Grading Gets An F: A Mathematician's Guide To The Absurdity of Numerical Assessment

My least favorite memory of being a teacher was calculating marks for students. While my calculator was getting a workout, it would be pretty disingenuous to infer that what I was doing was anywhere near the statistical analysis that I was ostensibly doing.

Sure, my gradebook was littered with numerical grades for students–that’s actually an appropriate word to describe the garbage that I was doing–but while they were truthful entries, they would be used fraudulently to come up with one final two-digit entry for student achievement.

Even former math colleagues would hum and haw about “bumping” a student’s mark from something like 77 to 80. First of all, the second number only has aesthetic value in that it is tied to honor rolls, A’s, and those awful bumper stickers proclaiming being a proud parent of this statistical nonsense. However, the worst infraction is the gatekeeper pausing done by teachers in believing that they have statistical jurisdiction to not get fast and loose with these numbers.

Are you kidding me?

The calculation of grades must be one of the most ludicrous beliefs that statistical validity, hence integrity is being maintained.

First off, let’s start with any assessment outline handed out in any subject in the history of education. Every mark breakdown always has numbers that end with a 0 or a 5. You know, 10% for quizzes, 15% for assignments, 50% for tests, and 25% for the final exam. Funny, I have never found a mark breakdown that had something like “23%”. Because, you know, we would laugh at that arbitrary precision. But, if we have our numbers being base 10 or base 5, somehow that randomness gets to inherit mathematical literacy. And so, the madness now officially begins.

How many assessment pieces shall we have? 5? 11? 23? What’s the “magic number” that will inform how well a student is learning? I used to have the bare minimum because I knew that I had to “show something”, but no way was I going to roll out more than that and contribute more to this numerical folly.

So what do you do with your dice-roll number of assessments? Well, of course, you throw them in the mark breakdown blender, where some comical debate must have occurred as to how much everything is worth. Just pray there isn’t some small percentage attached to homework completion or class participation, because quantifying that is a red flag that your school is a hot mess of 20th century authoritarianism. 

But, nonetheless, homage to the statistical notion of average needs to be attended to, which has no purpose other than to report one number and not thirty-seven. How does “averaging” even describe real-time learning? I am a pretty decent cook now, but there was a time I was, at least figuratively, burning toast. I don’t “average” my poor performances with my much better ones–the better ones are the status update of what I have learned and can do today. If a student performs better on the final exam, that should always be their mark. Always. What if they do worse? Keep reading…

Speaking of the final exam, it was the worst violation of learning and statistics. Yes, it was always worth some confident amount ending in the aforementioned 0’s and 5’s. Help me out here. How can this assessment piece over 2 hours–which is usually a K-Tel Greatest Hits of the whole year–be fairly compared to the knowledge assessed over the whole year? 75% for 8 months and 25% for 2 hours. How is it that calculators are not made to barf at this gross input of statistical sloppiness?

Let’s stop before the exam. Do you really need more information as to what the student has learned? Haven’t three seasons of grade mania been enough to commit to a number? Nope. Need the final exam. Not because of any logical merit, but because it is tradition and students need to learn to write exams in college and universities, where the silliness continues, albeit less embarrassingly with GPA–which at least tries to factor in the variance of grades to begin with.

While I did mark thousands of tests and exams, my grading practices were sloppy–so I could mirror the sloppiness that was already baked into the system of grades. The best I could muster in terms of demarcation was something like pass, 60ish, 70ish, etc. Even schools themselves quietly admit the silliness in grades. In one of my schools, you were not allowed to report a mark of “50”. If the student honestly passed(not sure what that means), they were assigned a mark of 51. If they had a mark between 45 to 49, it was at the discretion of the teacher to pass or fail them. Somehow, grading has a slippery zone when deciding a steeper academic fate of a student.

All of this was what I have just written put to the test over a decade ago, when one of my calculus students did poorly on a final exam, falling far below the required grade needed for his baseball scholarship in the United States. We all have bad days. And those bad days are more likely to happen during high pressure exams, where your whole future unfairly rests with.

So, I gave him the mark that he needed. And, to be honest, even I doubted my own decision a little bit. 

A decade later, that student contacted me on Facebook. The message he sent is below, and I shared it on Twitter. It got 5000 Likes. 

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Grades are not only statistically useless, they have been acting as academic gatekeepers for millions of students, unjustly sorting, sifting, and selecting which students get to go where and why. 

It’s reassuring to know that so many teachers and schools are going gradeless. It’s not just a moral decision, it’s a mathematical one. Continuing to apply grades are visible reminders that schools are not only amoral–and anachronistic–in their philosophy, they are also mathematically illiterate.

The first one can be debated, the second one cannot. 

Checkmate.