Promoting Deep Thought in the Classroom

An important part of the Common Core State Standards is helping students to be deeper math thinkers. By promoting the Standards for Mathematical Practice and recommending deeper exploration, educators are advised to spend less time on drilling skills and procedures. Below are a few tips for creating thoughtful learning experiences.

Start and End with Thought Provoking Questions

Traditionally, most math lessons have started with instruction of a new procedure, practice and finally an application at the end. Instead, lessons can be much more engaging if both the introduction and the conclusion challenge students to think critically and apply their own understanding to problem solving. Instead of culminating in a story of one train going east and one train going west, try giving one story at the start and one at the end (and some in the middle?!), and see how their thinking evolves on its own.

Plan for Strategic Skill-Practice

Think of how both thoughtful problem solving and practice of key skills can fit into the learning experience. Do the students really need 30 minutes of homework for practice? Are they already practicing enough in class? Math learning software not only makes practice more engaging, but also infuses the experience with helpful visuals, interactivity and opportunities for independent thought and exploration.

Keep Good Questions in Your Back Pocket

The internet holds great ideas for classroom problems and activities. Students should feel that math is not only about expediently finding the correct answer. Plan to ask great questions. The class is presented with “Maya has a circular pie of diameter 10 inches.” Before you ask, “What is the area of the pie?” have a grab bag of other open-ended questions. “What obvious thing can you tell me about this situation?” “What is not obvious?” “What can we use math to figure out?” “What questions might you ask about this situation?” “What other information might you want to know?” “How can this sentence be represented visually or graphically?” Let students know that problems do not start and end with the exact question the teacher is asking.

Joe Trahan

Peace Corps Volunteer in Guinea, West Africa | MEd in Secondary Mathematics from GWU, Washington DC | 6-year teacher of Mathematics in Bethesda, MD