Covariational reasoning has emerged as a productive construct to characterize students’ mathematical development. Researchers have illustrated its importance for major middle, secondary, and undergraduate mathematical concepts including rate of change, accumulation, and modeling. Within this line of work, several researchers have indicated differences between experiential and conceptual time with respect to the covariational relationships students construct. I draw on this body of literature and return to Piaget’s perspective of time to provide a framework for the role of time in students’ (co)variational reasoning. The framework also clarifies the nature of the multiplicative objects underlying students’ (co)variational relationships. To illustrate the framework and capture its emergence from second-order models of students’ mathematics, I also describe the framework as it relates to students’ engagement in a task.
Kevin Moore (Thu,) studied this question.