Over the past week, Ive seen this image multiple times on Facebook and elsewhere, a supposed denunciation of the Common Core version of math that kids are now learning:
That picture is especially popular onconservativesFacebookwalls and Im sure one of your relatives has said something about it, too.
On the surface, it seems ridiculous. The top makes sense; the bottom is silly;screw you, Common Core!
Except that the topdoesntmake sense, the bottomdoes, and the connection to Common Core is completely misunderstood. (Says this math teacher.)
Heres whats going on: The top is how most of us learned subtraction. Im sure your teachers taught you what was going on mathematically, but do you really remember what they said? Probably not. For us, its just an algorithm. You can do it without thinking. You hope theres 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 explainwhyit works, they'd have areallyhard 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, thats fine. For math teachers, thats a problem because it means a lot of students wont be able to grasp other math concepts in the future because they never really developed number sense.
Thats where the bottom solution comes into play. I admit its totally confusing but heres what its saying:
If you want to subtract 12 from 32, theres 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. Thats 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 arent going to get out a sheet of paper and do this:
Instead, youd just figure it out this way: Itd take 70 cents to get to $5 and another $15 to get to $20 so you should get back $15.70.
Thats it. Thats the sort of math most of us do on a regular basis and itsexactlythe sort of thinking the new way in the picture is attempting to explain. Granted that was an *awful* example to use, but thats the idea. If students can get a handle on thinkingthisway instead of just plugging numbers into a formula, the thinking goes, it'll make other math skills much easier to understand.