To Curve or Not to Curve?

[TheFez]

I have started teaching and I love it. But I struggle with how grades should turn out (in an ideal world).

Should the proper outcome of a class be a normal distribution of grades? Should the course material be developed so that some people will get A's and others will fail according to such a curve?

Idealists might (emotionally) suggest ..."just teach and let the chips fall where they may. If everybody gets an "A" then that's fine." But is it really?

If everybody failed they would be quick to criticize the teacher - either the material is too difficult, the exams are faulty, or the teaching is poor

But if everybody gets A's is the material too easy? The teacher not challenging students enough?

The scope of a course in many subjects (my area is economics) is not always clear cut. There's lots of gray area about what to include and what to omit from lectures. How rigorous to be, or how much material to cover. Look at posted Syllabi and you see a lot of heterogeneity.

I have found in my own limited teaching experience - a bimodal distribution of grades. One set of students seem to get it, work hard, do the readings, show up to class, study and get A's and B's.

The other group screws off, doesn't always turn in assignments, makes the same mistakes on tests as homework and quizzes (despite reviews of the correct answers). They get D's and F's. This suggests to me that the material is too easy - students who study mostly get A's students who have bad habits get Fs (and this may be unrelated to the difficulty of the material).

According to "the curve" most students should get C's... right? With a small portion getting the highest or lowest grades.

There's also external pressures on grading since professors get evaluations, and (I have been told) evaluation scores are positively correlated with expected grades.

On the other hand - I am sick of "grade inflation". (Worse in grad school where the options are even more limited by a minimum 3.0 standard that's so common.) Is it fair to top students to devalue their A's? Is it ruining the use of GPA as a standard for graduate Ad Comms (resulting in the dreaded dependence of standardized tests like the GMAT and GRE).

So - what does final grade distribution indicate? And what should it look like?

[emmm]

Grades need not be inflated for everyone to get As -- especially in grad school. If everyone works hard and learns the material, they should all be rewarded with the As their hard work earned. In grad school, especially, where students are already supposed to be among the best, what is wrong with everyone doing well? If they could not succeed in grad school, they should have never been admitted. Don't hand out As like Halloween candy, but don't be afraid to give them either.

[TheFez]

I may not have been clear.

As a PhD candidate I will be teaching Undergraduates, probably in lower level classes; so lots of students who are freshmen and sophomores.

But, even still emmm ... what would you say if I told you everybody in my class was failing? Wouldn't you think something was wrong? So why not question when everyone is getting an A? Is everybody really excellent?

[aberrant]

This is my experience as an undergrad TA:

The average of the class (for my school) is B/B- for lower division classes, B-/C+ for upper division classes. I would like to think of a scale that is roughly like this

94-100% = A/A+ (or minimum = 94%)

90-93% = A- (or minimum = 90%)

86-89% = B+ (or minimum = 86%)

82-85% = B (or minimum = 82%)

78-81% = B- (or minimum = 78%)

74-77% = C+ (or minimum = 74%)

70-73% = C (or minimum = 70%)

If my professor wants the average to be a B- then I'll curve the exams and quizzes to 78%. The easiest, not so accurate way to do that is to shift whatever the class average is to 78%. So if the class average for an exam was 70%, everyone will get this extra 8% for that exam. My professor would not curve down the average, however. So if the class does well throughout the quarter/semester then they'll get whatever grades they have, without curving it down.

[robot_hamster]

I guess I would only curve it if nobody was getting a good grade despite working really hard. So say a few students are obviously working really hard but still only get a B+ and then everyone else falls in a distribution below that. I would want to slide the scale so that those people with the highest scores would now have an A. I suppose there could be other reasons for doing it, like others have suggested above.

Another thing to consider might be adding different weights to different things.

Edited June 3, 2012 by robot_hamster

[emmm]

I guess it depends on the size of the class. I have never been in a large ( >10) person class where everyone got an A, but I have been in smaller classes where everyone got As, and they were generally wonderful classes where everyone was involved and enthusiastic (small, seminar style classes). They were a lot of work, though.

[kaykaykay]

if you have many additive scores that are graded strictly ,at the end grades will mostly naturally follow a curve.only really good students will do excellent work on every task. you just have to shift it if you feel like they deserve a better grade.

