• Journal of Educational Research in Mathematics
• /
• v.27 no.3
• /
• pp.391-410
• /
• 2017

This study aims to analyze mathematically gifted students' characteristics of generalization and justification for a given mathematical task and induce didactical implications for individual teaching methods by students' learning styles. To do this, we identified the learning styles of three mathematically gifted 6th graders and observed their processes in solving a given problem. Paper-pencil environment as well as dynamic geometrical environment using Geogebra were provided for three students respectively. We collected and analyzed qualitatively the research data such as the students' activity sheets, the students' records in Geogebra, our observation reports about the processes of generalization and justification, and the records of interview. The results of analysis show that the types of the students' generalization are various while the level of their justifications is identical. Futhermore, their preference of learning environment is also distinguished. Based on the results of analysis, we induced some implications for individual teaching for mathematically gifted students by learning styles.

• Education of Primary School Mathematics
• /
• v.22 no.1
• /
• pp.1-12
• /
• 2019

This study examined the attention and attention shift of general students and mathematically gifted students about pattern by the types of mathematical patterns. For this purpose, we analyzed eye movements during the problem solving process of 5th general and mathematically gifted students using eye tracker. The results were as follows: first, there was no significant difference in attentional style between the two groups. Second, there was no significant difference in attention according to the generation method between the two groups. The diversion was more frequent in the incremental strain generation method in both groups. Third, general students focused more on the comparison between non-contiguous terms in both attributes. Unlike general students, mathematically gifted students showed more diversion from geometric attributes. In order to effectively guide the various types of mathematical patterns, we must consider the distinction between attention and attention shift between the two groups.

• Journal of Gifted/Talented Education
• /
• v.27 no.1
• /
• pp.37-57
• /
• 2017

In terms of making more various geometrical figures than existing Tangram, Sphinx Puzzle has been used as a material for the gifted education. The main research subject of this paper is to verify how many convex polygons can be made by all pieces of a Sphinx Puzzle. There are several previous researches which dealt with this research subject, but they did not account for the clear reasons on the elementary level. In this thesis, I suggest using unit area and minimum area which can be proved on the elementary levels to account for this research subject. Also, I composed the program for the mathematically gifted elementary students, regarding the subject. I figured out whether they can make the mathematical justifications. I applied this program for three 6th grade students who are in the gifted class of the G district office of education. As a consequence, I found that it is possible for some mathematically gifted elementary students to justify that the number of convex polygons that can be made by a Sphinx Puzzle is at best 27 on elementary level.

• Research in Mathematical Education
• /
• v.13 no.1
• /
• pp.63-73
• /
• 2009

This paper reports on student, parent, and teacher perspectives of the characteristics of the mathematically gifted. The data are extracted from a two-year qualitative study that examined multiple perspectives, school policy documents and program provision for 15 mathematically gifted and talented students aged from 10 to 13 years. The findings have implications for identification and program provision.

• School Mathematics
• /
• v.6 no.4
• /
• pp.361-372
• /
• 2004

This study is designed to investigate intellectual, emotional, and creative characteristics of mathematically gifted students. In this paper, we analyze their proof examples, responses to questionnaire on mathematical aptitude and social coping, and scores for Torrance creativity test(figure) in comparison with scientific gifted and general students.

• Journal of Educational Research in Mathematics
• /
• v.27 no.3
• /
• pp.557-580
• /
• 2017

The purpose of this study is developing the manifestation process model of group creativity among mathematically gifted students. Therefore, I designed the manifestation process model of group creativity by researching the existing literatures on group creativity and mathematical creativity. The manifestation process model of group creativity was applied to mathematically gifted students' class. By analyzing students' response, the manifestation process model of group creativity was improved and concretized. In conclusion, the process of a combination of contributions was concretized and the major variables on group creativity such as a diversity, conflict, emotionally supportive environment and social comparison were verified. In addition, some reflective processes was discovered from a case study.

• Education of Primary School Mathematics
• /
• v.14 no.1
• /
• pp.13-26
• /
• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Journal of Educational Research in Mathematics
• /
• v.20 no.3
• /
• pp.203-219
• /
• 2010

Several studies have reported on how and what mathematically gifted students develop superior ability or creativity in geometry and algebra. However, there are lack of studies in probability area, though there are a few trials of probability education for mathematically gifted students. Moreover, less attention has paid to the strategies to develop gifted students' creativity. This study has drawn three teaching strategies for creativity development based on literature review embedding: cognitive conflict, multiple representations, and social interaction. We designed a series of tasks via reconstructing, so called Simpson's paradox to meet these strategies. The findings showed that the gifted students made Quite a bit of improvement in creativity while participating in reflective thinking and active discussion, doing internal and external connection, translating representations, and investigating basic assumption.

• Journal of Educational Research in Mathematics
• /
• v.19 no.4
• /
• pp.479-491
• /
• 2009

This paper researches the possibility of introducing Descartes' theorem to mathematically gifted students. Not only is Descartes' theorem logically equivalent to Euler's theorem but is hierarchically connected with Gauss-Bonnet theorem which is the core concept on differential geometry. It is possible to teach mathematically gifted students Descartes' theorem by generalizing mathematical property in solid geometry through analogical reasoning, that is, so in a polyhedrons the sum of the deficient angles is $720^\circ$ as in an polygon the sum of the exterior angles is $360^\circ$. This study introduces an alternative method of instruction that we enable mathematically gifted students to reinvent Descartes' theorem through analogical reasoning instead of deductive reasoning.

• Communications of Mathematical Education
• /
• v.31 no.1
• /
• pp.49-70
• /
• 2017

The purpose of this study was to investigate the relative influence of multiple error sources and to find optimal measurement conditions that obtain a desired level of reliability of a creative attitude test in mathematical creativity. This study analyzed the scores of the Creative Attitude Scale-Korea allowed to access publicly of 125 general students and 109 mathematically gifted students by performing a multivariate generalizability analysis. The main results were as follows. First, based on reliability, the Creative Attitude Scale-Korea was measured less precisely for mathematically gifted students. On the contrary, based on the conditional standard error of measurement, it was measured less precisely for general students. However, the Creative Attitude Scale-Korea showed strong reliability in both groups. Second, the optimal weights should adjust to .3, .3, .4 in mathematically gifted students and .4, .4, .2 in general students with three scoring components of divergent attitude, problem solving attitude, and convergent attitude based on the maximum reliability. Third, to approach desirable reliability, it is possible to use one component of divergent attitude in general students but three components of divergent attitude, problem solving attitude, and convergent attitude in mathematically gifted students. Finally this study proposed application plans for the Creative Attitude Scale-Korea and future directions of research.