Academic journal article Peer Review

Everything I Needed to Know about Averages . . . I Learned in College

Academic journal article Peer Review

Everything I Needed to Know about Averages . . . I Learned in College

Article excerpt

Several months ago, the conservative-leaning American Council of Trustees and Alumni (ACTA) excoriated America's leading colleges and universities with a report documenting the "failure of general education" (ACTA 2004). Among many cited shortcomings, one-emphasized in bold face in the opening paragraph-is that "mathematics is no longer required at 62% of the examined institutions."

Much could be said about the educational merits of traditional core curricula or the political agendas served by debates about the core. But that is not what I found most interesting about this report. Rather, it was the messages hidden in the fine print. There, in the endnotes, lie intriguing clues about collegiate mathematics-both about its place in general education and its role in the ACTA study.

First, many colleges and universities call this core requirement not "mathematics" but "quantitative reasoning," although variations abound: "quantitative or formal reasoning," "mathematical thinking," "mathematical and logical analysis," "quantitative and deductive sciences," "formal reasoning and analysis," or "quantitative and deductive reasoning." All of these stress the processes of mathematics (reasoning, deduction, analysis) rather than its components (algebra, geometry, statistics, calculus).

Second, these requirements are often fulfilled with courses that help students build connections between mathematics and other subjects, courses that reveal how quantitative reasoning is used across the entire spectrum of collegiate studies:

* Counting People;

* Economics and the Environment;

* Health Economics;

* Introduction to Energy Sources;

* Introduction to Population Studies;

* Language and Formal Reasoning;

* Limnology: Freshwater Ecology;

* Maps, Visualization, and Geographical Reasoning;

* Practical Physics: How Things Work;

* Quantifying Judgments of Human Behavior.

Here's what caught my attention: in every case where colleges allowed students to fulfill a quantitative reasoning requirement with courses such as these, the ACTA study judged the institutions as not including "mathematics" in its core curriculum. These colleges wound up on the 62 percent blacklist. But colleges that required a course in college algebra-whose pièce de résistance is the manipulation of negative fractional exponents-were checked off for having a suitable "mathematics" core requirement.

Quantitative Literacy

This ACTA analysis demonstrates the presence of "two mathematics" (see Bernard Madison's article in this issue). One is an abstract, deductive discipline created by the Greeks, refined through the centuries, and employed in every corner of science, technology, and engineering. The other is a practical, robust habit of mind anchored in data, nourished by computers, and employed in every aspect of an alert, informed life. This is what these many colleges call "quantitative reasoning," what many other countries call "numeracy," or what I'll call "quantitative literacy" (or QL for short).

Although clearly related, quantitative literacy and mathematics are not the same. Whereas mathematics rises above context, QL is anchored in context. Whereas the objects of mathematical study are ideals (in the Platonic sense), the objects of QL are data, generally measurements retrieved from some computers data warehouse. Because quantitative reasoning relies on concepts first introduced in middle school-averages, percentages, graphs-many believe that QL is just watered down mathematics (and thus should not satisfy a "mathematics" requirement). Some academics, typically mathematicians, argue that students should complete QL by the end of high school; in this view, it is not a central (or even proper) responsibility of higher education. Others, typically not mathematicians, argue that QL is too important to be left to mathematicians, whose training inclines them more toward Platonism than earthly practicality. …

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