Mathematical thinking is a fundamental aspect of human cognition. Cognitive scientists have investigated the mechanisms that underlie our ability to thinking geometrically and numerically, to take two prominent examples, and developmental scientists have documented the trajectories of these abilities over the lifespan. Prior research has shown that computer vision (CV) models trained on the unrelated task of image classification nevertheless learn latent representations of geometric and numerical concepts similar to those of adults. Building on this demonstrated cognitive alignment, the current study investigates whether CV models also show developmental alignment: whether their performance improvements across training to match the developmental progressions observed in children. In a detailed case study of the ResNet-50 model, we show that this is the case. For the case of geometry and topology, we find developmental alignment for some classes of concepts (Euclidean Geometry, Geometrical Figures, Metric Properties, Topology) but not others (Chiral Figures, Geometric Transformations, Symmetrical Figures). For the case of number, we find developmental alignment in the emergence of a human-like ``mental number line'' representation with experience. These findings show the promise of computer vision models for understanding the development of mathematical understanding in humans. They point the way to future research exploring additional model architectures and building larger benchmarks.

AI and ML are poised to provide new insights into mathematical cognition and development. Here, we focus on the domains of geometry and topology (GT). According to one prominent developmental perspective, infants possess core knowledge of GT concepts, presumably underwritten by dedicated neural circuitry. We use the alignment between human cognition and computer vision models to evaluate an alternate proposal: that these concepts are learned “for free” through experience with the visual world. Specifically, we measure the sensitivity of five convolutional neural network (CNN) models to 43 GT concepts that aggregate into seven classes. We focus on CNNs over other architectures (e.g., vision transformers) because their neural plausibility has been established through studies mapping their layers to areas of the brain’s ventral visual stream. We find evidence that the CNNs are sensitive to some classes (e.g., Euclidean Geometry) but not others (e.g., Geometric Transformations). The models’ sensitivity is generally lower at lower layers and maximal at the final fully-connected layer. Experiments with models from the ResNet family show that increasing model depth does not necessarily increase sensitivity to GT concepts. The models’ profiles of sensitivity to the seven classes roughly align with the profile shown by humans, with ResNet-18 corresponding best to Western adults and DenseNet to Western children ages 3-6 years. This case study shows how CNNs can provide sufficiency proofs for the learnability of mathematical concepts and thus inform theoretical debates in cognitive and developmental science. These findings set the stage for future experiments with other vision model architectures.

Recent studies show evidence for emergent cognitive abilities in Large Pre-trained Language Models (PLMs).The increasing cognitive alignment of these models has made them candidates for cognitive science theories.Prior research into the emergent cognitive abilities of PLMs has largely been path independent to model training, i.e., has focused on the final model weights and not the intermediate steps.However, building plausible models of human cognition using PLMs would benefit from considering the developmental alignment of their performance during training to the trajectories of children's thinking.Guided by psychometric tests of human intelligence, we choose four sets of tasks to investigate the alignment of ten popular families of PLMs and evaluate their available intermediate and final training steps.These tasks are Numerical ability, Linguistic abilities, Conceptual understanding, and Fluid reasoning.We find a striking regularity: regardless of model size, the developmental trajectories of PLMs consistently exhibit a window of maximal alignment to human cognitive development.Before that window, training appears to endow models with the requisite structure to be poised to rapidly learn from experience.After that window, training appears to serve the engineering goal of reducing loss but not the scientific goal of increasing alignment with human cognition.

The Every Student Succeeds Act (ESSA) prescribes holistic measures of schools for student success and well-being. However, many early warning systems rely exclusively on the "Attendance, Behavior, Course" (ABC) taxonomy, which misses potentially crucial determinants such as school climate and students' socioemotional learning. We report early findings from a larger project that aims to apply machine learning methods to improve an early warning system by incorporating factors related to school climate and socioemotional learning. These preliminary analyses suggest that a culturally inclusive, socially supportive, and emotionally and physically safe school climate is related to academic success and fewer engagement/behavior problems at the school level. They suggest the promise of integrating these features into early warning systems to help schools change their practices to better support student well-being.

In MOOCs, both instructors and students invest substantial effort into discussion forums. However, those discussions are abandoned when instructors start a new session in session-based courses. In an observational field study through a popular online Coursera course, we evaluate an approach that directly embeds high-value past discussion threads into future lecture videos to reuse them. Survey feedback shows that this approach can be useful to a large proportion of learners. We find that instructor involvement increases learners' chance of reading the threads, reduces learners' negative reactions, but is not associated with more perceived usefulness. Learners perceive enhancing threads embedded in the middle of videos less enhancing but more explanatory compared with at the end. Embedding explanatory threads at the end is rated less distracting and more helpful to understand the video compared with in the middle, right after the related content is lectured.