How a beer teaches functional modelling


Ismael Cabero, Universitat Jaume I, Castelló, Spain


We present a Study and Research Path (SRP) design, based on the Paradigm of Questioning the World (PQW), which seeks to relate functional modelling to motivating extra-mathematical contexts. By investigating the time it takes for a beer to warm up in summer, a functional modelling is presented with a required function notion that surpasses those that are usually worked on in high school with a single variable. This approach breaks away from the usual way of dealing with Newton's cooling law in teaching, which focuses on finding particular solutions to problems with concrete initial data. We believe that our approach could enhance the students' knowledge about Newton's cooling law, and of functional modelling in general, by explore how several variables may appear in the model, when ‘parameters’ are considered themselves as functions.

Self-intro of the speaker:

I am a university lecturer in mathematics didactics at the Jaume I University in Castelló (Spain), but I have been, for 20 years, a secondary school mathematics teacher.  My research focuses on the didactics of mathematics, and in archetype analysis (an unsupervised statistical analysis), which was the subject of my PhD.