Conceptualization of function as a covariational relationship between two quantities through modeling tasks

Abstract

In this paper we use learning trajectories to study 11th grade students’ conceptualization of function as a covariational relationship between two quantities while they engaged in modeling tasks to support their experimentation and conceptualizations. Pairs of students used digital tools that offer integrated representations of functions while working on an instructional sequence of modeling tasks in their mathematics classrooms. The analysis shows students’ progressive conceptualization of functional relationships starting from quantitative and covariational relationships using learning trajectories. The findings indicate the potential of upper secondary students to conceptualize function as a covariational relationship involving the rate of change, as well as the role of the available tools and the role of models and their connections in students’ conceptualizations.