Many of the students said that they had become more aware of their thinking process and spent time judging whether they were pursuing the correct path. This was not universal, however, and several students said they rarely reflected on their thinking process. Excerpts follow:

"I'm starting to recognize when I'm off in a wrong direction. I can figure out where I am if I understand the problem."

"I often evaluate my choices when working on a problem."

"I am more open to taking a new approach. I can now step back and look at the bigger picture and make sense of the problem. I don't get stuck in a rut and I am more apt to listen to others opinions about how to do a problem."

"Don't do that very much at all. There is some use in evaluating my strategy and methods."

"Most problems that I am now working on have no novelty and so I don't get stuck and have to think about my choices."

"This happens for me alot since I like to solve problems. I write down ideas. I come back to them. I check to see if they are on target. Math 30 contributed to making this more effective."

"I have been applying these methods but I am not consciously being reflective."

"I usually spend about 20 thinking about a problem, about the methods. Often in the middle of a problem I get stuck and then I go to a different approach."

"I tend to not reflect too much until I get into a deep hole. I believe in myself enough to think that what I am doing will work."

"I spend a lot of time going over problems looking for the best approach, the quickest way, the most efficient way."

"I think I do this more when the problem is interestiing. Generally I did not step back and think about my thinking. I do this more when I worked on problems that I chose to do."

"I always have a monitoring system to keep on the path."