The Importance of Ordinal Information in Interpreting Number/Letter Line Data

Abstract

The degree to which the ability to mark the location of numbers on a number-to-position (NP) task reflects a mental number line (MNL) representation, or a representation that supports ordered lists more generally, is yet to be resolved. Some argue that findings from linear equation modeling, often used to characterize NP task judgments, support the MNL hypothesis. Others claim that NP task judgments reflect strategic processes; while others suggest the MNL proposition could be extended to include ordered list processing more generally. Insofar as the latter two claims are supported, it would suggest a more nuanced account of the MNL hypothesis is required. To investigate these claims, 84 participants completed a NP and an alphabet-to-position task in which they marked the position of numbers/letters on a horizontal line. Of interest was whether: (1) similar judgment deviations from linearity occurred for number/letter stimuli; (2) left-to-right or right-to-left lines similarly, affected number/letter judgments; and (3) response times (RTs) differed as a function of number/letter stimuli and/or reverse/standard lines. While RTs were slower marking letter stimuli compared to number stimuli, they did not differ in the standard compared to the reverse number/letter lines. Furthermore, similar patterns of non-linear RTs were found marking stimuli on the number/letter lines, suggesting that similar strategic processes were at play. These findings suggest that a general mental representation may underlie ordered list processing and that a linear mental representation is not a unique feature of number per se . This is consistent with the hypothesis that number is supported by a representation that lends itself to processing ordered sequences in general.

Numerical magnitude understanding in kindergartners: A specific and sensitive predictor of later mathematical difficulties?

“…We presented it here as a measure of magnitude understanding that provides insight into the child’s understanding of symbol-symbol ordinal and linear relations, particularly for larger value numbers. Others argue that number-line estimation is a reflection of spatial reasoning that allows the use of proportional estimation and references points (Barth & Paladino, 2011; Sasanguie, Verschaffel, Reynvoet, & Luwel, 2016; Slusser, Santiago, & Barth, 2013), or that it simply reflects list order learning of numbers in formal education (Podwysocki, Reeve, & Forte, 2019) in which the symbol position within an ordered list is used to map a symbol to a location on a horizontal line. Dackermann, Huber, Bahnmueller, Nuerk, and Moeller (2015) put forward an integrative account suggesting that children’s number-line estimation reflect different developmental stages of their understanding of multidigit numbers (i.e., familiarity and place-value structuring) and proportional relations.…”

Spatial complexity facilitates ordinal mapping with a novel symbol set

“…This is an important issue, since it is claimed that ordinality is fundamental to numerical ability. Indeed, recent research has found that non-numerical ordered lists (i.e., letters of the alphabet) are represented in a similar manner to numerical information [1]. The authors interpreted this finding as implying ordinal lists share a common representational format.…”

“…Researchers have examined the representation of ordinal sequences using letters of the alphabet, or other ordinal lists, such as months of the calendar year [1,[9][10][11][12][13]. For example, Podwysocki, Reeve, and Forte [1] compared judgements of numerical stimuli and letter stimuli on a number-to-position task for numbers, and an alphabet-to-position task for letters. Specifically, participants were shown a horizontal line anchored by 1 to 26 for numbers, and A to Z for letters, and were required to estimate the location of a target number or letter respectively.…”

Influence of different spatial representations on the SNARC effect for letters: Electrophysiological evidence

“…When numbers are used as experimental materials, it is impossible to determine whether the effect is caused by their quantity or sequence characteristics. Some investigators have found that sequence information may cause the SNARC effect (Gevers et al, 2003(Gevers et al, , 2004Podwysocki et al, 2019;Previtali et al, 2010;Zhu & Wang, 2014). Since a number may contain quantity information, it can also represent a positional relation and sequential order, which appears to indicate the quantity and sequence characteristics of a number to be related directly.…”

“…When the mental spatial position of numbers on this line, referred to as the mental number line, was consistent with the response position, the response was fast; otherwise, the response was slow (Dehaene et al, 1993; Gevers et al, 2003). Podwysocki et al (2019) believed that the mental number line was a general phenomenon that could be applied to any ordered list. Other studies have examined the relationship between number and space (for a recent review see Guida & Campitelli, 2019).…”