Children's Mathematics Book Study: Part 4

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Welcome to the second to last week of our book study on Children's Mathematics.   If you missed this week's Monday Math Literature post, you might want to check it out.  I took a suggestion from the book about using children's literature to inspire story problems that help build place value understanding and wrote some story problems to go along with Bear Snores On.  Head over to read more about it and grab a free set of problems.  

If you are just joining us, it is not to late to join our book study.  Grab a copy of the book and maybe a friend or two and jump in when you are ready.  Also, if this December is just to hectic for you, I will be starting another book study the second week in January.  Read more details about both book studies here.  

Here is the posting schedule for Children's Mathematics:
December 7: Chapters 1- 3
December 14: Chapters 4 & 5
December 21: Chapters 6 & 7
December 28: Chapters 8 - 10
January 4: Chapters 11 - 13

I will post each Sunday morning and share it on my Facebook page.  Please join in by leaving a comment on my blog post or Facebook page.  If you have your own blog and want to write a post about the book that works too!  Add your link in the comments section here.  Thank you to all who shared last week!

Chapter 8: Problem Solving as Modeling

To me, this chapter is kind of the anthem to who I am as a math teacher.  I so strongly believe that kids learn best through problem solving and modeling situations rather than learning procedures and then applying the procedures to solve problems.  While working with kids of all ability levels I have seen that "Children who are progressing more slowly than their classmates are better served by being supported in generating their own models to solve problems than by being taught problem-solving strategies that have no inherent meaning for them and simply become procedures to follow." One of the things that saddens me the greatest as a teacher is when I find a kid who is so far removed from this sense making idea that they solve a problem like 300-299 using a procedure.  The fact that math has become all about procedures to them is just a shame.  

Chapter 9: Developing Classroom Practice: Posing Problems and eliciting Thinking

I think starting Cognitively Guided Instruction can be intimidating.  When teachers first see CGI being done it can look effortless but it certainly takes a change of practice for most teachers to get to that level.  Moving your classroom to one where kids are sharing strategies and a range of ideas are celebrated certainly takes some effort but is so worth it in the long run.  The ability to know what problems to pose, how to unpack those situations and how to question kids about their strategies develops over time.  There really isn't a wrong way to do these things.  If you are new to CGI, the hardest part can just be getting started.

Chapter 10: Developing Classroom Practice: Engaging Students with Each Other's Ideas

I love listening to students share ideas about math.  I think it is such a vital part of getting kids to develop a conceptual understanding of a topic.  There is so much power in hearing kids talk to each other about math and to make statements that compare and contrast strategies.  I love the ideas in this chapter about getting kids to think about other students thinking.

One thing that has made having students share strategies easier over the last few years is the availability of document cameras.  When I read the first edition of this book, I had an overhead projector and a small chalkboard.  Now many classrooms have access to document cameras thus allowing kids to share their work instantly without having to copy it to the board or a transparency.  While watching the video of Mr. Graces's class, I was thinking about how nice it was that the entire class of students could see multiple strategies at the same time and how the kids who were not writing on the board were talking about different strategies while they were being written up there.  I think I have gone a bit to far away from this with using document cameras and need to remind myself that the time invested in having kids show their work on the board is valuable in itself.  I need to find a better balance between the efficiency of the document camera and the breadth of possibilities I get by having multiple kids show their work on the board.

What are your thoughts about this week's reading?  Feel free to comment below or head over to Facebook and leave your thoughts there!