Five Design Steps to Scaffold Covariational Reasoning in STEM Graph Interpretation

Interpreting graphs is a critical skill for STEM students; however, many find this task challenging. This article introduces five design steps to help STEM instructors structure tasks that support students’ graphical interpretation, emphasizing quantitative and covariational reasoning. Covariational reasoning—understanding how quantities change in relation to one another—can be cognitively demanding, particularly in scientific contexts where students must also comprehend the underlying phenomena. Nevertheless, this challenge can promote a deeper disciplinary understanding, as we illustrate here in a task involving the graphing of potential energy in two springs in physics. The design steps follow a sequence: (1) Identifying graph quantities, (2) Recognizing how quantities change, (3) Coordinating changes among quantities, (4) Exploring the average rate of change, and (5) Exploring the instantaneous rate of change. These steps are flexible and applicable across various disciplines, as demonstrated by examples in physics (springs), chemistry (titration), and biology (population growth). By implementing these steps, instructors can assist students in developing quantitative and covariational reasoning skills that transcend specific contexts, allowing them to interpret graphs in complex or unfamiliar situations. These reasoning skills help students understand scientific phenomena by allowing them to link observed patterns and relationships to the mathematical models that depict those phenomena.