Four of Pepperdine’s five schools, including the arts and sciences school, Seaver College, use the Blackboard learning management system, and I personally use it extensively in my courses. Recently, however, Blackboard has given me no end of difficulties in the form of student complaints about grades. The problem arises from a disconnect between Blackboard’s mathematical operations and my expectations about what would happen when I selected certain operations. In my Spring 2009 Religion 101 classes, several students received grades lower than they expected, because I didn’t understand beforehand how Blackboard calculates “averages.”

In my Religion 101 courses, students earn six grades: four unit tests (100 points each), a final exam (100 points), and optional daily quizzes (up to 100 points total). Students may choose whether to complete the daily quizzes or not; at the end of the semester, if a student’s quiz total is higher than that student’s lowest test grade (including the final exam), I drop the lowest test grade and use the quiz grade instead. Mathematically—though not conceptually—that works out to students’ grades deriving from the best five of their six grades.

As an intentional consequence of my grading system, the final exam in Religion 101 cannot lower a student’s grade. In effect, the final exam only affects a student’s grade if it is higher than one of the other five grades the student has already earned up to that point in the semester. I do this by design; I prefer to see the final examination as one last chance for students to show what they know rather than for the professor to see what student’s don’t know. These are really two sides of the same coin, but I prefer a “glass half full” attitude toward grading.

At any rate, in Spring 2009, I tried to help students anticipate their final grades—and understand the benefits of taking the final exam—by adding a “Minimum Possible Grade” column to the Blackboard Grade Center. In previous semesters, I just told students the formula and let them work things out themselves, but I thought I might also find it helpful to see the figures at a glance. Therefore, I set up a calculated column in Blackboard, and populated it, using Blackboard’s standard calculation tools, as an average of the Test 1, Test 2, Test 4, and Quiz Total columns. For readers unaware of this, Blackboard’s “calculated columns” don’t allow you to assign variable names to columns and type in a formula. Instead, you choose from “weighted,” “total,” “average,” and “minimum/maximum,” and then select the columns you wish to include in the calculation. Blackboard keeps the actual mathematical formulae invisible to the user.

For the sake of convenience, let’s use the following annotations:

When I asked Blackboard to calculate the average of the first four tests and the quiz total, I assumed that it would use the formula

(t₁ + t₂ + t₃ + t₄ + q)/5

It turns out, however, that my assumption didn’t hold true. Instead, Blackboard calculates the average based on the raw point values. So let’s introduce some new variables:

Of course, one gets the same result from the formula cited above and

t₁/u₁ + t₂/u₂ + t₃/u₃ + t₄/u₄ + q/r

But Blackboard didn’t use this second formula either. Instead, Blackboard calculated another behind-the-scenes value:

Then, Blackboard used this new value to calculate an “average” as follows:

t₁/u₁ + t₂/u₂ + t₃/u₃ + t₄/u₄ + q/s

In short, if a student skipped a quiz, Blackboard didn’t count that quiz as a 0 for that student. Instead, Blackboard eliminated that quiz from consideration entirely.

For students who took all of the optional quizzes, then, Blackboard displayed the accurate “minimum possible grade.” Students who had skipped any quizzes, though, were somewhat misled by the way Blackboard calculated averages. For example, if Pat made a perfect score on every quiz Pat attempted, but Pat only attempted half of the quizzes, Blackboard calculated Pat’s “average” as

(t₁ + t₂ + t₃ + t₄ + q)/450

(subsequently multiplied by 100 to yield a percentage, of course) whereas I wanted it to calculate Pat’s average as

(t₁ + t₂ + t₃ + t₄ + q)/500

Poor Pat, then, expected to receive a higher grade than the real calculations yielded.

I can’t really blame Blackboard for this; the problem arises from one tiny control that I didn’t set properly. When I set up the calculated column for quiz totals, I should have marked the “No” button for “Running Total.” That would have saved me a lot of headaches. Despite this post’s catchy title, I’m not dissing Blackboard. Rather, I’m underscoring for myself the importance of understanding how your tools work before using them for mission-critical tasks. You (by which I mean “I”) have been warned.