# How much of symbolic manipulation is just symbol pushing?

- David Landy,
*University of Illinois*
- Robert Goldstone,
*Indiana University*

## Abstract

This paper explores the hypothesis that schematic
abstraction—rule following—is 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.

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