Are Vegetables Normal??


The new California Master Plan for Education 2002 contains an interesting assertion in the middle of the flowery vision statements of the Executive Summary. In the section on accountability it states:

"We envision an education system which will categorically reject the notion that student achievement must be distributed along a bell curve."

How should we interpret this?

An immediate flippant response from anyone just slightly familiar with the bell curve (or Normal Distribution) might be "are they suggesting that California students are not normal?"

A reader in search of deeper political meaning would probably think back to the arguments surrounding the 1994 book The Bell Curve: Intelligence and Class Structure in American Life by Hernstein and Murray. Publication of this book was funded by the right wing think tank, the Pioneer Fund. It attempted to use a controversial theory that human behavior is explained by a single factor called "intelligence" to prove that low IQ scores of African Americans are due to genetic factors. Amongst the many heated responses, a reanalysis by Raymond Carroll concluded that behavior and test correlations are explained by multiple factors that include skills that may indeed be changed by both environment and education.

So perhaps the authors of the Master Plan were implying support for an educational system that does not prejudge individuals and that provides equal opportunities for all of California's diverse population. The Academic Senate would certainly support this lofty ideal.

Currently, however, this ideal is far from being realized. The Academic Senate President has consistently called attention to the discriminatory funding to which the California Community College System is subject. Our students are automatically provided with fewer state resources just because they do not take their classes at a four-year university. Unfortunately, the Master Plan does not propose to change that.

But even worse, the plan is full of the same mindless accountability language of learner outcomes and institutional performance that we have strongly opposed in the new accreditation standards. Every thought and movement is to be recorded and graded and combined into scores that rate the individual human being, or instructor, or class, or institution. The disastrous K-12 model is to be imported to higher education.

But this is exactly where the Master Plan's statement about "rejecting the bell curve" gets interesting to a mathematician. In order to compile a single score for an individual student, for example, you have to calculate some type of average from this vast collection of separate outcome measurements. However, the Central Limit Theorem from statistics essentially states that when you use such an average, it is guaranteed to have a Normal Distribution.

If you measure student (or institutional performance) the way we're all being told we must, then you are absolutely guaranteeing that the result will be a bell curve. You can't avoid it.

So much for "categorically rejecting the notion!"

Or perhaps, as we used to say at U.C. Santa Cruz, "grades are for vegetables."