Proceedings of the Annual Meeting of the Cognitive Science Society

Initial perceptions of math problems are critical for performance; novices tend to fixate on surface structures, while experts look deeper towards strategies. However, it remains unclear how these early representations change across problem-solving phases and explain performance. In this study, 126 undergraduates solved 20 SAT-level math problems: 10 timed (90sec time-limit) and 10 untimed. For each problem, participants rated perceived calculation—a surface feature of problem representation—after brief (3sec) exposure and again after attempting the problem. Participants substantially overestimated calculation demand at first exposure and revised these judgments downward after solving (Cohen's d=0.84). Participants with lower self-efficacy showed even larger revisions (Cohen's d=0.61). Critically, only pre-solving perceived calculation demand predicted performance (partial r=-0.45), an effect primarily mediated by task-specific self-efficacy (49.65% of the total effect). Math-anxiety also contributed explanatory power, particularly under time-pressure. Overall, effective problem-solving appears to rely on rapid, structure-based representations that guide strategy selection.