This paper explores the hypothesis that schematic abstractionrule followingis partially implemented through processes and knowledge used to understand motion. Two experiments explore the mechanisms used by reasoners solving simple linear equations with one variable. Participants solved problems displayed against a background that moved rightward or leftward. Solving was facilitated when the background motion moved in the direction of the numeric transposition required to solve for the unknown variable. Previous theorizing has usually assumed that such formal problems are solved through the repeated application of abstract transformation patterns (rules) to equations, replicating the steps produced in typical worked solutions. However, the current results suggest that in addition to such strategies, advanced reasoners often employ a mental motion strategy when manipulating algebraic forms: elements of the problem are picked up and moved across the equation line. This demonstration supports the suggestion that genuinely schematic reasoning could be implemented in perceptual-motor systems through the simulated transformation of referential (but physical) symbol systems.