Often times, there is a disconnect between the way in which mathematics education courses suggest the teaching and learning of mathematics should occur and the way mathematics education doctoral students actually experience mathematics teaching and learning. By asking mathematics education doctoral students to reflect on their mathematical experiences, I was able to further understand the nature of and impact of these experiences. In this study, I engaged in conversations with five other mathematics education doctoral students asking them to share their mathematics experiences in their doctoral preparation. Several factors influenced doctoral student mathematical experiences such as their perceptions of the nature of authority in the classroom, the level of interaction (between student and instructor, among students, and between the students and the mathematics), and nature and purpose of the mathematics in the course.

The most typical experiences that doctoral students identified were consistent with traditional lecture courses where the instructor deposited knowledge upon students. Several participants reported on courses that broke the traditional mode and offered some authority to students in the decision-making in the classroom or encouraged a higher level of interaction by engaging students in group work. One particular set of courses deemed "influential", "transformational", and "empowering" embodied a classroom where inquiry reigned and the course environment allowed, required, and supported students to explore their own mathematical questions. This special set of courses featured a shared authority between instructors and students, engaged students in a high level of interaction, and explored mathematical questions and problems that came from the students' questions and ideas rather than from a textbook. The purpose of the course was a place where students could have an authentic opportunity to do mathematics. The importance of the mathematical inquiry in these courses, according to participants, was not only important for themselves as learners of mathematics but also necessary for their preparation of becoming mathematics educators.