Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

Mr. Carter is about to start a two-day lesson on subtraction of integers with his sixth-grade prealgebra students. He plans to use contextualized problems that will allow his students to develop an interpretation of subtraction that involves the idea of "difference." This article outlines one way to teach students develop number line…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…