Networking Theories on Giftedness—What We Can Learn from Synthesizing Renzulli’s Domain General and Krutetskii’s Mathematics-Specific Theory

Abstract

Giftedness is an increasingly important research topic in educational sciences and mathematics education in particular. In this paper, we contribute to further theorizing mathematical giftedness through illustrating how networking processes can be conducted and illustrating their potential benefits. The paper focuses on two theories: Renzulli's domain-general theory on giftedness as an interplay of creativity, above-average ability, and task commitment; and Krutetskii's mathematics-specific theory on gifted students' abilities. In a "proof of concept", we illustrate how the abilities offered in Krutetskii's theory can be mapped to the three traits described by Renzulli. This is realized through a mapping process in which two raters independently mapped the abilities offered by Krutetskii to Renzulli's traits. The results of this mapping give first insights into (a) possible mappings of Krutetskii's abilities to Renzulli's traits and, thus, (b) a possible domain-specific specification of Renzulli's theory. This mapping hints at interesting potential phenomena: in Krutetskii's theory, above-average ability appears to be the trait that predominantly is addressed, whereas creativity and especially task-commitment seem less represented. Our mapping demonstrates what a mathematics-specific specification of Renzulli's theory can look like. Finally, we elaborate on the consequences of our findings, restrictions of our methodology, and on possible future research.

Interdisciplinary approach to the study of giftedness

“…• mismatch between the learners' perception of their potential for creativity, imagination and innovation, their appreciation of creative personality, with the perception of teachers -specialists in "gifted education"; related under-representation of gifted children in groups with improved learning conditions [37][38][39][40]; • differences between gifted underachievers and other gifted learners in terms of perfectionism and ability to overcome difficulties (41); • specification of giftedness against retaining the basic models [42];…”

Giftedness, Gender and Motivation – The Impact of Mathematics Self-Efficacy, Interest and Attitudes as Determinants to Identify Mathematical Giftedness

“…The approach of Fuchs and Käpnick shown in Figure 1 provides a representative example of concurrent modeling considering the consensus mentioned [19,[33][34][35][36]. The model describes the development of mg at primary-school age; it includes at its center a system of criteria that operationalizes mg with children in the third and fourth grade [30].…”

As contribuições de Vadim Andreevich Krutetskii para o campo das altas habilidades/superdotação em matemática

“…Consentaneamente, pesquisadores de diferentes países apontam como pioneira a teoria de superdotação matemática proposta por Vadim Andreevich Krutetskii 4 apresentada em meados do século XX (LEIKIN, 2011;PARISH, 2014;SCHINDLER;ROTT, 2017) e que esta permanece sendo, até os dias atuais, a mais completa tentativa de explicar esse construto dada a riqueza e amplitude do estudo realizado (LEIKIN, 2021).…”

“…Dessa forma, o contexto de desenvolvimento da pesquisa científica na antiga URSS seguiu caminhos distintos quando comparados com EUA e Europa de modo que o trabalho de V. A. Krutetskii possui nuances que merecem nossa atenção e podem nos ajudar a refletir sobre o futuro da pesquisa e educação de superdotados matematicamente habilidosos.No campo de pesquisa da educação de superdotados observa-se a distinção entre as chamadas teorias de domínio geral, que conceituam a superdotação entre domínios e as teorias de domínio específico, que conceituam a superdotação em um domínio particular. Dessa maneira, a teoria de V. A. Krutetskii é considerada de domínio específico (SCHINDLER;ROTT, 2017).Reconhecendo o crescente interesse de diferentes países, incluindo a URSS, sobre problemas enfrentados na Educação Matemática e a matemática como área essencial para o desenvolvimento de outras ciências,Krutetskii (1976) parte dos princípios de que o problema das habilidades é um problema de diferenças individuais e de que as habilidades não são inatas, mas, sim, desenvolvidas por meio das vivências e do trabalho, ou seja, depende de fatores sociais. Além disso, considerava equivocada a noção de que a atenção especial ao desenvolvimento de crianças superdotadas entra em conflito com o objetivo do desenvolvimento integral das habilidades das crianças em geral.…”