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Assessing whether learning in one domain is transferable to abilities in other domains often eludes traditional testing. Thus, a question with bearing on the promise of neuroscience for education is whether neural changes that accompany in-school curriculum learning can improve prediction of learning transfer. Separately, debate in philosophy and psychology has long concerned whether spatial processes underlie seemingly nonspatial/verbal human reasoning (e.g., mental model theory; MMT). If so, education that fosters spatial cognition might yield transfer to improved verbal reasoning. Here, in real-world classrooms studied in a quasi-experimental design, a STEM curriculum devised to foster spatial cognition yielded improved spatial abilities and-consistent with MMT-transferred beyond the spatial domain to improved verbal reasoning. Further supporting MMT, the more students’ spatial ability improved, the more their verbal reasoning improved, and spatial ability improvement mediated curriculum transfer. At the neural level, longitudinal fMRI detected curriculum-driven changes in activity, connectivity, and representational similarity of brain regions implicated in spatial cognition. Critically, changes in spatial cognition-linked neural activity robustly predicted curriculum transfer-more accurately than testing and grades-and mediated this transfer. Reports by the National Research Council and others note that spatial abilities reliably predict STEM achievement, but that broad adoption of spatial cognition-focused curricula depends on classroom-based evidence of efficacy and mechanisms-of-change. The present findings support the real-world application of MMT to classrooms via “spatial education.” Further, demonstrating that in-school neural change can predict transfer over-and-above performance-based assessment suggests the long-term achievability of neurally-informed curriculum development that leverages neural change to identify and design transferable curricula.