Even when people are manipulating algebraic equations, they still associate numerical magnitude with space

The development of symbolic algebra transformed civilization. Since algebra is a recent cultural invention, however, algebraic reasoning must build on a foundation of more basic capacities. Past work suggests that spatial representations of number may be part of that foundation, but recent studies have failed to find relations between spatial-numerical associations and higher mathematical skills. One possible explanation of this failure is that spatial representations of number are not activated during complex mathematics. We tested this possibility by collecting dense behavioral recordings while participants manipulated equations. When interacting with an equation’s greatest [/least] number, participants’ movements were deflected upward [/downward] and rightward [/leftward]. This occurred even when the task was purely algebraic and could thus be solved without attending to magnitude (although the deflection was reduced). This is the first evidence that spatial representations of number are activated during algebra. Algebraic reasoning may require coordinating a variety of spatial processes.