Rules of Order: Evidence for a Novel Influence on Ordinal Processing of Numbers

Research on how people process numerical order carries implications for our theoretical understanding of what a number means and our practical understanding of the foundation upon which more sophisticated mathematics is built. Current thinking posits that ordinal processing of numbers is linked to repeated practice with the integer count list, but the mechanisms underlying this link remain unclear. For instance, in standard ordinal verification paradigms, participants more rapidly and accurately verify that count-list sequences (e.g., 3-4-5) are "in-order" than non-count-list sequences (e.g., 2-4-6), although it remains unclear whether this is due to strong count-list processing or poor non-count-list processing. If the count list primarily facilitates ordinal processing of count-list sequences, then forcing participants to classify sequences like 3-4-5 as "not-in-order" should adversely affect ordinal verification performance. We found that it does, but only moderately in single-digit sequences (d = −.26), and not at all in the case of double-digit sequences (d = −.02). Alternatively, the count list may influence ordinal processing in an exclusionary manner, creating a tendency to view anything that does not match the count-list as not-in-order. If so, then allowing participants to classify ordered (but non-count-list) sequences like 2-4-6 as not-in-order should improve ordinal verification performance. It did, with strong effects for both single-digit (d = .74) and double-digit sequences (d = 1.04). Furthermore, we demonstrated that the reverse distance effect found in standard ordinal verification paradigms is driven primarily by poor non-count-list processing. Taken together, our results advance our understanding of the mechanisms by which the count list shapes ordinal processing, even in highly numerate adults.