We hear a lot about educational entrepreneurs these days. As a service to these bright young innovators, I have here a proposed product that can revolutionize the teaching of mathematics: the bobblehead instructor. Given a gentle nudge, the instructor will nod reassuringly and repeat one of the following phrases:
"And now what do you do?"
"Let's try that."
All kidding aside, when I was a high school math teacher, a substantial part of my day was spent doing just that. I generally reserved the last section of class for individual or in-pair work. Kids would finish up their worksheets and start on their homework while I would walk around the room.
When a kid was stuck on a problem, it was usually enough just to stand there and, in an encouraging tone of voice, say some combination of the phrases listed above. The students basically needed someone to hold their hand.
Learning to be the bobblehead can be surprisingly difficult for new teachers. You have spent years preparing for this job, mastering your subject, learning to be an effective teacher. The natural impulse is to jump in and start instructing. Most of the time, however, that is not what the students need.
Students often attempt problems as if their desk were wired to deliver electrical shocks whenever they made a misstep. They have to learn to be patient with themselves and to relax a little bit. Having a teacher who stands there reassuringly is often the ideal form of assistance.