Vol. 33 No. 1 (2025):
Articles

A Framework for Time and Covariational Reasoning

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  • Kevin Moore
DOI: https://doi.org/10.63301/tme.v33i1.3573

Published 2025-05-29

Keywords

  • Covariational Reasoning

Copyright (c) 2025 Kevin Moore

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Abstract

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.

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