Twenty-four students who scored 650 or more on the SAT-M were asked to think aloud while solving 13 mathematics items in either multiple-choice or free- response format. Strategies students used to solve the items were classified as either algorithmic or insightful. Data analyses indicated that items in the free-response format were significantly more difficult for females than multiple-choice items. No significant difference was found for males. Females were more likely than males to use algorithmic strategies in both the multiple-choice and free-response formats, with no significant difference in types of strategies used in either format. Males were more likely to use insightful strategies in the multiple-choice format than in the free-response format. Finally, on multiple-choice items, both males and females used options to detect calculation errors, however, with females using this strategy somewhat more than males. (45pp.)