Tangible Mathematics: 3D-Printing Manipulatives as a Tool in Mathematics Teacher Education

While manipulatives, physical learning materials reifying mathematical concepts, have been discussed for a long time, 3D-printing revitalized the discussion and allows teachers to have new manipulatives at their disposal, as well as to design their own using a fraction of the effort. How this can be achieved, i.e., how teachers need to be prepared to utilize 3D-printing, is being tested and implemented in current research. In this study, we report findings and the three-year-long design evolution of an elective seminar where student teachers, beginning in the third semester, are trained to use OpenSCAD programming to 3D-model and then print their own manipulatives, guided by scaffolding elements such as cookie stamps in the second session or a design profile. Each student conceives, models, prints, and didactically embeds their manipulatives over three phases during the semester: the input phase, resembling a “normal” seminar; the hands-on phase, akin to a makerspace; and a presentation phase, tying the project work together. This concept combines technical elements, mathematics didactics, constructionism, and modern teaching technologies innovatively, inviting other educators to adapt it based on the provided structure.