Spatial grounding of symbolic arithmetic: an investigation with optokinetic stimulation

Elvio Blini,Marco Zorzi,Marco Pitteri

doi:10.1007/s00426-018-1053-0

Abstract

Growing evidence suggests that mental calculation might involve movements of attention along a spatial representation of numerical magnitude. Addition and subtraction on nonsymbolic numbers (numerosities) seem to induce a “momentum” effect, and have been linked to distinct patterns of neural activity in cortical regions subserving attention and eye movements. We investigated whether mental arithmetic on symbolic numbers, a cornerstone of abstract mathematical reasoning, can be affected by the manipulation of overt spatial attention induced by optokinetic stimulation (OKS). Participants performed additions or subtractions of auditory two-digit numbers during horizontal (experiment 1) or vertical OKS (experiment 2), and eye movements were concurrently recorded. In both experiments, the results of addition problems were underestimated, whereas results of subtractions were overestimated (a pattern that is opposite to the classic Operational Momentum effect). While this tendency was unaffected by OKS, vertical OKS modulated the occurrence of decade errors during subtractions (i.e., fewer during downward OKS and more frequent during upward OKS). Eye movements, on top of the classic effect induced by OKS, were affected by the type of operation during the calculation phase, with subtraction consistently leading to a downward shift of gaze position and addition leading to an upward shift. These results highlight the pervasive nature of spatial processing in mental arithmetic. Furthermore, the preeminent effect of vertical OKS is in line with the hypothesis that the vertical dimension of space–number associations is grounded in universal (physical) constraints and, thereby, more robust than situated and culture-dependent associations with the horizontal dimension.

Highlights

IntroductionIRCCS San Camillo Hospital Foundation, Lido‐Venice, Italy number–space interactions
The Spatial Numerical Association of Response Codes (SNARC) effect (Dehaene, Bossini, & Giraux, 1993) is a classic paradigm used in experimental psychology to probeElectronic supplementary material The online version of this article contains supplementary material, which is available to authorized users.ImpAct Team, Lyon Neuroscience Research Center, INSERM U1028, CNRS UMR5292, University of Lyon 1, Lyon, FranceNeurology section, Department of Neurosciences, Biomedicine and Movement Sciences, University of Verona, Verona, ItalyDepartment of General Psychology and Padova Neuroscience Center, University of Padova, via Venezia 8, 35131 Padova, ItalyIRCCS San Camillo Hospital Foundation, Lido‐Venice, Italy number–space interactions
As mental operations with the tens represent a crucial aspect in both procedures, we operationally considered decade errors as a signature of procedural errors, which are known to be affected by spatial deficits (Dormal et al, 2014)

Summary

Introduction

IRCCS San Camillo Hospital Foundation, Lido‐Venice, Italy number–space interactions. It has been proposed that numerical magnitudes are mentally represented in a spatially ordered manner along a continuum, referred to as the Mental Number Line (MNL; Dehaene, 1992; Restle, 1970; Zorzi, Priftis, & Umiltà, 2002), and that number processing involves orienting of attention in this “number space” (Hubbard, Piazza, Pinel, & Dehaene, 2005; Umiltà, Priftis, & Zorzi, 2009; Zorzi et al, 2012; 2002). The link has been traced back to infancy in the form

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