Mathematics in play: exploring curriculum integration and professional growth through playing, modelling and printing games

Abstract Integrating playful and maker-oriented approaches into mathematics teacher education remains challenging, particularly in relation to curricular alignment and teacher agency. This design-based research examines a workshop centred on the Hidden Blocks game, structured in three stages: play, digital modelling, and fabrication through 3D printing. The intervention was designed to support teachers’ mathematical reasoning, their articulation of links between the activity and the curriculum, and their professional agency as designers of resources and learning experiences. Across four cycles in Austria, Brazil, and Uruguay involving mathematics teachers, we analysed interviews, workshop recordings, facilitators’ notes, and lesson plans. Through iterative refinement, we developed a set of design principles organised into three interrelated dimensions: (a) mathematics, focusing on eliciting and formalising mathematical reasoning through play, modelling, and fabrication; (b) curriculum, focusing on explicit connections between mathematical ideas and curricular aims; and (c) professional agency, focusing on teachers’ ownership, authorship, and adaptation of resources for classroom use. These principles show how a technology-enhanced intervention that combines gameplay, modelling, and fabrication can support mathematisation, curriculum articulation, and teacher agency in mathematics teacher education.