• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.95-111
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• 2015

The purpose of this study is to analyze cases on teaching solutions exploration of Wythoff's game through using the analogy for the gifted elementary students, to suggest useful teaching methods. Students recognized structural similarity among problems on the basis of relevance of conditions of problems. The discovery of structural similarity improves the ability to solve problems. Although 2 groups-NIM game with surface similarity is not helpful in solving Wythoff's game, Queen's move game with structural similarity makes it easier for students to solve Wythoff's game. Useful teaching methods to find solutions of Wythoff's game through using the analogy are as follow. Encoding process helps students make sense of the game. It is significant to help students realize how many stones are remained and how the location of Queen can be expressed by the ordered pair. Inferring process helps students find a solution of 2 groups-NIM game and Queen's move game. It is necessary to find a winning strategy through reversely solving method. Mapping process helps students discover surface similarity and structural similarity through identifying commonalities between the two games. It is crucial to recognize the relationship among the two games based on the teaching in the Encoding process. Application process encourages students to find a solution of Wythoff's game. It is more important to find a solution by using the structural similarity of the Queen's move game rather than reversely solving method.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.7 no.12
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• pp.177-185
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• 2017

In order to succeed in gifted education, it is necessary to educate teachers with professional skills and qualities that meet the psychological characteristics of gifted students and satisfy their educational desires. The purpose of this study is to explore the characteristics of the science/mathematics gifted students the preservice teachers who participated in the service learning in the hothousing center annexed to the university, and the direction in which the Korean hothousing should proceed. For this, the service learning was conducted in the hothousing institution targeting three students attending A education college for 12 weeks. As a result of study, the gifted children showed the outstanding cognitive, affective, and creative natures which were expressed positively or negatively according to the situation. The study participants recognized the teachers had a duty to admit the distinctive nature of the individual gifted children and to provide the specially contrived education for them for the qualitative improvement of the Korean hothousing. Simultaneously they thought the gifted children should be regarded as ordinary children before the gifted persons and treated as the children. The necessity for preservice teachers to take the hothousing lectures requisitely and provide the learning chance focusing on the practical contents beyond the hothousing teacher training was brought forward in order to develop the systematic hothousing curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.341-355
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• 2014

The purpose of this study was to analyze the research trends of elementary mathematics education in Japan. For this purpose, 192 papers published by Japan Society of Mathematics Education for the last 10 years(2004-2013) were analyzed according to there criteria. First, as for research topics, the frequent topics in order were instructional design and methods (36.7%), analysis of curriculum and textbook, general studies, learners' perspectives and abilities, evaluation, teacher education, education engineering and parish. Second, the contents were researched by the order of number and operations (47.4%), geometry, regularity, measurement and probability and statistics. Finally, research subjects of this study were researched by the order of students(39.3%), teachers. Papers dealing with lower graders as well as pre-service teachers were rare. And article dealing with low-achievers and gifted students were not founded. On the basis of this result, we hope it will provide the follow-up and the idea of the elementary mathematics education in Korea and also help various and balanced development.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.179-199
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• 2007

The purpose of this study was to discover differences between mathematically gifted students (MGS) and non-gifted students (NGS) when making probability judgments. For this purpose, the following research questions were selected: 1. How do MGS differ from NGS when making probability judgments(answer correctness, answer confidence)? 2. When tackling probability problems, what effect do differences in probability judgment factors have? To solve these research questions, this study employed a survey and interview type investigation. A probability test program was developed to investigate the first research question, and the second research question was addressed by interviews regarding the Program. Analysis of collected data revealed the following results. First, both MGS and NGS justified their answers using six probability judgment factors: mathematical knowledge, use of logical reasoning, experience, phenomenon of chance, intuition, and problem understanding ability. Second, MGS produced more correct answers than NGS, and MGS also had higher confidence that answers were right. Third, in case of MGS, mathematical knowledge and logical reasoning usage were the main factors of probability judgment, but the main factors for NGS were use of logical reasoning, phenomenon of chance and intuition. From findings the following conclusions were obtained. First, MGS employ different factors from NGS when making probability judgments. This suggests that MGS may be more intellectual than NGS, because MGS could easily adopt probability subject matter, something not learnt until later in school, into their mathematical schemata. Second, probability learning could be taught earlier than the current elementary curriculum requires. Lastly, NGS need reassurance from educators that they can understand and accumulate mathematical reasoning.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.419-443
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• 2018

The purpose of this study was to analyze the problem solving strategies of ordinary students, gifted students, pre-service teachers, and in-service teachers with the 'chicken and pig problem,' which has multiple strategies to obtain the solution. For this study, 98 students in the 6th grade elementary schools, 96 gifted students in a gifted institution, 72 pre-service teachers, and 60 in-service teachers were selected. The researcher presented the "chicken and pig" problem and requested them the solution strategies as many as possible for 30 minutes in a free atmosphere. As a result of the study, the gifted students used relatively various and efficient strategies compared to the ordinary students, and there was a difference in the most used strategies among the groups. In addition, the percentage of respondents who suggested four or more strategies was 1% for the ordinary students, 54% for the gifted students, 42% for the pre-service teachers, and 43% for the in-service teachers. As suggestions, the researcher asserted that various kinds of high-quality mathematical problems and solving experiences should be provided to students and teachers and have students develop multi-strategy problems. As a follow-up study, the researcher suggested that multi-strategy mathematical problems should be applied to classroom teaching in a collaborative learning environment and reflected them in teacher training program.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.229-250
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• 2013

