Posted by: Gregory Linton | 05/07/2010

The Case for Quantitative Literacy

Many colleges and universities require a course in College Algebra or College Mathematics. Students generally dislike these courses intensely. Usually, these courses are just a re-hash of material the students studied in high school. Except for those going into a mathematics-related field, most students do not see the relevance of this course for their future careers. To address these problems, many colleges and universities are replacing their College Algebra course with a course in Quantitative Literacy. Quantitative Literacy courses address the use of numbers in real-world situations. In this post, I want to state the case for adopting this change in the college curriculum.

Several important publications have promoted requiring quantitative literacy in postsecondary education. One is the set of essays called Mathematics and Democracy: The Case for Quantitative Literacy, which was prepared by the National Council on Education and the Disciplines in 2001. The other publication was the Summer 2004 issue of Peer Review, a quarterly publication by the Association of American Colleges and Universities, which was dedicated to the subject of quantitative literacy. In addition, the Mathematical Association of American published Quantitative Literacy: Why Numeracy Matters for Schools and Colleges in 2003 and Achieving Quantitative Literacy: An Urgent Challenge for Higher Education in 2004. The National Numeracy Network has been developed by the NCED to promote initiatives in quantitative literacy.

What Is Quantitative Literacy?

“Quantitative literacy” is also called “quantitative reasoning” and “mathematical literacy.” In European countries, it is called “numeracy.” It emphasizes the practical use of numbers in everyday, real-world situations. L. A. Steen describes it as “a habit of mind, an approach to problems that employs and enhances both statistics and mathematics” (2001, p. 3). He lists the following elements of QL: confidence and comfort with quantitative methods, appreciation for the role of mathematics in science and culture, ability to understand and interpret data, logical thinking, decision making, ability to apply mathematics appropriately in a given context, ability to estimate numbers accurately, practical skills in solving real-world mathematical problems, the ability to use a wide range of mathematical and statistical tools, and understanding of mathematical symbols (2001, pp. 8-9).

The real-world contexts in which QL must be applied include citizenship, culture, education, professions, personal finance, personal health, management, and work (Steen, 2001, pp. 10-15). Examples of the application of QL include splitting a lunch bill, comparing price options for leasing or purchasing a car, reconciling a bank statement, estimating discounts and tips, understanding the effects of compound interest, comparing credit card offers, appreciating common biases in surveys, analyzing candidates’ proposals for reducing the national debt, understanding medical dosages, understanding the terms and conditions of different health insurance policies, developing a business plan, gathering and analyzing data to improve profits, producing a schedule for a complicated project, using spreadsheets to present data, etc. The possibilities seem almost endless.

QL is distinguished from typical college mathematics, which tends to be abstract and theoretical. Mathematics focuses on school-based knowledge, but QL focuses on mathematics acting in the real world. The primary difference between the two is that QL is anchored in real contexts. In fact, one can have a rigorous education in mathematics along traditional lines and still be innumerate. R. Orrill explains that “once basic arithmetic is left behind early in a student’s education, the mathematics curriculum moves on to more abstract concepts that are most applicable for future work in a limited number of technical professions” (2001, p. xviii).

Improving and intensifying the traditional mathematics curriculum will not necessarily translate into increased competency with quantitative data and numbers. Orrill summarizes the difference between the two fields in this way: “Unlike mathematics, numeracy does not so much lead upward in an ascending pursuit of abstraction as it moves outward toward an ever richer engagement with life’s diverse contexts and situations” (2001, p. xviii). Steen also notes that “even individuals who have studied trigonometry and calculus often remain largely ignorant of common abuses of data and all too often find themselves unable to comprehend (much less to articulate) the nuances of quantitative inferences” (2001, p. 2).

QL is best viewed not as a separate subject but as an integral part of all subjects in the curriculum. Steen summarizes the practical difference this makes in the curriculum: “Whereas, typically, college-level mathematics serves primarily preprofessional purposes (as prerequisites for particular courses), quantitative literacy is essential for all graduates’ personal and civic lives” (2004, p. 5).

Why is Quantitative Literacy Important?

To function successfully in a democratic society, citizens must possess the ability to search out information, understand it, critique it, reflect upon it, and apply it in making decisions. Unfortunately, American students do poorly on tests of literacy skills in comparison to students of other nations. For example, The National Assessment of Educational Progress found that the average mathematics performance of seventeen-year-old students was in the lower half of the “basic” range and well below the “proficient” range (Steen, 2001, p. 2).

Because we live in the Computer Age and the Knowledge Age, citizens are inundated with numbers and data. Until very recently, people had to make do with sparse and incomplete information about the world because data were difficult to obtain. The increased availability of data has made it imperative for people to know how to understand and interpret it in order to make sound decisions. For those who are competent and comfortable in thinking with numbers, this increased information is liberating and empowering. Those who do not possess this kind of mathematical literacy (those who are “innumerate”) will increasingly be disadvantaged in the workplace and in their personal lives. Steen (1997) warns that “an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg’s time.”

How Can Quantitative Literacy Be Taught?

QL is becoming such an accepted subject for higher education that publishers are providing textbooks for such courses. I have provided a list below. Typically, these books include units on management science, statistics, the digital revolution, social choice and decision making, fairness and game theory, sizes and shapes, and consumer finance models.

Here is a proposed course description for a Quantitative Literacy course: “This course develops the student’s ability to apply mathematical reasoning in the everyday world. It emphasizes the practical use of numbers in real-world contexts such as business, consumer finances, politics, history, and social sciences.” Practical, hands-on projects such as conducting surveys, analyzing poll results, calculating the total costs of different types of loans, and tracking investments will engage the students and show them the relevance of numbers in their everyday life.

Sources:

Orrill, R. (2001). Mathematics, numeracy, and democracy. In L. A. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. xiii-xx). N.p.: National Council on Education and the Disciplines.

Steen, L. A. (Ed.). (1997). Why numbers count: Quantitative literacy for tomorrow’s America. New York: The College Board.

Steen, L. A. (2001). The case for quantitative literacy. In L. A. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 1-22). N.p.: National Council on Education and the Disciplines.

Steen, L. A. (2004). Everything I needed to know about averages… I learned in college. Peer Review, 6(4), 4-8.

Websites:

Briggs, William. Quantitative Literacy/Reasoning

Mathematical Association of America. Quantitative Literacy

National Numeracy Network. Numeracy: Advancing Education in Quantitative Literacy (online journal)

Steen, L. A. Quantitative Literacy Web Sites

Textbooks:

Bennett, J. O., & Briggs, W. L. (2011). Using and understanding mathematics: A quantitative reasoning approach (5th ed.). Pearson.

COMAP. (2009). For all practical purposes: Mathematical literacy in today’s world (8th ed.). W. H. Freeman.

Sobecki, D., Bluman, A. G., & Matthews, A. (2011). Math in our world (2nd ed.). McGraw-Hill.

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