On the competence of programming animated linear curvature models to print

This study explores how students conceptualize mathematical ideas related to curvature and rate of change, and develop mathematical competence through 3D design, programming, and physical modeling. Curvature is approached as a rich conceptual field for developing students’ mathematical thinking through an intrinsically defined approach. Drawing on the theoretical frameworks of constructionism, reification and the KOM framework, and focusing on students’ engagement with the MaLT2 programming environment, we investigate how students build and use mathematically meaningful ideas through iterative processes of ‘imaging, seeing and touching’. The findings reveal educational opportunities arising from the interplay between digital and physical artifacts, especially when programming serves as a medium for design and mathematical exploration.