The project was designed to study factors within secondary schools that tend to affect young women's enrollment, perseverance, and achievement in extensive programs in mathematics, since mathematics is the "critical filter" to entrance and advancement in an increasing number of academic and professional fields. A sample of eight high schools that had a significant number of advanced placement (AP) mathematics candidates was chosen; with two selected to represent each of the following patterns: (A) high participation by females in AP classes and taking the AP examination; (B) high female participation in AP classes, low proportion taking the exam; (C) average female participation in AP classes, with high proportion taking the AP exam; and (D) average female AP class participation, average or low proportion taking the examination. Among the results, the questionnaires and interviews were seen to confirm the importance of AP and other mathematics teachers as counselors and mentors in the lives of students. Further, both the male and female students sampled tended to regard discouragement as a challenge to be overcome by extra effort. (MP)