I just finished a midterm exam. It was very easy but I was only able to finish about 3/4 of it. And I rushed through some parts in the final moments.
Talking with other students, there's a consensus that there wasn't enough time. Some of us mentioned this to the professor as we were leaving, and he acknowledged it.
What can the professor do to remedy this situation?
I found myself in a position similar to your instructor's. I considered and rejected several possibilities:
Ultimately, I decided that the fairest approach is to give students another opportunity (but not in the form of a required assessment) to demonstrate mastery of the course material. Depending on the course format, the size of the class, etc., several possibilities are:
As you can see, none of these are perfectly fair, either. Depending on the particular circumstances (and possibly with input from the class), an instructor may decide which is the least unfair.
This is an excellent example of when a professor may choose to grade on a curve. Grading on a curve normalizes the exam against observed performance rather than an absolute standard, and is a good way to re-normalizing when an exam proves unexpectedly challenging.
Your professor, however, might not choose to do so, or might choose to set the curve in a way that doesn't help you as much as you might like. The key is what's happening in the class relative to the actual educational goals of the professor.
If the exam was harder or longer than intended, and the professor believes that the lower grades reflect that, rather than the knowledge of the students, then they are likely to grade on a curve.
If, on the other hand, the students are showing evidence that they do not understand things as deeply as they are required to, then the professor may not curve or may adjust with a curve less than you hope.
It's really impossible to know which case without knowing the details of the exam and peoples' performance. A "long but easy" test sometimes is testing for deep facility that allows people to be extremely fast. For example, think of the arithmetic exercises sometimes done in elementary school, which can only be solved quickly enough if the student has effectively memorized and internalized arithmetic, rather than working out answers from first principles (e.g., counting on fingers). The same principle can sometimes apply in undergraduate and graduate education as well.
Bottom line: maybe the professor will choose a generous curve, but there are reasons that may argue against it as well, depending on the circumstances.
I have faced this a few times. (Once there was a general insistence that there was not enough time, though the number and difficulty of the questions was not noticeably different than in previous years; another time large numbers of students emailed me after the exam to say they had not known there was a question 5 on the back of the last page, despite the obligatory "THIS EXAM HAS FIVE PARTS" boilerplate on the first page.)
The first thing you do is to mark the exam in the usual way. Then you observe. Did many people leave the last question blank? Or just scribble a few quick points in a way that suggests a lack of time? If someone did the questions out of order, did they do worst on whatever question they left for last? Is there any kind of noticeable pattern to the exams that is not like the pattern you usually see for that course (eg every year, the X question might be the one everyone finds hardest; if this year the Y question, which was last on the paper, appears to have been more of a challenge then you have something observable.)
If you see no pattern and the average mark is about what you expected you don't need to do anything. If you see no pattern and the average mark is low, you can either work harder at getting the material through the heads of this particular cohort, or set an easier final to keep the average up (an approach I reject, but mention because some people do it.)
When I did see a pattern, I made the following offer to my class:
Do you think your performance on the midterm truly reflects your knowledge of the material? If you do not (for example if you feel you were constrained by a too-short time limit) then you may use your mark on the final exam as a replacement for your mark on the midterm. You must request this accommodation within one week from today.
That last constraint was very deliberate. You have written the midterm. You have received your marked midterm. We have taken up solutions to the midterm questions and discussed particular areas where you may not have known something or may have been in error. You have a good grasp right now of what part of your mark deficit (my students always seem to have some mark they believe they deserve, and want to know why they didn't get that mark, as though I start at 100 and subtract) comes from "not getting it" and what part comes from "running out of time". If you think the real issue was running out of time, then you know that right now.
There was always someone who wanted me to mark their final exam and then only use that mark if it was better than the midterm. No way. This isn't some sort of bet or optimizing technique. This is a one-time offer: if you're so sure that midterm was not a reasonable instrument for assessing you, I'll throw it out. I'll use my remaining instrument, the final exam, for assessing that part of your mark. (Assignments in my class were group work and in any event assignments and exams assess different skills and knowledge; I would only be willing to substitute exam for exam.)
In years where there were many complaints, some (but not all) of the complainers would take the deal. Rarely, it would be really good for them. Say 50% on the midterm and 90% on the final exam. Often, it would be a small improvement - 60% on the midterm and 70% on the final exam. Over half the time, it didn't help them at all. They got 50% on the midterm and 50% on the final exam too, even though there were no time complaints on the final and they may have left early (I write finishing times on all final exam papers as I receive them.) So I'm not entirely sure this approach solves the actual problem of some students getting lower marks than they deserve on the midterm due to lack of time. However it completely solves the problem of students complaining because they believe they got a lower mark on the midterm than they deserve. And where there has been a true mismeasurement, it does fix that.
