I first started reading these chapters online from the posting and found them difficult to follow for two reasons. First some of the content was cut off by the scanning and second because I felt as if I was missing some important aspect that had been introduced in chapter one. So once I had an actual copy of the book I read chapter one before proceeding to chapters two and three. This was much better and my insights follow.
Phases of Work
I particularly like how the authors set out the three phases in this chapter and spend most of it focused on phase one. Even though we subconsciously realize we often walk through the three aspects of the entry phase it was great to have it put into words. I appreciated how each aspect was expounded on and more ideas and examples were given to help develop them. I think students would benefit from spending some time pursuing this as well. It may formalize it in their understanding better than anything else we could do.
The review phase is something that we often overlook, even as teachers. How often do we ask our students to look back over what they've done and justify their solutions. We rarely spend any time actually teaching them how to critically look back at what they have done. This chapter gives me some ideas of how I could focus less on the answer and more on helping students justify their work.
Responses to Being Stuck
I really identified with this chapter. Recently in the Problem Solving class we were given a set of five problems to solve, of which we had to hand two in. There was only one question that I felt at all capable of doing on my own. It was very difficult to admit that I could not do the rest of them without help. I was hopelessly stuck and felt extremely defeated. It was only through this experience that I could identify with students who may often feel the same way about any math questions. This chapter showed me that it was okay to be stuck and that being stuck is perhaps the best place to be to truly learn something.
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