Calculus Cognitive Diagnostic: Mathematics skills tested in first semester calculus courses

Physics instructors and education researchers use research-based assessments (RBAs) to evaluate students' preparation for physics courses.This preparation and learning can cover a range of topics, including algebra, pre-calculus and calculus.To meet the need for high quality, adaptable assessments, we are developing a cognitive diagnostic for calculus as an online test using Evidence Centered Design.Using cognitive diagnostic models and computerized adaptive testing allows the users to customize which skills are assessed and when they are assessed.In this article, we investigate the extent to which our model of the students calculus skills fit the data from three mathematics RBAs.Our model included five calculus skills students often use in physics courses: pre-calculus knowledge, limits, derivatives, applications of derivatives, and integration.The data came from the LASSO platform and includes 4,132 responses from the Calculus Concept Assessment, Calculus Concept Inventory, and Pre-calculus Concept Assessment.The "Deterministic Input, Noisy 'And' gate" (DINA) analyses demonstrated a good fit for the five skills to the data.These results provide validity for our model of mathematics skills students develop.Including items from these RBAs will provide a foundation for developing a flexible assessment of a range of mathematics skills that can adapt to instructors' and researchers' needs.