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Physics instructors and education researchers use research-based assessments (RBAs) to evaluate students' preparation for physics courses. This preparation can cover a wide range of constructs including mathematics and physics content. Using separate mathematics and physics RBAs consumes course time. We are developing a new RBA for introductory mechanics as an online test using both computerized adaptive testing and cognitive diagnostic models. This design allows the adaptive RBA to assess mathematics and physics content knowledge within a single assessment. In this article, we used an evidence-centered design framework to inform the extent to which our models of skills students develop in physics courses fit the data from three mathematics RBAs. Our dataset came from the LASSO platform and includes 3,491 responses from the Calculus Concept Assessment, Calculus Concept Inventory, and Pre-calculus Concept Assessment. Our model included five skills: apply vectors, conceptual relationships, algebra, visualizations, and calculus. The "deterministic inputs, noisy 'and' gate'' (DINA) analyses demonstrated a good fit for the five skills. The classification accuracies for the skills were satisfactory. Including items from the three mathematics RBAs in the item bank for the adaptive RBA will provide a flexible assessment of these skills across mathematics and physics content areas that can adapt to instructors' needs. 

In physics education research, instructors and researchers often use research-based assessments (RBAs) to assess students’ skills and knowledge. In this paper, we support the development of a mechanics cognitive diagnostic to test and implement effective and equitable pedagogies for physics instruction. Adaptive assessments using cognitive diagnostic models provide significant advantages over fixed-length RBAs commonly used in physics education research. As part of a broader project to develop a cognitive diagnostic assessment for introductory mechanics within an evidence-centered design framework, we identified and tested the student models of four skills that cross content areas in introductory physics: apply vectors, conceptual relationships, algebra, and visualizations. We developed the student models in three steps. First, we based the model on learning objectives from instructors. Second, we coded the items on RBAs using the student models. Finally, we then tested and refined this coding using a common cognitive diagnostic model, the deterministic inputs, noisy “and” gate model. The data included 19 889 students who completed either the Force Concept Inventory, Force and Motion Conceptual Evaluation, or Energy and Momentum Conceptual Survey on the LASSO platform. The results indicated a good to adequate fit for the student models with high accuracies for classifying students with many of the skills. The items from these three RBAs do not cover all of the skills in enough detail, however, they will form a useful initial item bank for the development of the mechanics cognitive diagnostic. 

We analyzed the essays that were written on various topics in an introductory physics course using two unsupervised machine learning algorithms. One of them was Latent Dirichlet Allocation (LDA). This algorithm is used for extracting abstract topics from a collection of text documents. The other algorithm was Non-negative Matrix Factorization (NMF). It is used for similar purposes but also in other domains such as image recognition. We applied these two algorithms to the dataset that consisted of N=683 student essays. Although there were some built-in, important differences between LDA and NMF, they both found similar topics in our data by large. This offers instructors a promising and productive way of accessing useful information about their students' written work, especially in large-enrollment classes.