I actually took these photos right after the whole What Common Core is NOT controversy, but decided to wait until now to post it. The big argument that everyone had regarding the following math problem is that we should just ‘subtract down’ as we always did.

With this particular problem, it appears as though that can be done. We don’t have to borrow from a different column, so we can follow a simple algorithm. That’s all great… until problems get more complex, and children do not understand the rationale behind borrowing (that you are taking one group of 10 and breaking it into individual 1’s to be able to subtract).

So here’s this simple problem, using one method to solve it using manipulatives.

Children need to understand place value to recognize why we subtract in the manner in which we subtract.

A lot of people told me to just subtract 2 – 2 and 3 – 1. Well, that’s not even the problem that’s being presented. Here is why.

This is what 32 actually looks like.

Then we must do the same thing with 12.

Now we can actually solve the problem. Begin with the right column – directionality does not appear to matter in this problem, but it will matter when you have to borrow in future problems. Better to teach the right way from the beginning!

Move to the left column. This required two sheets of paper.

So now we can actually understand and solve the problem correctly. Does it appear to be a lot of extra steps? Sure! but will it help children to have a deeper understanding of what we’re actually doing, rather than teaching them to follow a simple algorithm, that long works for this specific type of problem? Absolutely!

Jim Lambert says

I came across the original graphic on Facebook and followed a link to your original ‘Core’ article. I wanted to point out an assumption you made in this demonstration: “Begin with the right column” and your statement to teach the right way (because of the possibility of borrowing in subtraction).

A few years ago I picked up an abacus and learned the basics of how to use it. Abacus subtraction starts on the left and works to the right, the final subtraction being the ‘ones column’. This allows you to ‘borrow’ from the final result of subtracting earlier columns, rather than ‘borrowing’ from one of the numbers before performing further subtraction on it. I won’t say it’s better, although it has advantages with the abacus, but it shows that our right way may not be the only or even best way.