Anyone who has worked with students learning algebra knows the truth to the maxim: MISTAKES HAPPEN.
This is the first in a series of posts offering PRACTICAL SUGGESTIONS for decreasing the number of algebraic mistakes students make.
First, it’s useful to recognize a key fact: we can’t help students with mistakes if we don’t know what causes those mistakes.
Years of tutoring have taught me a lot about why students make mistakes. And one major cause of mistakes in algebra is that students combine terms that should not be combined. Not all their fault, though. Students are often confused about what they may and may not combine. And it is tricky!
Take a problem like this: 8 – 2(3x – 7)
Certainly some kids can simplify this expression with no trouble. But in my experience, many struggle with a problem like this (when first learning it), and quite a few stay befuddled for quite some time.
The biggest mistake is that students think they can and should combine the 8 and the 2 through subtraction, proceeding like this:
8 – 2(3x – 7)
= 6(3x – 7)
= 18x – 42
Q: How can we help students avoid this mistake?
A: Use a mark that show students what gets combined and what stays separate.
I will start to elaborate on how I do this in tomorrow’s post.
Extra, extra! I thought it would be interesting for you readers to send in comments on the kinds of algebraic mistakes that “drive you up the wall” the most. When I get a number of comments in, I will conduct a poll to see which mistakes people find most vexing. Should be “fun.”