[TakeruK]

I think you have to be really careful with curving when the class size is small. Things only fall in a "normal distribution" when the number of samples is large. The theory (http://en.wikipedia....l_limit_theorem) says that given some distribution of grades (i.e. the class actual skill), numbers drawn from this distribution (i.e. the mark of each student) will tend towards a normal distribution given some conditions (including large sample size). This usually gets distilled to "students grades are normally distributed" but it's important to remember the conditions for this theory aren't always met!

So I think if there are less than say, 100 students in the class, I would be really hesitant to apply a normal curve onto the grades. I might still want to scale the grades if I don't think the numbers work out "fairly" (whatever that means). Maybe having that midterm worth 30% is too high. Or maybe instead of having 2 midterms each worth 15%, for each student, count the higher mark with 20% weight and the lower mark at 10% weight. Or maybe only count the best 6 out of 7 assignments, etc. Or allow students to do an extra assignment and replace their lowest mark. Or if an exam went poorly, allow the students to take it home and make corrections and let their final mark be the average of actual mark and take-home mark (should be 100%). Or you can adjust the difficulty of assignments/exams later on to compensate for students doing too poorly/too well. These are just as arbitrary as applying a normal curve to a situation where normally distributed values are not expected. I chose the number 100 before, arbitrarily, because I think it's feasible to do adjustments like this for ~100 or less students. More than that, I guess I'd rely on the bell curve.

Another question to consider is what you want the grade to actually represent. If you do no scaling, then the grade truly shows the students' ability according to your metric. If I didn't teach them anything and they all got Fs, the grade is still valid -- according to my metric, they don't know anything. On the other hand, I could just really lower the standards and everyone can get As -- the grade itself is also right. The grade doesn't actually measure the student's actual ability -- it's a subjective measurement based on the instructor's metric. Unfortunately, transcripts only show the final grade usually.

My solution would be to very clearly define what is expected for my students. For example, decide what you want your A students to accomplish. Then your B students etc. Then set up the marking scheme so that you get this to work out. Then I won't feel bad about giving a whole class of As if I think they meet my standard of what an A is. As a TA, I discuss these standards with the prof of course! When I eventually teach my own courses, it will probably take many years before I'm happy with the balance, but I guess that's part of the process.

Edited June 3, 2012 by TakeruK

[RosamundReage]

I personally think curving grades is unfair. I know I would be very upset when I was in undergrad if a TA gave me a lower mark because they wanted to meet a certain average (actually I think this happened once and the prof changed my mark).

I was also concerned with the distributions of my marks, and was worried that I would end up having to use a curve even though I desperately did not want to. I found that my concerns were unwarranted and the average marks for my first year course ended up naturally being in the -B range, which is generally what it should be. For my upper year course, which was very specialized and small I had a much higher average at a +B, but for me this was understandable based on having a high concentration of strong students. I think you have to recognize the type of class you have (again if it is a upper year seminar type class the marks will naturally be higher and it would be unfair to curve their marks) and generally the marks will just naturally fall into place.

Now if the average was super low I still would have a hard time curving the marks, and I think it would be more fair to reassess the difficulty of the assignments and maybe make the next one less difficult. I think you can also just be more lenient with the marks if the average seems to be super low. For example if it is a first year course you shouldn’t mark them like they are a fourth year course, and I think this is often the reason for very low averages.

[TheFez]

Fascinating.

I really could have posed the question this way -- "Should courses be designed so that the final grades will tend to have a normal distribution?".

Funny too that people object more to curving grades downward than upward. (This seems a lot like behavioral economics where people are risk averse).

I sense that people seem to feel if that if all the grades are low - then the material was too hard. But if all the grades are high - the students are just too smart and not that the material was too easy.

I am sure I could design a course so that even the smartest bunch of students would all fail. So the point isn't how smart the students are - but whether material should be geared to the "average" student so that the average student gets an average grade.

Again, my experience is that I see a bimodal distribution of grades. But I attribute that more to commitment and study habits than academic ability.

[aberrant]

As a student, it is not my problem if an instructor / TA give me an evaluation that is piece of cake and I do well at it. However, I would find it unfair if getting a 96% in an exam, for example, turn out to be a C, because clearly whoever wrote that exam didn't do a good job to differentiate the top students / bad students from the norm (or, into a normal distribution).

