Calculators Throw Teachers a Curve.

Graphing calculators have taken high school math to a new level, forcing teachers to change the rules to keep up with the students

Like hundreds of thousands of other high school students, Greg Myers, 16, began using a graphing calculator in freshman algebra. Graphing calculators are sophisticated devices that can run small computer programs and draw the graph represented by complex equations in an instant. In the last few years, they have become mandatory in many high school math classes and can be used on the SAT and advanced placement exams and other standardized tests.

"I use graphing calculators all the time, and am a big enthusiast," Greg says. "In my math class last year, I was known as the expert on graphing calculators."

And like many of his high school peers, Greg has found another use for his calculator, a Texas Instruments TI-83. He has gone into business with his brother, Douglas, 17, writing 20 programs that can be fed into graphing calculators to help solve math problems in the SAT exam and SAT II subject tests.

"There is no work involved, you just run the program, plug in the known values, and watch your answers appear," they claim on their Web site. The brothers charge $35 for the programs and guarantee that a student's score will rise by 160 points or more. They haven't had many takers so far. "Right now, we don't take credit cards," Greg explains.

ONE-UPPING THE TEACHERS

Graphing calculators, which cost around $100, are lauded as the greatest innovation in math classrooms in a generation. Proponents say they lift students' confidence, cultivate their analytical skills, and make math more tangible. But they have also given students new ways to one-up their teachers and the rules. In response, adults have been forced to develop more sophisticated defenses, tests, and regulations.

Texas Instruments, which dominates the market for high school graphing calculators, estimates that one quarter to one half of all high school math students use graphing calculators.

"These calculators are handheld computers," says Ellen Hook of Norfolk, Virginia, who has been teaching high school math for 20 years. "They are marvelous. I can do more mathematics better now than I could 15 years ago. Students' critical thinking skills have changed."

APPRECIATING MATH'S ELEGANCE

Charles Sullivan, 15, of Georgetown, Texas, uses his calculator to explore the structure of triangles in trigonometry. The algorithms that compute the intricate relations among cosines, angles, and lengths give him an appreciation for the elegance of math. "You can understand how math comes together more," Charles says.

But once he is convinced that he understands the math, he simply programs his calculator to do the number crunching for him. "In math class, a lot of the homework is routine," he says. "If you know it, you can whip out your calculator, write a program, and press enter a couple of times, and you've got your answer."

The graphing calculator is also Charles's weapon against boredom. He keeps Space Invaders and Tetris on his calculator, and he has no qualms about playing them in class. But teachers are not easily fooled. "If the kids are moving the keys real fast On the calculator, you know something's up," says Sam Powell, a math and computer teacher from Middlebury, Indiana. "You walk around the class and quietly ask the kid not to play on the calculator, and they usually comply."

Many teachers make students erase programs from their calculators before exams, and some standardized tests make clear calculator memories mandatory.

Rather than fighting students' programs, some teachers are redesigning their exams to take the programs into account. "I never ask a question that just depends on calculator use," Hooks says. "You want to mix the question with analysis." Occasionally, she will even distribute programs for the graphing calculators for students to use on tests.

HELP ON TESTS

The Educational Testing Service, which offers the SAT, says students who use calculators on the SAT I, the general college admission test, do slightly better than students who do not. But that is because those students can avoid computational errors, not because of the design of the test. "There is nothing about the test that is geared to the calculator," says Kevin Gonzalez, a spokesman for the service. "This is mathematical reasoning--it's not one plus one equal two. It's not a test of what you know, it's how you apply what you know."

To Hook, the more power in the hands of her students, the better. "I think that is exactly what we need for this generation," she says. "They need to be in control."