EVERYTHING IS PROPORTIONAL

The Committee on Undergraduate Education (CUE) doesn't have any professors of mathematics as members. This fact has become painfully obvious in its ongoing and bumbling efforts to smooth out Harvard's grading scale.

At present, we have the following scale in the upper echelons of grades: A (15 points), A- (14 points), B+ (12 points), B (11 points), B- (10 points), etc. Notice the large gap between A- and B+. Some people view this gap as a good thing--it puts a real premium on any A grades. But the CUE has decided to close the gap. Exactly how to do so has become a quagmire of arithmetic, almost geometric, nay, exponential proportions.

Some CUE members have recommended adding the grade A-/B+ to the scale, giving it a weight of 13 points. This change would allegedly make our grading system "proportional."

What does this mean? Perhaps that a 14-point A- does not contain seven-sixths as many points on a 100-point grading scale as a 12-point B+? The average A- is a 91; the average B+ is an 88. We have to normalize the scales, since an F is worth zero points on Harvard's scale; thus, 60 is the zero point for the 100-point scale. Of course the ratio on this 40-point scale is not correct (test (91-60)/14 against (88-60)/12)--but it wouldn't be with a 13-point A-/B+ assigned to a numerical grade anywhere in between! The fact is that our 15-point scale cannot possibly be proportional in either manifestation.

Many colleges--in fact, almost all other colleges in this country--have the same letter grades that we do. And, miraculously, they manage to have a proportional system for calculating grade point averages. Yes, the old four-point scale seems to work pretty well there. Having 3.67 points for an A- and 3.33 for a B+ is far more "proportional" on the 40-point scale: (91-60)/3.67=8.45 while (88-60)/3.33=8.4.

However, neither of these systems can be truly and perfectly proportional until the underlying system of converting numerical grades to letter grades is changed. As it stands, the regular letter grades have four points on the 100-point scale devoted to them while the plus and minus grades only have three. For example, 83-86 is the range for a B, but 87-89 is the smaller range for a B+. Both systems have the added problem that an A+ has no separate grade; thus a 15-point or four-point A stands for the huge range 93-100.

Clearly, some CUE members have not considered the intracacies of the grading process. Until the fundamental disparities discussed above are eradicated, no grading system will satisfy the CUE's lofty if misconceived ideals.