## PERC 2021 Abstract Detail Page

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Abstract Title: | Assessing Covariational Reasoning in College Calculus and Physics Courses: The Use of Graphs |
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Abstract: | Both calculus and physics were invented to describe how quantities change together. For example, calculus can help us specify precisely the difference between the rate of change of a quadratic function and the rate of change of an exponential function. College instructors use many methods to help students represent relationships between quantities and to help students make sense of new ideas such as rate of change functions (derivatives). Graphs are often used in calculus to convey new concepts and covariational relationships to students. For example, teachers often use graphical representations to convey why derivatives find the rate of change of one quantity with respect to another. Additionally, graphs are often part of assessments in calculus and physics class. For example, given a graph that shows the amount of a quantity at any moment in time, can the students produce a graph that shows the rate of change of that quantity at any moment in time. In both of these teaching situations-using students' graphs to assess their understanding and using teachers graphs to convey new concepts-there is often an implicit assumption that students understand graphs as representing and emergent trace of the covariation of two quantities (Moore et. al., 2017). If students do not understand a graph as representing covariation of two quantities, and the teacher primarily explains the meaning of a derivative graphically, the students are not likely to learn the meaning for derivative the teacher intended to convey. Our research team has also found that calculus students are often able to describe covariational relationships using words and gestures that they are not able to correctly represent graphically on assessments of covariational reasoning (Tyburski et. al., 2021; Drimalla et. al., 2020). This talk will discuss the importance of helping calculus and physics students' understand graphs as covariational relationships between two quantities. |

Abstract Type: | Symposium Talk |

Parallel Session: | Considering covariational reasoning in math and physics |

## Author/Organizer Information | |

Primary Contact: |
Cameron Byerley University of Georgia |