abstract
- Proportional reasoning is a crosscutting concept identified as necessary for student success in upper-level mathematics as well as science, technology, and engineering. Research on middle-grade mathematics learning shows that students tend to develop stronger understandings of mathematical concepts when they learn through constructionist real-world projects that are relevant and meaningful to them. In this qualitative exploratory research study, we developed and implemented a Challenge-Based Learning through Making project for a middle school engineering class to investigate how students demonstrate their understanding of proportional reasoning through designing and making physical and digital artifacts, mentored by industry experts, and within the context of a school makerspace. Our findings showed that students accurately represented their understanding of proportionality through their digital artifacts more than any other modality available, contrasting previous findings in the relevant literature. Findings regarding the integration of professional technology for digital 3D modeling, mentorship of industry experts, and the prevalence of mathematical estimation in digital modeling provide avenues for further research vis-a-vis the role of expert mentorship in middle school STEM design challenges and mathematical estimation in spatial reasoning for design. Implications for the practice and the field of STEM learning are discussed. © 2025 by the authors.