Do your students recognize a square if the base is oriented horizontally but call it a “diamond” if it is turned 45 degrees? Do they claim that a shape is a triangle because it “looks like” one? Do they say that one object is “bigger” than another without attending more precisely to the attribute they are comparing?

What tasks can you offer—what questions can you ask—to determine what they know or don’t know—and move them forward in their thinking?

This book focuses on the specialized pedagogical content knowledge that you need to teach geometry and measurement effectively in prekindergarten to grade 2. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these concepts—not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts.

Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of fractions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.

You have essential understanding. It’s time to put it into practice in your teaching.

The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics—topics that are challenging to learn and teach but are critical to the development of mathematical understanding.

Classroom vignettes and samples of student work bring each topic to life, and questions for reader reflection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at More4U.

Maximize the potential of student-centered learning and teaching by putting essential understanding into practice.