Factorial number system as an example of substantial learning environment for pre- and in-service teachers of mathematics

This article draws on the work of Wittmann and his followers who conceived and developed the notion of substantial learning environment (SLE). The paper contains a proposal of a teaching unit based on the definition of Factorial Number System (FNS). First, we illustrate the process of conversion from FNS to the Decimal Number System (DNS) and back. Secondly, we provide theorems on the divisibility rules for several numbers in FNS. The main aim of this paper is to present FNS as an example of a~mathematically rich environment wherein pre-service teachers of mathematics may be actively engaged in the process of discovering subjectively new mathematics.