Wednesday, May 14, 2008

Writing a Final Exam

For me, one of the hardest challenges of teaching is making up homework assignments and final exams. For homework assignments, there's some assistance from the textbooks (and I re-use problems a lot), but final exams are very challenging: coming up with problems that test a student's learning but under a 3 hour time limitation. Making a final exam usually takes me several hours.

For my final exam, usually about 1/2 is True-False, Multiple-Choice, Give-an-Example-or-Counterexample, or Execute-the-Algorithm-on-This-Small-Example type problem. These are very different from the homework assignments, which are usually proof/computation/programming-oriented, and hence have "bigger" problems. The other 1/2 is more like the homework assignments -- proof-type-problems -- but sufficiently easier (or with sufficient hints) that students can hopefully get through them quickly. Interestingly, although you might think the first kinds of problems are easier, on both halves, student averages are about 70%.

I've toyed with the idea of giving take-home finals (which I do sometimes in my graduate classes), but these days it's just too easy for students to cheat. I know I've had students anonymously mail questions around looking for people to answer them. And arguably it's useful to have the final exam test something different than the type of problem-solving that they do on the homework.

When I think of the time spent making a final, I know I'd be happier not to give one. And of course the students would be happier too. Not better off, I think, but happier. Perhaps there's a different solution....

10 comments:

Anonymous said...

I frequently feel that exams are good at identifying students who *don't* understand the material, but are not very good at distinguishing students who do know the material.

AC said...

I've toyed with the idea of giving take-home finals (which I do sometimes in my graduate classes), but these days it's just too easy for students to cheat.

Surely this is not a concern at such an esteemed university as Harvard! I have been routinely giving take home finals in the undergrad Theory of Computation course at Dartmouth and I do not think there's been a single instance of cheating. Am I naive?

-- Amit Chakrabarti

Michael Mitzenmacher said...

Amit: Yes.

Harry Lewis said...

Amit is right. Dartmouth students don't cheat.

Paul Beame said...

I always have difficulty starting grading because I dread the possibility that I screwed up in assigning a question or that a significant number of students misinterpreted a question on which nobody asked for clarification during the exam.

This last fall I made a small tweak on a question that I had asked on a previous exam. The tweak eliminated an accidentally correct answer but did very little to change the problem. The number of correct answers plummeted, by much more than the number of accidentally correct answers.

Anonymous said...

I used to inform the students that at least one exam question would be very similar to one of the homework assignments - typically proving a slightly modified version of a claim previously given as homework. That made my life easier (one question is easy to write) and it also had the positive affect of making the students reread their assignments and (hopefully) understand them better in light of subsequent material.

Udi

Norman Ramsey said...

I'm not a big fan of final exams, but ironically the main reason I give a final is to give me an idea which students are doing their own homework. I try to make my final-exam problems very similar to homework problems.

I also always have at least one final-exam question that introduces an interesting new topic. One year it was using continuation-passing style to build an automaton to recognize very simple regular expressions. This makes the exam more interesting for me and more interesting for the students.

Don't ask me about the year I got carried away and made every question on the final 'interseting'...

Anonymous said...

Half the reason I give in-class exams is so the students will study the material. Students are busy, and wonderful optimizers-- how are they going to allocate their precious time when they have many other classes, extra curricular activities, friend, and maybe even jobs. If they have an exam coming up, they will allocate some of their precious time to try to ensure they have what they think I think is mastery of the material I want them to know (and will be testing). In fact, I think they learn twice as much if we go through the exercise of in-class exams. Grad students are a completely different story-- they are in fewer classes, and often what you want is for them to demonstrate sufficient mastery that they can take the material someplace entirely new, and not everyone has the particular skill set that allows them to produce creative thought on a timed in class exam-- so takehome exams are often best for graduate classes.

Anonymous said...

Adding to Udi's suggestion, it is good practice to ask a question that would have a thirty second answer if the student did the assignment on his/her own, while taking 10-15 minutes (at best) to answer if they had never thought about it before.

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