To investigate the teaching undergraduate mathematics that strives to allow students to develop personally meaningful understandings of the mathematics in typical undergraduate curricula through a case study of one teacher; and To develop a professional development program for graduate teaching assistants from a theoretically based perspective.  In addition, this teaching assistant certification program will be a site for research in teacher development through a teacher development experiment. In particular, the work on this project is toward developing models of teaching at the undergraduate level that both extend and inform what is known about teaching at the K-12 level. These models then form a basis for implementing professional development programs that can affect reform at the undergraduate level, leading to a cohesive K-16 mathematics education program.The first phase of the project, underway in the 2001-2002 academic year is an intensive case study of one mathematics faculty member, teaching calculus, noted for innovative instruction that leads to meaningful mathematical participation among his students.  The case study involves daily interviews with the instructor on his plans and the results of his interactions with the students in class, which are also videotaped and observed.  The focus of the analysis on this teacher looks at: ways in which this teacher uses his content knowledge in practice; ways in which he incorporates technology into teaching calculus, and the ways in which he deals with the dilemmas of teaching in the university setting.  In addition, analysis of student work provides insight on the possible impact that instruction has on student learning.The second phase of the project is the developmental research on graduate teaching assistant professional development.  Using a Teacher Development Experiment [TDE] (Simon, 1999) model and emergent and situative theoretical perspectives, the research and development focuses on developing and testing instructional tasks used with graduate teaching assistants in a university-sponsored Teaching Assistant Certification Program.The results of this research lead to both a better understanding by the field of the processes involved in teaching at the university level, in understanding the professional growth as teaching assistants of future faculty, and in materials to use to foster growth of future faculty.