Current debate surrounds the promise of neuroscience for education, including whether learning-related neural changes can predict learning transfer better than traditional performance-based learning assessments. Longstanding debate in philosophy and psychology concerns the proposition that spatial processes underlie seemingly nonspatial/verbal reasoning (mental model theory). If so, education that fosters spatial cognition might improve verbal reasoning. Here, in a quasi-experimental design in real-world STEM classrooms, a curriculum devised to foster spatial cognition yielded transfer to improved verbal reasoning. Further indicating a spatial basis for verbal transfer, students’ spatial cognition gains predicted and mediated their reasoning improvement. Longitudinal fMRI detected learning-related changes in neural activity, connectivity, and representational similarity in spatial cognition–implicated regions. Neural changes predicted and mediated learning transfer. Ensemble modeling demonstrated better prediction of transfer from neural change than from traditional measures (tests and grades). Results support in-school “spatial education” and suggest that neural change can inform future development of transferable curricula.