Doing Arithmetic by Hand: Hand Movements during Exact Arithmetic Reveal Systematic,Dynamic Spatial Processing

Abstract

Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world—in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental “number-line”, the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial–arithmetical bias, moreover, was distinct from—but correlated with—individuals’ spatial–numerical biases (i.e., spatial–numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes.