Computational geology 25: Quantitative literacy - drug testing, cancer screening, and the identification of igneous rocks

Journal of Geoscience Education, May 2003 by Vacher, H L

Keywords: Education - geoscience; education undergraduate; miscellaneous and mathematical geology.

Topics this issue

Mathematics: The mathematics of false positives, probability trees; conditional probability; intersection of sets; Bayes' rule.

Geology: IUGS classification of plutonic rocks.

INTRODUCTION

Mathematics and Democracy (Steen, 2001) makes the case for quantitative literacy. We, as citizens, are surrounded by numbers. People try to persuade us with arguments using numbers. Decisions are based upon numbers. Yet many people are quite willing to say, 'I can't do a thing with numbers."

Math anxiety, math phobia, and math avoidance are real. They manifest a condition that is so common and so accepted that it is a punch line. November 15, 2001, Russia's Prime Minister Vladimir Putin and our own President Bush visited Crawford High School during their meeting at the President's nearby ranch. Teachers told the students that their distinguished visitors would be happy to answer questions. Putin, with an impish look, volunteered, "No math questions." Bush chuckled and didn't correct him - instead adding "No fuzzy math." The local news here in Tampa (and presumably around the country) featured the incident. It was cute. The newscasters were jolly. It was a real human interest story - the great, human common denominator in the U.S. We don t do math.

Math anxiety, math phobia, and math avoidance affect the way science is taught to nonscience majors in college. Although scientific evidence and interpretation are based on data and analyses of a quantitative nature, many professors avoid equations or anything that might remind the students of a math course. To do otherwise would affect student evaluations, threaten tenure, and demolish enrollments. So, science for these students becomes a collection of stories and pictures. Although the stories and pictures are informative, engaging and even spectacular, they are still only stories and pictures. They are exposure, not deep understanding of how we know. Stories can easily be replaced by other, faithbased stories as soon as the students hear a more compelling story-teller. After all, one story is as good as any other - or so students are told elsewhere on campus.

Pandering to math anxiety, math phobia, and math avoidance in the academy produces a work force that is anxious about math, phobic of it, and avoids it. American business "pours millions of dollars" into developing their human resources (Dare, 1996), presumably much of it to remediate basic education. For technological jobs, business imports people from China, India, and Germany, for example. In the same way, geology and other science professors are finding that only international graduate students are likely to be sufficiently capable mathematically to do the work required in their research grants.

We hear of the great economic divide. The technological divide is also well known. There is also a quantitative literacy divide.

QUANTITATIVE LITERACY VS. MATHEMATICS

Our national mathematics curriculum is like a great Pleistocene landscape reluctantly coming into equilibrium with a new climate. The mathematics curriculum, which reflects the engineering orientation of West Point alumni who populated American engineering, science and mathematics education in the first half of the 19th century (Arney, 2000), aims to prepare students for calculus. Calculus has become the great gate-keeper. AP calculus is on the to-do list for college-bound students - not to mention their parents. Calculus is a gate-keeper for many college geology curricula as well. How many students have to take calculus to get a B.S. degree in geology and never see it in their undergraduate geology courses? When asked why they don't drop the requirement, how many calculus-nonusers on geology faculties say, "Well, we want to know that the student is degree material"? True, calculus teaches reason, discipline, and perseverance, as well as the mathematics of rates (differentiation) and sums (integration). And true, calculus is essential to geology - precisely because it deals with rates and sums (see Computational Geology 5, "If geology, then calculus," March, 1999). But just how essential are the skills of calculus to being an informed, thoughtful, and discerning citizen? The concepts and insight, yes, they are crucial, I believe. But so are concepts and insight of other forms of mathematics.

Quantitative literacy (QL) is the application of mathematical energy in everyday context. It is a habit of mind, an attitude, a disposition. It is the opposite of the condition manifested by math anxiety, math phobia, and math avoidance.

QL involves elementary mathematics. It is mathematics for all students. It is mathematics all citizens can use.

The range of QL is broad. It involves some aspects of mathematics that are not seen in the "march to calculus." Ironically, many students - and many professors - who are very sophisticated calculus-users can be quantitatively illiterate in some respects.