Over the past week, I’ve seen this image multiple times on Facebook and elsewhere, a supposed denunciation of the Common Core version of math that kids are now learning:
On the surface, it seems ridiculous. The top makes sense; the bottom is silly; screw you, Common Core!
Except that the top doesn’t make sense, the bottom does, and the connection to Common Core is completely misunderstood. (Says this math teacher.)
Here’s what’s going on: The top is how most of us learned subtraction. I’m sure your teachers taught you what was going on mathematically, but do you really remember what they said? Probably not. For us, it’s just an algorithm. You can do it without thinking. You hope there’s no “borrowing” of numbers involved, but if you had to do it by hand, you could probably pull it off.
The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”
That’s where the bottom solution comes into play. I admit it’s totally confusing but here’s what it’s saying:
If you want to subtract 12 from 32, there’s a better way to think about it. Forget the algorithm. Instead, count up from 12 to an “easier” number like 15. (You’ve gone up 3.) Then, go up to 20. (You’ve gone up another 5.) Then jump to 30. (Another 10). Then, finally, to 32. (Another 2.)
I know. That’s still ridiculous. Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)
You sure as hell aren’t going to get out a sheet of paper and do this:
Instead, you’d just figure it out this way: It’d take 70 cents to get to $5… and another $15 to get to $20… so you should get back $15.70.
That’s it. That’s the sort of math most of us do on a regular basis and it’s exactly the sort of thinking the “new” way in the picture is attempting to explain. Granted that was an *awful* example to use, but that’s the idea. If students can get a handle on thinking this way instead of just plugging numbers into a formula, the thinking goes, it’ll make other math skills much easier to understand.
This image from Reddit clarifies the situation even more (click to enlarge):
As that image also points out, Common Core doesn’t say, “Do this.” Rather, it suggests some general standards that students at each grade level should meet and most states have agreed to adopt those standards.
But none of that matters to the people who would rather complain about the “new” math without taking a second to understand what they’re even looking at.
There may be plenty of reasons to criticize Common Core (such as the standardized testing component of it), but this isn’t one of them.
***Update*** (3/9/14): I should point out that the Common Core standards do include teaching students the “old way.” The “new way” is just one suggested method of teaching students how to add/subtract numbers.