Recently I read this post and I wondered what would happen if I stood silent in front of my class. Yesterday I had the perfect opportunity to give it a try in my calculus class.
I had just finished introducing optimization, and I gave them a new problem. I told them that I wasn't going to say anything, but I would write down whatever the class agreed on (easy since there are only 10 students in my calc class).
Someone suggested a primary equation and the rest agreed, so I wrote it down. Then someone else suggested an (incorrect) secondary equation. Everyone agreed, so I wrote it down. At this point I was smiling inside because I was really interested in how this would go. They continued through the rest of the problem, and I was pleased that everyone was really into it and participating.
Then, of course, a wrong answer at the end. They figured out it was wrong because it didn't make sense in the context of the problem. Someone suggested that they had done something wrong, and someone else found that it was the secondary equation. At this point there were moans and groans, especially from the kid who had forgotten his pencil and was doing the whole thing in pen.
They were completely shocked that I hadn't (gasp) STOPPED them at the point of the mistake and kept them from doing the ENTIRE problem WRONG! I remained silent, smiling, and they did a bunch of erasing and correcting and fixed everything.
Of course the experience was more meaningful because they had an opportunity to make a mistake, find it, and correct it. And Mrs. G didn't jump right in to save the day at first glimpse of their error.
I am not sure that I would do this again in exactly the same way, and I am sure I wouldn't get entire class participation if I did it in a bigger class. But the beauty of this whole experiment is that it got me to thinking about how often I say too much. I am always trying to explain things really thoroughly so that they can understand, but then they miss out on the opportunity of making their own conclusions, making their own mistakes, and figuring out how to fix them.
p.s. I have a calc student who is planning to be a high school math teacher, and he says "Silence, I am totally going to use that when I am a teacher."