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This question is similar to "Should I design my exams to have time-pressure or not?", but is, I think, sufficiently different to deserve its own space.

Naively, there are two benefits to placing (any, or at least strict) time limits on tests:

  1. It saves me time giving tests (not a noble end, but not so ignoble it deserves to be completely discarded either), and
  2. Students who really really "get" the material will have not struggle with time limits, so I can single those students out by placing (severe-enough) time restrictions on the exam.

I've found ways to make item 1 less important, but I've come to suspect item 2 is just plain false in many cases. I am curious if there is any research supporting this. So we have

Question 1: is there any research relating to performance on time-restricted mathematics tests and (somehow suitably defined) a student's grasp of the material they are being tested over. (Both positive and negative results on the efficacy of time-restriction are welcome.)


However, on a slightly different note, I'm also dubious whether it's all that important to separate those who really really "get" the material from those who are "merely competent enough." So we also have

Question 2: is it all that important to separate the "ultra-high-performing" students from the "pretty-darn-good" students, and if not, is there any other reason at all (aside from item 1 above) for giving time-restricted mathematics exams?

((Please feel free to edit the question, I feel its clarity can be improved.))

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    $\begingroup$ Not an answer since I don't have proof, but an extreme counterexample for question 1 would be a student who successfully rederives everything they can from first principles every test. Absolutely brilliant (though not necessarily smarter than anyone who has things memorized, just different), also really slow. Obviously that's a bit extreme, but I've met students who certainly edge closer to that side of the spectrum and I'd hesitate to call them worse at math than the guy who memorized every special case in the textbook. $\endgroup$ – LinearZoetrope Apr 10 '14 at 20:29
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    $\begingroup$ Math itself is a challenge with a wide time-pressure spectrum: On the short end is the Kangaroo, on the long end is Fermat's last theorem. A well designed math education model should incorporate both ends without making either too important. You as a single math educator: If there are no restrictions of your institution, ask yourself where your field lies in that spectrum and time-pressure accordingly. $\endgroup$ – Toscho Apr 10 '14 at 21:08
  • $\begingroup$ I'd add a thought to the mix. If time is considered important, is there some percent you'd expect to finish the test to be considered a well-constructed exam? 70%? 80%? As a student, my style was to go full speed, and then go back and check my work. Now, it seems that most students are lucky to just finish. $\endgroup$ – JoeTaxpayer Nov 25 '14 at 22:59
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I think that it is important, in this situation, to ask yourself the question "why am I even giving students tests at all?", and the answer to this question will shed light onto the question of timing your exams.

Obviously we're giving students tests to ensure that they learn the material, but the reason we are ensuring that they learn the material is an economics problem. High Schools want their students to be accepted to colleges, so they need a grading system, and Colleges want their students to get good jobs. If there was not a system for telling whether a student learned the material, then employers would not care that a student had a degree or not.

As educators, we naturally want students to learn the material because 1. We think that the material is important in and of itself and 2. We assume that students will love the material for what it is. Usually 2 is simply false, especially in high school and undergraduate mathematics, and in any case, neither of these is really a good reason to give exams at all. We would give interesting homework problems for the students to ponder in order to learn deeply, instead of exams which don't really teach a student anything, but are simply a measurement tool.

So if we're giving exams (whether we like it or not) because we are measuring students so that employers can fill positions more efficiently, and you're the sort of person who thinks that this is important, then timed exams ensure that not only does a student know the material, but can utilize the material in a meaningful way in a reasonable amount of time, which is crucial for the 'real world'.

If you're the sort of person who doesn't care about being a sorter for the industrial world, then there's no reason to give exams at all. At least, to me, it seems that there are better instructional tools for students than exams. Even if one does view exams as an effective instructional tool, there's no good reason to time them, outside of a reasonable constraint to ensure that the undisciplined student actually completes the exam.

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    $\begingroup$ I sort-of-agree. Just that one of our responsibilities as educators/evaluators is to do the "sorting for the industrial world," so we can't get around exams. Much as I dislike them (as you seem to). Necessary evil and all that. $\endgroup$ – vonbrand Apr 11 '14 at 0:51
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    $\begingroup$ What constitutes a "reasonable time" is a large part of where the argument lies, though. There's certainly a gulf in skill between someone who takes an hour of trial and error to find the answer to a problem vs two people who know how to solve it instantly but have varying degrees of special cases memorized to speed it up. Some tests like the GRE, IMO, go way overboard in selecting for those who memorize special cases, independent of actual problem solving ability. There's also some selecting for people who are confident in their heuristics vs people who prove everything to themselves. $\endgroup$ – LinearZoetrope Apr 11 '14 at 9:52
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    $\begingroup$ I should say that I don't care at all about being a sorter for the industrial world, but I do view exams as a useful instructional tool. In my experience, students in a course without exams tend to develop only a hazy understanding of a subject, since they are never really forced to clarify their understanding enough to answer questions on cue. After using almost exclusively takehome exams in upper-level courses for several years, I have been working may way back to having in-class exams and even weekly quizzes. $\endgroup$ – Jim Belk Apr 13 '14 at 4:12
  • $\begingroup$ @JimBelk I'd love to hear more about this; would you consider expanding this comment into an answer? $\endgroup$ – Shay Apr 14 '14 at 0:13
  • $\begingroup$ @Shay I'd be happy to talk more about this, but I think it would be off-topic for this question. Perhaps you could start a new question? Something like "Do exams have pedagogical value?" $\endgroup$ – Jim Belk Apr 14 '14 at 0:18

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