The Disappearing Bell Curve

Article excerpt

The way in which we determine the population distribution of intellectual ability is an important issue for the field of gifted education because it greatly influences decisions we make about identification, justifications for provision of (limited availability) services, numbers to be served, and ultimately assumptions about the distinctive needs of one group in contrast to others. We are a field based on the notion of attending to individual differences; hence, our beliefs about the distribution and nature of these differences are fundamental to our practice.

The Construction of the Bell Curve

The bell curve is so frequently used to describe the distribution of intelligence that we seem to have forgotten that it is a construction, rather than an empirical fact. In 1733, Abraham DeMoivre developed the concept of the normal curve through his work with Stirling's formula. Pierre Simon de Laplace and Karl Friedrich Gauss, both active in the early 19th century, used the normal curve in different domains, ranging from calculating hospital mortality rates to evolution (Boyer, 1999; O'Connor & Robertson, 1999). Their work provided empirical support for the appropriateness of the normal curve as the expected distribution of data for the various domains they studied. Sir Francis Galton, in the latter half of the 19th century, used statistics to explore the distribution of mental and physical characteristics and also found the normal curve to approximate the distribution of characteristics. Through Galton's work, the application of the bell curve to human intelligence became inextricably connected, despite t he fact that he measured simple reaction times and physical features, rather than higher psychological processes.

Working in France, Binet read of Galton's theories of a general intelligence and decided that testing an array of intellectual abilities would best capture general intellectual functioning. Binet's initial goal in developing an intelligence test was to have a means of identifying children who were in need of remediation or alternative schooling. Through his extensive research, Binet had come to realize that complex mental activities, rather than simple measures of intelligence such as reaction times, provided the best opportunity for distinguishing intellectual ability levels. Building on the work of Dr. Blin and his student Demaye (Binet & Simon, 1905b), who had come to realize the value of a test that included items too difficult for all students to master, Binet's test methodically sorted students based on their ability to complete items successfully. In constructing the test, Binet and Simon set items at a particular age level based on whether 75% of the students of that age would pass it (Freeman, 1962) . Additionally, each item was expected to be passed by those students who overall were chronologically older and of normal or high ability (Aiken, 1994). In developing classifications of subnormal intelligence, Binet's assertion was that one must first "establish how a normal child replies" (Binet & Simon, 1905a, p. 73). Although this seems self-evident, during the early 20th century Binet's use of the comparative approach, one he had gained from the natural sciences, was not the norm. Binet's approach to standardization is still the norm today (Freeman, 1962).

From Classification to Quantification

Binet's goal was to develop a "measuring scale of intelligence," but he warned that "this scale, properly speaking, does not permit the measure of the intelligence, because intellectual qualities are not superposable, and therefore cannot be measured as linear surfaces are measured, but are, on the contrary, a classification, a hierarchy among diverse intelligences; and for the necessities of practice this classification is equivalent to a measure" (Binet & Simon, 1905a, p. 40-41). The distinction of whether intelligence scores serve to classify or measure has become increasingly blurred over time by the change in terms used to describe individual results and the popularization of Stevens' scales of measurement (Stevens, 1946), which appeared to support the assumptions required to make those changes. …