Children’s Mathematics – The Book That Changed My Teaching Forever

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Blog Hoppers

My journey to become a Recovering Traditionalist started with the book Children’s Mathematics: Cognitively Guided Instruction by Thomas Carpenter et al.  So, when I was invited to participate in the blog hop entitled “Math Books That Will Change Your Teaching,” that book instantly came to mind.  This blog hop was organized by The Research Based Classroom and all the participants are shown above.  At the end of my blog is a link to the next blog in the hop.  I encourage you to hop all the way through as each person is giving away the book that Changed Their Teaching.  Here is mine:

Children's Mathematics

In my first years of teaching I quickly discovered I didn’t know anything about teaching math.  I could DO math but I was horrible at teaching it.  When I went back to school to get my master’s degree, my supervising professor had me read Children’s Mathematics.  Now coming from teaching middle school, I wasn’t super excited about reading a book focused on how K-3 kids do math…I wanted to know what to do to help MY students.  What I quickly learned was that the root of their problems and the root of why I was so bad at teaching them was because teachers (myself included) didn’t stop to listen to them.

I was teaching with the mindset that my students’ didn’t know anything and it was my job to tell them everything they needed to know.  But when I watched one of the videos (there are CDs with the book) of a 1st grader solving a division problem, I was amazed.  Now she didn’t know how to do formal division like you expect older kids to do, but she did know how to model the situation.  My problem was I was expecting students to work at the “formal” level when they really were down at an informal level like she was.  She was solving this problem:

Rodney is having some kids over for jelly donuts. 7 donuts can fit on one plate. How many plates will Rodney need for 28 donuts? 

What I saw still amazes me every time…she counted out 7 “donuts” represented by blocks, slid them into a pile and said “That’s one plate.”  Then she counted out 7 more, “that’s another plate,” counts out another 7 and then she goes back and counts them all to see if she is at 28 yet.  She isn’t so she makes another pile of 7, but goes back and recounts each pile to ensure they all have 7, then finally goes back and recounts them all and has 28 donuts accounted for and says “4 plates.”

So why did this amaze me…it’s a kid counting…NO, it’s a kid using what they know to solve a problem.  She knows how to count (and count again, and count again) and she used her skill set to solve a problem.  The teacher didn’t have to tell her what to do and the teacher didn’t interrupt her to suggest a more efficient strategy.  Children’s Mathematics gives teachers insight into how to write story problems that children can solve in their own informal way and shows you the progressions kids go through from using informal strategies like Direct Modeling (counting and recounting everything) to more efficient strategies like Derived Facts (using what you know to help you; 7+8 is like having 5+2+8 because 8 and 2 make 10). The first few lines on the back cover of the book sums up what I took away from reading the book:

By the time they begin school, most children have already developed a sophisticated, informal understanding of basic mathematical concepts and problem-solving strategies.  Too often, however, the mathematics instruction that we impose upon them in the classroom fails to connect with this informal knowledge. 

From the book, I began to realize that I wasn’t letting my students use the knowledge about mathematics that they already had in order to make connections to the mathematics they needed to learn.  Children’s Mathematics shows how teaching through problem solving allows students to approach problems at their own level.  Plus it gives teachers insight into the progressions kids go through when solving addition & subtraction, multiplication & division, and multi digit addition & subtraction.  Knowing the progressions allows teachers to identify what stage children are working in and how to help them move to a more formal/efficient strategy.  The mathematical concepts discussed in Children’s Mathematics are K-2, but teachers of all levels can benefit from knowing how kids approach problems informally.

Part of this Math Books That Will Change Your Teaching Blog Hop is giving away the book that changed our teaching.  So scroll down and enter for your chances to win this wonderful book and be prepared to have it change the way you teach.  There is a Second Edition of Children’s Mathematics that will be released in October (super excited to read it!) and so whoever wins my raffle will have a chance to decide if they want to get the old version right now or I will pre-order them the 2nd edition and have it delivered to them when it is released.

Sarah over at Adventures in Guided Math is next in the blog hop line up:

 

 

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