In my college classes I teach, it’s often the case that the first test is one that students struggle on. It’s not unusual for this to be the only test they fail – classes vary wildly from instructor to instructor, and learning the difficulty curve of the class often takes a bit of time. So I fully expect students to struggle on their first test as they feel me out as a teacher.
This is unfortunate in many such classes, though, because making a 50 or 60 on 1 test in a college class can ensure you don’t get an A, or in some cases, even a B.
This applies in the high school realm as well, where I used to teach. Even though there’s usually many more tests and opportunities for grades, a 0 for a grade (which is a practice I disagree with and can spend a post writing on) or a bad test grade or two can really tank a student’s grade.
This gets to the real question of this post: What do we want grades to mean? My view is that grades should represent a student’s overall level of mastery. If this is the case, should a bad day or one poor performance really do severe harm to a student’s grade?
Consider this: A student scores 80, 90, 90, 40, and 100 on 5 different tests. What would you say is the best number to encapsulate this person’s level of mastery? If we used the traditional average, it would yield 80. This is perhaps a fine and fair number, but I see 80, 90, 90, and 100 indicative of probably an A level knowledge. There’s one bad outlier, but overall, this person shows mastery. This is why I use the median.
The median is the middle number when the data is ordered. (There is a weighted version of the median, too, which I do use, but I won’t get into that here.) The median yields a grade of 90, an A.
To me, the data yields a fairer grade that “softens” the blow of extreme outliers from someone’s grade. The mean (average) is extremely influenced by such outliers. Grades are almost always negatively skewed, so from a statistical standpoint, the median is a more accurate measure of center anyway.
Using the median in high school or college will allow students to recover from a bad day or any attempt that greatly deviates from their displayed mastery level. It’s so simple to compute also, that most students can do it themselves, which (surprisnigly) most students have trouble with when calculating mean.
If we are serious about using grades to truly demonstrate mastery, we should at least give using the median instead of the mean an earnest nod. It’s all about the mastery, and that’s the entire point.