• Education of Primary School Mathematics
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• v.16 no.2
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• pp.123-145
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• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).

• Communications of Mathematical Education
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• v.23 no.3
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• pp.803-822
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• 2009

Creativity is emerging as one of the key components in every areas. In mathematics education, creativity or mathematical creativity is emphasized even though the definition of the term is inconsistence among every research. The purpose of this research was to identify the nature of mathematical creativity and provide the ways of strengthening it in the mathematics classroom. For this, students' mathematical strategies and problems in the elementary mathematics textbook were analyzed. The results showed that mathematically gifted students used a limited strategies and the problems in the textbooks were too simple to stimulate students' mathematical creativity. For the enhancement of students' mathematical creativity, we need to develop mathematically rich tasks and refine teacher education programs.

• School Mathematics
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• v.16 no.3
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• pp.613-631
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• 2014

The aim of this study was to investigate how the small group activity system influences individual to form concepts of prime number and composite number through activity theory on learning process of mathematically gifted 5th-grade students. Student's worksheets, recorded video, and interview were gathered and transcribed for analyzing data. Process of concept formation and using symbol behavior were used to derive the stage of mathematical concept from students, and the activity system and stage of concept formation process were schematized through analysis of whole class activity system and small group activity system based on activity theory. According to the results of this study, two students who were in different activity groups separated into the state of semi-concept and the stage of complex thinking respectively, and therefore, social context and the activity system had effects on process of concept formation among the students.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.327-344
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• 2006

This study examined the proof levels and understanding of constituents of proving by three mathematically gifted 6th grade korean students, who belonged to the highest 1% in elementary school, through observation and interviews on the problem-solving process in relation to constructing a rectangle of which area equals the sum of two other rectangles. We assigned the students with Clairaut's geometric problems and analyzed their proof levels and their difficulties in thinking related to the understanding of constituents of proving. Analysis of data was made based on the proof level suggested by Waring (2000) and the constituents of proving presented by Galbraith(1981), Dreyfus & Hadas(1987), Seo(1999). As a result, we found out that the students recognized the meaning and necessity of proof, and they peformed some geometric proofs if only they had teacher's proper intervention.

• The Journal of the Korea Contents Association
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• v.11 no.1
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• pp.448-457
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• 2011

In this study, the teaching material has been developed based on Polya's Problem Solving Techniques for preparing Korea Information Olympiad qualification and studying principle of computer. the basis of discrete mathematics and data structures were selected as the content of textbooks for students to learn computer programming principles. After the developed textbooks were applied to elementary school students of Science Gifted Education Center of J University, the result of study proves that textbook helps improve problem-solving ability using the testing tool restructured sample questions from previous test. We need guidebook and training course for teachers and realistic conditions for teaching the principles of computer.

• Journal of Gifted/Talented Education
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• v.18 no.1
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• pp.79-109
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• 2008

In most curricular model for gifted children, independent study is included as an important element for developing students' study ability and producing creative production Gifted children also prefers this style of learning and they study more easily and with more fun when they learn in the learning style they prefer. This study aims to find out how gifted children in math area performs independent study and how teachers who teach them recognize independent study; survey study was used to analyze the reality of the production in relation to independent study. In result, gifted children's independent study ability was rather very low and teachers recognized the necessity of independent study but lacked understanding of the method of independent study.

• The Mathematical Education
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• v.48 no.4
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• pp.455-467
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• 2009

During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The test questions are formulated into several areas of questioning-types which can reveal rather different result. The lower level questions are to investigate individual ability to solve multiple mathematical problems while using "mathematical thought." During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The scope of this case study is to present a desirable model in solving mathematical problems and to improve teaching methods for math teachers.

• 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.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.389-413
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• 2011

This study had suggested the direction and implications of mathematics education for the gifted student by looking into domestic research trends in relation with mathematics education for the talented children from 2000 to 2010. 168 theses were analyzed by researching theses about mathematics education for the talented children and the total 10 kinds of special journals that are registered or to be registered at National Research Foundation of Korea in order to find a research trend about mathematics education for the talented children. As a result of analyzing theses of each year, the number of theses on mathematics education for the talented children has been increasing largely since2004 and it is steadily being conducted until now. As a result of analyzing theses for each research theme, frequency was shown in order of development research about educational course program for mathematics education for the talented children and research on characteristics of the talented children. For analysis result of research target, research targeting elementary school students has taken great importance. For the aspect of research methods, research about development of program and research tool was used in theses and qualitative research method was mainly used in journals and therefore a direction of mathematics education for the talented children was discussed according to this.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.771-804
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• 2014

The concept of the center of gravity is presently being introduced in elementary school curriculums and is broadly applied to Mathematics, Physics, and the Engineering field in University education which are mostly theoretical classes much separated from actual life in the practical educational field. In 2013, ${\bigcirc}{\bigcirc}$ University of Science and Gifted Education, had developed the multidisciplinary approach program of verifying the center of gravity for gifted students, but this program was reconstructed and applied to ordinary students and the effectiveness was analyzed to lay the foundation and generalize this convergence education. Including experiments for verifying the center of gravity in an object with a hollow interior and the existence of a center of gravity outside an object, I proposed realizing the calculations by considering the weight of the lever, the Principle of the lever being a core factor when finding the center of gravity. We altered the existing 8 step program to a 4 step program for the told 65 students from elementary, Junior and High School students, letting them freely select the class lecture by themselves. The analysis attained from surveys, debates and interviews showed that by precise error analysis, students achieved a higher success experience, showing us the importance of the development of a new convergence program.