Homework is Hardwork

Each year, I struggle more with my homework policy more than anything else. This is really the most important part of a math course, the individual practice that will allow the student to master the concepts and algorithms; however, it is not the “big game.” The tests are where the real assessment comes. This is where students must "stand and deliver" or "sit" and deliver, whatever the case may be. Many college math courses’ grades come solely from 2 or 3 tests each semester. Homework often counts very little as part of the final assessment. In some classes, it counts for nothing.

This is why I really do not like the current grading system enforced unilaterally for our high school, which not only puts such little emphasis on homework, but also allows students to turn it in late (imagining practicing for a football game AFTER you've lost the game!). When students arrive at the university, professors expect that the student knows the importance of homework as a means to mastery, and that they have the prerequisite skills through the practice of homework. Although this is obviously not the case for all upper-level high school students, we should be preparing them for such an assessment system.

However ideal, it becomes an overwhelming burden to personally grade each student’s homework daily and provide critical feedback. To have each student grade his own in class allows them to immediately see their errors and correct them, but this is a serious chunk of time, meaning less time for the new material, to play with the mathematical kittens, so to speak. I have found that this creates a downward spiral: the more time we spend covering homework, the less time we have for the lesson, the less they understand the new information, the more questions they have the next class period, the less time we have for the new material, ad infinitum. The difficulty comes in finding the balance between holding their feet to the fire, getting them to do the homework everyday and not spending a lot of time going over things they should have picked up on their own. The challenge is to create an upward spiral.

I have found that a combination of completion and accuracy grades, depending on the difficulty of the lesson, the complexity of the solutions, etc., works the best for me. We have a homework assignment daily, without fail. The homework grade should be a reward for the student who exerts the daily discipline required to master the subject. In addition, homework is due at the beginning of class, as soon as the bell rings. Quick quizzes every other class period give me a good idea of who is doing quality individual practice, and who is copying their homework from another student. I never permit students to use notes or homework on quizzes (even though they lobby for this consistently.) This forces students, those that are motivated my grades, at least, not only to go through the mechanics of the homework, but to do it for comprehension as well. When done right, math homework is a very long, arduous, personal triumph of a student over his own limitations, and he walks away from the session sweaty and in possession of something he will never lose.

This is something that is ostensibly lacking in classrooms across the world. I have found that students go through the routine of completing the assignment as if the completion itself was the goal, rather than an opportunity for them to get a better return on their investment of time, energy, and resources. In the end, students reap what they sow. Good grades do not equal learning.