Just a little input from personal experience in the UK:
We had one exam where we were told in advance that it would be near impossible to finish/complete perfectly. (I did actually get through it, made a little mistake at the end and other little mistakes too.) From my point of view, it is or was doable in the time - but you couldn't stop to think about a problem in depth or make mistakes.
The reason for this was to draw the marks down as modules/courses that receive too high marks may be regraded by an external examiner which the university wants to avoid. So offering one hard exam that the best might get 60-80% on (with 70% the criteria for a First) is a way of avoiding that. (And from other people's comments, I believe exams were or are graded on a curve there too.)
Now this can work the other way too - a course/group that receives marks that are too low are remarked by an external which raises their grades (happened to people in statistics I believe).
Now one can argue about the pros and cons (and I find this rather stupid), but that's another discussion. The gist of my comment is that there may very well be a specific intention behind that exam, especially if it only one and not a regular occurrence.
The most obvious thing the professor can do is to take the time constraints into account when grading the exam, for instance by 'grading on a curve'. I have taken at least one exam where the professor announced this beforehand, stating he was sure the exam would be too long, and that he would scale the grades students obtained.
In the long run, unless the professor has very good reasons to keep the time constraints (too) strict, he can of course make any new exams easier or shorter, or give the students more time to complete them.
If most students had issues finishing the test, then having the professor weight the questions differently may be a fair way to handle it. For example, if the test was 4 pages long, weight the questions on page 1 and 2 normal, page 3 half-weight, and page 4 quarter-weight. This way, people that did finish the test get credit for finishing the test. People that didn't finish, or rushed through the last page, are not penalized as much.
Grading on a curve compensates for a test where all of the questions are uniformly hard, and the scores (graded normally) would be uniformly very low. That isn't the case here: everyone made it through page 1 just fine, the questions were not hard, so a missed question there should be the full penalty it normally is.
A possibility that I'm surprised hasn't been mentioned yet:
If you think the students had adequate time to complete only 8 out of the 10 problems (for example) then you could drop the two lowest-scoring questions on each student's exam, and base the exam score solely on the highest-scoring 8 questions. (If different questions have different point values then you could do something similar but a bit more complicated.)
It's not a perfect solution, but it seems natural and is easy to justify. The only students it really lets down are the students who spread out their effort so as to write equally poor answers for all the questions, rather than properly concentrating and writing good answers for any of the questions. That's not something I would want to encourage anyway (although some people might disagree, I suppose.)
One can add a bonus note to each student's grade, measuring the overall quality of answers. So, someone who did very good job but did only 3/4th of a 4/3 too long exam would receive a perfect grade. Someone doing a reasonably good, unfinished exam would have its grade improved compared to the planned grading, and someone doing a very poor job would have a very low grade no matter how many questions he answered.
I have built certification systems and most of our expert level certifications are built to make sure the average person who passes does not finish the certification test.
So if we asked 100 questions we would estimate how many we think the user could do in the 2 hours. We might formulate this as 80.
We then put a weight on the extra answers or incorrectly answered question. Based on a 100 question test we would normally give the student 1 extra point for each correctly answered question after 80 and minus 2 points for each incorrectly answered question.
Scenarios:
A. Student A answers 80 questions. She gets an 80% on those questions. Her final grade is an 80%.
B. Student B answers 60 questions. She gets 90% on those questions. So she answered 54/60 right. But she did not get to 20 questions. Her final grade would be calculated using 54/80 so a 67.5%.
C. Student C answers all 100 questions. The first 80 questions she got an 80%. She then got 15 of the last 20 questions right. The 15 right answers got her 15 points and the 5 wrong answers deducted 10 points. She got a bonus 5%. Final score is 85%.
D. Student D answers 90 questions. She got a 100% on the first 80 questions. And then missed 5 of the 10 last questions. She will get minus 5 points for the questions past 80. So her final score is a 95%.
E. Student E answers 95 question. She got a 100% on all 95 questions. Receives a 115%. This is how you pull your true experts from your really good students.
What you do
I would tend to think you made a big mistake in making the test or teaching your students. You should pay for the mistake by having to give out MUCH higher grades. You can use a scale like mine to grade but your number of questions needed to answered needs to be ridiculously low. I would even go so far as to say - whatever test had the least amount of answers. I don't want to be ridiculous on this so you may have to take several factors into account but I would rethink your test and think how many questions could they answer in 80% of the time - use that.
In a similar situation what I did was to adjust grades on a question by question basis, adjusting to give full points for those who got the most points on each question. Not really fair, and some students complained; but I didn't see any better method. In the end, some of the questions were easy/fast to do, others turned out too hard/long, and I was trying to adjust for the later ones.
