The Check-Your-Work Battle
Let’s assume that students want to get the right answer. It follows that they would be willing to check their work. But this is a constant battle for many teachers. There must be something more to students’ unwillingness to take our great advice.
When solving systems of equations, I teach students to set up four boxes to separate the steps. The fourth step is to check the solution by plugging it back into the original equations. Most of my students complete all four steps because they know that they will get detention otherwise. But they still get the wrong answer.
I noticed that even though they are checking their work, they will often fudge the check at the end so that it looks like their solution worked even though it didn’t. Or sometimes they will check their work, see that it is wrong and leave the entire problem anyway. When I asked someone why they did this, they said, “Well, I’d written in pen.” This is a separate battle that we will save for another day. I refuse to believe that most students are checking their work and still getting it wrong because they are lazy. They must not understand how checking their work helps them get the right answer. And if you think about it, this makes sense. Checking one’s work just tells you if you’ve got the wrong answer.
This is why it is not enough to teach students to check their work. We must teach them how to go back and fix their work after they realize it is wrong. And how do students learn? By watching us do something? No. They learn by having to do it themselves.
This is how I realized that my feedback was actually teaching students bad habits. In my attempt to be the very best teacher ever, I was running around from desk to desk catching silly mistakes and telling each student exactly where they went wrong. “You missed a negative sign.” “Seven times five isn’t thirty.” “You substituted for y instead of x.” It got to the point where after a student checked their work and saw they’d made a mistake, they’d raise their hand and ask for help.
But if this is how students practice checking their work then why would they do it when they’re on their own and I am not there to tell them where they went wrong? Instead, they must learn to do this for themselves. That means that I am not being Super Teacher when I give them very specific feedback. It would actually be more helpful to say, “Nope. Find the mistake.”
This kind of feedback involves a different battle that usually sounds like this:
Me: There’s a mistake. Go back and find it.
Student: Taking one millisecond to look at their paper… I can’t.
Me: It’s there. You’ll find it.
Student: Making taking a few milliseconds… I still can’t find it!
Me: It’s there. Go back to the beginning and look at each step. It’s a little mistake.
Student: Seriously, please! Help me! It’s not there! I’ve BEEN trying!
Me: Of course it’s there. You checked your work and saw it was wrong. Keep looking.
Student: After a few minutes… Ohhh!
It’s kind of nice when you realize that you can actually teach better by doing less. At first, this new kind of feedback might frustrate students. But ultimately it is setting them up to be more independent mathematicians.