The study investigated the development of 48 gifted adolescents' competencies and achievement related cognitions in mathematical skill development and examined the effects of school achievement level and sex. Ss completed a self instructional packet on mathematical residues (remainders) and were periodically assessed on perceived ability, task difficulty, effort, general expectancy, and perceived efficacy. Compared with Ss who performed well in school, underachievers judged ability, general expectancy, and perceived efficacy lower, and rated task difficulty and effort higher. Contrary to prediction, there were no sex differences on any measure. Three possible reasons for the lack of sex differences were noted. (Author/CL)