Infants and young children can solve "arithmetic-like problems" using non-symbolic representations of quantity (e.g. solving "one object" + "one object"), and these early non-symbolic abilities are thought to support the acquisition of formal mathematics in school. How do untutored children perform non-symbolic "arithmetic-like" computations? Formal symbolic arithmetic is defined by function rules that specify how operators operate over inputs to produce outputs, and these function rules allow for the principled combination and manipulation of numerals. In this talk, I will present recent research from my lab that suggests that human's early, non-symbolic "arithmetic" abilities are much more computationally limited. Our results provide new insights into the computations underlying early numeracy abilities, and suggest computational limitations on early non-symbolic numerical competencies that could limit their effectiveness as scaffolding for the acquisition of formal arithmetic knowledge.