There are many things you can do to mitigate the damage (offer another exam, grade differently, add a fixed percentage to all grades, “grade on a curve”) but there is no perfect solution. Students have to manage their time during the exam, some will be stressed out when they realize they won't be able to do everything, others might rush and compromise quality or not take the time to fully understand each question in an effort to finish in time. You simply cannot compensate for all that after the fact.
I have experienced this when teaching courses. Setting an exam at the correct level of difficulty is difficult, since most subject-matter experts find it hard to gauge the appropriate level of difficulty for students who know much less than them. I have found it helpful to adopt the following processes:
Make your assessment schedule robust to errors: Academics are human and they make mistakes and errors of judgment. Assume that you will misjudge the difficulty of an exam at some point. Make your assessment schedule robust by having multiple assessment items prior to the final exam. I like having redeemable tests during the semester, since this allows me to set some tests, and gauge whether they were too easy/hard prior to writing the final exam.
Give yourself maximum discretion for scaling of marks, but avoid if possible: To the extent that university policy allows it, always include explicit statements in your course outline that gives you the maximum discretion to scale marks in your assessments. If it is allowed by university policy, then a statement to the effect that you have discretion to scale results up or down is useful. I also like to include a statement to the effect that I have discretion to award additional marks, beyond the stated marks, for work of exceptional quality. (Rare, but occasionally it happens.) You are in a stronger position to engage in scaling of marks if you have put students on notice of this in the course outline.
Although you want the discretion to do this, it is best not to have to scale marks if this can be avoided. If your assessment schedule is robust, then an excessively easy/hard assessment can be dealt with by changing the level of difficulty of later assessments. If you set a test too hard, you can correct this in the next test. Your goal is to set a reasonable level of difficulty in the overall course, even if an individual assessment was not calibrated correctly.
Exam length for undergraduate-level courses: As a rule-of-thumb, the teacher should be able to correctly complete the exam in one-third of the time allocated to students, from a position of initial ignorance of the answers. So if you are setting a three-hour exam, you should be able to do the whole thing, including all working out and writing up of answers, in one hour.
Exam length postgraduate-level courses: As a rule-of-thumb, the teacher should be able to correctly complete the exam in one-half of the time allocated to students, from a position of initial ignorance of the answers. So if you are setting a three-hour exam, you should be able to do the whole thing, including all working out and writing up of answers, in one-and-a-half hours.
Sit your own exams: After you have written an exam, let it sit for a while to try to forget the answers (if you haven't been naughty and left it too late to do this), then do the exam yourself under exam conditions, adjusting your working to "forget" everything and work it out from scratch. Keep track of the times you start each new question so that you can see how long each one took. Compare this to the above rules-of-thumb to see if your exam is too long, and if so, look for questions that are taking more than their share of the time.
Get student feedback on length/difficult after each test: After each in-class test I get my students to tell me about the length and difficulty, usually just by a show of hands. Was this exam more difficult than you expected, about as difficult as you expected, or less difficult than you expected? Did you find you had more time than you could constructively use, about the right amount of time, or less time than you needed?
Usually I just get this information on the in-class tests during semester, by show of hands after the test. It would also be easy to have feedback boxes at the end of the exam if you don't have an opportunity to address your students (e.g., in some final exams). I find that this helps me calibrate whether the length and difficulty were reasonable. Bear in mind that most students will usually say they didn't have as much time as they needed, but you will know when this is really the case because the response will be overwhelming.
These processes have generally held me in good stead with writing exams. Occasionally I still write one that turns out too hard, but because I have a robust assessment schedule, this does not stuff up the whole course. My experience is that there is no post hoc solution - if you write an exam that takes too long, take it as a learning experience and write a better one next time. You can scale if necessary, but this should be a last resort.
So...All of these responses are from the perspective of the student taking the exam. What of the professor's perspective?
Students today think that the criteria of excellence on an examination is 100 percent. They fundamentally misunderstand what a "test" is, and what information it gives the professor.
A well-designed test isn't given so that the student can feel "awesomesauce" about themselves. It's given to assess the student's grasp of the coursework. If every student finishes everything and gets an A, what has been evaluated? On some level, we can look at such a test as assurance that our students have met some "floor" criteria, but we haven't actually tested exactly what they know. A well-designed test is one that "brackets" the expected student performance, such that most, if not all of the students will not touch the upper boundary...by this, we can assess what they know, and where their knowledge stops. This is magnitudes more valuable to an instructor than giving the student a feel-good "all will ace" test. The test INTENDS to drop you somewhere before the end. And, the test is graded accordingly...getting an A doesn't necessarily mean you answered everything.
This concept will be anathema to the entering freshman and sophmores who were in elementary school when "no child left behind" was enacted, because when that happened, the whole constellation of what testing was actually for was bastardized.
