve mathematical problem, stir up motivation of learning and learn knowledge of mathematics become familiar with real life.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.129-144
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• 2009

The purpose of the study was to investigate the effects of the use of RNP curriculum based on Lesh translation model on third grade students' understandings of fraction concepts and problem solving ability. Students' conceptual understandings of fractions and problem solving ability were improved by the use of the curriculum. Various manipulative experiences and translation processes between and among representations facilitated students' conceptual understandings of fractions and contributed to the development of problem solving strategies. Expecially, in problem situations including fraction ordering which was not covered during the study, mental images of fractions constructed by the experiences with manipulatives played a central role as a problem solving strategy.

• Communications of Mathematical Education
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• v.18 no.3 s.20
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• pp.23-28
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• 2004

이 논문은 네덜란드의 4학년 학생들에게 시행된 문제 해결 시험에서 얻은 첫 번째 결과이다. 참여한 학생들은 수학에서 높은 성취도를 얻은 학생들이었다. 학생들의 응답을 분석한 결과 성취도가 높은 학생들에게 관심을 가져야 하는 이유를 알게 되었다. 교사는 우수한 학생에 대해서는 걱정할 필요가 없다는 일반적인 믿음을 수정해야 한다는 것이 분명해졌다. 수학에서 높은 성취도를 보인 학생들이 비전형적인 문제에 직면할 때 그들의 능력은 기대했던 것보다 저조하게 나타났다. 이 연구에서 학생들은 특정 문제를 풀 때 여분의 노트에 거의 아무것도 적지 않음을 발견하였다. 또한 학생들이 답을 찾는 과정을 참고 견디지 않는다는 것도 알 수 있었다. 이 논문에서는 시험 문제 중 한 문제의 결과를 논의하면서 이러한 결과를 보여줄 것이다.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.205-224
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• 2010

This paper examined what structural relationship metacognition and flow, which are identified as major variables that positively influence creative problem solving ability, had with mathematics creative problem solving ability. For this purpose, the Mathematics Creative Problem Solving Ability Test (MCPSAT) was given go 196 general second-year middle school students, and their cognitive and affective states were measured with metacognition and flow tests. The three variables' relationships were examined through a correlation analysis and, through structural equation modeling, the mediating effect of flow was tested in the structural relationships between the three variables and in the relationship between metacognition and mathematics creative problem solving ability. The results of the research show that metacognition did not directly influence mathematics creative solving ability, but exerted influence through the mediating variable of flow. A more detailed examination shows that while metacognition did not influence fluency and originality from among the measured variables for mathematics creative problem solving ability, it did directly influence flexibility. In particular, metacognition's indirect influence through the mediating variable of flow was shown to be much stronger than its direct influence on flexibility. This research showed that the students' high metacognition ability increased flow degree in the problem solving process, and problem solving in this state of flow increased their mathematics creative problem solving ability.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.239-250
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• 2004

수학적 힘의 함양과 문제해결력의 신장을 위한 수학교육에서 확률영역은 중요한 학습소재임에도 불구하고, 확률영역은 어려운 것으로 고착되었다. 이 연구에서는 학생들이 확률영역의 어떤 부분을 어려워하고 이해하기 힘들어하는지를 구체적 문항분석을 통하여 알아봄으로서 교수-학습의 기초자료를 제공하고자한다. 이를 위하여, 지난 10년간 출제되었던 대학수학능력시험의 확률영역 16문항을 고등학교 학생 220명에게 실시하고, 고전검사이론과 문항반응이론울 적용하여 그 결과를 분석하였다. 고전검사이론에서는 신뢰도와 변별도를 측정하였고, 문항반응이론에서는 Rasch 1-모수 문항반응모형에 근거한 BIGSTEP을 사용하여 내적타당도와 난이도를 측정하였다.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.59-75
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• 2012

This study aims to find whether the solutions for well-structured problems learned in school can be transferred to the moderately-structured problem and ill-structured problem. For these purpose, research questions were set up as follows: First, what are the patterns of changes in strategies used in solving the mathematics problems with different level of structuredness? Second, From the group using and not using proportion algorithm strategy in solving moderately-structured problem and ill-structured problem, what features were observed when they were solving that problems? Followings are the findings from this study. First, for the lower level of structuredness, the frequency of using multiplicative strategy was increased and frequency of proportion algorithm strategy use was decreased. Second, the students who used multiplicative strategies and proportion algorithm strategies to solve structured and ill-structured problems exhibited qualitative differences in the degree of understanding concept of ratio and proportion. This study has an important meaning in that it provided new direction for transfer and analogical problem solving study in mathematics education.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.381-395
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• 2010

The purpose of this paper is to examine the competence and the methods of problem solving in four operations word problems based on the informal knowledges by five-year-old children. The numbers which are contained in problems consist of the numbers bigger than 5 and smaller than 10. The subjects were 21 five-year-old children who didn't learn four operations. The interview with observation was used in this research. Researcher gave the various materials to children and permitted to use them for problem solving. And researcher read the word problems to children and children solved the problems. The results are as follows: five-year-old children have the competence of problem solving in four operations word problems. They used mental computation or counting all materials strategy in addition problem. The methods of problem solving were similar to that of addition in subtraction, multiplication and division, but the rate of success was different. Children performed poor1y in division word problems. According to this research, we know that kindergarten educators should be interested in children's informal knowledges of four operations including shapes, patterns, statistics and probability. For this, it is needed to developed the curriculum and programs for informal mathematical experiences.