This chapter is about the different types of math problems we (can/should/do?) pose to students. This is actually something I remember learning in university, in a “How to teach math” class. That, by the way, was the first math class I ever earned an A in! I remember us having to learn the types of problems, and then create problems of each type. This still felt like new information to me, rather than a review. Perhaps I have been out of university longer than I realize? Say it isn’t so!! I will say that I am in the habit of thinking about the math required to solve the problems I ask, and wondering if they will help move us toward our goal. I think this information will help me refine that process, ask more specific questions, and move kids along on a mapped out course, instead of that “Let’s see if this road takes us to where we want to go!” way of posing problems that I will admit to sometimes using. And I also drive that way sometimes. But that’s a blog post for another day.
One of the things that stood out for me in this chapter is the fact that each type of problem creates different mathematical demands on the learner. As I was reading, I kept thinking of how Cathy Fosnot stresses that children need to be given a chance to answer problems on their own without the teacher telling them how to do it. The act of puzzling their way through the problem is an important part of them developing an understanding of when it makes sense to add, or when subtraction is required, or how to figure out the unknown without someone showing them what is unknown in the problem.
I also noticed that once again Lawson points out that students will fall back (she says “fold back”) on less efficient strategies that they feel more confident about when they encounter more complex problems. Again this makes a lot of sense to me. Once they figure out the answer and are confident about being right, then they can consider solving the problem again with a strategy they still feel apprehensive about. I am reading Cathy Fosnot’s book about conferring, she she says that when we see students falling back on one of their tried and true strategies, that is the perfect time to push them ahead to a new spot on the landscape by suggesting a strategy they could consider trying. For example, “I know you solved this by counting all the blocks by ones. The other day I saw you solve a problem by making groups of 5. Do you think that could try that here and see what happens?” That prompt does not tell them how to solve a problem, but rather suggests they use a strategy you have already seen them use in other situations.
I made a little graphic of the information from this chapter about the types of math problems we can pose in class. I think I am going to print it off, put a copy in my day book, and use it to help me with my planning. Hopefully after a few months it will become second nature and I can make them up on the fly.