Symbolic Number Ordering and its Underlying Strategies Examined Through Self-Reports.

Natalia Dubinkina,Francesco Sella,Bert Reynvoet

doi:10.5334/joc.157

Abstract

Symbolic number ordering has been related to arithmetic fluency; however, the nature of this relation remains unclear. Here we investigate whether the implementation of strategies can explain the relation between number ordering and arithmetic fluency. In the first study, participants (N = 16) performed a symbolic number ordering task (i.e., “is a triplet of digits presented in order or not?”) and verbally reported the strategy they used after each trial. The analysis of the verbal responses led to the identification of three main strategies: memory retrieval, triplet decomposition, and arithmetic operation. All the remaining strategies were grouped in the fourth category “other”. In the second study, participants were presented with a description of the four strategies. Afterwards, they (N = 61) judged the order of triplets of digits as fast and as accurately as possible and, after each trial, they indicated the implemented strategy by selecting one of the four pre-determined strategies. Participants also completed a standardized test to assess their arithmetic fluency. Memory retrieval strategy was used more often for ordered trials than for non-ordered trials and more for consecutive than non-consecutive triplets. Reaction times on trials solved by memory retrieval were related to the participants’ arithmetic fluency score. For the first time, we provide evidence that the relation between symbolic number ordering and arithmetic fluency is related to faster execution of memory retrieval strategies.

Highlights

The processing of ordinality is typically assessed with a symbolic number ordering task in which participants indicate whether numbers of a triplet are in order or not (e.g., 1-2-3 vs 2-1-3; Lyons et al, 2016; Sury & Rubinsten, 2012)
Individuals are faster in responding when digits in ordered triplets are consecutive compared to non-consecutive ones (e.g., 1-4-7). This phenomenon is known as the reversed distance effect (RDE) as a small distance between digits in the triplets leads to faster reaction times (Goffin & Ansari, 2016; Lyons & Ansari, 2015; Lyons & Beilock, 2013; Sasanguie et al, 2017; Vogel et al, 2017; Vogel et al, 2019)
We examined the presence of reversed distance effect (RDE) and distance effect (DE) in the response times (RTs) across conditions

Summary

Introduction

For notordered triplets (e.g. 3-1-2), individuals are slower in responding when triplets entail numbers with a small (e.g. 2-3-1) compared to large distance (e.g., 1-7-4) This difference is usually called standard distance effect (SDE; Morsanyi, O’Mahoney, & McCormack, 2017) as it mirrors the classic distance effect observed in digit comparison task (e.g., Moyer & Landauer, 1967; Buckley & Gillman, 1974), whereby reaction times are faster when comparing the magnitude of digits that are far apart (Moyer & Landauer, 1967)

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