Guest Blog: She likes math, but she hates math homework

Emma, 6th grade, likes math (does math circle voluntarily on Saturdays, for example), but hates math homework.  When I asked her why, she sent me the following well-thought-out response--unedited by me (okay, I deleted two commas).  Math teachers, take note!
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As a 6th grader, here are the reasons I hate math homework, and solutions to the problems:

1) Quantity- Homework is supposed to be for us to practice what we've learned. So if you know the material, then it's a waste of time to do 20 similar problems when all you need to prove that you know the material is 4 or 5. And if you don't know, then you'll practice incorrectly, and it really won't help you to learn how to graph inequalities if you're repeating incorrect steps for any number of problems greater than that needed to prove that you know the material.

2) Quality- Having similar problems doesn't help anyone. Sure, if you want to memorize steps, it may be helpful, but in order to understand the math behind the equation and prove why you need to take the steps, you should have a variety of problems. Because in order to understand how to use a method, you should take the time to practice with different types of problems, or else you run across a slightly different problem and you don't know how to do it. 

3) Comprehension- Having problems to solve like "x+2=5. x=?" doesn't help you learn math. That's arithmetic. Arithmetic is something that you can do with a calculator. Math is knowing why x=3. And just showing your work doesn't help, because again, you're just showing your calculations, which again, could be done with a calculator. What helps is asking, "Why does x=3?" Because then you have to look up from your calculator and think about what makes the problem work.

4) Grading (as a class)- When homework is being graded as a class, then you should again focus on the logic hidden behind the problem. Ask a kid to come up to the board and prove why their answer is correct (having fewer problems would also prove to be helpful here). When you go over them by just stating the answer, it doesn't help the kids who got the answers wrong. Unless they just made an arithmetic error, they still don't get why it works, still don't understand the material, and now only know that they were wrong, which doesn't help. And as teachers, your job is not to make kids pass or fail, but to get them to learn something.