The long-running REU-program is tacitly intended to increase retention and provide "an important educational experience" for undergraduates, particularly women, minorities and underrepresented groups. This longitudinal, two-stage study was designed to explore the ways in which REUs acted as educational experiences for 51 women in the field of astronomy, in an attempt to develop a theory of experience related to the REU. Stage-1 consisted of an ex post facto analysis of data collected over 8 years, including multiple interviews with each participant during their REU, annual open-ended alumni surveys, faculty interviews, and extensive field notes. All data were analyzed using a theoretical framework of continuity and interaction, in a search for transformative experiences. Four findings emerged, related to developing understandings of the nature of professional scientific work, the scientific process, the culture of academia, and an understanding of the "self." Analysis provided an initial theory that was used to design the Stage-2 interview protocol. In Stage-2, over 10 hours of interviews were conducted with 8 participants selected for their potential to disconfirm the initial theory. Results indicate that the REU provided a limited impact in terms of participants' knowledge of professional astronomy as a largely computer-based endeavor. The REU did not provide a substantive educational experience related to the nature of scientific work, the scientific process, the culture of academia, participants' conceptions about themselves as situated in science, or other aspects of the "self". Instead, the data suggests that these women began the REU with pre-existing and remarkably strong conceptions in these areas, and that the REU did not function to alter those states. These conceptions were frequently associated with other mentors/scientist interactions, from middle school into the undergraduate years. Instructors and family members also served as crucial forces in shaping highly developed, stable science identities. Sustained relationships with mentors were particularly transformational. These findings motivate an ongoing research agenda of long-term mentoring relationships for women in the sciences, at a variety of stages and across multiple disciplines.