This is the third, and perhaps final, post concerning the mathematical and statistical validity of grades. You can view the other ones here: How Grades Are Damaging Students and The True Injustice of Grades
The last post was so well received, I have been thoroughly enjoying developing this final post. Over the past two weeks, I have been reading and combing through two fantastic older books about grades, the first Teaching Without Grades (1968) and the second Making Sense of College Grades (1986). Both are excellent, and even though the second tome deals with college, in particular, 85%+ of the book is still applicable to K12 realms.
I think it would be a shame to spend two posts lamenting the travesty of our current grading system without also proposing some solutions. Granted, the 5-letter, 100-point 4.00 GPA system is fully ingrained, but little by little, we can dream about chipping away at it.
At issue is that evaluation is essentially a qualitative subjective action, not an objective quantitative one, so any measurement assigning numbers to people will have limitations in usefulness at best and abhorrent misuses at worst. My solution, melded together from the two books and some self-study in the matter, attempts to establish grading (evaluation is really the better word) on a firm footing.
Proposal #1: Remove GPA entirely and convert to a new letter system. GPA is a derived statistic of derived statistics and has essentially lost any relevant information carried to it by the dead carcasses of other statistics, so it’s an easy call to toss – it is meaningless in every conceivable way.
The new letter system reduces the number of letters from 5 to 4 (wait, here me out! It truly is a reduction!), but in practice, the system only utilizes 2 letters heavily – N for No Credit and C for Credit. On any assignment, a student can be given no credit or given credit…and that’s essentially it, no 100-point scale, no convoluted curve, no magical mathematical genie lamp to make the teacher’s implicit wishes come true.
There are two other letters that are used on occasion, P and H. H is for Honors, which is given rarely (~5%) to assignments that exceed expectations and showcase high mastery. The other letter, P, is a temporary assignment of Pending and is for the gray middle areas where a clean cut from N or C cannot be had. A student who receives an assignment grade of Pending must produce evidence of further mastery (in whatever way is mutually agreed upon) to successfully receive credit (C). Failure to do so or inaction, and the P reverts to an N.
Proposal #2: Alongside the letter evaluation system, each assignment will also be accompanied by a Narrative as well. This seeks to give detailed information to the student, the teacher’s future memory, and any other stakeholders a vivid descriptive picture of the student’s mastery and how it has evolved over time. Suggested lengths of 1 medium-to-large paragraph seems doable. Granted, this will add time and effort on the teacher, but I feel the effort would be worthwhile.
There is a temptation among traditionalists that this system will blur the lines and delete valuable information about a student’s progress (such as the 78 the student made last week or the 3.7 GPA that the student has). Yet, this is a smoke-and-mirrors fantasy. The truth is that the math and stats are being bastardized by the education system in the name of “objectivity” and “fairness” when it really is anything but. Honestly, the Narrative along with the evaluation letter gives far MORE information to students and stakeholders about where a student stands and paints a far more complete picture than a unidimensional number can ever hope to do so. Realize “academic ability” is a very multidimensional trait, so expecting a unidimensional stat to tell you what you need is naive and perhaps far worse.
We do still live in a world of grades, though, and districts, software programs, and parents and students will still demand/require numeric grades, sadly. Until a no-numbers-grading can take foot, I suggest the following: For No Credit, this is an F/50%. For Credit, this is a B/85%. For Honors, this is an A/100%. Pending skips over the C/75% range and isn’t recorded. (In my view, C’s and 70’s are one of the greatest criminals in the grading system – in the murky gray middle, no one really knows if a student has mastered the standard or not and thus slips by to repeat the tragedy next course.)
When calculating end-of-semester/course grades, it is INCORRECT to use the mean (average), since grades are (by definition) ordinal data. (So if you take away nothing else from all this, stop using the mean/average to calculate grades!) The median is better if you have to use numeric grades. However, if using qualitative data such as letters, the mode is the most appropriate to use. Simply find the most commonly-occurring letter, and take that as the overall evaluation for the semester/grading period/course. Don’t weight everything different amounts; that only introduces huge subjectivity and biases the evaluation to your personal preference. The best practice is, if you don’t want to count a daily grade the same as a test, just don’t count the daily work as a grade – simple as that! (Those saying “but…then the students won’t work!” have to ask themselves what the real purpose of grades is anyway…the books above will help tremendously.)
Finally, for any wishing to take the dive into this radical realm of evaluation, I have enjoyingly spent some time creating a gradebook that accomplishes all of everything in this post. This gradebook allows you to fill out narratives and assign evaluations, and the excel VBA code takes care of most of the tiny details for you. It’ll even create Microsoft Word reports for you based on the students, or you can produce entire folders of reports all at once for an entire class.
I’ve included the zipped file at the end of this post. You’ll have to unzip it to use it. There are two files in the folder – both of these MUST remain in the folder for the coding to work. Simply make copies of the Gradebook file for each of your classes. Also, since it contains macros, you must enable and click through the Warning messages for the code to work.
Thanks everyone for such a warm response to this series of posts, and I truly hope we can work together to change math, stats, and education for the better!