By REBECCA CATALANELLO
Published November 23, 2003
[Times photos: Ken Helle]
Tiffany Jones, 17, uses a calculator during calculus class at Middleton High School in Tampa. Students in Jones' class use TI-89 calculators, like the one shown below.
TAMPA - Nine calculus students. Eight calculators. Twelve homework problems. And one teacher who wouldn't stop repeating her command.
"Now do it without a calculator," Middleton High School teacher Pamela Allison said.
Hrmph. Fluster. Roll of eyes.
"What's all this "without a calculator' stuff?" 17-year-old Tiffany Jones asked.
"I want to know if you can do it without a calculator," Allison said.
With 24 years experience, Allison sees calculators as a tool and isn't worried about Computer Algebra Systems, which lets users type in a formula and get instant answers.
"I just say, "Put them away.' And their little hands twitch toward them. And I say, "No,"' Allison said. These days, calculators are almost as common as pencils in K-12 math classes. But the advent of CAS technology is adding new fuel to an ongoing debate about their impact on math education.
Those who favor using the latest generation of graphing calculators say they allow students to move past the tedium of paper-and-pencil calculation into the depth and breadth of mathematical concepts.
But others worry that the high-tech devices are crippling basic math comprehension.
The newest $100 to $150 CAS devices can solve and graph equations, store formulas, answer true/false math questions and download text.
"You don't want a calculator that tells you everything," said Louise Albritton, math department chairwoman at Citrus High School.
She said she likes graphing calculators but has stayed away from CAS, because "a student doesn't really have to know any math" to use them.
Already in Florida, students schooled in largely calculator-friendly math courses are scoring poorly on the state's college math placement test, which does not allow the use of calculators.
Students must score higher than a 72 on the elementary algebra test to avoid being placed in remediation.
The median score has hovered in the mid 50s for the past five years.
Susan McAveety, an adjunct math professor at the University of South Florida, said most students coming to her are well-versed in calculator math. But many flinch when asked about formulas that students used to commit to memory - the quadratic formula, for example.
"And when it comes to fractions, they just fall apart," said McAveety, who also tutors high school students.
* * *
The Hillsborough, Pasco and Hernando school districts use CAS calculators in some math classes.
Pinellas classrooms don't have them yet, because the district still is working to equip students with the more common, non-CAS graphing calculators.
The Citrus district's three high schools also are going without, although officials there said they are open to using the new devices if they can be convinced they enhance learning.
Even Texas Instruments, which makes the CAS-equipped TI-89 used in local schools, is urging caution.
"It's important that students learn the basic concepts first," Texas Instruments spokeswoman Linda Beheler said.
The debate over calculator use is not a new one.
Since the 1970s, supporters have argued that they allow students to do difficult calculations without frustration, expanding math's appeal to even traditionally math-poor students.
Opponents think calculators are crutches that allow students to glaze over important concepts, undermining a true understanding of math.
The pro-calculator forces clearly have the upper hand.
The National Council of Teachers of Mathematics has endorsed calculator use since 1974 and now says they are okay to use as early as prekindergarten.
Most math textbooks are written specifically for calculator use. For example, the textbook Allison's calculus class uses is Venture Publishing's Calculus: Concepts and Calcula tors.
The nation's leading standardized tests permit calculators in the exam room. The College Board has encouraged calculator use on the SAT and Advanced Placement algebra tests since 1994. The ACT followed suit in 1996.
And the state of Florida doles out Casio four-function calculators to students taking the math portion of the FCAT in grades 7-10.
But after CAS calculators came on the market, ACT officials decided to bar their use.
"The skills necessary to do algebra manipulation are skills colleges believe students should have," ACT spokesman Ken Gullette said.
If CAS calculators were permitted, he said, there would be no way to determine whether a student knows what is being tested.
College Board officials used similar logic to explain why they encourage calculator use.
They say calculators are an essential part of college and high school math instruction.
"If you looked to see what all the best schools were doing, they were using calculators in math classes," said Amy Schmidt, the College Board's executive director of higher education research.
Robin O'Callaghan, the math curriculum specialist for the Educational Testing Service, the company that writes the SAT, said the exam is designed so calculators are effective only if students have a clear idea of the concepts.
She said CAS calculators provide an edge only to students who are familiar with them: "It's important that students be able to use the calculators they're comfortable with."
But California State University math education professor Wayne Bishop called such logic "flat wrong."
"It's comparable to hiring someone who knows the answers," he said. "If you're allowed to bring someone with you who knows, then I don't think that does the job."
And sometimes even the calculator isn't right.
Two years ago, students sitting down to the FCAT discovered their state-issued Casios were spitting out wrong answers.
* * *
So what impact do calculators have on a student's math comprehension?
Researchers from the Brookings Institution recently determined that students who use calculators moderately are likely to score higher than their counterparts who use calculators daily or never.
"It's a tool that's appropriate sometimes and not in others," said Jill Neilson, secondary math supervisor for Pasco County Schools. "I don't think all day, every day is appropriate."
Bishop criticized the research for its lack of depth, especially its focus on test scores and surveys, and its failure to look at student learning over time.
"Do you understand arithmetic better if you press keys and get an answer, or do you understand arithmetic better if you do arithmetic?" he asked. "Follow these kids for years and see what you find."
Even ardent calculator proponents agree that students should not leave elementary classes without a firm grasp of the basics.
"We're getting some kids in the high school level in Algebra I who don't know their times tables," Allison said.
But because of calculators, she said, it's still possible for those students to earn high grades.
What research says
During the past 25 years, research into the effect of calculator use on student performance has reached different conclusions:
- 1979: Calculators do not undermine basic skills. (Suydam)
- 1985: Calculators have neither a negative nor a positive effect on the paper-and-pencil skills of low- or high-ability students. They have positive effects on math understanding for average students, except in the fourth grade. (Hembree and Dessart)
- 1997: Calculators have a positive effect on learning, but should be used "on a limited basis" in elementary grades and for exploratory purposes. (Smith)
- 2000: Frequent calculator users score lower on math assessment tests than those who use them less frequently. Calculators are more commonly used by black and Hispanic fourth-graders than by their white peers. (Brookings Institution)
- 2002: Students who use calculators on the SAT to answer a third to half of the questions scored higher than those who either used it more or less frequently. Students who used the calculators frequently were less likely to complete the test in the allotted time. (Educational Testing Service: Scheuneman and Camara)
- 2003: A study of about 500,000 SAT test takers revealed white and Asian students were more likely to have studied math using graphing calculators in the previous two years than were black, American Indian and Hispanic students. The less expensive scientific and four-function calculators were more common among black and Hispanic students than in the other student groups. Researchers did not link the type of calculator used with test performance. (Educational Testing Service: Wendler, Zeller and Allspach)
- Sources: Brown Center Report on American Education; Educational Testing Service; Brookings Institution
