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I have recently completed a Multivariable Calculus class. I struggle a lot with math, and failed the first and second midterms and I feel that I failed the final exam as well. The first midterm was worth 25% of my grade, the second was worth 30% and and the final was 35%. I am absolutely convinced that I failed the final, yet I passed the course with a C, although homework was worth 10% and I maintained a 96% on it.

My question is, how often do professors alter their grading scale such that they don't fail someone? My professor did mention that if we do very poorly on the final exam, he would just give us a 'C'. How often does this happen?

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    Many professors never intend for the grading to follow this scale. I certainly don't, in my classes - that scale has too much compression at the top for my taste, it makes it hard for "really outstanding" students to distinguish themselves from "very good" students. – ff524 Dec 16 '15 at 9:00
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    When you say that you failed the first two exams - did you receive a letter grade on the exams, or just a numerical grade? – Oswald Veblen Dec 16 '15 at 12:25
  • First, please consider removing the school's name. It contributes no extra information but provides enough information to identify the faculty member(s). Second, what is the mechanism of grade assignment? Was it based on absolute or relative scale? If it's relative, it's hard to judge if grading scheme has been changed. – Penguin_Knight Dec 16 '15 at 12:59
  • As pointed out in the comments by ff524 and Oswald Veblen, we don't have enough information to answer the question. – Ben Crowell Dec 16 '15 at 14:43
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    I've had professors in the US who were willing to bump you a half-letter grade if you prove that you're putting the effort in and are just having difficulty with the material. My own multivariable calc prof actually did this for me after I brought my grade from a D- to a B+. It was painful, but the prof appreciated the effort I put in for the rest of the course. TL;DR: sometimes profs are nice people too! ;) – tonysdg Dec 16 '15 at 19:15
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Teaching is hard, and writing exams is hard. Anyone who thinks they can set the exact criteria in advance is probably being arrogant. At Chicago (at least in the 1980s) every single course is graded on a curve so essentially every course had its criteria set by the performance of the students. On the one hand this compensates for mistakes in teaching or in writing an exam, on the other hand your performance is partly determined by how good your classmates happen to be.

One of the professors at MIT I tutored under was very angry that students had demanded (so the Institute regulated) that the percentages given to the various midterms and exams were set out in advance, because before that "innovation" he'd been able to adjust the percentages if he'd written an exam not up to his own standards, something you can often only find out after you've given it.

In the UK, these sorts of practices are banned. Every student is supposed to be marked to criteria set up when the course was approved. To make this work, UK universities require the exam to be written very early in the term, checked by a colleague, and then checked again by an external examiner. Then at the end of the year there is something called an exam board, where a panel decides if something went wrong in a course and moves all the marks for the whole course up or down in response. This is better than marking on a curve because the students can help each other learn without hurting themselves, but in other ways it's worse in that the professors cannot innovate and it can be very difficult to update material.

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    The Chicago style seems really bewildering to me (and never encountered it in my own academics); personally I don't find writing college math exams very hard, and I after one or two semesters I can usually predict within 5% what the course average will be. I have an acquaintance at a top school who used the Chicago method and the students figured out the following: if none of them took the final then everyone would get 100% by default, and they actually did follow through on this, much to my friend's embarrassment. – Daniel R. Collins Dec 16 '15 at 19:32
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    @SnakeDoc: Yes, that's exactly what my friend thought too, right up until his students called his bluff, and then he wound up in the national news for it. Magister cave. – Daniel R. Collins Dec 16 '15 at 21:38
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    @DanielR.Collins Well, that's a first for me! If I were the professor, I would have called their bluff back and failed everyone ;-P If it's in the syllabus, you can fall back to it (at least in principal). I suppose we can say "majority of the time" it works out as intended. – SnakeDoc Dec 16 '15 at 21:44
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    (1) My friend was asked about that implication in advance, and verbally confirmed the conclusion to the students, thinking it would be a non-issue. (2) The students stood as a block outside the exam room to monitor if anyone actually went in and were ready to all file in if anyone "broke the strike". – Daniel R. Collins Dec 16 '15 at 21:54
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    About M.I.T.s regulations: If you say the homework is worth 10% of your grade, students will skip assignments in weeks when they are overwhelmed by the workload in the rest of their classes. If you then decide at the end of the term to make the homework worth 40% of the grade, the students will be upset and complain to the administration. I don't see anything wrong with this regulation. (And I have been told that things like this have happened.) – Peter Shor Dec 16 '15 at 23:17
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The Predetermined Minimum Scale

In general, at least in the US and according to my experience with a few institutions, grading often goes like this:

  1. The professor sets up a grading scale (generally percentage to letter grade conversion) and puts it in their course syllabus at the beginning of the semester. This commonly goes something like 94% >= A, 90% = A-, 87% = B+ ... < 60% = F.

