Rules of order: Evidence for a novel influence on ordinal processing of numbers.

Abstract

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 = À.26), and not at all in the case of double-digit sequences (d = À.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.

Familiar Sequences Are Processed Faster Than Unfamiliar Sequences, Even When They Do Not Match the Count‐List

“…Reconceptualizing the reverse distance effect as a byproduct of this familiarity effect is, however, at odds with the view that nonconsecutive sequences are processed slower due to conflicting with an intuition that only count‐list sequences are correctly ordered (e.g., Gattas et al., 2021). From this perspective, non‐count‐list (i.e., nonconsecutive) sequences should always be processed slowly due to not matching the count‐list.…”

“…Therefore, it is unknown whether these findings will generalize to double‐digit sequences. In fact, reverse distance effects have actually been found to be stronger in double‐digit sequences than in single‐digit sequences (e.g., Gattas et al., 2021; Lyons & Ansari, 2015). These findings are seemingly inconsistent with the familiarity perspective since one would perhaps expect the difference in familiarity between consecutive and nonconsecutive sequences to be lesser in double‐digit sequences than in single‐digit sequences; therefore, one may expect a weaker rather than stronger reverse distance effect in double‐digit sequences.…”

“…Although this familiarity account of the reverse distance effect can potentially explain these absences, recent studies have challenged this perspective. For instance, it has been suggested that both children and adults likely possess an intuition that only count‐list (i.e., ascending consecutive) sequences are correctly ordered (Hutchison, Ansari, Zheng, De Jesus, & Lyons, 2022); therefore, slower processing of nonconsecutive (i.e., non‐count‐list) sequences is argued to result from having to suppress this intuition (Gattas, Bugden, & Lyons, 2021). Dissociating between the familiarity and count‐list interpretations of the reverse distance effect is challenging, however, when we use sequence types (e.g., consecutive vs. nonconsecutive) as a proxy for familiarity (Devlin et al., 2022).…”

Concepts of order: Why is ordinality processed slower and less accurately for non-consecutive sequences?

“…One proposed alternative to the facilitation account stems from suggestions that young children may initially believe that “in order” refers only to sequences that directly match the count-list ( Gilmore & Batchelor, 2021 ; Hutchison et al, 2022 ). Therefore, it has been argued that the reverse distance effect might actually result from the processing of non-consecutive sequences being impeded due to conflicting with this intuition, rather than from consecutive sequences being facilitated by memory retrieval ( Gattas et al, 2021 ). However, although both the facilitation and count-list interpretations of the reverse distance effect seem plausible, there has been limited direct comparison between them ( Devlin et al, 2022 ).…”

“…To test whether people are predisposed to consider non-consecutive sequences as not in order, Gattas et al (2021) varied the instructions given to participants taking an order judgement task. Surprisingly, they found that adult participants were faster at classifying non-consecutive sequences as not in order than they were at classifying them as in order.…”