So, Sunday, I started a horror story about math over at Virginia is For Teachers. This was prompted by a few things.
First, that I'm in grad school to get certified as a math specialist. (I'm thinking I might have bitten off more than I could chew there)
Second, that I'm teaching fifth grade this year after a ten year hiatus and I'm having to get re-familiar with multiplication and decimals.
And third, my school is trying really hard to move away from traditional math teaching to a conceptualized approach where kids really UNDERSTAND why numbers work the way they should.
When I was teaching second grade- this wasn't too huge of a deal. Young kids- relatively new to math anyway, and we're just in addition and subtraction.
The focus is on manipulating the numbers:
Short little bits like this- parents don't mind. It's when you start messing with "regrouping" that they get upset.
Can you remember when we stopped saying borrow and carry and drop down and started using the word regrouping? Parents really got upset then too- but fifteen years later, they've adjusted. So just think of it this way- 15 years from now, they'll stop being upset about expanded form and new math. But why wait that long? Let's look at educating parents as well as our kids to build a bridge between the two systems.
The first thing that sends chills of horror through those raised on the algorithm is the horizontal equation. What adds the fingers down the chalk-board cringe to the entire situation is when the smaller of the numbers comes FIRST.
This one right here- might make your brain hurt:
47 + 89 =
However- any algorithm loving math nerd can solve this in a wink. We just do this:
And now children learning "new" old math all over the country begin to weep. Because they've just solved the problem doing simply this:
What's missing is the bridge between the two. A middle ground so that the kids can see how to get to the traditional algorithm, and the parents can see there is a method to the madness.
Here's one possibility:
Fewer steps decomposing a number looking for friendly numbers.
Or this one:
Decomposing just the bottom number and using the ones place to create friendly numbers.
Either way, eventually the step needs to be taken to explain that the "1" that unceremoniously got plopped on top of that 8 in the first example of the traditional algorithm, actually means, "1 group of 10". Here's one easy way for parents to show that in their own traditional algorithm style:
Now let's look at subtraction.
Same horror story, just reversed:
87 - 49 =
Good old traditional getting it's borrow and carry on!
So here is a decomposing method used to keep the integrity of place value when the student is manipulating the numbers. Parents REALLY really hate this one:
Both students and parents hate this black magic right here - adding when you're supposed to subtract! Whaaa??? (Although it is probably the coolest):
There are two different ways to bridge this to the traditional algorithm. Note that both attempt to keep the student focused on place value:
What's important to remember is that the end game is for students to understand numbers so well, that they can do much of it mentally. It's not to actually slow down calculation. When students AND parents can see the progression from one method to the traditional algorithm, life gets better, The magic kitchen table gets more magical.