So...we all know of it, we all love it (or love to hate it). Math homework, an old time friend of some of us, eventually rears its ugly head sometime or another in a high school student's life. The question is, what's it good for, really? Why does it have to exist, and why don't teachers take it for credit most of the time?
Well, honestly, I have no idea. But should I go out on a limb (specifically, my right leg) I would come up with some reason why math homework needs to exist to make this world a better place. (OK, not quite that far.)
When we start out math, we learn the basics, and I mean the basics. Like that 2 comes right after one (integer wise) and that adding is the opposite of subtracting. Think about it for a second; would we really have the time to repeat that much over and over again today, when we are learning how to factor and graph polynomial equations to the nth degree???
No. So that's why there's homework, to buy teachers time outside of class so they can cover the truckloads of coursework that they need to teach within America's amazingly short average school year of 180 days. This is the main reason why we cannot go through homework in class as much as we used to as recently as 6th grade! We'd still be in Algebra I should we have spent that much time reviewing stuff we should already be familiar with.
But why isn't it counted for credit in most of our classes? Well, in honors classes, students are supposedly intrinsically motivated to do their work; they work not for the points, but for their own self-improvement. If teachers counted homework for credit, they also run the risk of people cheating on it and learning nothing at all. By putting the pressure on the students individually to do their homework, they save themselves the time, effort, and potential hassle of counting homework for grades. This also helps out those students who can get 100% in math on everything without even trying one bit. "More power to them," my math teacher says. Of course.
But... in higher level math classes, preparation for college is one of the topmost priorities. If the teachers do not count homework for credit, they are giving a "demo," if you will, of college. There, all you have are a midterm and a final, give or take any other small assignments. If you don't have your act together there, the teachers won't care. You're spending the money, right? By having just tests and quizzes make up your grade, the teachers make it very difficult to scrape by on some HW that you obviously BS'ed the period before.
And a final reason why math homework exists is to frustrate the hell out of students when there's a pop quiz on the homework topic that the teachers "know everyone did" the night before.