About Homework

Most of the time and energy devoted to a mathematics, science, or engineering course will go into homework. This means reading the text, reviewing class notes, and doing assigned exercises. Some classes have special projects, labs, or other activities, but most rely mostly on homework -- or on tests for which homework is rehearsal.

So what is there to say about homework?

First of all, what is homework good for, anyway? There's the basic advantage: in a well-run class, doing the homework prepares students for taking the exams. This does not mean that exam problems are like homework exercises; it means that students who put a lot of time and effort into homework tend to do better in exams than students who do not. But there's an additional advantage: doing the homework helps students to learn the material better. By reading a text, a student can memorize facts; by doing homework, a student can learn how to use those facts. For more on this, click here.

So if homework is necessary, how does one do homework?

One must find time to homework. The standard rule is that in a university course, homework and studying take at least two hours out of class for each hour in class; note that this is a minimum. Thus each 3-hour class presumes a minimum of 6 hours out of class, so that a full-time 15-hour load presumes a minimum of 30 hours out of class, for a total of at least 45 hours on courses each week. This requires a certain amount of time management: note that there are only 168 hours in a week, and since sleep deprivation reduces one's ability to function, after setting aside 8 hours per night, there are 112 hours in a week, of which at least 45 should be committed to classes. For more on this, click here.

There is more to time than just selecting some number of hours each week. One must make time during which homework will actually get done. It is better to work regularly instead of fitfully. This makes it less likely that one will fall behind (and it is especially dangerous to fall behind in a math class --- or indeed any class with lots of regular homework).

• Working regularly is habit-forming.
• If you are behind, you have practically no margin for error.

But homework involves more than just putting in the hours. You may not want to hear this, but attitude has a powerful effect on performance. This is a problem because we've been taught to loath homework. But the most effective approach to homework is with an attitude that is clear and focussed: one should be conscious of the material, not of one's reaction to it. For more on this, click here.

So now you've set up a schedule and you are working on your attitude; what do you do when homework time comes?

There are the mechanics of actually doing the homework. A typical homework assignment will consist of a variety of exercises, some easy, a few hard, and some in between. Read through an entire problem carefully first: many mistakes and much lost time arise from misunderstanding problems. Write out the problem and solution in a first draft (perhaps, in a notebook you keep) and then write up a second draft which you turn in. And some problems are hard, and cannot be solved rapidly. Word problems and proofs (and tricky computations) often require a different approach from easy problems: they cannot be solved in a few minutes, or even in a single sitting. These problems must be solved by returning to them repeatedly: not by obsessing over them (much less worrying about them), but by trying to make a little progress each time. Problems can be hard because (a) they require a trick (and finding the trick may involve a lot of brainstorming and false starts) or (b) it is very long (in which case, just keep going). For more on this, click here.

Some final comments:

• Neatness counts: it forces you to think more clearly and is easier to grade.
• Use lots of paper: don't try to squeeze lots of stuff into a small space.
• Write things down: skipping steps and doing things in your head leads to mistakes.
• Draw pictures: it makes the situation more clear.
• Minimize distractions: music, TV, etc, get in the way.