  2. The syllabus also includes an outline of weighting of grades - for instance 10% "attendance and participation", 40% assignments, 50% midterm + final.

These guidelines as noted in the syllabus reflect a "guaranteed minimum grade". This means that if you get 90% in this course you are guaranteed at least an A-. However, this also means that the professor generally reserves the right to adjust grades upwards, especially in borderline cases. If you got a 93.7% and participated actively in class, they might bump it up to an A solely at their discretion!

In this scheme, students are protected against wanton harshness, like a professor suddenly decides the final wasn't hard enough and so suddenly anyone with less than a 95% gets a B.

Please be aware this is not the only grading system!

Forced Curve Grading

Another system uses what is sometimes called a "forced curve", and is designed such that - for instance - only 10% of students can get an A of any kind. It doesn't matter what your score is - just that your relative ranking is compared to other classmates that semester. I'm told the Airforce Academy uses this system extensively (or at least use to), among other institutions and sometimes even individual professors choose this system.

So you can theoretically bomb the final and get a miserable score, and if everyone else did too then your grade might still be excellent.

Hybrid Grading Systems

Bespoke systems implemented by various professors abound across the USA, which is part of the reason most graduate schools take GPA with at least a few grains of salt (it is understood that a 4.0 in one program might be equivalent to a 3.5 in another, to say nothing of whether or not a 4.0 student in one program might be otherwise inferior to a 3.5 student in the same program due to different student focus).

One system I've found somewhat common is using the predetermined grading scale, setting the scale strict as shown above, but then giving very difficult exams where they note that even they themselves would not be able to score 100% if they didn't have their answer key at hand. In these classes getting even a 90% is truly difficult. The goal is perhaps to be more discriminating, and a score of 100% isn't very informative in this outlook. I found math professors much more likely to fall into this category!

So what the professors do is at the end of the semester they plot out all the grades (in a histogram, scatter plot, or sorted-by-grade spreadsheet), and then take a look. They find some sort of 'gap' in the actual grades, and decide anyone above that gap gets the maximum score of A. The next 'segment' gets the next highest grade, on down to the end. No one gets bumped down to a lower grade, but many students can/do get bumped up.

Discounting Aberrant Grades

Many professors also compare the grades on a final exam to scores in the rest of the course, and adjust grades up in certain cases. One example is if you did well all semester long, then somehow did poorly on the final. If this seems like a weird aberration and you participated and clearly worked hard in class, sometimes a professor will think the grade is a poor reflection of your understanding of the material and will lower its weight - effectively giving you a better grade than your final would indicate.

Other professors look at the final as the most important/difficult test, and if you did significantly better on the final than in the rest of the class they will assume you must have learned the material (or you wouldn't have done so well on the hardest test!) and bump your grade up - effectively discounting your earlier less-spectacular grades.

Of course, some professors do none of this. Some give lots of extra credit, or "easy A" assignments so you just have to turn something in, etc. In the USA professors usually have a tremendous amount of independence in determining grades, and they often just have to have a sensible system they can defend if 'challenged'. But some don't really care and pretty much do what they want. YMMV.

Your Specific Case

In your specific case of wondering how you got a good grade even though you thought you bombed the final, it's possible you did not actually bomb the final - and it's also possible you did and got 'curved' up, or the professor discounted your grade on the final because you otherwise did so well in the course.

If you are really concerned or wondering, you can generally ask the professor or meet with them to share your concern that you bombed the final, etc. I personally wouldn't "look a gift horse in the mouth" (question someone who graded you kindly), but if you really feel uncomfortable with the grade then by all means you can politely ask to go over the final with the professor or discuss your grade more generally.

One final note- I have known a number of people exhibit a mentality I like to call "reverse paranoia": the belief that people are secretly out to help you even though you don't deserve it! It's very possible you did better than you think or even that you earned the grade you got (I know, crazy right?), and the professor just gave you the grade you deserved. This may or may not be related to the impostor syndrome, or just a past experiences that were negative. But this is just a pet theory/observation of mine!

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There are some very high reputation schools where they still will have very loose pass criteria, for a basic pass (i.e. a C). However, what is very hard to achieve there are the high marks.

