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.
