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.

Dumber by the Test

Overuse and misuse of standardized tests are dumbing down the curriculum in our public schools.

Standardized tests are not bad per se. Some standardized tests are useful—for diagnosis, for research, and so on. But the wholesale use of mass standardized testing—essentially every student in every school—and the misuse of test results to judge individual students, teachers, schools, and entire districts is reductionist. Complex qualities such as student achievement, teacher quality, and school and district effectiveness cannot be reduced to a number or a set of numbers. No test score (or group of scores) should ever constitute more than a small fraction of the information used to evaluate a student’s learning or a teacher’s effectiveness. There are simply too many other factors that must be considered, many of them beyond the scope of the school to control or influence.

As standardized tests proliferate, teachers concentrate more time (often required by their supervisors) on direct test preparation, drilling their students on a narrow set of tested concepts and shunting aside richer learning opportunities that may, in fact, be lost forever. Researcher Qiuyun Lin comments:

Standardized tests create a system of education that reduces student learning to scores on a single test, rules out the possibility of discussing student learning in terms of cognitive and intellectual development, growth, social awareness and social conscience, and social and emotional development. (in “Beyond Standardization: Testing and Assessment in Standards-Based Reform.” Action in Teacher Education 23 (4): 43-49)

Over-testing limits students to acquiring basic knowledge at the expense of skills such as critical and creative thinking. When the goal is to determine answer A, B, C, or none of the above, there is no place left in the curriculum for students to develop higher-level thinking. So-called 21st-century skills don’t make the cut, however much they are touted by pundits and policymakers far from actual classrooms.

Bluntly stated, educators are running scared, faced with lawmakers, bureaucrats, and ideologues whose ramping up of standardized testing on a claim of “school improvement” is thin cover for a broad-scale effort to degrade public schooling and thereby validate the movement toward privatization. This takeover of public education is being orchestrated on the backs of children whose education is being impoverished, educators whose good work is under attack, and communities whose depressed education systems are graduating less well-educated students and, over time, whose schools will be seen as less attractive to potential new businesses. The health of a community’s schools and the health of a community’s business and industry run parallel. Indeed, the very fabric of our community is intimately connected to the wellbeing of our public schools.

Standardized tests do not improve education. Apart from their overuse narrowing the curriculum—dumbing down students’ learning—after getting test results education authorities at the state, and sometimes federal, level spend more time punishing schools and students that don’t do well (by taking over schools, for example), instead of spending time and money helping students and schools to improve. After all, in Indiana more than $46 million goes to testing, most of it paid to testing corporations, rather than to real school improvement. That’s a great deal of money that could be better invested in teaching than testing.

If our schools are to recover ground lost to over-testing, then mass standardized testing in the name of “school improvement” has to stop. There are better ways to use taxpayers’ money; there are more effective ways to use students’ learning time, and there are better ways to help teachers improve our schools.