• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.115-123
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• 2001

In its seventh revision to start in 2001, mathematics will have a new emphasis in the middle school curriculum. Mathematics subject is now composed of practical things in the use of mathematics. Also, the future of new generation, which has been known as the information age, places much focus on problem-solving in order to collect, analyze, synthesize, and judge various kinds informations. This demand of problem-solving ability is not only related with mathematical education but, along the entire educational process, its related to actual life. With this change of social structure, the importance of school education is increasing rapidly. Therefore, in order to grow abilities and create new knowledge, adapted this new method of self-oriented learning in groups to middle school 2nd graders for one year, the results were as follows : 1. Students developed their ability of the use of mathematical terms and signs correctly. 2. Students' mathematical knowledge and problem-solving ability improved as they had increased interest in mathematics. 3. Students' peership was enhanced through their communication and cooperative activities in groups during the class. 4. Students themselves were more willing to volunteer and participate during the class.

• The Mathematical Education
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• v.47 no.4
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• pp.421-436
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• 2008

Mathematics assessment doesn't mean examining in the traditional sense of written examination. Mathematics assessment has to give the various information of grade and development of students as well as teaching of teachers. To achieve this purpose of assessment, we have to search the methods of assessment. This paper is aimed to develop the open-ended problems that are the alternative to traditional test, apply them to classroom and analyze the result of assessment. 4-types open-ended problems are developed by criteria of development. It is open process problem, open result problem, problem posing problem, open decision problem. 6 grade elementary students who are picked in 2 schools participated in assessment using open-ended problems. Scoring depends on the fluency, flexibility, originality The result are as follows; The rate of fluency is 2.14, The rate of flexibility is 1.30, and The rate of originality is 0.11 Furthermore, the rate of originality is very low. Problem posing problem is the highest in the flexibility and open result problem is the highest in the flexibility. Between general mathematical problem solving ability and fluency, flexibility have the positive correlation. And Pearson correlational coefficient of between general mathematical problem solving ability and fluency is 0.437 and that of between general mathematical problem solving ability and flexibility is 0.573. So I conclude that open ended problems are useful and effective in mathematics assessment.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.1-17
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• 2006

This thesis analyzed the effects of cooperative learning blended with TAI(Team Assisted Individualization) and STAD(Student Team Achievement Division) models on the students' ability of problem solving in mathematics in order to discover what kind of effects would give to their ability of that, and would promote their disposition and attitude to learn mathematics. The results of this study were as follows : First, the learning method blended with TAI and STAD models was more effective in the students' ability of problem solving in mathematics than traditional learning method because of the blended model's characteristics; positive interdependence, individual accountability, team recognition, curriculum materials. Second, the learning method blended with TAI and STAD models was more effective in sub-elements - self-confidence, adaptability, will, curiosity and value - of mathematical disposition than traditional learning method. And the learning method blended with TAI and STAD models was more effective in sub-elements - self-consciousness of mathematics and interests - of mathematical attitude than traditional learning method. In conclusion, the learning method blended with TAI and STAD models could affect to not only the students' ability of problem solving in mathematics but also the students' several affective factors.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.315-335
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• 2010

The goal of this research was to study the effects of the Mathematical Problem Generating Program on problem solving ability and learning attitude. The experiment was carried out between two classes. One class was applied with the experimental program (treatment group), and the other continued with normal teaching and learning methods (comparative group). In this study, two 5th grade elementary classes participated in Seoul city. In this study, the students were tested their problem solving abilities by the IPSP test and learning attitude by the Korean Education Development Institute (KEDI) before and after use of the program. The collected results were t-tested to find any meaningful changes. The results showed the followings. First, use of the mathematical generating program showed meaningful progressive results in problem solving ability. Second, the students that used the program showed positive results in learning attitude. In conclusion, learning mathematics using the problem generating method helps students deeper understand and solve complex problems. In addition, problem solving abilities can be improved and the attitude towards mathematics can be changed while students are using an active and positive approach in problem solving processes.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.663-686
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• 2017

The purpose of this study was to identify the effects of convergent approach of mathematics education on students' problem-solving ability and self-efficacy by designing and applying mathematics curriculum based on STEAM. The results are as follows. First, the test results between the two groups did not show any statistically significant difference in terms of problem solving ability, but the experimental group showed a higher average score than the comparative group. Compared with the standard deviation of the experimental group, It can be seen that the level of difference between students is great. This suggests that STEAM-based mathematics lessons have a positive effect on the problem solving ability of low-level students. Second, the results of the self-efficacy t-test of STEAM-based mathematics class showed statistically significant results at a 5% significance level. In the sub-domain, the preference for the difficulty of the mathematics task, except math self-confidence and the math self-regulation efficacy, were statistically significant at a 5% significance level. This study shows that STEAM-based mathematics classes have a positive effect on the students' positive aspects. Through the STEAM program, students learn that mathematics is connected with other fields, and it provides an opportunity to explore on their own, and they more became interested, motivated, and achievement. Also, through the results of the STEAM-based mathematics class, it can be seen that the expressive power and self-confidence are increased by using the non-formal representation outside of the existing formal representation center. The result of this study can be summarized as follows: A STEAM-based mathematics class has a positive effect on problem solving ability and self-efficacy. Therefore, it is interpreted that the application of the STEAM program focusing on mathematics accounts for education effectives.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.361-374
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• 2005

