Mistakes are a big fixation in the life of a piano teacher. Students come to piano lessons and play their pieces and sooner or later they play wrong notes, wrong rhythms, wrong articulations, wrong dynamic shapes, and so forth.

Once upon a not-so-long-time ago (let’s say 50 years ago) a particular breed of teacher would respond to a mistake with a physical action – a smack across the knuckles with a ruler, say – with the idea that this would focus the student’s mind on not making mistakes. (It’s more likely that this focussed the student’s mind on not being tortured, but, well, we’ll talk about that another time.)

Even though piano teachers don’t do that now, this idea of not making mistakes still looms large in the learning-to-play-the-piano scene. Students are taught to avoid them. When they do make a mistake the teacher puts a big circle around the…