Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image—not the whole plane? Do they understand that examples—no matter how many they find—cannot prove a conjecture but one counterexample is sufficient to disprove it?

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 effectively in grades 9–12. The authors demonstrate how to use this multifaceted knowledge to dispel students’ misconceptions and replace them with the steadily developing understanding that students need for success with geometry—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 diagrams and definitions, transformations, and proof. Use the opportunities that these and similar tasks provide to build on their understanding and guide them in taking the next steps in learning.

Putting Essential Understanding of Geometry into Practice in Grades 9–12 is the seventh title in NCTM’s highly useful and very readable Putting Essential Understanding into Practice Series, edited by Barbara J. Dougherty. Each volume in the series builds on the companion volume in the earlier Essential Understanding Series to show teachers how to implement their understanding of mathematics in the classroom.