Assessing the integration of mathematical and physical conceptual reasoning in introductory physics problem solving

The creation of new assessments has been a cornerstone of Physics Education Research (PER). These research-based assessments operationalize the learning goals of physics education and continue to drive instructional innovations that improve student learning and academic success. In this talk, I will discuss a past and current direction in physics problem-solving assessment: coherence between physical concepts and mathematics. I will present three novel assessments that measure students’ skills at detecting errors, finding conceptual shortcuts, and choosing to use calculations on qualitative questions. These skills each indicate the integration of mathematical and physical reasoning. I will share the results of a quasi-experimental teaching comparison where these assessments were instrumental in detecting the learning benefits of a course focused on developing mathematical sensemaking. Finally, I will discuss potential connections between conceptual/mathematical coherence and physics students’ long-term success and retention in STEM.