Learning a novel number system: The role of compositional rules & counting procedures

When children learn to count, they are exposed to a finite list of words, as well as rules for combining them - e.g., that any decade label, like “seventy” can be combined with the unit labels “one” through “nine”. Additive, multiplicative, and other rules allow the creation of indefinitely large numbers, beyond those that children experience directly in their input. However, while children begin to use number words by the age of 2, they generally don’t acquire rules for combining them until much later. One possible reason for this late learning of rules is that it exceeds the cognitive capacities of younger children, or depends on information acquired at earlier stages of learning. Another possibility, however, is that these rules are hard to learn because they’re not readily available in children’s input, and that other forms of input might lead to earlier learning. Here, we simulated the problem of number word learning in adult participants by training them on a series of artificial number “languages”. We find that (1) training adults on rote counting facilitates memory for number words, but (2) may actually inhibit the acquisition of rules that govern them. We also find that whereas additive rules are relatively easy to learn (e.g., the number after “twenty” is “twenty-one”), adults struggle to acquire new multiplicative rules (e.g., “seventy” is seven tens). Finally, we find that the size of a base - e.g., base 2 vs. base 5 - has little effect on learning when learned via a rote counting procedure, despite the fact that larger bases require more memorization of words, and provide less exposure to rules.