What Is Normal? The Curse of the Bell Curve

Popularized ideas often end up misconstrued and misinterpreted. Consider the biblical allegory in Revelation 7:1, in which the narrator says, “I saw four angels standing on the four corners of the earth….” For centuries, and even within small pockets of believers today, biblical literalists have taken this statement as fact and thus concluded that the Earth is flat. After all, a spherical Earth would not have corners on which angels, which perforce must exist, could stand.

On a slightly less biblical scale, inamorati of the bell curve, formally the Gaussian function, have broadly misinterpreted the normal distribution in probability theory and then misapplied it to circumstances for which it was never intended. Perhaps the most egregious error committed by bell curve enthusiasts is the use of the normal distribution as a prescription—that is, to establish how variations ought to be distributed—rather than as a description of possible, or probable, distributions of variation. Bell curve prescriptionists are the flat-earthers of statistics, except that unlike actual flat-earthers who are relatively harmless, bell curve prescriptionists can do quite a bit of harm—especially in the present age of test mania.

High-stakes tests, in themselves, harm many students because the tests do not accurately or adequately capture a true portrait of students’ knowledge, understandings, or abilities. When an overlay of prescriptive “normality” is imposed, the results are even less reliable as indicators of, well, anything. And application of the bell curve to classroom practice is truly a curse worth lifting.

Consider, instead, O’Boyle and Aguinis’ (2012) “The Best and the Rest: Revisiting the Norm of Normality of Individual Performance.” These researchers studied the performance of individuals involved in four broad areas of human endeavor: academics writing papers, athletes at the professional and collegiate levels, politicians, and entertainers. Their findings challenge the “‘norm of normality’ where individual performance follows a normal distribution and deviations from normality are seen as ‘data problems’ that must be ‘fixed.’”

O’Boyle and Aguinis suggest, alternatively, that distributions of individual performance—such as the learning of students at various levels of schooling—do not follow a Gaussian distribution but, rather, a Paretian distribution (see illustration of a normal distribution overlaying one type of Paretian distribution). Named for Italian economist Vilfredo Pareto (1848 – 1923), this “power law” distribution, sometimes referred to as the “80/20 rule” was originally used to describe the allocation of wealth in Italian society—i.e., 80 percent of the wealth generally rests in the hands of 20 percent of the population. The distribution has broader applicability. The 80/20 rule is shorthand, not a fixed distribution; but it is consistent over many activities involving large groups of people and often fairly describes smaller groups as well. For example, in a given classroom a small percentage of students is often responsible for achieving a large percentage of the top marks, on a sports team a small percentage of players is often responsible for garnering a large percentage of goals or points, and so forth.

In education contexts the so-called Pareto Principle, rather than prescribing how students ought to perform, can be used to help students monitor their own learning. “Documenting a learner’s errors using Pareto charts is an interesting way for learners to see evidence of growth, especially when they are working on discrete skills,” according to staff development trainer Donna Curry (2001) at the EFF National Center.

As practice experience and research like the work done by O’Boyle and Aguinis continues to accumulate, it seems hopeful that thoughtful educators and education policy makers may eventually be able to throw off the curse of the bell curve and thereby move away from prescribing how students ought to perform—whether on high-stakes standardized tests or teacher-made, end-of-unit exams—in favor of examining how students actually do perform and how learning can be encouraged, supported, and expanded for all students. At the very least, notions like the Pareto Principle ought to help educators reconsider what constitutes “normal” when it comes to teaching and learning.

This summary is excerpted from a longer article titled, “The Curse of the Bell Curve,” which can be accessed at https://www.academia.edu/7488772/The_Curse_of_the_Bell_Curve. The full article contains the references omitted from this excerpt.