Mathematical modelling and covariational reasoning: a multiple case study

This research aims to investigate the relationships between the mathematical modelling process and the levels of covariational reasoning through a multiple instrumental case study with six college students solving a task in the context of science. We designed a modelling task based on a problem faced by Newton: obtaining higher temperature values than a thermometer could register; and analysed the participants' modelling processes and covariational reasoning as they solved the task. The results show that the modelling task promoted covariational reasoning. The results also show that participants used covariational reasoning to solve the task, and the participants were unaware of nonlinear covariational reasoning which prevented them from making mathematical models closer to reality. Furthermore, participants required specific levels of covariational reasoning at specific steps in the mathematical modelling process, and as they advanced in the mathematical modelling process they exhibited more sophisticated levels of covariational reasoning.