Mathematical modelling and covariational reasoning in college students: the case of modelling the cooling phenomenon with a function

Abstract

This research aims to explore the relationships between the mathematical modelling process from a realistic perspective and the levels of covariational reasoning through an instrumental case study with three college students while modelling the phenomenon of cooling. To achieve such an aim, we have relied on a theoretical framework of mathematical modelling that describes the typical ways of solving modelling tasks step by step, and a framework that describes covariational reasoning by levels of sophistication. We designed an instructional module for the participants in two parts: the first part was about analyzing patterns of change in functions and the second part was about solving a modelling task, where they were asked to find a function that models the behaviour of cooling water based on their own measuring instruments of time and temperature variables, stopwatch and thermometer. The results show that the cooling of the water modelling task, together with the measurement tools and the instructional module part about patterns of change, favoured covariational reasoning at the highest levels and that the participants’ covariational reasoning was necessary for the modelling task.