I work with a lot of students after school, many of who are struggling. I always say it’s the best place to learn about issues students are having. Students are more open to discussing their frustrations and you can watch a particular student work for much longer periods of time. I hear this from students (and parents) all the time: “My son seemed to understand it even when I went over the problems with him but he gets it wrong on the test. I can’t understand it”. So what is going on?
One of the first things I learned years ago is that students learn to solve problems by (smartly) recognizing patterns. It’s tough at his age to have a real desire to understand “why something works the way it does” (I didn’t have it at 15 years old). But the problem with pattern learning is that it falls apart as soon as a problem looks a little different.
Example of common mistakes with distributive property
Let me give my first example that I see very frequently that involves the distributive property (of multiplication).
On the left is how students are typically are shown how to distribute. All of the problems they practice look like this so they learn to distribute whenever they see a number next to a parenthesis – without a thought as to why they should do it. But when they number appears on the right side of the parenthesis, they don’t know what to do (even though it is still multiplication and the 2 should be distributed).
