ABSTRACT
The content area of mathematics compels educators to pry open the lid of that chest full of years-old patterns of instruction, to sift through them and examine them, using a new and perhaps unfamiliar lens. Complex problems, which are the “game” in mathematics, help students understand why they need fluent skills, solid concepts, and efficient procedures. The Common Core State Standards for Mathematics require students to become deeply engaged in thinking, to persist in making sense of content, to apply their learning, and to reason critically and eventually abstractly. A classroom environment rich with models can turn into wallpaper that disappears into the background, unless teachers and students consistently use it. Mathematics lessons should have three parts: an introduction, an investigation, and a discussion. Students must become fluent in mathematical language both receptively (understanding when others speak) and productively (using the language themselves).
