Wednesday, February 25, 2015

Mathematical Nonsense from Education Professionals

When I started as an assistant professor, our Provost insisted that to be tenured, all tenure-track faculty had to have scores on their anonymous student evaluations that were above their department’s averages. I tried to explain to him that if this were sustained over time, the result would be that all tenure-track faculty would be required to have perfect scores. After that happened, no one would get tenure, since it would no longer be possible to score higher than average. He gave me a deer-in-the-headlights look.

Anonymous student evaluations are of course notorious for statistical nonsense. They should be controlled for the type of course (large, general-ed courses often get lower ratings than upper-level courses for majors), subject, major, and attendance. Small-number statistics also matter: if only four students do the evaluation, if the one premed is mad at you for having earned any grade other than an A, it will affect the average significantly. My first Provost understood this. The second one, who arrived three years later, did not: it’s a miracle I got tenure.

Now, my administration is clucking about “student success.” They expect us to improve graduation rates by 2% per year and by 10% over the next ten years, never mind that these goals are not mathematically equivalent. The effect this has on standards is anyone’s guess, of course.

Recently, a talented undergraduate told me that her high-school GPA was 4.3. Her high school counted AP courses on a five-point scale, and simply added this to the conventional four-point grade-point average. This, statistically, is nonsense. What strikes me is that exactly this was done when I was in high school, in the mid-‘70s. After 40 years, am I the only one to point out this is mathematical nonsense?

I tried to tell my student this. She got upset, insisting that she worked hard in her AP courses, so she deserved the extra points to her GPA. I told her that this doesn’t help when applying for jobs: when I was an undergraduate, telling a prospective employer that I’d had a 4.20 GPA in high school would get a glazed look, and I would not be hired. These non-academic employers understood this was mathematical nonsense.

I told my student that she should therefore go over her high-school transcript carefully and calculate what her GPA would be, if she had gotten nothing but grades of A, and then express her GPA as a ratio of this number. This would make my high-school GPA a 4.20/4.46, which is equivalent to a 3.77/4.0, which employers could understand. Wouldn’t you know that when I did find a job as an undergraduate, it was compiling statistics for some academics on campus, who never did ask my high-school GPA.

It’s bad enough for a 19-year-old undergraduate to do this. It’s less excusable for education professionals. (Mencken called them “pedagogues.”) What is it about education professionals and mathematical nonsense? It’s a wonderful illustration of the saying that, “It’s difficult to get people to understand something when their livelihood relies on their not understanding it.”


  1. Maybe the criteria are impossible to meet just because nobody is supposed to. Then, tenure or any other advantage will be a discretionary matter. You may get it if they like you. If they don't, you'll be told that you have not met the criteria and maybe even that you got more than you deserve based on the criteria.

    1. Or as they used to say on "Whose Line is it Anyway?"

      Everything's made up and the points don't matter.

    2. They have more than enough wiggle room to deny tenure even if the numeric criteria are reasonable. All that having numerically nonsensical criteria accomplishes is exposing the adminiflakes as the idiots they are. I am fortunate that they are not so innumerate at my joint.

  2. I recently had reason to spend several hours in the company of one of my more social-science-oriented colleagues, who decided to support a point not only with reference to the Site That Shall Not Be Named, but also mentioned student evals as a source of information. When questioned, (s)he seemed completely oblivious to the statistical problems associated with such data. Apparently statistical innumeracy is not limited to the statistically untrained.

    Of course, I can't claim any great expertise myself. There are really only two (three, depending on how you count) classes I regret not taking in college: economics (both micro and macro), and statistics.

    Also, I should have gone to church more often (to hear a preacher who turned out to be one of the greats of his generation, but we were busy making fun of what we took to be his affected British accent. Oh, the stupidity of youth.)

  3. OK, I'm right there with you about the administrative misuse of evaluations and statistics. That the adminiflakes are superbly wrong is almost tautology. However, I don't 100% agree that the treatment of AP grades is necessarily "mathematical nonsense".

