Exploring creativity in pattern generalization: a study of future teachers in Brazil and Portugal

Abstract

Addressing the needs of talented students presents a significant challenge in today's society and consequently in schools, where creativity plays an important role. Creativity is a dynamic characteristic that students can develop, particularly in mathematics education, where solving problems involving the generalization of mathematical relations through the identification of figurative patterns is key. These patterns are the foundation of algebra, which is important across many disciplines and in some professional challenges. This study investigated how future teachers from Brazil and Portugal, during their initial teacher training, solve problems involving the generalization of mathematical patterns, with an emphasis on multiple solutions and creativity. The research adopted a qualitative and exploratory approach, characterizing the participants’ performance in solving tasks involving figurative patterns, identifying dimensions of creativity that emerge from their solutions, and analyzing distinctions between the two contexts. The findings highlight the importance of integrating visualization and the exploration of multiple representations in the training of future teachers. This approach contributes to the identification of some dimensions of creativity (fluency, flexibility, and originality) that emerged in different ways in the participants’ productions. It is evident that the focus on visualization in Portugal promoted a more robust understanding of regularities and algebraic generalizations, while in Brazil, the use of symbolic notation favors the early development of formal skills.