In order to increase women's representation among quantitative degrees, Berryman (1985) suggested two strategies: (1) increase women's share of the initial mathematical/scientific pool; or (2) reduce attrition from the pool. However, current research indicates that the decision to enter a quantitative field of study for women is the result of a complex interaction of many factors. This study examines the manner in which these factors influence women's choice of undergraduate fields of study by proposing a model indicating hypothesized patterns of effects. The estimation of the model resulted in the exogenous background variables producing the predominant influences in the model. Data for this study were drawn from the 1980 sophomore cohort of the national longitudinal "High School and Beyond" survey. The analyses reported here were based on 1,893 women who participated in all waves of that study, who had attended a postsecondary educational institution, and for whom data for all variables were available. Results suggest that while parents encourage academic performance in general, they tend to discourage daughters from entering quantitative fields of study in college. It is suggested that intervention strategies targeted no later than junior high school be developed for use with females and their parents to increase awareness of opportunities for women and to effect change in attitudes and course-taking patterns. (Author/KM)