“No curve” – the name of this blog. I’m not against curves, though I am against grading practices that knowingly or unknowingly serve to detach the student’s grade from a complete assessment of their work.
Most of my blog posts will likely be about structural and methodological issues in education, why engineering education is under-research yet also misunderstood, and why the liberal arts have an identity crisis. But I feel this first post on this blog needs to explain the chosen domain name. Besides that it was short, easy to remember, and not already taken!
The experiences described in this post are biased to the science/engineering world. In my English courses in college, professors presumably read my papers, supposedly gave deep thought and analyzed what I wrote, and ultimately applied a grade that an assessment of my work – usually a letter grade. So this critique really does not apply to such courses. Though my solution gets back to what the English professor (theoretically) is likely doing inside his head when he grades an assignment …
Ask a university professor or student – what is a curve? You will get a lot of answers. It usually means one of a two things:
- Course grades (ABCDF) are assigned based on your standing within the class. No matter what your numerical grade. Many have written on the subject pro and con, like here and here.
- The notion, by students, that the common designation of A=90 B=80 etc is an arbitrary ideal. To account for poor student performance, poor exam preparation, or a variety of other reasons why the exam “results” did not live up to the ideal, some sort of upward remapping of the grades is performed. This is the commonly accepted student notion at my university (students – correct me if I’m wrong, but you all seem to use it in this context).
This blog post accurate highlights the differences and consequences of these mismatched definitions.
For this blog – I am talking about the second item. To put it in plain context, here is a not uncommon statement to be heard among students while walking across campus: “I got a 56 on my calculus test. But the highest grade is a 67, so maybe I still got a B.”
Let’s deconstruct this.
- Why is the highest grade a 67? Were the students unprepared? Was the exam too difficult? Was the exam material not the same as what as taught (e.g. core exam, individual lecturers)?
- Just because the highest grade is a 67, does that mean the 67 should receive an A?
- Note that the student seems to have no clue what their grade even means in terms of a course grade.
I am speaking from personal experience. Over 20 years ago while an undergraduate engineering student at Georgia Tech, I took a senior math course called “Complex Analysis.” Like many engineering students, I soon learned that only math majors should take senior level math courses, unless they have taken one or two other courses beyond the standard two-year calculus/differential equations sequence. Over half the students in the course were graduate students. On my first exam, I receive a grade of maybe a 60. I dropped the course.
A week later, the professor happened to cross my path and was surprised that I dropped it. I told him my grade. He continued to express surprise, and told me that put me in the top 1/3 of the class. He wished I had not dropped it.
Note that by his metric (I was in the top 1/3), I was doing well. By my metric (I got a 60) I was doing poorly. But something else bothered me even more – I didn’t have a clue what was going on in that class! I really should have dropped it. (I know, I should have taken Real Analysis first!) So we have several disconnects here in terms of who is communicating what to whom about class performance. I thought I was doing horribly. I know I was doing horribly. My grade reflected it. But the professor, who apparently was used to such low grades and grades “on a curve” thought I was doing reasonably well!
Why does this happen? Seemingly a lot, in some disciplines?
I will not make blanket statements about student performance, and will leave that out of it. There are good students, bad students, those who try hard, those who are lazy, those who whine about every last point no matter what, and those who question an exam grade out of a genuine concern that something was not graded right. A topic for another day.
- The 100 point grading system is easy to set up and use. Assign points to problems. Start grading. Take off a few points for minor mistakes, a lot for big mistakes. But the process of doing this often results in mis-scaled grades. In my early years as a professor, I’d do this and look at the end result and say “this exam performance doesn’t really deserve a 67 – these answers definitely reflect B-level thinking.”
- Some faculty do not tailor exam size or difficulty, both of which affect the time it takes to complete. They forget what it is like to be a student who has never seen the material before. If I tell my students “I took this exam and it only took me 10 minutes to complete” that should not please them. I made the exam. I might know this material as well as you can recite your home telephone number. It really is not useful information for the students!
- Some faculty don’t spend a lot of time grading. Their job depends on a lot of other things that take up their time. Even when dedicated and committed, they may be doing it in a hurry if other deadlines are conflicting and the students are clamoring for their grades back.
- Thoughtful grading takes more time than “just strike points off” grading. The classic example is messing up on the first step of the problem, but getting the right concept after that. Depending how hard the grader is looking at it, they may or may not recognize such situations. Or the grader may just cite the classic “you built the bridge upside down. Signs are important.”
- It takes some level of experience to estimate the common big and small errors students will make on a exam. I have found that while I THINK I know what some of the common errors made by students will be, and this thinking might bias how I create the exam, sometimes I’m really off. And I discover common misunderstandings (errors that occur by many students when I grade) that I hadn’t considered before.
