Talking about Rates Conceptually, Part I: A Teacher's Struggle

Classroom discourse and communication are issues central to current reform in mathematics education. For reform to happen in classrooms, teachers will have to teach from a conceptual curriculum. To do so they must be sensitive to children's thinking during instruction and shape their instructional actions accordingly—to ensure that children hear what they intend them to hear. This article examines how one teacher's way of knowing mathematics was reflected in the language he used in teaching concepts of rate to one student during a teaching experiment. The 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 conceptually. We examine the teacher's language in light of his intentions and the 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.