When I was a child in school, we were taught that using our fingers to figure out the answer to an arthmetic problem was wrong. Some kids even got their hands slapped for doing it.
But it looks as if in this case it was the teachers who were wrong. Research is showing that using gestures while one is thinking about a math problem actually improves thinking. This seems to apply whether we are trying to solve a problem, being taught how to solve it by someone else, or explaining how we solved it.
So hand shakes all around.