- The act of curving causes some faculty to start playing crazy games of data analysis, when the real underlying problem is a lack of quality information. I have co-taught classes where this has occurred, and I realized in the end that the real problem was not enough good data on the students (our fault – either more assignments, or more meaningful grades, were needed). This blog post is an example of the lengths I have seen some faculty go through. To the author’s credit of that blog, they do write about not losing sight of what you are trying to achieve. But the extensive study of mathematical techniques for curving come grading time is something I have seen faculty spend too much time on, and again distracts from the base question – what is the student’s performance, and from my assessment of it, what grade do they deserve and why?
So what is the solution? My approach is simple.
- Use the full dynamic range. Why compress our entire scoring system to one tight end of the 0-100 scale.
- Give students meaningful grades. They should never wonder if a 67 is a D or an F. The biggest dilemma they should have is “is this a B or C, and where is the cutoff?” A student should always have a good idea of the general grade range they are sitting at (high B, BC, low A, etc).
This is not hard to do. My approach is simple. I grade every individual problem on an A/B/C/D/F scale. My grade is based, after reading this answer, on their demonstrated level of understanding of the problem and the core underlying concepts, and the accuracy of their answer. This works a lot better than “-2 for that, -12 for that.” I turn that into a 0-4 scale (A=4, B=3, …) and the exam grade is a weighted sum of the answers to the individual problems. Sometimes I do mark points off on a given problem but it is totally within this context. So when they get their exam back, the grade might be a 3.3. That is a meaningful number. It will not be curved. The student knows it is a high B or low A. The syllabus can fully explain the grading system.
This approach takes into account exam difficulty. If I notice that everyone in the class got a certain problem wrong, there is probably a good reason. I try to figure it out and take that into account when grading that problem with my letter grade system (or in rare cases, eliminate the problem if I really goofed!)
This sounds arbitrary, but is not. We can ascribe meaning to what those letters actually mean. WE ARE SUPPOSED TO.
So what do the grades mean? My university/employer is not particularly helpful in this regard. They say little more than ABCDF -> (excellent, good, satisfactory, passing, failure).
So let’s put some words around these terms from my engineering-centric bias.
A: Excellent understanding of the material. I want to hire you as a grad student. Or encourage you to continue coursework in this area leading to a senior thesis or design project.
B: Solid understanding of the material. You understood all the core concepts, and only had trouble with the tough or deep ones or were prone to lots of minor mistakes that really added up.
C: Adequate understanding of the material. Good enough to pass the FE exam. If you study hard. Some important concepts were missed, but most were understood to an acceptable degree. Often associated with excessive carelessness, not checking work, not answering questions, etc.
D: I hate D’s. Many majors don’t allow D’s for classes in their major. So it implies a higher standard for those who major in it. It means you barely scraped by, and it certainly was inadequate if this is a class in your chosen major. Why the double standard?
F: You were in this class? Your performance suggests you really don’t understand even the basic concepts of the course.
In a perfect world with infinite time, I would replace all quizzes with 15 minute verbal exams. I can usually accurately assess a student’s understanding of course material in a 15 minute conversation in my office. But a 50 person undergraduate course means 12.5 hours per exam … plus the scheduling issues (try scheduling a meeting among even 3 students!)
This is all from my own personal experience as both a student and university professor.
In my experience, this grading system really does not take any longer to implement. Students like the meaning of a 0-4 grade. The number is immediately meaningful, and no translation is required.
Some professors do a great job with the 100 point system. I knew a professor who had taught the same circuits course for almost 40 years. He could tell the class “the average will be a 72” while handing out the exam. He was always correct within a point at predicting the average. He didn’t curve – he taught the course for so long that he really understood how students would perform under his grading system. And he used the usual 90/80/70 cutoff.
Students, for the most part, really do fall along a bell curve, especially classes of 50 or more students. I tell my students “you can all get an A in this class.” I am not lying. But I also know it will never happen.
Finally, I’m not opposed to grading on a curve (the first definition), if it is commonly accepted by all parties (students, faculty, employers) that this is the purpose and design of the grading system. This might apply to some graduate level professions or particular disciplines. But most undergraduate college majors fail this “commonly accepted” test.
One more note — there are many reasons why a professor may not spend as much time on your class, or your grading, than a student may like. Some professors are quite dedicated to their students, even if they are squeezed for time! I’m not asking for an apology, but just trying to place things in perspective. If truly high quality teaching really were rewarded by the university, then being widely acknowledged as a great teacher would result in such faculty being paid as well as the top 50 researchers on campus in terms of research dollars. But they are not. There are many reasons, one of which is often overlooked – we don’t have good metrics for what a high quality teacher is. We cannot reward what we cannot measure. And if you think the measure is student teaching evaluations, read more here.