Validating a measure of graph selection and graph reasoning for dynamic situations

Abstract

Using a mixed methods approach, we report results from the evaluation and validation stages of a fully online Measure of Graph Selection and Reasoning for Dynamic Situations, implemented with undergraduate college algebra students across three U.S universities. The measure contains six items; each includes a video animation of a dynamic situation (e.g., a fishbowl filling with water), a declaration of understanding, four Cartesian graphs from which to select, and a text box for explanation. In the evaluation stage, we demonstrate usability and content validity, drawing on individual cognitive interviews (n = 31 students). In the validation stage (n = 673 students), we use Rasch modeling to evidence reliability and internal structure, establishing a continuum of item difficulty and confirming the viability of a partial credit scoring approach for graph selection. Rasch results provide statistical support that the theorized graph reasoning framework (Iconic, Motion, Variation, Covariation) from Johnson et al. (2020) forms a hierarchical scale.