# Calculators in class: freedom from scratch paper or 'crutch'?

OKEMOS, MICH.

It's just after 8 a.m., and Jacqueline Stewart is closely monitoring calculator use in her first-hour math class at Okemos High School.

Students are graphing: y=(x-3)n.

"Alright, you can use calculators on this problem," she says with a light Scottish lilt, "but I want you to conjecture about the expected shape [first]."

This isn't just any math class. It is Core-Plus Mathematics, one of only five math programs designated as "exemplary" by the US Department of Education. The course emphasizes real-life problems, group learning, and weaving together subjects from algebra to trigonometry. It also uses calculators. A lot.

Ms. Stewart and others say calculators are needed to engage students with problems like figuring out how fast college costs are growing, or working out statistical problems in manufacturing processes.

Critics, however, say calculators are overused in US middle and high schools. They warn that a wave of "new new math" programs that employ calculators much more than traditional approaches are entering grade schools, threatening basic math skills.

David Klein, a math professor at California State University in Northridge, says calculators should "not be used at all in grades K-5, and only sparingly in higher grades." That's not where America's schools are headed, however. Calculators are an important part of Mathland, Everyday Math, Connected Math, and other new math-reform programs touted by the Education Department last fall as "exemplary" or "promising." One reason such programs use calculators more than traditional math is that they are aligned with the 1989 National Council of Teachers of Mathematics standards. Those standards strongly advocated using more "technology."

"Do we really need to do long division with decimals, with pencil and paper? Calculators give kids the tools for thinking about math ideas they didn't have before," says James Fey, a math professor at University of Maryland and co-author of Core-Plus and Connected Mathematics textbooks. With Mr. Fey on the calculator side of the program was Core-Plus codirector Franklin Demana, a math professor emeritus at Ohio State University. Dr. Demana also serves as an academic coordinator for Texas Instruments, a leading maker of calculators.

Another possible reason calculators are favored by new programs touted by the Department of Education is that members of its expert panel supported the technology. "It's time to recognize that, for many students, real [math] power .... and facility with multidigit pencil-and-paper computational algorithms ... are mutually exclusive," wrote Steven Leinwand, consultant to the Connecticut Department of Education and later part of the expert panel, in a 1994 article.

Such views may ultimately impact students like John and Sean, in Stewart's class. In a few minutes, the two decide they've ruminated enough. So John taps buttons on his TI-82 calculator. A perfect parabolic curve appears. "That looks good," Stewart says.

Stewart does tell students when not to use calculators. John offers to solve another equation - and reaches for his calculator. "Trust yourself first," Stewart chides. "Don't trust the calculator."

But not all teachers are as conscientious. And as calculators become cheaper and more powerful, even some college students question their impact on learning. "I feel as though three years of math at high school were lost," says Amir Emami, a freshman at Kalamazoo College. Even though he graduated with a 3.4 grade point average, he says he has a weak understanding of math. "The answers [in high school] were written paragraphs, not equations or number crunching. You learn to depend on our TI-82 calculator."

In a nod to critics and parents, NCTM's 2000 standards unveiled last month recommended "guided work" with calculators in grades K-2, and a "principled approach to technology." That, it says, will ensure calculators don't become "a crutch."

Of course, math performance is tied to many factors, Klein notes, but the highest-performing countries on international math tests used calculators less. At the eighth-grade level, students from three of the top five performing nations in math (Japan, Korea, Belgium) rarely or never used calculators. But in the US and 10 of 11 nations with scores below the international average, many used calculators every day.

Down the highway from Okemos is the city of Portland, where Portland Middle School is a pilot for Connected Math. A sixth-grader recalls that at his elementary school kids used calculators in every grade. "I can't even do division without a calculator," he says. "Last year we did this weird type of division, I think they called it 'long' ... I didn't really get it. The teacher told us 'don't worry, you're doing the work. The calculator is just showing you the answer.' "

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