by Glenda Lappan, NCTM President 1998-2000
NCTM News Bulletin, February 1999

We have arranged a civilization in which most crucial elements profoundly depend on science and technology. We have also arranged things so that almost no one understands science and technology. This is a prescription for disaster. We can get away with it for a while, but sooner or later this combustible mixture of ignorance and power is going to blow up in our faces.--Carl Sagan

This provocative statement is especially significant for those of us who teach mathematics because we are in the thick of the matter. Mathematics is a part of the sciences and also fundamental to all of science and technology. Mathematics is the key to the future of the students who are in our classes today.

The need for a higher level of mathematical literacy pervades modern life. In Education for What? (1998), the Educational Testing Service reports that in the United States, the new office economy is changing the face of work. Forty-one percent of U.S. workers are office workers. The vast majority of these office jobs are good, well-paying jobs, and the majority of such workers hold college degrees. These professionals use mathematics, and they do so in ways that are not always predictable.

The modern office worker's success depends mainly on flexibility, learning on the job, keeping up-to-date--and an ever increasing level of technical skill. Many tasks require the use of computers and various aspects of mathematics, from word processing to controlling machines, to analyzing complicated sets of data, to ensuring quality control in production processes. Yet our current high school academic preparation in mathematics barely prepares our students to apply mathematics in these ways. To quote a National Research Council workshop report (1995):

"Mathematics in the workplace is quite different from mathematics in school. It is more concrete and more intuitive, yet at the same time more exacting and more unpredictable. It is rich in data and inextricably linked with technology. Technicians and other workers are routinely expected to carry out multistep applications of simple mathematics--especially three-dimensional geometry, triangle trigonometry, and elementary data analysis."

Is there evidence that more education really helps? The National Center on the Educational Quality of the Workforce reported in 1995 that a 10 percent increase--about one year--in the educational level of a company's workforce increased productivity by 8.6 percent, whereas a comparable increase in capital equipment investment increased productivity by just 3.4 percent. Mathematics proficiency boosted a worker's earning power by a remarkable margin--28-year-old workers in the top quartile of mathematics skills earned, on average, 37 percent more than those in the lower quartiles.

These data show clearly that mathematics education is important. Yet we have no crystal ball that can be used to predict exactly what a particular student will actually do in life. Nor do we know how to predict exactly what mathematics will be needed in a technical job in the future.

What we do know is that mathematics outside of school arises from a context that often has ambiguous elements. There is no label at the top of a page giving a clue, such as "Solving Two Equations in Two Unknowns." Adults in numerous fields have to develop the problem that needs solving, make the measures or collect the data that might be needed, put together a strategy for attacking the problem, carry out the strategy, and then ask if the solution makes sense in the real context of the problem. If not, they try again. Clever, creative strategies count in the real world, but what counts even more is good solutions.

Our mathematical programs must teach all that. To do so, we cannot be satisfied teaching mathematical techniques alone. We have to teach the reasoning, the understanding, the flexibility, and the perseverance as well. Focusing on the basics until students master them and only then moving on to solving interesting problems yields very disappointing results. Although drill and practice have their place, the heart of a successful mathematics program must focus on good, challenging problems that motivate students to acquire skills--skills that will in turn open the door to new insights into mathematics problems. Such experiences will prepare our students to work in a technological and complex world that offers no easy answers. They will prepare them to be citizens who understand and can harness the power of science and technology.