“There is nothing in the middle of the road but yellow stripes and dead armadillos”
There used to be a time, not so long ago, when exam scores of students taking college physics were distributed on a curve resembling the usual Normal distribution. This was almost invariably the case in large introductory physics classes, but the same observation also applied to advanced senior courses, typically attended by relatively few (e.g., ten or less) students per year (as one could ascertain by lumping together data from a few consecutive years).
This meant that the bulk of the students would perform comparably, as one would intuitively expect. In turn, this allowed an instructor to gauge the level of the material covered in class, as well as the presentation thereof, based on how well most of the students seemed to assimilate it (and rendered grading much easier too).
Increasingly, however, over the past decade I have been observing Bimodal distributions of student achievement, in the classes that I have taught, including at the graduate level.
A “Bimodal” distribution
Extensive discussions with colleagues, as well as with friends who teach subjects other than physics, have led me to believe that bimodal distributions are in fact rather common, these days. I have heard several theories purporting to explain why this would be happening. Whatever the explanation, though, bimodal distribution pose significant challenges to instructors.
The simplest example of a bimodal distribution (BD) is shown in the figure above (courtesy of Wikipedia). The difference with respect to the normal distribution is clear. In the case of a normal distribution, most of the students perform near the average (i.e., right in the middle of the distribution itself), whereas in the case of a BD the majority of the students perform either above, or below average. In fact, I have seen instances in which the “dip” in the middle was quite pronounced, i.e., there was a clear separation between the two groups of students.
What is a teacher to do, in the presence of a BD of student achievement, especially if both groups of students (i.e., performing above or below the average) are large enough in size that one cannot simply forget about either one ?
I can only think of three alternatives, none of which seem particularly satisfactory:
1) Keep the level of the course high, i.e., gear it toward the minority of “overachievers”. This will likely result in a large number of students failing the class. Is this a desirable outcome ? Admittedly, often times the purpose of a course (especially at the introductory level) is that of “weeding out” those students who may not have chosen the best academic path. Still, failing over half of a class seems harsh, especially if one wishes to encourage breadth, i.e., have students with diverse backgrounds and interests take also classes in subjects that are far from their academic focus .
2) At the opposite extreme, lower the level to the point where most students will pass. This seems to be equally unfair, as it seriously short-changes students with a strong background and interest for the subject matter, who wish to be challenged, in the process possibly learning something that they do not already know. Some of these students will be seeking admission to graduate programs later on, and expect to acquire knowledge comparable to that of their competitors, i.e., students from other institutions. Why water down the course material to a point where it may lose much of its meaning, only to keep afloat students who will often not learn anyway ?
3) Adjust the level to be somewhere in the middle. This would be the optimal solution in the case of a normal distribution, but in the case of a BD it is a surefire way to dissatisfy everyone, making the course either too difficult or too easy for just about every student.
I wish I had a better idea…
 It is often the case, especially in physics, that departments offer classes that are very qualitative, essentially only descriptive, aimed at attracting students who are not majoring in science. In my opinion, this type of course does not really give students a real taste of what doing science is like.