What is the Lowest "F" grade?

At St. Michael Catholic High School, the lowest “F” grade we record in our grade book program is a 50. That’s true if a student scores less than than a 50 for a test or quiz, or if a student skips an assignment.

Let me guess what you might be thinking: This is yet another example of a misplaced sense of compassion, whereby we give students something they don’t deserve in order to build up their self-esteem, resulting in inflated grades. Or maybe you think it’s because we’re trying to help our weakest students and “give them a chance” if they bomb a major assignment.

You may think these things, but you’d be wrong. We give grades of 50 because it’s the lowest possible “F” we can give a student on a 100 point scale that is valid. We do it for reasons of cold, hard mathematics!

The mathematical problem with giving grades lower than 50 is caused by trying to translate a one hundred point scale based on percentages into a 4 point GPA scale. Though each school might define these ranges a bit differently, for the sake of example, let’s say a school defines 90-100 as an A or 4.0, 80-89 as a B or 3.0, 70-79 as a C or 2.0, 60-69 as a D or 1.0, and anything less than 60% as an F or 0.0.

What does a “zero” on a 100 point scale, then, translate to on a 4 point GPA scale? Mathematically, a 50 is a 0.0, a 40 is a -1.0, a 30 is a -.2, a 20 is a -3, a 10 is a -4 and a “0” is a negative -5 on a “point” scale. We’re giving -5’s each time we enter a zero!

Let’s look at it in a different way. If a student gets a perfect score on test #1 and a misses every single question on test #2 and both tests were equally weighted, what should his grade be? Well, logically, the average between a high A (4.0) and low F (0.0) should be a C (2.0). But if we entered "0" for test #1 and "100" for test #2, the average would be a 50--or a flat F. In fact, if a student received a score of zero for the first test, he or she would have to get three perfect test scores to equal 300/400 points, or 75%, or a middle C. But that’s simply wrong! Three A’s and an F should average to a B (3.0), due to the fact that (4+4+4+0)/4 equals 3.

In other words, when we give “percentage” scores of less than 50 and retranslate that to a 4 point GPA scale, we inadvertently “weaponize” that grade against the student.

Let me anticipate a few objections:

If we give 50’s for work that is less than 50% correct or 50's for missing assignments, we give them “something for nothing” and that’s the wrong message.

No, we give them the lowest possible F that is mathematically valid. We give them nothing, but we also do not take away what they already have! Suppose we only entered grades as letter grades, as perhaps an English teacher might do for essays.  What letter would we give a kid who missed an assignment? An F, right? A zero on a 4.0 scale. That’s our lowest grade! But if we give zeroes on a 100 point scale, we are destroying their grade disproportionately to what they've already gained.

If I give nothing lower than 50 on missed assignments, kids would  rarely do homework or turn in minor assignments. It’s not enough of a penalty to make them do it.

If getting 50's for missing homework doesn't impact a student’s grade, then the “homework” portion of a quarter grade is likely weighted too low. Homework as 10% of a final grade won’t have much impact, and kids will figure out pretty quickly that doing it doesn’t matter! But at St. Michael, homework counts anywhere from 25% to 40% of the final average. Logging a series of “50’s” has real impact.

I support a higher percentage of grade for homework from a pedagogical viewpoint as well. One of the most important lessons we must teach students is to “earn” their success through hard work.  If I allow a student sit through a class, never pick up a book to study, ace the test and get a good grade, I have contributed to this student’s moral delinquency as an adult. Homework forces a kid to “own”his or her education, without the teacher at that moment being the main engine that “drives” the car. We should hold onto its importance by weighting it sufficiently.

Giving 50’s instead of zeroes flies in the face of long standing educational practice.

It may be long-standing, but that doesn’t make it right! The problem developed over time, I think, when we morphed from a predominantly “lettered” grading system in our schools (A through F) to a predominantly “numbered” system (1-100) due to the predominance of spreadsheets and computer averaging. Computers need numbers. If we were only giving letter grades, then it would be entirely appropriate to give “zeroes" on a four point scale.

Is there any mathematically sound alternative? It just feels wrong.

If a faculty is adamant about recording the exact percentage, even if less than 50%, were I their principal, I’d insist they multiply whatever percent that was times 4, then enter that number in the gradebook, with “4” being the maximum total points. All grades must also be recorded as a number between 0-4. Zeroes would then be mathematically sound. But doing it this way would also be a nuisance!

We prefer to simply keep the lowest grade at 50.