An unexpected event in the last week has caused me to have to write three tests in less than two days. It often takes me at least that long to write one test, and I started thinking (now that they’re finished) about the test writing process. If you’ve ever written a test before, you probably know what I’m talking about, but if not, let me give you a little insight.
The first thing I do is create an outline. Well, not so much an outline as a list of problem types I’d like to have in the test. Almost immediately after that, I have to pare down the list because the second thing I consider is time. It’s difficult to ask more than about 10 questions on a 50-minute test, and if there are proofs involved—yeesh. Then there are the times when I already have a great problem in mind but soon realize that it would have to be the only problem on the test. At this point I have a tentative-but-probable list of problem types.
The next step is the hardest part: actually writing the problems. Fortunately, it’s usually the most fun, too. I am a firm believer in “nice” answers, so I often reverse engineer my problems. This typically involves starting with a problem, solving it, then tweaking coefficients or other parameters to give the desired result. If I’m feeling particularly adventurous, I’ll solve the problem with variable parameters, then solve an equation to find the necessary values for those parameters. For example, if I want a Laplace transform to end up having a nice partial fraction decomposition like
then I can rearrange the equation to get
and this now suggests possible differential equations that will lead to this form. Say
By starting with a solution I’m happy with, I can work backwards to create a problem that will give that solution. (Actually, I started with a different partial fraction decomposition:
but that leads to the wrong kind of differential equation. See, I even tweak my examples!)
Once the problems are written, it’s time to organize them. Spacing and problem order can take a surprising amount of time. I like to put a relatively easy problem on the first page so students get off to a good start. (Of course, that can backfire, so I try to be very careful with what I call “easy”.) The last page almost always has the hardest question(s) because they often require the most space. I also tell my students that it is possible to judge (my evaluation of) problem difficulty based on the amount of space provided. If you only have 0.5″ to answer the question, if probably wasn’t meant to be hard. On the other hand, if you only took three lines to answer that full-page problem, you might want to go over it again.
The last step is assigning points. I used to make every test worth 100 points, but that meant for a 10-question test, the questions averaged 10 points each. Sometimes that makes sense, but “Compute the derivative of cos(2x)” doesn’t really feel like a 10-point problem, does it? Now I assign point values based on how much I think the problem is worth, and the test is worth whatever the total is. A 62-point test? OK. Maybe 48 points? No problem.
So there you have it. Writing tests takes more work than you might have thought. How about all you teachers out there? What do you do when you write tests?