• The Mathematical Education
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• v.48 no.2
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• pp.149-167
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• 2009

This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

• Korean Journal of Human Ecology
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• v.19 no.2
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• pp.271-283
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• 2010

This study was planned to investigate the effects of mathematical games with motion on young children's development. The study was performed to compose mathematical games with motion and just mathematical games for young children. The games were set up to be executed 16 times for 8 weeks. The results of this study were as follows: Mathematical games with motion had a significant effect on young children's mathematical problem-solving ability. Mathematical games with motion had a significant effect in every category on young children's ability for motion competence and mathematical games with motion had a significant effect on young children's socio-emotional development. There were significant differences between the control group and the experimental group except for the independence from teachers and peer interaction. Mathematical games with motion had a significant effect on young children's language ability.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.401-420
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• 2010

The purpose of this research is to find out effectiveness of geometry learning through spatial reasoning activities on mathematical problem solving ability and mathematical attitude. In order to proof this research problem, the controlled experiment was done on two groups of 6th graders in N elementary school; one group went through the geometry learning style through spatial reasoning activities, and the other group went through the general geometry learning style. As a result, the experimental group and the comparing group on mathematical problem solving ability have statistically meaningful difference. However, the experimental group and the comparing group have not statistically meaningful difference on mathematical attitude. But the mathematical attitude in the experimental group has improved clearly after all the process of experiment. With these results we came up with this conclusion. First, the geometry learning through spatial reasoning activities enhances the ability of analyzing, spatial sensibility and logical ability, which is effective in increasing the mathematical problem solving ability. Second, the geometry learning through spatial reasoning activities enhances confidence in problem solving and an interest in mathematics, which has a positive influence on the mathematical attitude.

• 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.

• 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.

• East Asian mathematical journal
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• v.33 no.4
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• pp.381-411
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• 2017

The purpose of this study is to investigate how students' mathematical creativity changes through problem-solving instruction using problem-posing for elementary school students and to explore instructional methods to improve students' mathematical creativity in school curriculum. In this study, nonequivalent control group design was adopted, and the followings are main results. First, problem-solving lessons with problem-posing had a significant effect on students' mathematical creativity, and all three factors of mathematical creativity(fluency, flexibility, originality) were also significant. Second, the lessons showed meaningful results for all upper, middle, and lower groups of pupils according to the level of mathematical creativity. When analyzing the effects of sub-factors of mathematical creativity, there was no significant effect on fluency in the upper and middle groups. Based on the results, we suggest followings: First, there is a need for a systematic guidance plan that combines problem-solving and problem-posing, Second, a long-term lesson plan to help students cultivate novel mathematical problem-solving ability through insights. Third, research on teaching and learning methods that can improve mathematical creativity even for students with relatively high mathematical creativity is necessary. Lastly, various student-centered activities in math classes are important to enhance creativity.

• The Mathematical Education
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• v.31 no.2
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• pp.109-119
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• 1992

The primary purpose of the present study is to provide the sources to improve the mathematical problem solving performance by analyzing the effects of the belief systems and the misconceptions of the middle school students in solving the problems. To attain the purpose of this study, the reserch is designed to find out the belief systems of the middle school students in solving the mathematical problems, to analyze the effects of the belief systems and the attitude on the process of the problem solving, and to identify the misconceptions which are observed in the problem solving. The sample of 295 students (boys 145, girls 150) was drawn out of 9th grade students from three middle schools selected in the Kangdong district of Seoul. Three kinds of tests were administered in the present study: the tests to investigate (1) the belief systems, (2) the mathematical problem solving performance, and (3) the attitude in solving mathematical problems. The frequencies of each of the test items on belief systems and attitude, and the scores on the problem solving performance test were collected for statistical analyses. The protocals written by all subjects on the paper sheets to investigate the misconceptions were analyzed. The statistical analysis has been tabulated on the scale of 100. On the analysis of written protocals, misconception patterns has been identified. The conclusions drawn from the results obtained in the present study are as follows; First, the belief systems in solving problems is splited almost equally, 52.95% students with the belief vs 47.05% students with lack of the belief in their efforts to tackle the problems. Almost half of them lose their belief in solving the problems as soon as they given. Therefore, it is suggested that they should be motivated with the mathematical problems derived from the daily life which drew their interests, and the individual difference should be taken into account in teaching mathematical problem solving. Second. the students who readily approach the problems are full of confidence. About 56% students of all subjects told that they enjoyed them and studied hard, while about 26% students answered that they studied bard because of the importance of the mathematics. In total, 81.5% students built their confidence by studying hard. Meanwhile, the students who are poor in mathematics are lack of belief. Among are the students accounting for 59.4% who didn't remember how to solve the problems and 21.4% lost their interest in mathematics because of lack of belief. Consequently, the internal factor accounts for 80.8%. Thus, this suggests both of the cognitive and the affective objectives should be emphasized to help them build the belief on mathematical problem solving. Third, the effects of the belief systems in problem solving ability show that the students with high belief demonstrate higher ability despite the lack of the memory of the problem solving than the students who depend upon their memory. This suggests that we develop the mathematical problems which require the diverse problem solving strategies rather than depend upon the simple memory. Fourth, the analysis of the misconceptions shows that the students tend to depend upon the formula or technical computation rather than to approach the problems with efforts to fully understand them This tendency was generally observed in the processes of the problem solving. In conclusion, the students should be taught to clearly understand the mathematical concepts and the problems requiring the diverse strategies should be developed to improve the mathematical abilities.

• East Asian mathematical journal
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• v.40 no.2
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• pp.167-181
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• 2024

This study explored the characteristics of elementary gifted students' creative problem-solving skills combining creativity and problem-solving ability based on their work on Fermi estimation problems. The analysis revealed that gifted students exhibited strong logical validity and breadth but showed some weaknesses in divergent thinking abilities (fluency, flexibility, originality).

• 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.

• The Journal of Korea Robotics Society
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• v.12 no.3
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• pp.287-296
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• 2017

Robots are used in early childhood education as a new instructional media, and educational activities using robots have been increased. So the purpose of this study is to investigate the effect of educational activities using hands-on robots on logic-mathematical knowledge and creative problem-solving ability of young children. The total number of subjects was 43, and they were all five-year-old children. The experimental group and control group did activities with hands-on robots and general free activities, respectively. Results using ANCONA have shown that the activities with hands-on robots positively affected logic-mathematical knowledge and creative problem-solving ability of young children. These meaningful results have shown the possibility of early childhood educational use as the effectiveness of hands-on robots has come out.