Engaging in covariational reasoning when modelling a real phenomenon: the case of the psychrometric chart

The mathematical modelling of a real-life phenomenon is an elaborated activity, and it often requires complex forms of covariational reasoning, such as second-order covariation. This study aims to characterize how students use several forms of covariational reasoning when modelling a real-life phenomenon. To achieve this research goal, it is proposed the analysis of a teaching experiment conducted in an 11th-grade classroom and focused on the mathematical modelling of the relationship between three quantities, temperature, absolute humidity, and relative humidity, which is mathematically represented in the psychrometric chart. The qualitative analysis was focused on covariational reasoning and the students’ processes of mathematical modelling of the real-life phenomenon under investigation. Findings from five representative episodes showed an interlacing of several forms of covariational reasoning, the emergence of qualitative, quantitative, and global characterizations of covariational reasoning, and three different roles of covariation throughout the various steps of the modelling activities. From an educational point of view, the modelling activities described here offer practical insights for the design of activities aimed at promoting the modelling of real-life phenomena through a covariational approach.