Moving students through steps of mathematical knowing: An account of the practice of an elementary mathematics teacher in transition

We present an account of a sixth-grade teacher's practice as she responds to the challenges of current reform initiatives. We analyzed classroom observations and interviews to understand how the teacher, Ivy, teaches and thinks about teaching mathematics to her students. For Ivy, mathematical meaning is available in particular experiences. She creates these experiences for her students by leading them through a predetermined sequence of steps of mathematical knowing. This account contributed to our postulation of a perspective on mathematics learning that we refer to as perception-based, in which the goal of instruction is to create opportunities for students to perceive, first hand, mathematics that exists as part of an external reality. We examine implications of this account of Ivy's practice for mathematics teacher development.