Is nativism sufficient in the acquisition of number word meanings?

Number word learning offers a unique window into the nature of cognition. Number words are not only abstract in nature, but they are defined by their participation in a rich system of logical inferences that transcend our perceptual experience of the world. Numerate children as young as 5 years of age can reason about relations between large exact number words despite being unable to perceptually discriminate the quantities they represent. And they can reason about infinite magnitudes, despite never having experienced them. How do these intuitions arise in cognition if not through the senses? Although developmental psychologists have made remarkable progress in documenting the stages according to which children learn number words and the principles that govern their use, the cognitive origins of this knowledge remains poorly understood. I argue that strong nativist accounts lack a workable causal theory that describes the role that innate primitives might play during development and actual learning episodes. I then reconsider constructivist accounts that seek to explain how children might create new representational resources that have greater expressive power than precursor states.