I just gave a quiz on solving systems with substitution. There are six problems, which doesn't sound like many, but the problems are long and it's so easy to make mistakes. Many students understand what they're doing, but they lose points on careless mistakes. It's rare to have a student get everything right...maybe two or three perfect papers per class.
This is especially frustrating because I reemphasize the meaning of their solutions. I ask them, "Why did I just solve for x and y? What the hell does any of this mean? Who cares?" This all sounds like common sense, but I've tutored too many kids who could follow algebraic procedures, but couldn't tell me what any of it meant or what it was used for.
And every year I would show them how to check their solutions by substituting them into each equation. And every year, on the quiz, they were too lazy to do it. It drove me nuts!
So last Wednesday, before I handed this quiz out to my last class of the day, I pleaded with the kids. "Please, check your solutions. Make sure they work. I'll be so proud of you. I'll take your quizzes and put them on my refrigerator. I'll take down my son's drawings to make room for them. Just do me this solid."
Some students finished early and tried to turn their quizzes in. I gave them dirty looks. "Did you check it? No? Go back and check it!" They grumbled, but did what they were told.
And it paid off!
I was happy to see that this particular class had eight perfect papers. And a number of other students had much higher grades. I have to believe that some of these students had some mistakes in their papers, saw that their solutions didn't work, and fixed their errors.
Emmett's drawings are coming down. These quizzes are going up. Sorry Emmett. :(
By the way, my favorite quiz was from a student who typically gets F's in my class. I could tell that he was working really hard on it. He was aggravated that a couple solutions weren't working. He was able to find the error in one of them and got a B on the quiz.