The calculator’s enthusiasts say its graphing capability is especially helpful to visual learners, who often struggle with the symbolic nature of math. Many teachers believe it opens the way to teach high school students not just the rudiments of computation and repetition but also the beauty and precision of such subdisciplines as probability and statistics.
“We can solve whole classes of equations that we’ve previously avoided in high school,’' explains Frank Eccles, who recently conducted a seminar on the new calculators at Phillips Academy in Andover, Mass.
Says Ellen Hook, a 20-year teaching veteran from Norfolk, Va., who has used graphing calculators for three years: “We are truly examining and talking about mathematics; we’re not doing arithmetic.’'
The first graphing calculator was introduced in the mid-1980s by Casio Inc., a New Jersey-based electronics firm. But the most popular one at the moment seems to be Texas Instruments Inc.'s TI-81, introduced last year. Texas Instruments actively sought the input of math teachers in developing its calculator, sending engineers to conferences to watch teachers use existing machines and to ask them how the device could be improved.
Teachers’ near-fanatic support for the TI-81, which sells for about $80, has not gone unnoticed by its competitors. Casio announced earlier this year that a new version of its graphing calculator would soon be available. And Hewlett-Packard Co. has been promoting its new models at math teachers’ conferences.
Several school districts around the country have made a major commitment to graphing calculators, thanks, in large part, to teacher enthusiasm. Last year, for example, the Pittsburgh public schools began supplying each student in upper-level math courses with a TI-81. The district had previously required pocket calculators in lower-level math classes and had used microcomputers in advanced classes to produce graphical representations of math functions. But teachers became enthusiastic about graphing calculators after some taught pilot courses with the early Casio models and experimented with others at conferences.
As a result, Diane Briars, director of the district’s math division, requested and received funding for 1,000 of the Texas Instruments machines for the upper-level students, as well as several classroom sets of the calculators to be used in algebra and other lower-level math courses. The district also adopted a textbook, written by mathematics professors Franklin Demana and Bert Waits of Ohio State University, that specifically incorporates the use of graphing calculators into the pedagogy.
“The pressure for these calculators is not coming from some administrator’s office,’' says David Molina, an assistant professor of education at Trinity University in San Antonio. “It’s very teacher driven.’' Molina has been awarded a grant to help teachers in the San Antonio Independent School District use graphing calculators.
Advocates of the technology, who sometimes refer to their uninitiated colleagues as “dinosaurs,’' concede that the new approach has its problems. Algebra and other courses, for example, lack textbooks that make use of the machine. Moreover, to use the calculators effectively, both teachers and students will have to do more work in the classroom. “To fully master this is going to take a great deal more than a couple of hours [of training] on a few afternoons,’' says Eccles of the Phillips Academy. “Teachers are going to have to think about their methods, to encourage kids to use discovery and cooperative methods.’'
Not everyone has been wowed by the new machines. Many teachers and administrators believe their students need a “back to basics’’ approach to arithmetic, not fancy technological aids. John Saxon, a nationally known former Air Force officer who espouses drill and practice, counts numerous math teachers among his adherents. And many schools have adopted Kumon math, a Japanese method that focuses heavily on basic and traditional computing skills.
Even teachers who have embraced the graphing calculator worry that students will use the devices to avoid learning the mathematical concepts involved. Hook of the Norfolk schools has addressed this concern by requiring her students to learn the basic concepts of the course before introducing the machine.
She remains, however, a true disciple. “For the price of a trendy pair of tennis shoes, we can put this very powerful piece of technology into our students’ hands,’' she says. “Mathematics is changing so much just because of this.’'
Peter West, Education Week
