How many times have you hear the phrase "Practice makes perfect."? I've heard it from my grandmother, my parents, my teachers, just about everyone. I even heard it the other day from another teacher. He commented the new math program did not have enough practice problems.
I realized one thing about practice and that is you have to learn to do it correctly the first few times or you will impress the wrong moves in your muscles or in your brain. If a student learns the process incorrectly, it takes about 21 days to relearn it correctly. Imagine 21 days.
Have you taken time to actually analyze the mistakes of your students? I haven't but I have noticed that certain students make the exact same mistake every time they do the problem. For instance, when rewriting a two variable equation into slope intercept form, they always combine the x variable and the constant into one term. Every time. This means they have the incorrect process imprinted in their brain and it becomes harder to reteach it.
This means you have to reteach the concept which is almost like having to break them of one bad habit and replace it with a better habit. This means you have to reteach the material and have students practice the correct process over a 21 day period so hey have a chance of learning to do it correctly.
Sometimes, they develop the incorrect process because they were absent while other times its because they didn't learn it properly the first time or perhaps they got careless and just started doing it wrong. It doesn't matter because we have to make sure students learn and practice it correctly.
I'm figuring out I have to break it down so they practice say the last step on their own, then I have them do another step plus the last step independently until they can work the whole problem on their own. In addition I try to spread the lesson over several days while practicing previously taught material. I use homework as another place to practice previously taught material so they have a better chance of learning it properly.
The current thought on this topic is not "Practice makes perfect" but "Perfect practice makes perfect." Next week I'll provide some ideas for helping students learn the material correctly the first time and looking at effective ways of reteaching.
Feel free to comment and let me know what you think about this idea.