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This first study of a multi-experiment project evaluating the efficacy of complete learning trajectories (LT, including a mathematical goal, a developmental progression of levels of thinking, and instructional activities for each level) in early mathematics education directly compared instruction based on a learning trajectory (LT) to a counterfactual designed to answer critical questions in the development and application of LTs. One group of preschoolers in the Cluster Randomized Trials design received instruction on shape composition based on an empirically-validated LT and the other, "skip-levels," group, received an equal amount of instruction focused only on the target level. We found significantly greater learning in the LT group, mainly on near transfer items.