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My question is, how often do professors alter their grading scale such that they don't fail someone?

I cannot easily answer this for the whole world as the frequency may differ wildly across universities as each may have different policies. However, based on studying in three different universities in three different countries, I can tell you that I think that this practice is very common as many professors (at least those in the institutions I attended) are required to have a certain pass rate for their classes. If, therefore, too many students fail, then they will find some way to ensure that a sufficient number pass.

Do you have a more specific follow up question that you would like to ask?

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I don't know if you're going to be able to get an answer for "how often". I would assume this varies heavily by country, university culture, department culture, and individual differences in teaching styles.

From my experience as a TA and other TA's I've worked with, it is fairly common in the department to modify the grading scale a little bit if necessary - a practice similar to curving. Whenever I've been involved in these discussions, there has always been a lot of very careful deliberation before the choice is made. Why? Because teaching and learning both have an element of subjectivity and imprecision. No question is absolutely perfect, no exam will perfectly represent the material, and sometimes it's difficult to know the problem is the students or the inability for some concepts to sink in.

Some other reasons:

  1. Equalizing between two different classes. In theory, both classes should have the exact same grade averages for all exams and for the final course grade. This never happens in practice. Sometimes the grade cutoffs need to be equalized between both classes to make up for this.
  2. Poor performance on the final exam. What if students are doing well the whole semester and they do poorly on the final? It's very difficult to know if this is because the exam was problematic or if the students were taught poorly or if they were lazy or a number of other reasons. Sometimes the exact same final will have totally different grades between two classes even if the material taught is the same.
  3. Unforeseen issues. Five years ago, I taught a course in which the fire alarm went off during an exam. As a result, we had to postpone the exam and give the students a make-up one week later. But then the other class that didn't have the fire alarm, complained incessantly and became rabid in their attempts to grab free points by badgering the TAs and arguing answers on test regrades. They claimed that it was not fair that the other class got an extra week. The average for the exam between the two classes was unequal by a large margin so adjusting cutoffs seemed fair.
  4. An alternative to curving. Many professors curve their exam in some way to alter the grade distributions. Some professors think this isn't necessary until the end of the semester and "curve" by altering cutoffs rather than adjusting final averages.
  5. Sometimes you, as a student, deserve the grade you got. I am always asked by my professors if the students I TAed really deserve the grade they received. What if a student comes to my office hours every week, does well on all the homeworks, participates in discussions, clearly knows their stuff, but performs poorly on exams? [I was one such student for my early undergrad so I can sympathize] And what about the student who crams the night before but understands little of the material and makes a really good grade on the exam because they are good test takers? Sometimes you need to adjust cutoffs for students who are on the cusp that deserve to be one letter grade up.
  6. The aim of Freshman courses is not to weed-out but to instruct. I find this is more common in Freshman courses. Freshman year is hard and just because you don't perform amazingly in your first semester doesn't mean you aren't cut out for your topic of study. Sophomore classes and beyond tend to be much more weed-out courses. If it's clear that that you understood the material then maybe you deserve to pass the class. The point of teaching is to encourage and not discourage. And if a student passes that shouldn't, it will catch up with them eventually. They will reach a course where a cutoff can't save them or they will find their upper-division courses are far harsher when it comes to passing students.

Summary: the overall aim for adjusting cutoffs is to strike a balance between creating a fair course for the students and ensuring the students learned the material. However, It is wholly unethical to only alter individual grades or cutoffs for specific students. The most important thing to ensure is that whatever changes you make apply to the entire class.

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How often does this happen? I have a feeling this happens quite frequently based upon my one personal experience/data-point that I have. This took place at a very well known, high-rep, American university. Most of the students in the class were probably engineering students.

I was taking a junior/senior level probability class. The class averages on the exams we utterly horrendous. We're talking in the 25%, 35% range. The averages showed the entire class to be in a state of utter failure. The professor was almost universally considered to be terrible...with the exception of one student who kept obliterating the exam averages by getting in the 90s each time. I knew that student personally. She was superb.

According to the class averages, I was in the "C" range. If a student had an "A" going into the final exam, they weren't required to take the final. Unfortunately, I had to take the final exam. I bashed my brains in preparation for that final.

Would you believe I ended up with an "A" for my final grade? It is the most undeserved "A" I ever received. You should have seen the totally confused look on my face when I found out! That "A" still stands out on my transcript as a diamond amongst coal.

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