I was recently struck by the idea of writing an exam that was purposefully too long. Basically, the instructor just writes down whatever problems they come up with, related to the subject at hand, and give the complete list of questions to the students. Tell the students they aren't expected to get through everything, that they should look through the list and attack problems they know how to do. And if students finish all the problems they know how to do before time is up, they just keep trying as many problems as possibly. Students have whatever fixed amount of time to get through as many problems as they possibly can.

I was wondering if anybody out there had tried this, or what people's thoughts were about this idea. It seems like setting up an exam this (kinda lazy) way, the instructor can easily see what topics students are comfortable with. I suppose this is possibly the case for more traditionally designed exams. Perhaps we should ask students to rate how confident they are about their answers on exams?

The first question about this method probably is about grading. I'd say each problem is assigned a point value, before being distributed to students. After the exam, the instructor grades whatever work students turn in, and this gives them a point distribution for the class. The highest grade gets an A (presumably), and then you work out what to do with lower grades, perhaps based on the distribution that arises. Perhaps you set a level of minimum points you're going to allow for a... C say, to make sure the students don't conspire to all just do one problem and all get the same grade?

To give credit where credit is due I should perhaps describe the circumstances that led me to the idea. There are 5 sections of the course I am teaching this semester (Calc 2), and we have coordinated exams. This means the 5 instructors all meet sometime before the exam, and write a common exam. The setup we have adopted this semester is to split up the sections that are on the exam, and have each instructor write questions from the sections they are assigned (and whatever other fun questions they want). Then when we meet we have 5 pages of questions, one from each instructor. We meet and decide which problems to keep, and then the exam gets written.

At this last meeting we had, Katherine, one of the other instructors, joked that we should just make copies of the sheets we were looking at, and hand the set to our students as their exam. Naturally, this was the inspiration for the idea asked about above.

So... thoughts? Anybody tried it?

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## 5 comments:

I believe that in Russia for a time they had very hard problems, but were given a long list beforehand some of which turned up in the exam, which reminds me a little of this. However not be Russian I am not sure that this is what happened and if so how general it was.

To be honest I think this plan is a little dangerous as it rewards fast thought over deep thought. It is also very susceptible to exam technique attack. Students should go through the exam and hoover up all the easy marks first. Not all will.

Finally your motivation seems to be to make exam setting easier, but the work is pushed to the marking. Maybe it would be better to construct an exam with appropriate amounts of easy, medium and hard questions. You can make this (carefully constructed) exam harder than the time easily allows if you wish, but most university exams need far more thought than they get.

Actually this sounds intriguing. I teach in the International Baccalaureate Middle Years Program and instead of grading by points or marks, etc., we use rubrics.

Most tests in mathematics fit into Criterion A, for example, which is Knowledge and Understanding. the descriptor for levels 7-8 (the best) is

"The student consistently makes appropriate deductions when solving challenging problems in a variety of contexts including unfamiliar situations."

This could make for an interesting evalution. We'd assign levels to the questions, according to the criterion, and students would attempt to answer as many of them as possible, perhaps even being required to search out what they consider the more challenging questions, looking for quality of answer, rather than quantity.

I think I'll think about this some more. Might make for an interesting open book exam, or perhaps a few days of individual work in class.

As a 46 year old college student, I think this is a horrendous idea. It essentially tests which students would feel overwhelmed and which wouldn't by such an exam. Are you trying to test knowledge, or are you trying to find out who has lest test anxiety?

Don't do it.

Thanks, all, for the feedback. I've been rolling this over in the back of my mind since my post, and thinking about your comments. I've also talked to some of the other graduate student teachers here at UVA about it.

I've been coming around to the idea that this setup requires at least as much care, in making the exam, as a more traditional style exam. Problems of many difficulty levels, covering all of the appropriate material, still need to be chosen (of course). And there seems to be more thought required in how to score such an exam, in terms of setting minimum point values for various grades or something.

I've started wondering how it would compare to setting up an exam where you pick several problems that you feel are about the same difficulty and on the same topic, and let the student do 1 of them (from each topic). So, for example (since I just gave a series exam): Here are 7 series, pick 5 and determine if they converge or diverge. And here are 3 functions, find the Taylor series for one of the functions and it's derivative. Etc.

This idea seems like it might help ease the test anxiety @Anonymous brings up. I would have thought that the original idea would have actually been less stressful than normal exams, as long as students go in with the understanding that they aren't expected to complete all of the problems. But perhaps I was mistaken.

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