Laurence Holt

Jocelyn Beauchesne, Christine Maroti, Jeshua Bratman et al.

Recent research demonstrated that students exhibit consistent learning rates across diverse educational contexts. We test these findings using a dataset of 1.8 million (366k post-filtering) student interactions from the digital platform Campus AI providing further evidence to the observation of regularity in learning rate among students. Unlike prior work requiring manual cognitive modeling, Campus AI automatically generates Knowledge Components (KCs) and corresponding exercises, both of which are validated by human experts. This one-to-many mapping facilitates the application of Additive Factors Models to measure learning parameters without complex cognitive modeling. Using mixed-effects logistic regression, we confirmed the core finding of prior work: students displayed substantial variation in initial knowledge ($\text{IQR} = [2.78, 12.18]$ practice opportunities to reach 80% mastery) but remarkably consistent learning rates ($\text{IQR} = [7.01, 8.25]$ opportunities). Furthermore, students using this fully automated system achieved 80% mastery in a median of 7.22 practice opportunities, comparable to the 6.54 reported for expert-designed curricula. These results suggest that automated, science-grounded content generation can support effective personalized learning at scale. Data and code are publicly available. https://github.com/Campus-edu-AI/learning-rate

Owen Henkel, Bill Roberts, Doug Jaffe et al.

Recent advances in multimodal large language models (MLLMs) raise the question of their potential for grading, analyzing, and offering feedback on handwritten student classwork. This capability would be particularly beneficial in elementary and middle-school mathematics education, where most work remains handwritten, because seeing students' full working of a problem provides valuable insights into their learning processes, but is extremely time-consuming to grade. We present two experiments investigating MLLM performance on handwritten student mathematics classwork. Experiment A examines 288 handwritten responses from Ghanaian middle school students solving arithmetic problems with objective answers. In this context, models achieved near-human accuracy (95%, k = 0.90) but exhibited occasional errors that human educators would be unlikely to make. Experiment B evaluates 150 mathematical illustrations from American elementary students, where the drawings are the answer to the question. These tasks lack single objective answers and require sophisticated visual interpretation as well as pedagogical judgment in order to analyze and evaluate them. We attempted to separate MLLMs' visual capabilities from their pedagogical abilities by first asking them to grade the student illustrations directly, and then by augmenting the image with a detailed human description of the illustration. We found that when the models had to analyze the student illustrations directly, they struggled, achieving only k = 0.20 with ground truth scores, but when given human descriptions, their agreement levels improved dramatically to k = 0.47, which was in line with human-to-human agreement levels. This gap suggests MLLMs can "see" and interpret arithmetic work relatively well, but still struggle to "see" student mathematical illustrations.