Second-order covariation: it is all about standpoints

Second-order covariation is a quite recent theoretical construct in the field of Mathematics Education: it differs from the already existing construct of covariation in placing greater emphasis on the role of parameters, with respect to the other variables, as characteristic of a certain family of functions and as relevant in modelling classes of real phenomena. In this contribution, we address the novelty and importance of this type of reasoning based on a teaching experiment concerning modelling of a thermodynamic situation. Starting from the analysis of three episodes, we highlight some features of this construct, and the emerging interpretation as a change in standpoint that results in different graphical representations suitable to interpret globally the specific mathematical situation.