If you don't have that in-depth mathematical understanding, then it's difficult to make those decisions. I had no idea what the students were going to ask. I had no idea what kind of questions I needed to ask that could help them. It is very difficult at first. People don't always talk about that.
Teachers are often distraught and worried.
They need to be able to tell the students that we're in this together, and we're going to learn together. If a teacher is able to say, 'Okay, now, I'm going to give some of this power to students,' then it's going to work. It's technology driven. We've got to change the way we teach mathematics because we have so much more to teach now. They understand the concept of division and can get an estimate so that when the answer comes up on their calculator, they have an idea of whether or not it is accurate.