Twenty-four students who scored 650 or more on the Scholastic Aptitude Test Mathematics test (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, with females using this strategy somewhat more than males. One table gives score distribution by sex. Appendix A contains multiple-choice and free-response versions of items used in the protocols. Appendix B provides samples of solution strategies. (Contains 31 references.) (Author/SLD)