The construction of artefacts with friezes and rosettes -connecting mathematics with visual arts

Resumo

Background: Geometry plays a central role in mathematics education by fostering visual reasoning and spatial awareness. Within geometry, symmetry provides meaningful opportunities to connect mathematics with artistic expression and cultural heritage. However, research has shown that students and pre-service teachers often experience difficulties in understanding and applying symmetry concepts beyond procedural approaches. Objectives: This study aims to understand how pre-service elementary school teachers solve symmetry tasks, including the construction and decoration of artefacts, based on frieze and rosette patterns, and how these experiences contribute to the development of visual reasoning. Design: The study followed a qualitative, interpretative, and exploratory research design, focused on a didactical intervention, combining progressively challenging tasks involving paper-and-pencil activities, manipulatives, digital tools, and the design of artistic artefacts based on friezes and rosettes. Setting and Participants: The participants were 26 pre-service elementary school teachers enrolled in a master's programme in Primary Education at a public higher education institution in Portugal, attending a Mathematics Education course, who voluntarily participated in the study. Data collection and analysis: Data were collected through participant observation, written documents, artefacts produced by the participants, and photographic records. The data were analysed inductively using content analysis. Results: The findings indicate that engaging with multiple symmetry tasks and constructing artistic artefacts enabled participants to overcome initial misconceptions, strengthen their understanding of symmetry transformations, and develop visual reasoning. The tasks also promoted creativity, motivation, and appreciation of the aesthetic and cultural dimensions of mathematics, while encouraging participants to establish meaningful connections between mathematical concepts and artistic production. These results extend previous research by demonstrating how aesthetic-constructionist learning environments can simultaneously support mathematical understanding and artistic expression in teacher education. Conclusions: Integrating art-based activities into mathematics teacher education can promote visual thinking, deepen conceptual understanding of symmetry, and encourage future teachers to view mathematics as a creative and cultural human endeavour. Engaging pre-service teachers in designing mathematically informed artefacts provides pedagogical experiences that can enrich future geometry teaching through meaningful connections between mathematics and the visual arts.