Guest Blogger: Tammy at Forever in First!!

Hi.  My name is Tammy from Forever in First.  If you're like me, I'm sure you love hearing all about teaching from across the Atlantic, but Kelli asked if this little teacher from Idaho would be her guest.  Idaho isn't quite as thrilling as England, but hopefully what I have to say will hold your attention.  Thanks Kelli for letting me drop by!   

I'm fully aware that it's summer and your brain is probably on vacation just like mine, but would you do me a favor?  I double dog dare you to compute the answer to this problem without using an algorithm.  In other words, carrying, borrowing, and all the tricks that you most likely learned as a student are illegal.  Grab a piece of paper if you need to and play along pretty please.  Here goes.

847 + 256

How'd it go?  Was it hard to ignore the rules of an algorithm or did you find it easy to think flexibly about computation?  If we were in my classroom, I'd ask several of you to draw your strategies on the board and ask you explain your thinking to the rest of us.  You would definitely notice the absence of any algorithms.  You would see several different strategies that originated from the students instead of the teacher.  You would hear the reasoning behind each strategy.  You would hopefully walk away with several new computational tools and a more complete concept of how addition works.  You would definitely know that there's never just one way to solve a math problem.

"Flexibility with a variety of computational strategies is an important tool for successful daily living.  It is time to broaden our perspective of what it means to compute."  John A. Van de Walle, Teaching Student-Centered Mathematics 158

You see, I've got math on my brain this summer.  I'm in the middle of this thought-provoking book.  (Get yourself a copy!) It definitely stretches my thinking and at times confirms what I had always thought.  I love books like that.  It covers about everything, but today I have just enough time to hit on the somewhat controversial topic of computation.  Who knew computation could be so controversial?  

Like most of us, I was taught algorithms in school, but as a teacher, I've simply never believed in them.  The book states that they're not evil, but Van de Walle also says,

"Far too many students learn them as meaningless procedures, develop error patterns, and require an excessive amount of reteaching or remediation."  (162)  

Does any of that sound familiar?  The premise of this book and of the math classes I've taken in the past few years is that students learn to compute more efficiently and understand what they're doing more completely when they invent their own strategies.  Teaching them to carry and borrow does not allow them the freedom to do this, even in classrooms where algorithms are conceptually taught well.  The book lays out several other reasons why invented strategies are more beneficial than prescribed algorithms but I'm afraid this post would get way too long and you'd never forgive me, so I'll let you get the book and read it for yourself.  When I allow my kids to think independently and flexibly about math, this is a taste of what they come up with.  (These strategies originated from contextual tasks.  I apologize that you don't know the contextual problem behind the strategy.  Also, notice that many equations are written in horizontal form.  This is on purpose.  It's harder for algorithms to sneak their way into the mix when the problems aren't written vertically.)

(Yep, this is my writing, but the kids told me all the steps.  I was simply their secretary.)

Stepping away from the safety of an algorithm might create a little fear in the hearts of some teachers out there and understandably so.  If that's you, you're in good company.  Look here to read about some of the leaps of faith I've taken on my journey as a math teacher.  If you're not ready to leap, then maybe this post has raised some questions or sparked some unexpected thinking.  I believe Van de Walle would be pleased with that, and his book would definitely fill in the holes that I've left wide open.  If you can get your hands on a copy, it will broaden your view of what it means to compute, and in my opinion, our students will be better mathematicians because of it.