Designing to transform: High school students’ reasoning with geometric transformations in an authentic real-world project
Description
As educators pursue more authentic and relevant approaches to mathematics instruction, it is essential to understand how students reason mathematically in innovative learning environments. This study examines students’ reasoning with geometric transformations during a summer camp, in which they used dynamic geometry environments (DGEs) to design transforming, multi-functional products. Student artifacts were analyzed using two frameworks on reasoning in transformational geometry. taxonomy of transformational reasoning. Findings show that students’ reasoning was closely tied to their product designs, with many using features of their prototypes to describe and justify geometric transformations. The open-ended, real-world challenge prompted students to engage with relevant transformations while navigating 2D and 3D representations in the DGE, fostering authentic mathematical reasoning across dimensions. These results suggest that positioning students as designers in meaningful, technology-supported contexts can deepen geometric reasoning and support conceptually rich engagement with transformations.
Suggested citation:
Borden, M. L., Belcher, M., Krupa, E. E., & Anderson, R. K. (2025). Designing to transform: High school students’ reasoning with geometric transformations in an authentic real-world project. The Journal of Educational Research, 1–14. https://doi.org/10.1080/00220671.2025.2557296