Using machine learning to measure evidence of students' sensemaking in physics courses

In the education system, problem-solving correctness is often inappropriately conflated with student learning. Advances in both Physics Education Research (PER) and Machine Learning (ML) provide the initial tools to develop a more meaningful and efficient measurement scheme for whether physics students are engaging in sensemaking: a learning process of figuring out the how and why for a particular phenomena. In this work, we contribute such a measurement scheme, which quantifies the evidence of students' physical sensemaking given their written explanations for their solutions to physics problems. We outline how the proposed human annotation scheme can be automated into a deployable ML model using language encoders and shared probabilistic classifiers. The procedure is scalable for a large number of problems and students. We implement three unique language encoders with logistic regression, and provide a deployability analysis on 385 real student explanations from the 2023 Introduction to Physics course at Tufts University. Furthermore, we compute sensemaking scores for all students, and analyze these measurements alongside their corresponding problem-solving accuracies. We find no linear relationship between these two variables, supporting the hypothesis that one is not a reliable proxy for the other. We discuss how sensemaking scores can be used alongside problem-solving accuracies to provide a more nuanced snapshot of student performance in physics class.

Decision-aware training of spatiotemporal forecasting models

Optimal allocation of scarce resources is a common problem for decision makers faced with choosing a limited number of locations for intervention. Spatiotemporal prediction models could make such decisions data-driven. A recent performance metric called fraction of best possible reach (BPR) measures the impact of using a model's recommended size K subset of sites compared to the best possible top-K in hindsight. We tackle two open problems related to BPR. First, we explore how to rank all sites numerically given a probabilistic model that predicts event counts jointly across sites. Ranking via the per-site mean is suboptimal for BPR. Instead, we offer a better ranking for BPR backed by decision theory. Second, we explore how to train a probabilistic model's parameters to maximize BPR. Discrete selection of K sites implies all-zero parameter gradients which prevent standard gradient training. We overcome this barrier via advances in perturbed optimizers. We further suggest a training objective that combines likelihood with a decision-aware BPR constraint to deliver high-quality top-K rankings as well as good forecasts for all sites. We demonstrate our approach on two where-to-intervene applications: mitigating opioid-related fatal overdoses for public health and monitoring endangered wildlife.