Will your situation be different if you give out exams/quizzes/assignments that are difficult in the first place, so that you will never have to consider "curving down" the average? Obviously, if the standard deviation of an evaluation (e.g. exam) is small, that means this particular evaluation does not differentiate good/bad students from the norm. Thus far, I don't have a trouble to maintain a SD around 20 (out of a 100).

ps. I'm TA'ing a class with +200 students. So all the comments that I've made are based on a class size of +200.

pps. bimodal distribution may occur if the difficult of a particular evaluation is mediocre / easy, and yet you have to categories of students -- 1) those who have talented/work hard and understand the material well; 2) those who gave up / slack off / fell behind

[TakeruK]

In many of my undergrad physics classes, there were bimodal distributions in our midterms. There was one memorable midterm were ~5 students had an average around 90% and the rest of us (~40 students) averaged around 35% !! There were many good students in the latter group (obviously the best students were in the first group though). The prof handled this by giving an optional midterm rewrite and the better mark would be counted. I didn't complain

There are also entire departments that had a "no downward curving" policy -- the raw mark you get back on your tests and assignments is your minimum grade. Another department curved between sections of a very large course -- the final was the same for all sections but the assignments+midterms were specific to each section/prof. So, to avoid giving an (dis-)advantage to people with (harder)/easier profs, the distribution of the section-specific grades were curved to match the final-exam grade distribution. Sometimes this came with a "safety net", despite how the curving happens, you are guaranteed to get a grade no less than your final exam grade minus 5%.

My point is that there are so many arbitrary policies, grade inflation/deflation and different grading practices that I don't think grades are very meaningful at all and even if one school adopts a very standardized system, it's going to vary from place to place anyways. And even if the grades were correct at identifying skill level, an outsider would not know the scope and material of the course anyways. So individual grades don't really mean too much and I don't worry whether the best mark really went to the best student, etc. In the end, the best students will, on average, get higher marks on all their courses and their GPA will smooth things out. Even so, GPAs should be considered with high error bars -- they can differentiate for example, a 3.9 and a 3.5 student, but I'm not convinced there is much difference between say, a 3.8 and 3.7.

[tocs1]

I could never get the whole curving thing. If a set of students works hard enough to get good grades, then why do you feel the need to artificially make their grades lower? As long as the material itself is what they need to know (based on external criteria, not the grades themselves) then fine.

[OregonGal]

I've had varied experiences with grading methods. As a liberal arts major (history, international studies) I was not often in classes graded on a curve because the graded portions were often subjective--grading a research paper or an in-class essay isn't the same as solving an equation correctly or answering multiple choice questions. Usually in those classes the syllabi broke down the grades into portions (attendance (usually assessed via pop quiz), homework, mid-term essay/exam/project(s), final essay/exam /project) with a percentage grade assigned to each, and no curving.

Now, I took a few econ classes with interesting results. In one, the professor told us since it was an international studies course he'd go easy on us and curve to a B instead of to a C as he would for his econ-major courses, and explained how the curve distribution worked (he hedged as others have mentioned, but I think that the hedge was predicated on your attendance--i.e. he would allow your final grade to be drastically lower than your final exam if you had poor attendance/homework turn ins). In another, the econ professor hadn't taught an introductory course in a decade and I was very, very happy he curved his exams because my midterm exam grade of 25% was a C--and then his final was a breeze because he over-corrected for his previous exam's rigor.

My final note is that my engineering school friends had extreme grade distributions because their intro courses were designed to crush their dreams--a 10% was an A in one of their exams that I remember them agonizing over. In that class I think the distribution was by making the top grade 100% and adjusting everyone else's accordingly, so that if everyone scored the same then they'd all have the same grade rather than the usual curve.

So I've seen everything--curved grade distribution, weighted non-curved grades, curve adjustments for bad tests/teaching, and redistributions for intentionally over-rigorous tests. I'm in favor of the objectively weighted grade myself, because then it's easier for students to see what they need to do to make up for blowing off an exam etc by seeing how deep a hole they dug in that subcategory, and therefore what their max possible grade is. It's also easier to justify when someone comes to you asking why their final grade is what it is when you can point to the syllabus and tell them that getting 95% on the final (worth 25%) doesn't make up for the missed 15% from never turning in homework.

[TakeruK]

I've had varied experiences with grading methods. As a liberal arts major (history, international studies) I was not often in classes graded on a curve because the graded portions were often subjective--grading a research paper or an in-class essay isn't the same as solving an equation correctly or answering multiple choice questions. Usually in those classes the syllabi broke down the grades into portions (attendance (usually assessed via pop quiz), homework, mid-term essay/exam/project(s), final essay/exam /project) with a percentage grade assigned to each, and no curving.

