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

Isabel Vale; Ana Barbosa; Jorge Gualandi; Isabel Vale; Ana Barbosa; Jorge Gualandi

doi:10.3934/steme.2025034

STEM Education

2025, Volume 5, Issue 5: 732-756. doi: 10.3934/steme.2025034

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

1.
Instituto Politécnico de Viana do Castelo, Rua Escola Industrial e Comercial Nun'Álvares, 34, 4900-347, Viana do Castelo, Portugal; isabel.vale@ese.ipvc.pt, anabarbosa@ese.ipvc.pt
2.
Instituto Federal do Espírito Santo, campus Cachoeiro de Itapemirim, Espírito Santo, Brasil; jhgualandi@ifes.edu.br
3.
CIEC, Centro de Investigação em Estudos da Criança, Universidade do Minho, Braga, Portugal
4.
inED, Centro de Investigação e Inovação em Educação, Instituto Politécnico de Viana do Castelo, Viana do Castelo, Portugal

Academic Editor: Maria Tatto

Received: 28 January 2025 Revised: 18 June 2025 Accepted: 26 June 2025 Published: 10 July 2025

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.
- pre-service mathematics teachers,
- creativity,
- figurative patterns,
- representations,
- generalization,
- algebraic thinking
Citation: Isabel Vale, Ana Barbosa, Jorge Gualandi. Exploring creativity in pattern generalization: A study of future teachers in Brazil and Portugal[J]. STEM Education, 2025, 5(5): 732-756. doi: 10.3934/steme.2025034

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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.

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Author's biography Dr. Isabel Vale is a professor of Mathematics Education at the School of Education of Instituto Politécnico de Viana do Castelo in Portugal. She specializes in didactics of mathematics. She is a researcher at the Research Centre on Child Studies (CIEC-UM). Among other topics, her research interests focus on didactics of mathematics, in particular, problem solving—patterns, creativity, visualization, connections in mathematics education, and teacher training. More recently, she is interested in the design of tasks and teaching strategies in diverse contexts that are more favorable to active learning of mathematics, such as STEAM education and learning outside the classroom; Dr. Ana Barbosa is a professor of Mathematics Education at the School of Education of Instituto Politécnico de Viana do Castelo in Portugal. She specializes in Child Studies, in the area of Elementary Mathematics. She is a researcher at the Centre for Research & Innovation in Education (inED). Among other topics, her research interests focus on didactics of mathematics, problem solving, visualization, algebraic thinking, active learning, outdoor mathematics education, and STEAM education; Dr. Jorge Gualandi is a professor of Mathematics at the Federal Institute of Espírito Santo in Brazil. He is a specialist in Mathematical Education, with a focus on Teacher Training. He is the leader of the Mathematics Teaching Research Group of Espírito Santo (GPEMES). Among other topics, his research interests focus on mathematics didactics, algebraic thinking, and teacher training

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