## Friday, May 06, 2005

### Meta-Exam Questions

Here’s an actual question from an exam I gave earlier this semester:
Professor Nerdburger is deciding what kind of exam to give. He considers multiple choice and essay exams just as good in terms of measuring students’ performance, so he only cares about minimizing the total time-cost of creating and grading exams. The opportunity cost of his time is \$60/hour (or \$1/minute). It takes one hour to create an essay exam, and it takes four hours to create a multiple choice exam, regardless of the number of students. It takes 20 minutes to grade each student’s essay exam, and it takes 5 minutes to grade each student’s multiple choice exam. (a) Find the total cost function for each type of exam. (b) State the type of exam Professor Nerdberger should choose, depending on the number of students in the class.

[Answer: TC(essay) = 60 + 20q; TC(mc) = 240 + 5q. Professor Nerdburger should give an essay exam for any class with fewer than 12 students, and a multiple choice exam for any class with more than 12 students. For a class of exactly 12, it doesn’t matter.]
The numbers are arbitrary, of course, but the problem actually does describe – at least to a first approximation – how I think about what kind of exam to give. Essays have a low fixed (preparation) cost but a high variable (grading) cost, whereas multiple choice exams have the reverse. The variable cost is dependent on the number of students in the class. Thus, the more students there are in a class, the more sensible it is to have a multiple choice exam.

However, this approach does leave out two main factors that I consider. First, if exam questions can be recycled from semester to semester, then the fixed preparation cost can be spread out over time. Instead of a decision-rule that depends on number of students in a class, the appropriate rule (when questions can be recycled) should depend on the number of students over time. Since that number is likely to be very large for any professor who plans to keep his job, this factor strongly shifts the balance toward multiple-choice tests.

But second, most professors (including me) disagree with Prof. Nerdburger’s judgment that essays and multiple-choice questions are “just as good in terms of measuring students’ performance.” Written answers convey some information about student learning that Scantron answers cannot. This factor points toward having more essays. As a result, professors have to make comparisons of dissimilar values. Unlike Prof. Nerdburger, who has the luxury of measuring everything in terms of time spent, we have to weigh the better information attributable to essays against the greater expenditure in time to grade them.

And then there’s the possibility of other question types. In most of my classes, I end up using a mix of multiple-choice and short-answer questions, since short answers convey most of the information I would glean from essays, but they are faster and easier to grade (though not as fast multiple choice).

Anonymous said...

You are a wise guy to continually seek to improve your teaching and grading methods.

How about bringing back oral exams? I think that they should be videotaped or recorded in case the student objects to the grade given. I'm envisioning an interactive sort of exam where you can interrupt the student and ask him to amplify on this or that. Okay so it was a bad idea...

I once had a friend who gave an oral report to his high school history class on the Holy Roman Empire. He spoke for a solid week before the stunned teacher finally remembered that their were other students in the class. He was a certifiable genius or idiot savant or something like that. He looked a lot like Herman Munster.

JB said...

But second, most professors (including me) disagree with Prof. Nerdburger’s judgment that essays and multiple-choice questions are “just as good in terms of measuring students’ performance.” Written answers convey some information about student learning that Scantron answers cannot. This factor points toward having more essays.

Being a fan of multiple choice personally...I'd make the case that the information that the essay conveys has a certain degree of signal, and noise in it. I think that often enough that information conveyed is more noise, than signal, and can mislead professors, just a different perspective.

Chris said...

Speaking from a purely student standpoint, I'd have to go with the essay. Besides, there's not much room for bullshit on a m/c. Though, maybe you can't bullshit in some courses as much as you can in others.

Jacqueline Mackie Paisley Passey said...

Don't most textbooks come with multiple choice question barks?

Anonymous said...

Of course, if you recycle questions, your students will pass on their tests to frat brothers in future classes, making student life much more efficient...