Proceedings of the Annual Meeting of the Cognitive Science Society

Mathematical cognition researchers have studied the mental representations of natural numbers, integers, and frac-tions extensively. We investigated the representations of irrational and perfect square numbers in a laboratory setting. Eightyparticipants performed (1) a magnitude comparison task (MC) by indicating which of two numbers is greater or lesser, (2) anumber line estimation task (NLE) that required subjects to estimate the positions of natural and radical numbers on a numberline, and (3) a numeracy test. On the MC task, participants were slower for radical expressions than for natural numbers andshowed distance and size effects for both. When comparing radical expressions, they were faster when both numbers wereperfect squares. This suggests a privileged mental representation for perfect squares. On the NLE task, participants wereless accurate when locating radical expressions. Performance on the numeracy test revealed broad deficits in conceptual andprocedural knowledge of irrational numbers.