Breaking with Experience in Learning to Teach Mathematics: The Role of a Preservice Methods Course.

This paper examines a particular problem in teacher education: helping prospective elementary teachers learn to teach mathematics. As a mathematics teacher educator, my goal is to help my students learn to do something different rom--and better than--what they experienced as pupils in mathematics classes. My problem is also framed by the kinds of experiences with mathematics and with the teaching and learning of mathematics that my students have had before I ever meet them and the ways in which those experiences influence the trajectories on which they move in becoming teachers. Although teacher educators sometimes speak of preservice teacher education as the first stage in learning to teach, nothing could be further from the truth. In fact, before they take their first professional course, future mathematics teachers have already clocked over 2,000 hours in a specialized "apprenticeship of observation " (Lortie, 1975, p. 61) which has instilled not only traditional images of teaching and learning but has also shaped their understandings of mathematics. My students are also almost all women, as are most prospective elementary teachers, a fact that is significant, given what we know about the widespread alienation of girls from mathematics during their precollege education. In considering the problem, I focus on the role of a methods course in helping prospective elementary teachers learn to teach mathematics. A methods course is a particular curricular occasion,