Imagine… a basketball coach (let’s say Coach K at Duke) and his team are in the gym. Coach K starts practice by demonstrating a new skill for his team to learn. He asks the two most experienced players on the team to demonstrate it again while the others watch. Then he tells all of the players to take the floor and try the skill. When Coach sees one of the players doing something wrong, he takes the ball from the player, demonstrates the skill again, and then hands the ball back and walks away. After about 15 minutes, he sends most of the team off the court and has his two most experienced players practice the skill for about 10 more minutes, with everyone else watching. Coach K repeats this process with other skills for the rest of practice.
Of course, we know that Coach K would never actually conduct practice like this. Coach K knows well that every player, regardless of experience level, has to be on the court for the whole practice, working on every skill and every part of the game in order to become a better basketball player. He knows that the players with less experience aren’t going to get better by mostly watching.
As mathematics teachers, we have to guard against the first scenario above. How often do we as teachers actually do/talk about more mathematics in class than any of our students? How often do we allow many of the students to sit and watch while a few confident ones do most of the thinking? It is our job to be sure that every student is as engaged in doing and talking about mathematics as possible – and it is our job to be continually checking their understanding as they work. I think Coach K would be proud of this kind of math class.
