• East Asian mathematical journal
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• v.27 no.4
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• pp.485-506
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• 2011

In this study we study Krutetskii and Krutetskii's monograph 'The Psychology of Mathematical Abilities in Schoolchidren' which is published in Russia(in Russian) and USA(in English). We describe Krutetskii's biography briefly, which was not published in Korea. We analyze the methods, procedures, and results which are presented in the Krutetskii' work, and systemize these. Our study will give a overview of Krutetskii' viewpoint about mathematical abilities.

• The Mathematical Education
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• v.53 no.1
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• pp.75-92
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• 2014

In this paper, we summarize briefly some of the most salient features of Repkina & Zaika's theory of learning action formation levels. We concretize Repkina & Zaika's theory by comparing various points of view of Uoo, Polya, Krutetskii, and Davydov et al. In this study we are able to diagnose students' learning action formation levels in the process of mathematics problem solving. In addition we use interview method to collect various information about students' levels. As a result we suggest data related with each level of learning action formation, and characteristics of students who belong to each level of learning action formation.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.365-382
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• 2003

This study intends to develope and apply mathematical activities for gifted students. According to the Polya's research and Krutetskii's study, mathematical activities were developed and observed. The activities were aimed at discovery of Euler's theorem through exploration of soccer ball at first. After the repeated application and reflection, the aim and the main activities were changed to the exploration of soccer ball itself and about related mathematical facts. All the students actively participated in the activities, proposed questions need to be proved, disproved by counter examples during the fourth program. Also observation, conjectures, inductive arguments played a prominent role.

• The Mathematical Education
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• v.53 no.4
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• pp.479-492
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• 2014

According to Krutetskii, the education of mathematically gifted students must be focused on the improvement of creative mathematical ability and the mathematically gifted students need to experience the research process like mathematician. Independent study is highly encouraged as the self-directed activity of highest level in the learning process which is similar to research process used by experts. We conducted independent study as a viable differentiation technique for gifted middle school students in the 3rd grade, which participated in mentorship program for 10 months. Based on the data through the research process, interview with a study participant and his parents, and his blog, we analyzed mathematical behavior characteristics of a study participant. This behavior characteristics are not found in all mathematically gifted students. But through this case study, we understand mathematically gifted students better and furthermore obtain the message for the selection and education of the mathematically gifted students and for the effective method of running mentorship program particularly.

• 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.