The art of the Wunderlich cube and the development of spatial abilities

Abstract This paper advocates for a future where the teaching of math and art are harmoniously intertwined as they were in the days of da Vinci. In this future, code provides the “brush” that enables the expression of artistic ideas and mathematical structures in digital and digitally-fabricated mediums. This educational idea is motivated by (1) literature supporting the position that visual thinking and spatial reasoning significantly impact STEAM disciplines, and (2) Piaget’s theory of cognitive development in which children, in the concrete operational stage, solve problems relating to physical objects (i.e., they learn-by-making). A project is then described involving the creation of a 3D artifact we call a Wunderlich cube — a mathematical artifact that embodies numerous spatial reasoning puzzles. An understanding of the properties of the Wunderlich cube is developed through manual construction using LEGO®, mathematical analysis, computational thinking, coding, and 3D printing.