TALKING ABOUT RATES CONCEPTUALLY .1. A TEACHERS STRUGGLE

Classroom discourse and communication are issues central to current re form in mathematics education. For reform to happen in classrooms, tea chers will have to teach from a conceptual curriculum. To do so they m ust be sensitive to children's thinking during instruction and shape t heir instructional actions accordingly-to ensure that children hear wh at they intend them to hear. This article examines how one teacher's w ay of knowing mathematics was reflected in the language he used in tea ching concepts of rate to one student during a teaching experiment. Th e teacher's conceptualizations of rate, although strong and elaborate, were encapsulated in the language of numbers and operations, and this undermined his effort to help the student understand rates conceptual ly. We examine the teacher's language in light of his intentions and t he student's interpretations of the tasks. We discuss implications for instruction that is based on a conceptual curriculum and is sensitive and responsive to children's thinking.