Helping Elementary Teachers Build Mathematical Generality into Curriculum and Instruction

This article explores how elementary teachers can use functional thinking to build algebraic reasoning into curriculum and instruction. In particular, we examine how children think about functions and how instructional materials and school activities can be extended to support students’ functional thinking. Data are taken from a five-year research and professional development project conducted in an urban school district as well as from a graduate course for elementary teachers taught by the first author. We propose that elementary grades mathematics should, from the start of formal schooling, extend beyond the fairly common focus on recursive patterning to include curriculum and instruction that deliberately attends to how two or more quantities vary in relation to each other. We discuss how teachers can transform and extend their current resources so that arithmetic content can become opportunities for pattern building, conjecturing, generalizing, and justifying mathematical relationships between quantities and how teachers might embed this mathematics within the kinds of sociomathematical norms that help children build mathematical