Developing spatial mathematical skills through 3D tools: augmented reality, virtual environments and 3D printing

In this paper, we show how to improve the mathematics teaching-learning process to enhance students' spatial visualization and orientation skills with the use of 3D tools; specifically, with augmented reality, virtual environments and 3D printing. Two of the tools presented in this work were especially developed for multivariable calculus courses. The inclusion of these materials in pedagogical activities integrates the senses of touch and sight to the learning process, favoring the understanding of important mathematical concepts related to three-dimensional space. This allowed instructors to present to students a natural way of modeling real world phenomena with proper mathematical language, thus achieving a significant increase in mathematics learning. Tests with control and experimental groups were conducted over four years, and students' final grades, failure rates and visualization-skills development were analyzed. Students and professors from several countries were interviewed and surveyed to assess perception and experience in the use of these tools. An analysis of variance with a sample of N=993 was performed, finding that the experimental group grades were seven points above those of the control group (on a 0-100 scale) and the failure rate dropped 14%. Moreover, from the spatial mathematical skills test with a sample of N=442 students, the experimental group obtained 15 points more than the control group, and the percentage of students achieving the minimum spatial skills level required to pass the course increased 36%. Our results reveal a positive impact in the use of these tools to develop spatial mathematical skills.