Generative syntax and a consistently ordered count routine are both understood to have central roles in learning a number system. However, there has been little experimental exploration of how the diversity of each of these features alters the inductive landscape of number learning, as most empirical work has been constrained to correlational studies. We present a causal manipulation both of syntactic structures and counting procedures, using an artificial language paradigm. Our findings suggest that (1) learners have a greater facility with conjunctive over multiplicative rules of composition, (2) counting procedures help learners to recall words independently of syntax, and (3) predictable syntax helps learners to use numerical concepts, independently of - and possibly despite - counting routines.