Dissociated Spatial-Arithmetic Associations in Horizontal and Vertical Dimensions

Abstract

Spatial–numerical associations (small numbers—left/lower space and large numbers—right/upper space) are regularly found in elementary number processing. Recently, the interest in this phenomenon has been extended from elementary number processing to mental arithmetic. Many studies have demonstrated horizontal spatial-arithmetic associations, i.e., solving addition or subtraction problems cause spatial shifts of attention rightward or leftward, respectively. However, the role of this effect in the vertical dimension has not been addressed. This is problematic because it leaves the analogy between elementary number processing and arithmetic incomplete. In order to make a strong case for a similarity between elementary number processing and mental arithmetic, a spatial-arithmetic association should be observed in the vertical dimension too. Here, we adopted the target detection paradigm from Liu et al. (2017) to replicate the horizontal spatial-arithmetic association, and meanwhile investigate whether this effect also exists in the vertical direction. Our results confirmed that addition could induce covert movement to right side and subtraction to left side. However, such a spatial-arithmetic association was not found in the vertical dimension. The implication of these findings is discussed.

Spatial grounding of symbolic arithmetic: an investigation with optokinetic stimulation

“…On the contrary, we suggest that both our results and those of Masson et al represent a signature of the spatial/attentional processes that take place during mental calculation: attentional shifts occurring in a direction that is compatible to the putative movement along the MNL (e.g., downward for subtractions) may have facilitatory effects on mental calculation that extend to procedural components. Finally, it is conceivable that we observed an effect of vertical OKS, but not of horizontal OKS, because addition and subtraction might be grounded in early experiences with the physical world along the vertical axis, such as the universal (and culture-independent) actions of stacking and removing items from a pile (Fischer, 2012 ; Myachykov et al, 2014 ; but see Liu, Verguts, Li, Ling, & Chen, 2017 , for contrasting results).…”

Addition and Subtraction but Not Multiplication and Division Cause Shifts of Spatial Attention

“…More recently, a number of studies have tested the hypothesis that addition and subtraction can cause shifts of spatial attention rightward or leftward, respectively ( Masson and Pesenti, 2014 ; Mathieu et al, 2016 ; Masson et al, 2017 ; Liu et al, 2017a , b ). Using a target detection task primed by an addition or subtraction operation, it was found that solving subtraction problems facilitates the detection of left-side targets, whereas solving addition problems facilitates the detection of right-side targets ( Masson and Pesenti, 2014 ).…”

“…Using a target detection task primed by an addition or subtraction operation, it was found that solving subtraction problems facilitates the detection of left-side targets, whereas solving addition problems facilitates the detection of right-side targets ( Masson and Pesenti, 2014 ). Liu et al (2017a , b ) modified the target detection paradigm of Fischer et al (2003) to reexamine the time course of the interaction between space and arithmetic (in particular, addition and subtraction). Their results confirmed that addition and subtraction can induce horizontal shifts of spatial attention (i.e., right-side targets are detected faster than left-side targets after solving addition problems, while left-side targets are detected faster than right-side targets after solving subtraction problems), and the spatial-arithmetic associations are shown robustly at 300 ms after the arithmetic operations ( Fischer et al, 2003 ; Mathieu et al, 2016 ; Liu et al, 2017a , b ).…”

“… Liu et al (2017a , b ) modified the target detection paradigm of Fischer et al (2003) to reexamine the time course of the interaction between space and arithmetic (in particular, addition and subtraction). Their results confirmed that addition and subtraction can induce horizontal shifts of spatial attention (i.e., right-side targets are detected faster than left-side targets after solving addition problems, while left-side targets are detected faster than right-side targets after solving subtraction problems), and the spatial-arithmetic associations are shown robustly at 300 ms after the arithmetic operations ( Fischer et al, 2003 ; Mathieu et al, 2016 ; Liu et al, 2017a , b ). These findings confirm that there is a close link between elementary arithmetic operations and visuospatial attention orientation ( Knops et al, 2009a , b ), and there are similarly recruited brain activation patterns of addition/subtraction operation to rightward/leftward eye movement ( Knops et al, 2009a ).…”

“…Although these studies have provided some evidence for a spatial-arithmetic association in multiplication or division, such work remains scarce, and the conclusions from earlier studies are controversial. In order to make a complete case for the interaction between space and mental arithmetic, it is worth considering whether multiplication or division operation can induce shifts of spatial attention similar to those found in addition and subtraction operations ( Masson and Pesenti, 2014 ; Mathieu et al, 2016 ; Liu et al, 2017a , b ). In the present study, we used symbolic magnitudes (Arabic numerals) to investigate shifts of spatial attention not only in addition and subtraction, but also in multiplication and division with a within-subject design.…”