Just want to add that most science classes are graded this way too (usually it's like 20% homework, 30% midterm(s), 50% final exam; with a redistribution for a laboratory grade if one exists). A curve can be applied to the final weighted grade or to each component separately. There are sometimes extra requirements that the student pass both the "in-course" (homework+exams) portion independently of the laboratory (so even if you get 100% on the tests but never show up to the lab classes, you'll still fail). Since curving can still happen and it's even less clear where the curving happens when it's split into components, objectively-weighted grading isn't always transparent. For example, in one course, I received all my midterms and homework back (so the only component I don't know was my final exam). In order to get the final overall grade that I saw on my transcript, I would have need to get something like 130% on the final (which I know I didn't ace, by any means). I have no idea how the prof curved this grade!

[Sigaba]

MOO, the answers to your questions should be driven by conversations with the professor supervising your work, a firm understanding of your department's vision for the courses you are teaching, and your school's overall approach to teaching undergraduates. Even if you've been given the latitude to run the class as you wish, your grading policies should still fall within the standards and practices of your department and your school.

Unless you receive specific instructions to hold the line on grades, think twice before turning your sections into strongholds against grade inflation. This is not to say that you should give any undergraduate a grade she hasn't earned. I am merely suggesting that you double check to make sure that your grading practices fit into the established contexts of your department and your school. By tradition if not also by design, some courses may be easier and others may be "weeders." You will save yourself (and your department) a lot of heartache if you do not endeavor to re-invent the wheel.

[TheFez]

OregonGal, you raise several interesting points.

I actually think it's easier to grade "subjective" work on a curve since you can rank order the work from best to worst and set the percentiles where they fall. It's more objectionable to students to differentiate tightly clustered numeric scores into different grades.

Sigaba, I did have complete latitude to grade as I saw fit (though I had frequent discussions with other faculty to solicit their opinions.) But since I did my undergrad and masters at the school, I had a pretty good feel for the department's approach to grading.

I used a breakdown as others suggested (X% homework, Y% exams, Z% final, and also included a small percentage (5%-10%) that was based on "participation". I did this to give myself wiggle room so I could nudge a grade slightly for a student if circumstances warranted. Otherwise I was afraid the grades would be completely formulaic and I would not be able to pass somebody who was one or two points shy, but showed good improvement, or give an "A" to a top student who screwed up on one test.

[OregonGal]

I actually think it's easier to grade "subjective" work on a curve since you can rank order the work from best to worst and set the percentiles where they fall. It's more objectionable to students to differentiate tightly clustered numeric scores into different grades.

Maybe it's because I come from a writing-intensive liberal arts/humanities background, but for me the idea of subjectively ranking people's writing is part of what's objectionable. Often there are at least 3 possible topics given for any paper, and in upper-division courses sometimes there are no specific topics given other than a basic subject--students choose their own research focus/thesis. That makes it more difficult to shake students out into rankings when you have a group of well-written, well-researched 15 page papers on different subjects. In my upper-division courses I often got a letter grade, rather than a rubric with x points for writing/research/clarity/analysis which makes it even harder to try and rank people within those letter clusters. It's just as hard as applying a curve to a tightly grouped set of scores. While I have no issues with an exam that included in-class essays being ranked/curved, I'd have a much harder time accepting the ranking of 15 different thesis/capstone papers without a detailed point breakdown to explain the rankings.

I used a breakdown as others suggested (X% homework, Y% exams, Z% final, and also included a small percentage (5%-10%) that was based on "participation". I did this to give myself wiggle room so I could nudge a grade slightly for a student if circumstances warranted. Otherwise I was afraid the grades would be completely formulaic and I would not be able to pass somebody who was one or two points shy, but showed good improvement, or give an "A" to a top student who screwed up on one test.

I think it's completely acceptable to build in slippage with a small percentage for attendance/participation as you decided to do. A lot of my professors did and it's always been clear that either those points are a student's to lose through their own apathy, or that they're there to adjust grades a fraction of a percent to the professor's satisfaction.

[herbertmarcuse]

When I first started teaching undergraduate classes I only gave 4 tests which determined the entire grade for the class. This was problematic for me because I had a number of outstanding students in the class who always participated in the lectures/discussions but sometimes did much worse on exams than the ones who showed up only on exam days. Hence, a few years ago I modified my grading method to 3 tests (with study guides), 1 major research paper (about 5-6 pages in length) , 4 group projects.