Conceptual Knowledge Falls through the Cracks: Complexities of Learning to Teach Mathematics for Understanding

Abstract

In this article we focus on two interrelated aspects of the process of learning to teach mathematics for understanding: (a) ideas and practices for teaching procedural knowledge and (b) ideas and practices for teaching conceptual knowledge. We explore one student teacher's ideas and practices, together with the messages about teaching for procedural and conceptual knowledge that were presented by the teacher education program in which the student teacher was enrolled and the placement schools in which she student taught. We reveal a pattern in which the student teacher, her mathematics methods course instructor, her cooperating teachers, and the administrators of her placement schools expressed a variety of strong commitments to teaching for both procedural and conceptual knowledge; but with these commitments, the student teacher taught, learned to teach, and had opportunities to learn to teach for procedural knowledge more often and more consistently than she did for conceptual knowledge. We find that the actual teaching pattern (what was done) was the product of unresolved tensions within the student teacher, the other key actors in her environment, and the learning-to-teach environment itself. We hypothesize that situational supports constructed to emphasize more consistently teaching for conceptual knowledge might help resolve at least some of the tensions, and we suggest that such supports should be developed if the national goal to increase the teaching of mathematics for understanding is to be achieved.