In teaching math, it can be very difficult to keep students engaged. Moving around the room and keeping proximity to students in mind during my "lecturing" is key. When I'm at the whiteboard, making eye contact with specific students and keeping up the back-and-forth discussion keeps them from drifting to sleep. Asking open ended opinion-based questions to students who are shy or may not be totally grasping the concept is a safe way to keep them included in what's going on. When students volunteer answers, I'll challenge those answers (even if they're correct) to see if the student can back up their conclusion. Again, asking for others' opinions about a student's justification keeps the class functioning as a group and encourages communication. Sprinkle some humor and levity into the mix and you have a successful math classroom with engaged students.