I analyzed the effect of problem posing teaching and teacher-centered teaching on mathematical problem-solving ability and creativity in order to know the efffct of problem posing teaching on mathematics study. After we gave problem posing lessons to the 3rd grade middle school students far 28 weeks, the evaluation result of problem solving ability test and creativity test is as fellows. First, problem posing teaching proved to be more effective in developing problem-solving ability than existing teacher-centered teaching. Second, problem posing teaching proved to be more effective than teacher-centered teaching in developing mathematical creativity, especially fluency and flexibility among the subordinate factors of mathematical creativity. Thus, 1 suggest the introduction of problem posing teaching activity for the development of problem-solving ability and mathematical creativity.

• Education of Primary School Mathematics
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• v.17 no.2
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• pp.95-111
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• 2014

The purpose of this study is to determine the relationship between metacognition and math creative problem solving ability. Specific research questions set up according to the purpose of this study are as follows. First, what relation does metacognition has with creative math problem-solving ability of mathematically gifted elementary students? Second, how does each component of metacognition (i.e. metacognitive knowledge, metacognitive regulation, metacognitive experiences) influences the math creative problem solving ability of mathematically gifted elementary students? The present study was conducted with a total of 80 fifth grade mathematically gifted elementary students. For assessment tools, the study used the Math Creative Problem Solving Ability Test and the Metacognition Test. Analyses of collected data involved descriptive statistics, computation of Pearson's product moment correlation coefficient, and multiple regression analysis by using the SPSS Statistics 20. The findings from the study were as follows. First, a great deal of variability between individuals was found in math creative problem solving ability and metacognition even within the group of mathematically gifted elementary students. Second, significant correlation was found between math creative problem solving ability and metacognition. Third, according to multiple regression analysis of math creative problem solving ability by component of metacognition, it was found that metacognitive knowledge is the metacognitive component that relatively has the greatest effect on overall math creative problem-solving ability. Fourth, results indicated that metacognitive knowledge has the greatest effect on fluency and originality among subelements of math creative problem solving ability, while metacognitive regulation has the greatest effect on flexibility. It was found that metacognitive experiences relatively has little effect on math creative problem solving ability. This findings suggests the possibility of metacognitive approach in math gifted curricula and programs for cultivating mathematically gifted students' math creative problem-solving ability.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.143-159
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• 2018

Since the mathematics learning achievement level is closely related to problem-solving ability, it is necessary to understand the relationship between problem-solving ability and meta-affect ability from the point of view of general mathematics learning ability. In this study, we compared the frequency analysis and the case analysis of the functional aspects of the meta-affect in elementary school students' problem-solving processes according to mathematics learning achievement level in parallel with frequency analysis and case analysis. In other words, the frequency of occurrence of meta-affect, the frequency of meta-affective type, and the frequency of meta-functional types of meta-affect were compared and analyzed according to the mathematics learning achievement level in the collaborative problem-solving activities of small group members with similar mathematics learning achievement level. In addition, we analyzed the representative cases of meta-affect by meta-functional types according to the mathematics learning achievement level in detail. As a result, meta-affect in problem-solving processes of the upper level group acted as relatively various types of meta-functions compared to the lower level group. And, the lower level group, the more affective factors acted in the problem-solving processes.

• 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.

• Research in Mathematical Education
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• v.7 no.3
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• pp.163-189
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• 2003

The purpose of this study is to develop a test, which can be used in creative problem solving ability in mathematics of the mathematically gifted and the regular students. This test tool is composed of three categories; fluency (number of responses), flexibility (number of different kinds of responses), and originality (degree of uniqueness of responses) which are the factors of the creativity. After applying to 462 middle school students, this test was analyzed into item analysis. As a results of item analysis, it turned out to be meaningful (reliability: 0.80, validity: item 1(1.05), item 2(1.10), item 3(0.85), item 4(0.90), item 5(1.08), item difficulty: item 1(-0.22), item 2(-0.41), item 3(0.23), item 4(0.40), item 5(-0.01), item discriminating power: item 1(0.73), item 2(0.73), item 3(0.67), item 4(0.51), item 5(0.56), over the level of a standard basis. This means that the test tool was useful in the test process of creative problem solving ability in mathematics