Abstract
This study was conducted from a perspective that adopts a broad vision of mathematical talent, defined as the potential that a subject manifests when confronting certain types of tasks, in a successful way, that generate creative mathematical activity. To analyse this, our study proposes a Praxeological Model of Mathematical Talent based on the Anthropological Theory of Didactics and the notion of mathematical creativity, which defines four technological functions: (1) producing new techniques; (2) optimizing those techniques (3); considering tasks from diverse angles; and (4) adapting techniques. Using this model, this study analyses the creative mathematical activity of students aged 10–12 years displayed as they sought to solve a series of infinite succession tasks proposed to encourage the construction of generalization processes. The setting is a Mathematics Club (a talent-promoting institution). The evaluation of results shows that the Praxeological Model of Mathematical Talent allows the emergence and analysis of mathematical creativity and, therefore, encourages the development of mathematical talent.
Highlights
For several decades, diverse models and definitions of talent have been proposed in the literature.Singer, Sheffield, Freiman and Brandl point out that most of those models and definitions describe talent as the potential to successfully perform a certain activity, and indicate that while a broad range of models of mathematical talent exist, they are still limited [1]
The results presented reflect our analysis of the mathematical activity of three pairs of students
This study chose situations 2, ”Origami Cubes”, and 4, ”Intersections and Regions”, which were developed in sessions 2 and 4–5, respectively, because they allowed the authors to analyse which were developed in sessions 2 and 4-5, respectively, because they allowed the authors to analyse the evolution of creative mathematical activity using the Praxeological Model of Mathematical Talent (PMMT) model
Summary
Sheffield, Freiman and Brandl point out that most of those models and definitions describe talent as the potential to successfully perform a certain activity, and indicate that while a broad range of models of mathematical talent exist, they are still limited [1]. Krutetskii specified that: Mathematical giftedness is the name we shall give to a unique aggregate of mathematical abilities that opens up the possibility of successful performance in mathematical activity (or with school children in mind, the possibility of a creative mastery of the subject). Krutetskii specified that: Mathematical giftedness is the name we shall give to a unique aggregate of mathematical abilities that opens up the possibility of successful performance in mathematical activity (or with school children in mind, the possibility of a creative mastery of the subject). [9] (p. 77)
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