by George W. Cobb, Mount Holyoke College
Excerpted with permission from "Why Numbers Count: Quantitative Literacy for Tomorrow's America," Copyright (c) College Entrance Examination Board, 1997. All rights reserved.
Why is it that for decades literacy rates have been recognized as important indicators, measured and reported for countries at all levels of economic development, yet comparable rates for quantitative literacy have only recently been measured in a way that permits cross-country comparisons, and even now only for a handful of the most developed countries?
For a short, simple answer, we need only one word: computers. However, this surface explanation conceals an asymmetry with unsettling implications: quantitative thinking is becoming more important mainly because of computers, but these same computers are cheapening the value of many traditional quantitative skills--precisely the ones that are easiest to learn and least concentrated among an educated elite.
Literacy, as defined and measured by various government agencies, reduces to answers to two simple questions: "Can you read? Can you write?" The phrase "quantitative literacy" tempts us to think of the analog for numbers: "Can you count? Can you calculate?" But these questions ask about the low end of a continuum, inhabited by those skills whose value is quickly eroding. Value is increasing only at the upper end, and there reasoning is a better description than literacy.
Quantitative reasoning requires a difficult integration of four very different kinds of thinking. This makes it a kind of cognitive emulsion, an unstable Hollandaise of the intellect that constantly threatens to separate into its more basic forms of thought. ... Any attempt to understand and define quantitative reasoning solely in terms of measurable skills is apt to overlook the dynamic tensions that hold the skills together. A far greater consequence is that essential elements of quantitative reasoning tend to be overlooked, misunderstood, and underemphasized in our school curricula. This underemphasis has costly consequences.
Quantitative reasoning is supported by mathematical thinking, but to embrace mathematics as the essence of quantitative reasoning comes no closer to reality than did the blind man who hugged the elephant's leg. Something else besides mathematics, something quite different from it, is needed to link mathematical thinking to civic discourse, [namely] contact with the real world.
Although mathematics often relies on applied context for motivation and as a source of problems, ultimately, the focus of mathematics is on abstract patterns. Context is part of the irrelevant detail that must be boiled away over the flame of abstraction in order to reveal the previously hidden crystal of pure structure. In mathematics, context obscures structure. Like mathematicians, those who reason with data also rely on patterns, but ultimately, in quantitative reasoning, whether patterns have meaning, and whether they have any value, depends on context. In quantitative reasoning, context provides meaning.
Thus in quantitative reasoning, context plays a dual role: In the formal mathematical aspects, context obscures structure. But in the interpretive aspects, context provides meaning. This fundamental conflict, I believe, is largely responsible for what gives quantitative reasoning its intellectual vitality, but is also what makes it so hard to define in operational terms.
George W. Cobb is professor of statistics at Mount Holyoke College and chair of the joint Committee on Undergraduate Statistics of the MAA and ASA. He can be reached by e-mail at email@example.com.
Last Update: July 17, 1997