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Sunday, December 7, 2014

Children's Mathematics Book Study: Part 1

I am so excited to be starting a book study on Children's Mathematics.  This is an excellent book for elementary teachers.  The first edition of this book helped set me on the path my career has taken from being a general K-6 teacher towards being a math specialist.  It helped me get started with making math meaningful for kids and has shaped me into the teacher I am today.  I am excited to be sharing the second edition on my blog and can't wait to hear what everyone else thought about this book. 
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.

Introduction and Chapter 1

"I have always known that it is important to listen to kids, but I never knew what questions to ask or what to listen for."  This is a quote from the opening paragraph of the book and does a great job demonstrating the journey I have taken over the past 9 years as a math specialist.  I have learned to stop teaching and start listening and I have learned how to seize teachable moments.  When reading the introduction and the opening chapter what struck me most is how much of a different place I am in than when I read the first edition of this book.  

Chapter 1 also reinforces my beliefs that students can and need to construct their own knowledge about mathematics rather than being taught a procedure.  "Without direct instruction on specific number facts, algorithms, or procedures, children can construct viable solutions to a variety of problems."  

Chapter 2: Addition and Subtraction: Problem Types

When the Common Core was first published and I took a look at Table 1 from the Glossary it was a real wake up call that my students were not being exposed to all the different problem types for addition and subtraction.  If you haven't checked out table 1, you will see there are TWELVE different problem types for addition and subtraction word problems.  When my students were first exposed to some of these problem types that I had been neglecting, they found them extremely challenging.  Now I have included them in problem sets starting in the primary grades, working on double digit addition and subtraction and going up through fraction operations.  What a difference it has made!  

Chapter 2 does such a great job of outlining these different problem types that I think anyone who has looked at Table 1 in the Common Core and been confused should definitely read this chapter.  It provides the detailed explanation about the different problem types and give some great ideas about how to make problems easier or more challenging by playing with the wording and the positions of the unknowns in the equations.   

Please make sure that you note distinguishing between the different types and knowing what they are called in a job for teachers, not for students.  Don't spend time trying to teach kids which kind of problem it is and what it is called! 

Chapter 3: Addition and Subtraction: Children's Solution Strategies 

I love this chapter and I think it has a lot of value for professional development.  It is great to read about different strategies and ideas kids have but it is even better to be able to watch the videos. I absolutely love the chart on page 41.  I think this will be something I refer to often.  

What are your thoughts and ideas about this week's reading?!


  1. I'm excited to read the second edition of Children's Mathematics, too! Here are a few key points/quotes that jumped out at me for this week's reading:

    “The better I get at listening to children, the clearer I hear them tell me how to teach them.”

    Good teaching isn’t just about giving children problems or knowing the standards; good teaching starts with knowing what the children understand and then purposefully crafting problems to deepen and extend that knowledge.

    Chapter 1:
    The structure of the problem influences the strategy that children use to solve it. Children do not have to be taught that a particular strategy goes with a particular type of problem. With opportunity and encouragement, children construct for themselves the strategies that model the action or relationships in a problem.

    Chapter 2:
    A classification scheme for addition & subtraction problems provides a structure for interpreting how children solve different problems and for selecting problems for instruction.

    The differences among the eleven problem types is important because they are related to how children solve the problems, which in turn affects the difficulty level of different problems.

    Chapter 3:
    Research has identified a remarkably coherent picture of strategies that children invent to solve addition & subtraction problems and how they evolve over time.

    Students who know facts from memory after going through Direct Modeling strategies, then Counting strategies, then Derived Fact strategies have a stronger understanding of addition and subtraction than children who learn facts through rote memorization.

    Thanks for organizing this book study. Looking forward to hearing what others have to say!

    1. Hi Lori,
      I love the quotes your picked out! I now have had the opportunity to see students who have built their knowledge by taking the path through direct modeling and counting and have ended up at derived facts. What a difference from the kids who learn through rote memorization! Kids who construct their knowledge have much more flexibility and fluency and are able to connect new learning to what they already know!

  2. I've Made an effort in the last four years to use different problem types because I sure didn't before that. Sounds like a great book! I'm looking forward to more posts.

    1. I feel the same! I am sure I didn't use all the problem types or even know about them. If I saw problems that were worded differently than I was used to, I was convinced they were problems meant to trick kids. If I only knew then what I know now....

  3. I loved the first book- it really changed my teaching. The second edition just came in the mail this week. I need to get reading. Once I saw you were going to be talking about it, I finally ordered it. Can't wait to read it.

    The Research Based Classroom