The purpose of this study is analyzing 'observation and recommendation letter by teacher', which is being submitted to screen and enhance the utilization of gifted students in accordance with recently introduced gifted students observation, recommendation and screening system. For the purpose, this study will provide with objective securing plan of 'observation and recommendation letter by teacher' by developing an optimum evaluation model. The research findings were as follows: First, the result of analysis on the mathematically gifted students behavior characteristic as appeared in 'observation and recommendation letter by teacher' suggested that the recommending teachers have the tendency of giving superficial statement instead of giving concrete case description. When it was analyzed for frequency by the 'observation and recommendation letter by teacher' analysis framework devised by the author, the teachers showed the tendency of concentrating on specific questions. Meanwhile, there was a tendency that teachers concentrate on specific gifted behavior characteristic or area for which concrete case had been suggested. The reason is believed that such part is easy to observe and state while others are not, or, teachers did not judge the other part as the characteristic of gifted students. Second, the gifted students behavior characteristics as appeared in 'observation and recommendation letter by teacher' were made into scores by Rubric model. When the interrater reliability was analyzed based on these scores, the correlation coefficient of 1st scoring was .641. After a discussion session was taken and 2nd scoring was done 3 weeks later, the correlation coefficient of 2nd scoring increased to .732. The reason is believed that; i) the severity among scorers was adjusted by the discussion session after the 1st scoring, ii) the scorers established detail judgment standard on various situations which can appear because of the descriptive nature, and, (iii) they found a consensus on scoring for a new situation appeared. It implies that thorough understanding and application of scorers on evaluation model is as important as the development of optimum model for the differentiation of mathematically gifted elementary students.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.67-86
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• 2013

The purpose of this study is to analyze selection of factors of Schoenfeld's problem solving behavior shown in problem solving process of mathematically gifted students based on brain preference of the students and to present suggestions related to hemispheric lateralization that should be considered in teaching such students. The conclusions based on the research questions are as follows. First, as for problem solving methods of the students in the Gifted Education Center based on brain preference, the students of left brain preference showed more characteristics of the left brain such as preferring general, logical decision, while the students of right brain preference showed more characteristics of the right brain such as preferring subjective, intuitive decision, indicating that there were differences based on brain preference. Second, in the factors of Schoenfeld's problem solving behavior, the students of left brain preference mainly showed factors including standardized procedures such as algorithm, logical and systematical process, and deliberation, while the students of right brain preference mainly showed factors including informal and intuitive knowledge, drawing for understanding problem situation, and overall examination of problem-solving process. Thus, the two types of students were different in selecting the factors of Schoenfeld's problem solving behavior based on the characteristics of their brain preference. Finally, based on the results showing that the factors of Schoenfeld's problem solving behavior were differently selected by brain preference, it may be suggested that teaching problem solving and feedback can be improved when presenting the factors of Schoenfeld's problem solving behavior selected more by students of left brain preference to students of right brain preference and vice versa.

• The Mathematical Education
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• v.45 no.4 s.115
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• pp.481-491
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• 2006

Diffy is a simple mathematical puzzle that provides elementary-school students with subtraction practice. The idea appears to have originated in the late nineteenth century with E. Ducci of Itali. Thirty years ago Professor J. Copley of the University of Houston introduced the diffy game to teachers in elementary schools and it widely spreaded out. During the diffy activity we naturally guess many interesting conjectures. First, does diffy always end? Second, does the head of diffy always exist? Third, for an arbitrary given natural number n, is there any possible method to find the diffy with the given length n? In this study I give the necessary and sufficient condition for the existence of the head of diffy. Using this condition I classify all possible heads of diffy and provide an algorithm to find the diffy with any given length n. With this algorithm I find four natural numbers with diffy length 200. To ensure my numbers are correct, I make a diffy program for Mathematica and check they are correct. I suggest the diffy game is good for enlarging the mathematical thinking to all graded students, especially gifted and talented students, It will produce rational consideration and synthetic judgement.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.621-636
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• 2013

In this paper we intended to present the case of mentorship program for the gifted in elementary mathematics education, which is related with Waldorf education. We installed the program to four six-grade students during six months. We focused on cultivating integrated perspective, aesthetic perspective and substantial skills. For the aim we dealt with the item, construction based on the aesthetic experiences. Finally we presented three main ideas, construction of regular polygons and flowers, construction of islamic design, and farmland cleanup with construction. We also contained the students' project in this paper.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.