Putting Essential Understanding of Geometry into Practice

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-imagenot the whole plane? Do they understand that examplesno matter how many they findcannot prove a conjecture but one counterexample is sufficient to disprove it? What tasks can you offerwhat questions can you askto determine what they know or dont knowand move them forward in their thinking This book focuses on the specialized pedagogical content knowledge that you need to teach geometry effectively in grades 912. 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 geometrynot 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 912 is the seventh title in NCTMs 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.