Introduction

As mathematicians and educators, we are faced with the challenge of preparing future generations of middle grades teachers of mathematics. This is a daunting task indeed, given that many prospective and practicing teachers reveal a paucity of mathematics content knowledge [1, 11] and have overtly authoritarian beliefs about the nature of mathematical behavior [18, 19]. We are left to wonder how to best design our programs for prospective middle grades teachers. Should we emphasize mathematics content or stress mathematics methods and connections to the school curriculum? What forms should our courses take and which faculty members are best qualified to teach them?

At the center of this problem lies a tension between the education and the mathematics communities over the types of mathematical knowledge that teachers need. The research literature distinguishes several components: content knowledge, knowledge of learning and the learner, general pedagogical knowledge, and pedagogical content knowledge. A synthesis of this literature can be found in [6], where the authors propose that teacher knowledge is both situated and changeable.