An Ode TO The Common Core

Do you remember how to divide fractions?

That’s what I taught last week in math, and it is a great example of why I love the Common Core. 

If you’re like me, when you learned how to do this, somebody taught you to flip the second fraction and multiply them.

It seems like a magic trick.  You’re dividing two numbers, but you never divide.  You do something else.

Did you ever ask why that’s how you do it?

You probably didn’t.  We didn’t ask those kinds of questions.  That’s how math is done.  Every kind of problem has a set of steps, and you memorize and do them.  We didn’t ask why in math.  Math is something you DO, not something you UNDERSTAND.

Dividing fractions has a different set of steps from multiplying fractions, which has a different set of steps from adding or subtracting fractions.  Dividing fractions also has a separate set of steps from dividing decimals, which is different from multiplying decimals, which is different adding and subtracting decimals.

Oh, and negative numbers all have different sets of steps to pile onto that, too.

Math is all about who can memorize the most sets of steps and who can keep straight which set of steps goes with which kind of problem.  Those who can miraculously do so are “good at math” and those who sometimes forget sets of steps or mix up which set of steps goes with which kind of numbers are “bad at math.”

Until the Common Core.

All of a sudden, instead of being told to memorize an unending list of sets of steps, kids started to learn HOW numbers and operations actually work BEFORE learning the official set of steps.  It all seemed so logical!  Before being told “just carry the one when you add because I said so (except the last 1 - don’t carry that one, because just don't, but carry all the other ones)” when adding large numbers, like this:

Trying to summon the correct set of magic steps.

Students learned WHY that one got carried, by learning a variation like this:

And everybody got real upset about that.  

Except for the kids who forgot which set of magic steps goes with this kind of problem and had something to fall back on that didn’t require memorizing.

This week, I taught my class the set of steps to divide fractions, like I showed you above (YES - the Common Core still teaches the magic steps - it just teaches you how to understand them first.  Weird, I know.).  Within a month, about ¼ of them will have forgotten that set of steps all together.  Another ¼ will not remember if dividing is the operation where you flip one of the fractions, or which fraction you flip, or if you just flip the division sign to multiplication.  Another ¼ will not remember whether dividing fractions is one of the operations where you need a common denominator or not.

Because people forget things they don’t understand.

And nobody understands why when you divide two fractions, you flip the second one and multiply.

Except for the kids who are shown other strategies for doing this, and why it works out that way.

In addition to learning the flip-the-second-fraction-and-multiply magic trick, my class learned two additional ways to think about this type of problem, both of which were based on other understanding-based Common Core strategies they learned when they learned how to divide whole numbers.

When students first learn to divide, say,

​

Did you know that it's possible to understand why long division works, too?  Prior to learning the magic steps of long division, students learn an understanding-based method for dividing large numbers.  ​

They learn to see it visually, like this:

​Pretty logical, huh?  Since I know they learned how to divide whole numbers like that in 3rd grade, I can show them how to use the same logic to divide fractions that way:

Additionally, in 3rd grade, they also learned to divide using “repeated subtraction:”

Knowing that, I could show them that the same idea applies to dividing fractions:

And now, a month from now when ¾ of the class has forgotten the “magic trick” for dividing fractions, they have TWO strategies to fall back on, both of which make sense, don’t need memorizing, and that relate back to how they’ve known to divide every other kind of number for the last four years.

The Common Core will probably be gone soon.  I know my state is in the process of moving away from it.  Understanding math is, apparently, "new math" and not "real math" in the eyes of too many voters.  We’ll soon be back to presenting math as an unending series of steps to memorize and magic tricks to learn.

All I can do is savor my remaining time with you, Common Core.

At least in my practice, you’ll be dearly missed.

​

(Note: for anyone interested in understanding how the Common Core unfolds mathematical concept, I highly recommend this extraordinary video series by Graham Fletcher:  https://gfletchy.com/progression-videos/)

If you enjoyed this post, please share it!

Want to make sure you never miss a new post?  Subscribe below for email notifications of new content.

Want to read more right now?  You're in luck - you can browse past posts by category:

• ​Building A Thinking Classroom
• Leaning Into The Science and Engineering Practices
• Classroom Practices
• Classroom Stories
• Ideas and Opinions
• Pandemic-Related Issues​​