These pieces originally appeared as a weekly column entitled “Lessons” in The New York Times between 1999 and 2003.

[ THIS ARTICLE FIRST APPEARED IN THE NEW YORK TIMES ON NOVEMBER 28, 2001 ]

## Statistics, a tool for life, is getting short shrift

BOGART, Ga. — Many educators want all high school seniors prepared for calculus. That means taking algebra in the eighth grade and covering geometry, intermediate algebra and trigonometry by the junior year. This leaves too little room for study of statistics and probability.

Yet students need grounding in data analysis. The push for universal calculus has relied on a false belief that colleges and future jobs would demand it. Yet while calculus is important for college students who major in science and for the scientific literacy of others, only a few jobs, mostly in technical fields, actually use it.

Nationwide, educators who recognize this imbalance are trying to get more statistics into the math curriculum.

One place this is happening is Malcom Bridge Middle School, about 60 miles east of Atlanta. There, Jamie Parker recently taught seventh graders to make graphs called scatterplots in which an X depicted the relationship between two aspects of body size the students had measured. The graphs showed each student’s wrist and ankle circumference, or height and arm span, or length of pointer finger and longest toe.

Mrs. Parker showed the 12-year-olds how someone (at a newspaper, for example) could report data accurately but display them deceptively — for example, by changing the scale on one side of a graph to make an apparent correlation seem less important.

Meanwhile, down the road at Oconee County High School, Steven Messig’s advanced placement statistics class used a list of random numbers to select five students from each of 20 math and science classes. The 100 subjects came to Mr. Messig’s room for a double-blind taste test of Pepsi and Coke. Two students poured drinks in random order. Others gave out cups, not knowing in which order they did so and then recording the taste each subject preferred.

Wouldn’t it have been easier to test a few complete classes rather than randomly select from many? Kelly Blount, a senior, explained that socially similar students might take the same classes, so each room might not be representative. For example, Kelly explained, students from wealthier families tend to value education more and might take more difficult classes. If those people also tend to have common tastes in what they drink, preferences of students in some rooms might differ from those of students chosen randomly.

Later, as these students analyze their data, Kelly may learn to say a “convenience sample” could be “biased” if drawn from a homogeneous subgroup. Students may be able to explain their “confidence” in the generalizability of results from a sample of the school’s 1,800 students — what the “interval,” or range of results, might be if other groups were randomly selected. Using computers and graphing calculators, Mr. Messig’s students will design several ways to display their findings.

In 2006, when Mrs. Parker’s seventh graders are ready for an advanced placement class in statistics, they could already know much of this math. This knowledge will be important because common debates about health, justice, economic and legal policy all assume familiarity with statistics. It is no longer possible to serve competently on some juries without more data skills than most college graduates have.

Clifford Konold, a professor at the University of Massachusetts, counted data displays in The New York Times. Dr. Konold found that in 1972 there were four graphs or tables in 10 consecutive weekday editions of The Times, excluding the sports and business sections. There were 8 in 1982 and 44 in 1992. Next year, he could find more than 100.

Interpreting these requires not only different skills from conventional mathematics, but a different way of thinking. Geometry and calculus concern proof. Statistics describe uncertainty. This change in orientation makes it hard to expand statistics instruction. Math teachers often resist placing it in the regular course of study because, despite having math degrees, they do not know how to teach statistics. Parents and counselors also balk, wanting no time taken from calculus.

Mr. Messig’s elective statistics course this year enrolled only nine students. Because their statistical backgrounds are weak, Mr. Messig is taking twice the typical time to cover the material.

But his students never benefited from Mrs. Parker’s middle school instruction. Her math class includes data analysis because the State of Georgia, influenced by standards of the National Council of Teachers of Mathematics, now tests if seventh graders are learning it. Mrs. Parker’s textbook this year includes more statistics than the old one.

If the trend continues nationwide, this newspaper could someday report that an apparently alarming cluster of cancer cases has arisen in an innocuous normal distribution, and students will be able to explain to their parents what that means.