Although number words are common in everyday speech, for most children, learning these words is an arduous, drawn out process. Here we present a formal, computational analysis of number learning that suggests that the unhelpful structure of the linguistic input available to children may be a large contributor to this delay, and that manipulating this structure should greatly facilitate learning. A training-experiment with three-year olds confirms these predictions, demonstrating that significant, rapid gains in numerical understanding and competence are possible given appropriately structured training. At the same time, the experiment illustrates how little benefit children derive from the usual training that parents and educators provide. Given the efficacy of our intervention, the ease with which it can be adopted by parents, and the large body of research showing how strongly early numerical ability predicts later educational outcomes, this simple discovery could have potentially far-reaching import.