The Bell Curve occurs when there is a random distribution along a matrix with two variables. My point is that after the deliberate homogenization of "streama", and the elimination of pure failures, the Bell Curve is no longer applicable. Thus, it not the way to determine the norm. An additional criticism is that the Curve shows up in a large population. In a small sample, it is "fudged in". In other words, just as you might have a run of heads in a probability experiment, but regression towards the mean the more trials performed, until 50/50 is vindicated, so a small sample will not necessarily reveal the Curve, although it may appear as one increases the population. In a small sample, then, one is trying to make the cluster come out in a curve- like configuration. Thus, in a class that grades on a curve, it is unlikely that grades will be based on standard deviations. Rather, a certain number of Fs, Ds, Cs, Bs, and As will be assigned, and whoever comes closest in the ranking will somewhat arbitrarily get the grade.
So, how do we derive our expectations of performance? Well, we already have a good idea of what is to be covered in algebra II or high school American literature, so we are not bereft of guideposts. We also have some idea of what level of detail would constitute mastery of the material. After that, there are a couple of questions: is it tolerable for the students' knowledge of the multiplication tables to be spotty past the 6th grade? If not, then you have to demand an A of every child by that time, at least on that material. 70% will not do. Is it tolerable to have a spotty knowledge of precise historical dates? Yes, in many instances it would do no harm to be inexact. But, on the other hand, one should have an approximate idea of when various things occurred. For example, it is intolerable not to be able to place the Civil War in the second half of the 19th century before graduating high- school. In other words, we need to think about what students should know, and how detailed it should be, and make sure that they meet reasonable standards at least, that is, that a C means that they know the material pretty well, that they know the essentials cold, and that they have a fair idea of the rest......... |
