Counting on Calculators Gives Mathematics a Wider Appeal

September 16, 2009

When it comes to calculations, does taking the fast route undermine rudimentary mathematical understanding? In one of its 2009 back-to-school stories about mathematics teaching and learning, the Pittsburgh Post-Gazette investigated the pros and cons of using calculators.

Calculator advocate and former high school instructor Henry Kepner, president of the National Council of Teachers of Mathematics (NCTM), commented that calculators enable students to explore mathematical objects such as quadratics in greater depth than would otherwise be possible, changing variables and seeing instantly how the graphs change accordingly. If students had to solve the problem by hand, Kepner argued, "we'd come to a stop for several minutes while everybody did the work."

On the opposing side, Robert Siegler, a member of the National Mathematics Advisory Panel, noted that "it doesn't make any sense to ask children (on an exam) to multiply 123 times 456 if they have a calculator." What teachers would be testing, he said, is merely whether students know how to use calculators.

Current information on the costs and benefits of calculator use is inconclusive. It "neither helps nor hurts learning of basic arithmetic," Siegler observed. "There is some evidence that it might do a little bit of good for learning functions and problem-solving skills, but basically research stopped (around) 1986."

Interested in remedying this gap in information, last year's mathematics panel recommended that the U.S. investigate the effects calculators have on students' computation, problem-solving abilities, and conceptual understanding.

Whatever their effect on computational ability, calculators have the benefit of bringing mathematics to a wider audience. One math teacher described the appeal of calculators to the gadget-loving side in many teenagers. Above and beyond handheld calculators are Internet search engines such as WolframAlpha, which can take verbal inquiries like "What is the square root of pi" and respond in seconds with a numerical answer carried out to more than 50 digits. Technological advancements like these have changed computation from drudgery reserved for mathematicians to an easily accessible form of exploration.

Other stories in the paper's series examined "Early Math," "Fractions," and "Algebra."

Source: Pittsburgh Post-Gazette, Sept. 2, 2009.