Why Do Professors Curve Exams in Math Courses?

[Dembadon]

I'm taking a combinatorics course this semester (from the math department), and my professor said the exams are usually devised so that the average score is a 60%, and then they're curved.

I've seen this method of exam development with other professors, so I wanted to get some input to help understand the reasoning behind this. I'm not disappointed or upset; I'm actually looking forward to the challenge. This is pure curiosity. Venturing a guess, it might be a way to identify potential research assistant candidates. The professor for my course does research in linear programming and combinatorics.

Not sure if this should go in the Educators subform or not.

 

[sweetpotato]

I had a professor who gave exams where the average scores were extremely low (he curved the grades afterwards, so if you got, say, 60%, that was an A). His reasoning was that he gave problems which were actually intellectually interesting, instead of designing the exam so that the average student could score 80% and not get his/her ego bruised.

I had another professor who gave exams where the average score was around 90%. There were questions on his exams that were purely to boost performance, i.e. someone who barely paid attention in class would get them right. However, asking these sorts of questions actually does very little to test the students' knowledge, so I personally do not like this testing approach.

 

[micromass]

This is my style of examination. I like to give quite difficult exam questions just to see what the student comes up with. When doing research or something similar, then the questions you need to tackle will be quite hard. If you never had a challenge before, then doing research will be impossible for you.

I think mathematical ability is best tested with difficult questions. I want students to understand what they're talking about and to be creative in the course. I don't want people memorizing the exercises to get an A on the final.

 

[Angry Citizen]

One of the advantages of using hard exams and then curving upwards is to give truly intelligent students a chance to shine. Easy exams can let highly intelligent students and above average students co-mingle in the grade distribution.

 

[R.P.F.]

i have had this professor for four classes. She gave exams whose average is below 50% and it has been lower in more recent classes. Taking exams like this was not fun. I was always very frustrated after the exams though my scores always turned out to be good enough to get me an A. But i have to say exams like this made me study harder and had a better mastering of the materials.

 

[nonequilibrium]

Interesting, my professors never mention their "method". I wonder what they have been doing :p

 

[Dembadon]

Thanks for the input, everyone. All of the reasons given make sense to me.

Well, after a couple sessions, I can tell that this will be my most difficult course to date. The examples we've been doing can be understood by a 10 year old, but finding a solution is complicated and it's easy to miss an important element and compromise the entire problem. There are a few graduate students in the class, so maybe I can get together with one of them and talk about some of the more challenging problems. I think this course will be very useful for developing my mathematical maturity.

 

[turbo]

My inorganic chemistry final was brutal! I thought that I had missed about 50% of the questions. I had missed a lot of lectures and labs due to back-to-back bronchitis and mono, and my grades were suffering. After that final, I thought I was toast. Luckily, the final was intended to be really tough, and after grade-curving I ended up with a B+ for the course. Not bad for someone who had missed 3 weeks of classes. Thank God for tough grading!

 

[Moonbear]

It really depends on your objectives. I don't like curving grades at all. But, I teach a subject where a minimum competency is required not to kill people, so my exams test those competencies and if students don't pass, they don't pass. This was actually the first year I had a skewed distribution of grades toward As and Bs, and I didn't make the tests easier. I just happened to have a really hard-working, motivated class. In other years, it actually wouldn't have mattered, because my grade distribution actually fit well with how people would normally curve grades. That's my other reason for not curving. I don't want to penalize a good student for having an outstanding, curve-busting classmate if she knows just as much as someone in a previous class year without a curve-busting classmate.

On the other hand, if you're teaching an upper level course and want to offer a challenge and find out if someone outstanding can meet that challenge, or need to sort out ability levels among a group of already top students, then curving makes sense.

One difficulty with curved grades, and I experienced this as a student, is that the student has no idea where they stand with their grade until the final grades are done. Again, in an upper level class, that could challenge them to work harder, but in a lower level class, more often leads to a false sense of security that they'll probably be okay once grades are curved. I like my students to know where they stand, so if they are at risk of failing, or even getting a C when they want an A or B, they know they need to seek help and work harder.

The biggest problem with curving grades is when it is used to compensate for bad test writing, which can make an exam more difficult in an unfair way.

So, there are a lot of reasons one might choose to curve or not curve grades. You'll probably figure out which it is once you take an exam in the course. If it's hard but fair, then there is probably sound reasoning behind the process. If it's hard because you can't even quite figure out what the question is asking, then just be happy it's curved and leave it at that.

 

[lisab]

Moonbear has some great points about the downside of curving. All, or nearly all, of my physics classes were curve graded and I was never quite sure where I stood until the final grade came.

