Running head: How abstract is symbolic thought? How abstract is symbolic thought?

In four experiments, we explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations testing their ability to apply the order of operations. In each experiment, a non-mathematical grouping pressure was manipulated to support or interfere with the mathematical convention. Despite the formal irrelevance of these grouping manipulations, accuracy in all experiments was highest when the non-mathematical pressure supported the mathematical grouping. The increase was significantly greater when the correct judgment depended on the order of operator precedence. The result that visual perception impacts rule application in mathematics has broad implications for relational reasoning generally. Our conclusion is that formally symbolic reasoning is at once more visual and more external than is usually proposed.