# Re-viewed: Children’s Mathematics. . . It’s a Beautiful Thing

About a month ago, I was asked to preview the new edition of Children’s Mathematics and write about it on this blog.  I was more than happy to oblige!  Children’s Mathematics is one of a select few books that I’ve read in the past decade that have really had an impact on how I teach mathematics.

Let me begin by saying that no matter which edition you read, it’s worth it.  If you’re a teacher (or parent) and have an unread edition of Children’s Mathematics sitting on your shelf (for whatever reason), do yourself and your students (or children) a huge favor and read it.  Then do exactly what it says to do!

The research-based approaches to teaching mathematics you’ll learn from the contents in this book are invaluable.  Cognitively Guided Instruction.  That’s what it’s called.  And it’s a beautiful thing to see in action.  And it’s even easier to see in action as you read the book (more on that later).  Empowering students to think, make sense of, and solve problems based on their own understanding.  Why don’t we all teach this way?  It makes so much sense.

To be clear, Cognitively Guided Instruction (CGI) is not a program or a curriculum.  It’s an approach to teaching and it’s based on research on children’s mathematical thinking and how it develops.  The idea that’s most intimidating to teachers (and parents) is that no direct instruction is used before giving students a problem.  Many would argue that students won’t know how to solve the problem unless they are shown how first.  This is so NOT TRUE.  The contexts of the problems give the students all they need to jump in to the problem.  Their pathways to solutions are defined by their own understandings.  For example, students may be given a problem such as:

Luke had 7 toy cars.  His friend gave him some more cars for his birthday.  Now Luke has 12 cars.  How many cars did his friend give him?

Students given this problem may solve it by counting down from 12 or up from seven,  They may begin by choosing 7 objects to represent the cars, then counting some more to get to 12.  They may even make two sets (one set of 12 and one set of 7). There are multiple ways students can represent the problem.  All of them valid.  Some are more efficient than others, but regardless of the strategies used, it’s a beautiful thing.  It’s especially beautiful when students share their strategies and learn from each other.  When we listen to students’ thinking we best know how to work with them in order to move them along their own mathematical journey.

Now this is all great, but you can get this and more from any of the earlier editions of this book.

Here’s some of the new goodness you get from the latest edition (out later this month):

• A chapter dedicated to Base-Ten number concepts – this was nice to see, since base-10 understanding is a huge part of elementary mathematics.
• Quotes from real teachers using CGI in the classroom.  These can be found at the beginning of each chapter.  Its a small part of the new edition, but really it’s one of the things I really enjoyed!
• Video clips that you can watch as you read! No more CDs to have to load, or lose or break.  When you’re reading and want to see the accompanying video, just scan the QR code in the book with your phone.  It just pops right up!

Overall, this new edition has some updated content and makes it easier (thanks to technology) to see in action.  As one teacher from the book put it:

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

Have I said this already?  Beautiful.  Absolutely beautiful!

What are you waiting for?  Go out and get Children’s Mathematics and read it.

And then, go out and get the “sequels”:

Extending Children’s Mathematics: Fractions and Decimals

and

Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School

Check out the new edition here:  http://heinemann.com/ChildrensMath

## 6 comments

1. This comes at a good time for me. I’m preparing to begin looking at solving equations to my 7th graders and the use of CGI to reintroduce the idea for determining the unknown seems like a brilliant idea. May I borrow your copy as mine was accidently left at my previous school?

2. I’m sure I have another copy at school! I can get it for you on Monday. I love the collaboration aspect of blogging! This kind of thing happens to me all the time. When I need an idea for a lesson or just can’t seem to make something work, I talk to you or Graham or Turtle or any number of other critical friends and one of you will say something and suddenly it’ll all make sense. That’s the power of collaboration! Let me know when/how I can get the book to you.

1. Perfect! I’ve been looking forward to getting reacquainted with CGI since Graham’s post about his love affair with it.

3. Turtle Toms says:

Woohoo! Lovely review. This book and the manner in which it helps you to see and further reveal children’s thinking is so fundamental to good teaching. Glad you are sharing, Mikey. You’ve always been extra good at that. You too, Jenise! Can’t wait to see the two of you at GCTM.