But my biggest issue with curve grading is the effect it has on the esprit de corps of the class. Especially in the tougher classes, it was hard to form study groups because no one wanted to help anyone else -- and how could you blame them, when doing so only hurt the student doing the helping? It made the whole experience a lot harder, and it was already pretty hard.

On the other hand, some people would help the poor folks who were just barely surviving -- because if they quit, that was a disaster for those on the wrong slope of the curve!

 

[bpatrick]

I have mixed feelings about curving. I was in an "Honors College" within a small / medium sized university. Most if not all of my classes through the honors college were curved. My class size average for my honors courses was about 3.5 students. There was a regulation where at most 20% of the class could get As (or if fewer than 5 students, only one could receive an A). So there was HUGE competition to be that one. Most students within the HC had GPAs of somewhere around 3.4 ... and on our transcripts there was separate class rankings for within the HC and for the university in general.

Now the bad part about this is that if anybody would ever ask me what my GPA was, I'd say oh, a 3.4 (which doesn't sound all that impressive) ... when that level of performance easily got me a 1540 GRE and 43 MCAT back when I took them ... without studying. I was not slacking when I was getting my Bs, it's just that I wasn't necessarily the #1 person in my class. I remember an ODE class where we had some super nasty stuff to solve for our final ... which was slotted for 6 hours on a Saturday. There were 4 of us in the class and the prof wrote up 7 questions, we had to pick 4 to submit ... I only solved 3 of them in the 6 hours. one person solved 4, another solved 3 and the 4th, solved only 2. Our grades that semester were A, B, B, C for the people who solved 4, 3, 3, and 2 respectively. Now I know that Nate (the one who got the C), knew ODE theory a hell of a lot better than 95% of the engineering students who took the regular ODE classes from the math department and got As in it ... I studied with him most of the semester and the following year I ended up TAing a regular section of ODEs so I knew the level of performance / comprehension of those classes.

I took 3 classes the summer between sophomore and junior year at a local (to where I grew up) college just to finish gen-eds. I was working 40 hours a week 3rd shift packing boxes. I didn't buy the required textbooks nor did I do any reading in them the entire summer. The exams were multiple choice and easy enough to ace without studying ... assuming you payed any attention during the lectures. Needless to say I got a 4.0 for those 11 credits (two classes were lab courses) without any effort. So there's something to be said about programs who drive their students to compete with each other and fight to earn an A by being the #1 performer in a class of 3-6 or give exams where the mean is somewhere around 50%. It's just a shame when nobody recognizes the difference in caliber of student (from one of the schools that truly challenges it's students) who has a 3.4 and the kid who has a 4.0 from some other college (that gives multiple choice, open book tests all the way through their degree) who actually knows next to nothing compared to the former.

 

[physics girl phd]

I tend to agree with Moonbear... curving seems to mostly compensate for poor test-writing (and I'll add... teaching!).

I don't "teach to my tests"... but I do make my expectations clear. I give students basic sample problems and assignments of standard types, which are important in the field. I pick from these many types for the test (maybe approaching from a different direction). I then throw in a few interesting ones (with a cool application or "real" numbers) that generally the outstanding students will still get... but those at competency-level won't get completely, so it will drop them down a grade. I generally get a test average of 72-78... especially in large enrollment classes (Intro Calc-based Physics Sequence). If it's lower... I think I need to be evaluating my own teaching or test-writing.

In some intro-intro classes, where my tests are multiple-choice and true/false, I sometimes give a small curve... but this is when one question might be particularly hard (or "experimental"... for me to see if people get the subtlety), or be worded odded or have a typo (and this goes to "poor test-writing", since it's rather hard to write those tests). But in these cases I can track that question to a low percentage of correct responses and use that question's points for the curve.

I'll also add... I think teaching engineers also teaching a large number of people in fields where "minimum competency is required not to kill people". I had a structural engineering student say that to me in an email just this morning (well, his exact statement was "When engineers make mistakes people die").

 

[physics girl phd]

I'll also note: I think my best grad school professors (since the OP talks about grad classes) also presented reasonable expectations and tests.

 

[Sankaku]

I tend to agree with Moonbear... curving seems to mostly compensate for poor test-writing (and I'll add... teaching!).

Yes, I agree as well.

There are two kinds of "curving." One is just adjusting all the grades upwards because the material was hard. The other is actually fitting to a bell-curve which, I think, should be completely outlawed. Although unlikely, if every person in the class has A-quality understanding, the whole class should get an A.

The other issue is a philosophical one. Are grades there to promote competition and sort people into winners and losers? For some in academia, this is a real goal. However, I think a more humane approach is to give people reasonable challenge that they can rise to with effort.

Hitting people with endless unsurmountable tests only promotes masochism or resignation.