Mathematics in Action: On the Who, Where and How of the Constructions and Use of Mathematical Models in Society

Mathematics in action refers to its prescriptive function in society, whereby the more or less explicit use of mathematical models assists in decisions and actions in extra-mathematical contexts. The Danish KOM (Competencies and the Learning of Mathematics) framework frames questions on who, where, and how these models are constructed and used as an overview and judgement about mathematics. In this chapter, we actualise this critical stance in the digital era by networking the notion of internal and external reflections regarding mathematical modelling and the instrumentation–instrumentalisation duality from the theory of instrumental genesis. We unfold two experiences from our teaching in higher education as illustrative cases. These are group projects on the statistical testing of hydroxychloroquine as a COVID-19 treatment and the modelling of influenza epidemics to design a vaccination programme. Our main argument is twofold. On the one hand, these theoretical constructs may address the same unit of analysis but, consistent with the literature, account for observable aspects at a different granularity. On the other hand, instrumental genesis can provoke critical reflections about the use of mathematical models in society through the pragmatic use of digital instruments.