    A 4.0 GPA means the student has achieved the highest level of competency expected of a high school student. How then to deal with students who opt in to courses at a level beyond the highest expected? If a 4 out of 5 in an AP course represents the same rigor as a 4 out of 4 in a "regular" course, is it correct for a student who gets a 4 in an AP course to have that count as less than a 4 towards the GPA if the AP 5-point scale is "normalized down"?

    Rather, I think the onus is on the student with a 4.5 GPA to explain what that means to those who might not initially understand it. My high school happened to grade on a A=1, B=2, etc. scale. I had to repeatedly explain why my 1 point something GPA didn't mean I was useful only as a donor of blood and/or organs; my audience generally understood, so I think it can be done. After college nobody gave a damn about my high school GPA and I could stop being defensive about it.

    However, "she worked hard in her AP courses, and so deserved the extra points to her GPA" is a shitty argument. I would hope an AP student would aspire to better.

    "IT WAS HELL", recalls former child. - B. Kliban.

    If we keep it in the realm of percentiles and competencies, we can have a better conversation.

    1. Then express the GPA as 4.20/4.46 = 3.77/4.0. With both, the 5-point classes are weighted 5/4 times more than the 4-point classes.

    2. I'd be concerned that someone whose eyes glaze over at a GPA > 4.0 would go catatonic at a denominator of 4.46. They will latch onto the 3.77 to preserve sanity, the likely result being that the student is numerically penalized for taking courses significantly harder than most of their peers. Explaining why my 3.77 is better than Joe's 3.83 because I took some AP courses and Joe didn't is, I think, a harder row to hoe than explaining a 4.20.

      I think I may be missing something, and an actual scenario might make this more concrete . How would you express the term GPAs for these four cases below? Each student takes the same courses, but two of them take the AP versions of some courses; their report cards are as follows.

      Peter: 3, 3.33, 3.67, 4, 4
      Janine: 3, 3.33, 3.67*, 4*, 4
      Ray: 4, 4, 4, 4, 4
      Egon: 4, 4, 4.5*, 4.5*, 4

      * AP course

      I am now reminded of my jobs while in college. My employers never asked for my high school GPA. Probably the fact that I was in that college spoke to my secondary academic qualifications well enough. I got the jobs by bringing samples of my work to the interviews, because that was the type of work mentioned in the job description and I thought the interviewers would want to know if I could actually do it. After I worked there for a bit, one of my employers told me that many of my classmates who interviewed had never heard of the tools one would use to do such work, much less had ever used them to produce anything.

    3. "Explaining why my 3.77 is better than Joe's 3.83 because I took some AP courses and Joe didn't is, I think, a harder row to hoe than explaining a 4.20."

      Sorry, but Joe's 3.83 is worth more than your 3.77. I learned that in high school. A kid in the same grade as me got an award that I didn't because his GPA was higher than mine, even though I was two years ahead of him in math, which was tracked.

      This has been said elsewhere as: 'A's from a community college are worth more than 'C's from Harvard.

  4. I am sorry that you were screwed royally out of that award. I have similar stories, but rather than depicting how it should be in all cases, like your story they only further highlight the problems of compressing a person's achievement into a single, contextless number. Someone who just clears the age-appropriate bar gets rewarded over the person who well surpasses that bar but falls some percent short of a higher one. The AP scheme used by high schools and accepted by colleges at least tries to address that.

    We were not talking about whether an A at one undergraduate institution is comparable to a C at another. We are talking about whether it makes sense for high school students who earn something like a B in a quasi-college-level course to have it count as an A on their high school transcripts, and whether an A in that course can count for even more to reflect the higher bar that was reached.

    I think the prospective employers who could not understand a 4.20 GPA did you a favor by passing you over. Good employers easily understand the concept of the "bonus" which may be given to workers who deliver ahead of schedule, under budget, higher quality, or any combination thereof, relative to their peers. Then again, at my joint, the brass knows what a bonus is, but they only give them to each other.

    1. Just to be clear, I'm saying that an employer who doesn't understand a 4.20 high school GPA probably also doesn't understand the concept of an earned bonus, thus there may be better ones to work for.