Rebuilding manipulatives through digital making in teacher education

The integration of digital making and computer-aided design (CAD) technologies, using 3D printing, in mathematics education has opened new opportunities for creating manipulatives that enhance conceptual understanding and problem-solving skills. Here, we explored how pre-service elementary teachers engage with the engineering design (ED) process while using Tinkercad and 3D printing to create customized manipulatives for mathematics education. A qualitative exploratory study was conducted with thirteen pre-service teachers enrolled in a master's program in Mathematics and Science Education at a Portuguese higher education institution. We employed multiple data sources, including classroom observations, participants' artifacts, written reports, and visual records, to capture the learning processes and challenges faced by the participants. Our findings indicated that participants developed a deeper understanding of content knowledge by analyzing mathematical properties and structures in the design of manipulatives, although some struggled with mathematical precision and curricular alignment. The iterative nature of ED reinforced technical knowledge, as participants engaged in CAD modeling and 3D printing. Despite initial difficulties, they refined their models through iterative redesign, recognizing the importance of spatial reasoning and precision. Pedagogical knowledge emerged as participants reflected on the educational use of manipulatives, proposing classroom applications and recognizing digital making's potential for active learning. However, some tasks lacked clear curricular connections, highlighting the need for further pedagogical scaffolding. Overall, the study underscores the potential of integrating ED, CAD environments, and 3D printing into teacher education to foster interdisciplinary STEAM learning and problem-solving skills.