My Response: Formula for Thinking Mathematically

I find these two chapters, "Phases of Work" and "Responses to being Stuck"  to be very-very interesting, and informative, as they have provided the detailed analysis of various stages of dealing with a problem. The three phases of work involved in solving a problem, are really crucial for developing of thinking mathematically, and a teacher must have the knowledge of these stages, as well as enough skill to apply the same during his or her teaching process, in order to achieve the required learning outcome. Although, I also feel that these stages occur naturally while we encounter a problem, but by highlighting them beforehand we can train our students to enjoy the process of discovering beyond the solutions. Consequently, their thinking will be more mathematical.
      I, especially, liked the analysis of the "Attack" phase in 2nd chapter, where the remarkable use of the words "stuck" and "aha" has provided a more practical illustration of a mind's activities while going through this significant stage of exploration. I just want to share my own practical experience of developing mathematical thinking. When I used to teach solving Mathematical problems in India, I always asked my students to write down all the steps involved in solving a problem, together with making down where they got stuck, and how they got the way to come out. These readings have really provided me with concrete information, and I can now use it more effectively to train myself and my students in actually thinking Mathematically.