I don't care about the problem in the moment. I'm looking ahead. I'm thinking about how they are approaching the problem. I'm thinking about the mathematics of the task while they are thinking about the performance of the task. I'm thinking about all of the things that puzzle me and wondering why they aren't puzzled.
As the year progresses, the feedback I receive from students becomes more and more positive. I feel like they are starting to get it. I feel like they are starting to think like mathematicians. I think this starts to change my approach a little bit because I start to believe that we are finally thinking alike. As I start assuming we are on the same page, the negative feedback comes in. Students are again focused on the performance of the task and the "right" way of doing things.
It's hard to gauge what's really happening though because I have to readjust how my gauge works. Why? Because that journey changed me. Yes, it changed students too, but in the process of converting students, I converted myself on a deeper level. Now I think differently. Which makes it harder to gauge where they are at.
As students change, the temptation is to change the focus in teaching. But the very things that helped students change their way of thinking, and, subsequently, my thinking, are the very things that will help them keep changing their way of thinking. "Are we there yet?!" This is where I have gone wrong. I have assumed that students would arrive at some end goal. That journey is never over. Learning to think is a task with no bounds. It's the task of a lifetime.