Math homework is necessary for the same reason practicing the piano is necessary: it’s one thing to “get” what the teacher taught during the lesson, but it’s another thing to be able to perform that same skill independently and fluently.
Yet, all too many students practice math incorrectly, and they therefore gain little benefit, or even worse, they solidify misunderstandings and bad habits.
Practice doesn’t necessarily make perfect, but enough practice does make permanent, which is why guitar teachers, ski instructors, and golf pros are all such sticklers for proper form; they know how hard it is to unlearn errors that have become ingrained.
Many students will do a whole page of math and never check their answers. How do they know they were doing the right procedures? (Answer: They don’t.)
Or, students check their answers after completing the entire assignment, and only then discover that their answers don’t match up with those in the back of the book. In both such cases students tend to declare: Oh, well, the teacher will go over it in class tomorrow.
But in each of these scenarios, the student has now thoroughly practiced BEING WRONG.
Here’s the right way to do math (or math-related) homework:
- Locate the answer key. If it’s in the back of the textbook, insert a bookmark or Post-it note for easy back-and-forth flipping.
- Do the first problem.
- Check it on the answer key.
- If you were correct, move on to the next problem.
- If you were incorrect, figure out what you did wrong before you move on.
- Check your arithmetic; did you make a careless mistake?
- If you realize you don’t understand how to do the problem, go to your notebook or your textbook and page through until you find the topic and carefully follow the explanation.
- Still stumped? You can get help on www.KhanAcademy.org. Or, ask a friend or parent or sibling for help.
- Only as a last resort, put a star next to the problem and make sure and ask the teacher for help tomorrow.
- Proceed to the next problem.
Remember, the reason for doing math homework is to train your brain into automatically performing the CORRECT procedures. This is why you need to check after every problem and make sure your thinking is on target, and, if you are off-track, to fix your misunderstandings right away.
In fact, it’s beneficial to make mistakes and learn from them. Research shows that when lessons are too easy, students don’t learn them very well!
Believe it or not, thinking hard and even battling with confusion will make you smarter in the end. These experiences may not feel good, but they’re good for your brain. (So many sports and music skills are also like this, such as learning to swing a bat properly or bow a violin correctly; tedious yet vital!)
And the last step in math homework should always be spiral review. This means going back and practicing a problem or two of older material from the night before, the week before, or the semester before. Math is cumulative, which means those older skills are always important and need to be kept honed.
Of course this method of doing math homework is more time-consuming and effortful up front, but students who follow this plan will then be thrilled to find that they hardly need to study for tests; they know the material already and feel prepared and confident.
Like so many things, doing math homework the right way is a pain at first, but developing this habit will have a huge payoff!
[sculpture on lawn at Tulane University]