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

Abstract

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 supported participants in revising some initial misconceptions, strengthening aspects of their understanding of symmetry transformations, and showing evidence of progression from predominantly intuitive visual approaches towards more analytical and justified reasoning. The tasks also promoted creativity and motivation, 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 visual art-based activities into mathematics teacher education can promote visual reasoning, deepen