Degree of Difficulty

We’ve been talking lately about how hard numbers are. Not to use them, but just to decide what they even mean.

Let’s shift for a moment to grades and the GPA. Grades have enormous communicative power, even though they mean almost nothing. They are symbols without significance.

Let’s take a single course, say Calculus 1. What does a B+ mean? Does it mean that a student got more than 83% but less than 87% of the homework and test questions correct over the course of the semester? (And does that calculation include partial credit for operations correctly done but with a trivial error somewhere? And do some questions have more points than others?) Or does it mean that the student was at the vaguely-better-than-average-but-not-at-the-top-of-this-semester’s-group level? Or does it mean we don’t hold out a lot of hope for you as a potential math major, but we aren’t quite ready to turn you away, so go ahead and try Calc 2? It’s quite likely that different faculty in the same department would calculate that grade a little differently, based on their interests and values—it could be a bookkeeping score, or a competitiveness score, or a communicative score.

Now let’s take two courses, Calculus 1 and Introduction to Racquetball. Does the same grade of B+ mean the same thing in both courses? They both weigh the same, 3.33 units…

Now let’s look at two different schools. I taught one online master’s course with ten students, three of whom at the end got what I considered to be reasonably justified grades of A or A–. But the work of those very best students—second-year master’s students, remember—at one school would have gotten them a B or B– in my first-year undergraduate writing courses at Duke.

The remarkable precision of the GPA, with all of its attendant stress, with its precise cutoffs for adequate or exemplary performance, is a ruse. It’s a nicely decorated cover for a complete conceptual shambles.

We can mess around with it, calculating “weighted GPAs” that offer more points for honors or AP courses, but that just shifts the artifice to a new location. How much harder is an honors class than a regular class? 18.4% harder? Should Organic Chemistry get an extra 24.91% grade boost over the far simpler Intro Chemistry in the same major sequence? If I transfer, should my A in my community college writing course be converted to a B on my University of California transcript?

Here’s the fact. When someone reads your college GPA, their thought process will look like this:

Hmm… degree from Smith College. Good school. Majored in economics, tough major. 3.34, pretty good student. We’ll call her in.

Or like this:

Degree from Wilton and Madison College? Never heard of it. Majored in business, GPA 2.81… naahh…

Or like this:

Degree from Michigan in philosophy? Wow, great program! But only a 3.15 GPA… Maybe he’s okay…

What we mean by a grade is this: within a specific context, this student was judged by a specific person to have been:

  • outstanding
  • strong
  • okay
  • disappointing
  • awful

It hardly seems warranted to average those across experiences, much less to imagine two places beyond the decimal. It’s a false precision that feels reassuring, like a stuffed bunny that can’t actually speak. Do I know my GPAs from college and from grad school? You bet I do. They have talismanic force to protect me in the face of a hostile world, an external validation that suffices, once in a while, in the absence of internal validation. Yes, you really were that good, they murmur, if only to me…