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

- Tyler Marghetis,
*Indiana University, Bloomington*
- Robert Goldstone,
*Indiana University, Bloomington*
- David Landy,
*Indiana University, Bloomington*

## Abstract

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.

Back to Table of Contents