Using an artistic approach to the teaching of non-Euclidean geometry in a professional development course for mathematics teachers

Elliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning [1]. This is true for any subject, including mathematics. Geometry related topics make a perfect setting for a deeper contribution of art to education and allow for a complete symbiosis between the teaching of mathematics and an artistic education. One such topic is the study of non-Euclidean geometry which is now briefly addressed in the middle school mathematics curriculum in Portugal [2]. We believe that the learning and teaching of non-Euclidean geometry can be facilitated by taking the role of an artist and creating works of art, eventually inspired by renowned artists such as M.C. Escher. In this paper, we present some results of a professional development course for mathematics teachers where the participants studied basic non-Euclidean geometry concepts and created ceramic pieces using the Poincaré disk. The course took place in a Portuguese university, from January to March 2018, and involved 20 teachers of grades 1 to 12. The authors have developed a qualitative case study to evaluate how an artistic approach to the teaching of non-Euclidean geometry is perceived, by the mathematics teachers, as a contribution to the learning process. Overall, the activities developed have proved to be successful examples of interdisciplinary methodologies that bring into the teaching of mathematics usual procedures in the teaching of the arts. Moreover, the artistic approach followed during the course helped the teachers develop their geometric competences concerning non-Euclidean geometry in a more solid appropriation and application of the geometric concepts involved.