Two experiments examined the content of novice and expert representations for both surface and deep structural elements of arithmetic equations. Experiment 1, which used a forcedchoice categorization task in which surface features of equations (e.g., digits) competed with deep structural principles of mathematics (associativity and commutativity), found that experts were more likely to focus on principles in their judgments than were novices, who focused more often on surface elements. Experiment 2, using a similar task, introduced trials in which only principled elements varied. Novices were able to focus on principled elements in this case, but failed to transfer these representations when surface features were reintroduced
