Proceedings of the Annual Meeting of the Cognitive Science Society

When do children understand that number words (such as ‘five’) refer to exact quantities and that the same number word can be used to label two sets whose items correspond 1-to-1 (e.g., if each bunny has a hat, and there are five hats, then there are five bunnies)? Two studies with English-speaking 2- to 5-year-olds revealed that children who could accurately count large sets (CP knowers) were able to infer that sets exhibiting 1-to-1 correspondence share the same number word, but not children who could not accurately count large sets (subset knowers). However, not all CP knowers made this inference, suggesting that learning to construct and label large sets is a critical but insufficient step in discovering that numbers represent exact quantities. CP knowers also failed to identify 1-to-1 corresponding sets when faced with sets that had an off-by-one difference, suggesting that children who could accurately count large sets used approximate magnitude to establish set equality, rather than 1-to-1 correspondence. These results suggest that children’s initial intuitions about numerical and set equality are based on approximation, not 1-to-1 correspondence, and that this occurs well after they have learned to count and construct large sets.