• Communications of Mathematical Education
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• v.3
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• pp.275-295
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• 1997

• 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.

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.219-233
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• 2012

Practicality and value of mathematics can be verified when different problems that we face in life are resolved through mathematical knowledge. This study intends to identify whether the fraction teaching is being taught and learned at current elementary schools for students to recognize practicality and value of mathematical knowledge and to have the ability to apply the concept when solving problems in the real world. Accordingly, contextual problems and noncontextual problems are proposed around fractional arithmetic area, and compared and analyze the achievement level and problem solving processes of them. Analysis showed that there was significant difference in achievement level and solving process between contextual problems and noncontextual problems. To instruct more meaningful learning for student, contextual problems including historical context or practical situation should be presented for students to experience mathematics of creating mathematical knowledge on their own.

• 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.

• 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 Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.211-229
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• 2009

The purpose of this study is analysis of to investigate relation proportion problem of mathematics textbooks of 7th curriculum to proportional reasoning(relative thinking, unitizing, partitioning, ratio sense, quantitative and change, rational number) of Lamon's proposal at sixth grade students. For this study, I develop two test papers; one is for proportion problem of mathematics textbooks test paper and the other is for proportional reasoning test paper which is devided in 6 by Lamon. I test it with 2 group of sixth graders who lived in different region. After that I analysis their correlation. The result of this study is following. At proportion problem of mathematics textbooks test, the mean score is 68.7 point and the score of this test is lower than that of another regular tests. The percentage of correct answers is high if the problem can be solved by proportional expression and the expression is in constant proportion. But the percentage of correct answers is low, if it is hard to student to know that the problem can be expressed with proportional expression and the expression is not in constant proportion. At proportion reasoning test, the highest percentage of correct answers is 73.7% at ratio sense province and the lowest percentage of that is 16.2% at quantitative and change province between 6 province. The Pearson correlation analysis shows that proportion problem of mathematics textbooks test and proportion reasoning test has correlation in 5% significance level between them. It means that if a student can solve more proportion problem of mathematics textbooks then he can solve more proportional reasoning problem, and he have same ability in reverse order. In detail, the problem solving ability level difference between students are small if they met similar problem in mathematics text book, and if they didn't met similar problem before then the differences are getting bigger.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.147-158
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• 2012

In this paper we introduced the reflection cluster problems. They are not well known in Korea education field. We used two reflection cluster problems and analysed the responses of the gifted students. Finally, we asked how they felt about reflection cluster problems. The results of this paper will help to make new assessment items and develop new programs for the gifted education.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.19-38
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• 2011

The purpose of this study was to analyze the responses and the behavioral characteristics between mathematically promising students and normal students in solving open-ended problems. For this study, 55 mathematically promising students were selected from the Science Education Institute for the Gifted at Seoul National University of Education as well as 100 normal students from three 6th grade classes of a regular elementary school. The students were given 50 minutes to complete a written test consisting of five open-ended problems. A post-test interview was also conducted and added to the results of the written test. The conclusions of this study were summarized as follows: First, analysis and grouping problems are the most suitable in an open-ended problem study to stimulate the creativity of mathematically promising students. Second, open-ended problems are helpful for mathematically promising students' generative learning. The mathematically promising students had a tendency to find a variety of creative methods when solving open-ended problems. Third, mathematically promising students need to improve their ability to make-up new conditions and change the conditions to solve the problems. Fourth, various topics and subjects can be integrated into the classes for mathematically promising students. Fifth, the quality of students' former education and its effect on their ability to solve open-ended problems must be taken into consideration. Finally, a creative thinking class can be introduce to the general class. A number of normal students had creativity score similar to those of the mathematically promising students, suggesting that the introduction of a more challenging mathematics curriculum similar to that of the mathematically promising students into the general curriculum may be needed and possible.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.73-83
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• 2009

Mathematics Olympiad aims to identify and encourage students who have superior ability in mathematics, to enhance students' understanding in mathematics while stimulating interest and challenge, to increase learning motivation through self-reflection, and to speed up the development of mathematical talent. Participating mathematical competition, students are going to solve a variety of types of mathematical problems and will be able to enlarge their understanding in mathematics and foster mathematical thinking and creative problem solving ability with logic and reasoning. In addition, parents could have an opportunity valuable information on their children's mathematical talents and guidance of them. Although there should be presenting diversified mathematical problems in competitions, the real situations is that resent most mathematics Olympiads present mathematical problems which narrowly focus on types of solving problems. In order to diversifying types of problems in mathematics Olympiads and making mathematics popular, this study will discuss a Olympiad for problem solving ability, a Olympiad for exploring mathematics, a Olympiad for task solving ability, and a mathematics fair, etc.

• The Journal of Korean Association of Computer Education
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• v.13 no.5
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• pp.71-80
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• 2010

A lot of studies in and outside the country says that robots can become an effective tool in developing creativity, problem solving skills and positive learning motivation in the knowledge and information era. This study aims to verify the educational effect of robots in mathematics education by applying robots to mathematics education as a learning tool in an effort to improve the teaching/learning environment. For this study, the mathematics curriculum of elementary school and robot programming were analyzed and then a robot integrated mathematics program was developed. The developed program was applied to the mathematics education of an elementary school year 5 over 16 times. The result of the study showed that the experimental group which used the robot integrated program has better learning attitude and problem solving skills than the group which used the traditional method. The result also showed that the mathematics activities that used robot programming contributed to developing problem solving skills and provided positive mathematics learning experience.