At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…

Tiering and scaffolding are two differentiation strategies that teachers use to support access to a high-quality mathematics curriculum for all students. This article provides examples demonstrating a thinking process for planning tiered activities that focus on important mathematical understandings. Also described are possible scaffolds that can…

Presents remarks adapted from the presidential address of the 1999 annual meeting of the National Council of Teachers of Mathematics (NCTM). Argues that the mathematics classroom teacher must create an environment that supports students' interests and mathematical growth at many different levels, and suggests ways to accomplish this. Considers…