In this article, we discuss the well-known Waldorf modular arithmetic circles, which have a pedagogical purpose in the teaching of mathematics, particularly in learning multiplication tables. However, the aim of this work is to rigorously present the mathematics behind this pedagogical concept by using modular arithmetic and explaining how the intuition involved in generating these circles can be formalized through equivalence. In doing so, we demonstrate which are the only groups of figures that can be formed within this framework. Modular arithmetic and graph theory are used to define Waldorf circles and their groups of shapes by establishing an equivalence relation on these figures. This allows us to determine the quotient set of this relation and, consequently, to uniquely characterize the different figures that can be generated according to their equivalences.
Keywords: Modular arithmetic, Waldorf pedagogy