• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.89-110
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• 2004

The purpose of this study is to identify the significant characteristics shown in the field of mathematics by a gifted child, the educational curriculum for this child, and to find what has to be set in place in the areas of teacher's teaching methods and programs. The important aspect of these ideas is that one has to completely understand and know the characteristics of the gifted in order to give them the opportunity to discover their underlying talents and to develop upon those skills by giving them suitable and appropriate education for their intellectual state. This study focuses on the thoughts and behavior of a gifted male child, from his third to fifth grade, and the study shows the results and analysis of data gathered from close observation and interview, and a collection of documents gathered from the child. This study is analyzed from three different perspectives: 1. The typical life and surroundings of this gifted child, and how he was raised in this particular environment. This also shows the significant event that allowed others to recognize him as gifted. 2. Identification of how a gifted child's mind works in the field of mathematics. This attempts to analyze methods the child uses to arrive at a solution to a problem. 3. Exploration of mathematical attitude of the child. This shows the child's interest in mathematics, and the willingness to find better and more efficient ways to reach a solution. This also shows the child's ability to explain his purpose and methods of problem solving in detail, and the focus and clarity in communication of mathematics. This study will enlighten the readers with information on the importance of advanced education specifically designed for the gifted. In development of advanced education programs, it is necessary to comprehend the minds of the mathematically gifted, and furthermore, this will help in defining an appropriate teaching method and curriculum for a better equipped educational system.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.339-356
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• 2010

It is important for children to develop statistical reasoning as they think through data. In particular, it is imperative to provide children instructional situations in which they are encouraged to consider variability in data because the ability to reason about variability is fundamental to the development of statistical reasoning. Many researchers argue that even highperforming mathematics students show low levels of statistical reasoning; interventions attending to pedagogical concerns about child ren's statistical reasoning are, thus, necessary. The purpose of this study was to investigate 15 gifted elementary students' various ways of understanding important statistical concepts, with particular attention given to 3 students' reasoning about data that emerged as they engaged in the process of generating and graphing data. Analysis revealed that in recognizing variability in a context involving data, mathematically gifted students did not show any difference from previous results with general students. The authors suggest that our current statistics education may not help elementary students understand variability in their development of statistical reasoning.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.163-177
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• 2007

Studies on mathematically gifted students have been conducted following Krutetskii. There still exists a necessity for a more detailed research on how these students' mathematical competence is actually displayed during the problem solving process. In this study, it was attempted to analyse the algebraic thinking process in the problem solving a peg puzzle in which 4 mathematically gifted students, who belong to the upper 0.01% group in their grade of elementary school in Korea. They solved and generalized the straight line peg puzzle. Mathematically gifted elementary school students had the tendency to find a general structure using generic examples rather than find inductive rules. They did not have difficulty in expressing their thoughts in letter expressions and in expressing their answers in written language; and though they could estimate general patterns while performing generalization of two factors, it was revealed that not all of them can solve the general formula of two factors. In addition, in the process of discovering a general pattern, it was confirmed that they prefer using diagrams to manipulating concrete objects or using tables. But as to whether or not they verify their generalization results using generalized concrete cases, individual difference was found. From this fact it was confirmed that repeated experiments, on the relationship between a child's generalization ability and his/her behavioral pattern that verifies his/her generalization result through application to a concrete case, are necessary.