Education for the Future: Crafting 3D Geometric Models and Building Mathematics Knowledge with 3D Printing
Abstract
This paper addresses the creation of 3D geometric models using 3D printers and introduces a newly designed and 3D-printed construction set of polygons for educational purposes.
The process of creating these geometric models encompasses steps such as design, 3D computer modeling with Constructive Solid Geometry (CSG), 3D computer modeling of parametric surfaces using principles of differential geometry, 3D scanning of real objects, and the process of manufacturing itself. Students can be involved in the entire process of crafting models for 3D printers, and these resulting printed models can be utilized in geometry education at all levels (university and secondary school in our scenario) as instructional aids. We explore the potential methods to design geometric objects using 3D computer modeling software; this covers both commercial options and open-source software like Tinkercad, a free web application for 3D design, electronics, and coding. We present the fabrication of a new construction set of polygons which consists of different shapes of regular and irregular polygons and it is intended for use in mathematics teaching to study polygon properties and create diverse types of tessellations at the secondary school level. The effects of using these instructional aids were tested with several groups of students.
All steps of the model design for 3D printing, in combination with the physical 3D printed models, shed new light on mathematics education and more broadly, to education as a whole. This process engages students in solving real-world problems and enhances their understanding of geometry, while familiarizing them with 3D computer modeling and 3D printing technologies. Both 3D virtual models and 3D printed models can act as manipulative instructional aids.