Dissociated Spatial-Arithmetic Associations in Horizontal and Vertical Dimensions

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.