John F. Kennedy High School
Cougar Crier
2002 Volume 16, Issue 2

Bellmore, New York 11710
December, 2002

cougarcrier@hotmail.com

Do Other Schools Have an Unfair Advantage on SATs and AP Exams?

By Sarah Brown,
Co-Editor-in-Chief

Most Kennedy students are unaware that upper-level math classes in Port Washington, Jericho, Great Neck, and other high schools across Long Island and the country are using the Texas Instruments-89 calculator, a far more advanced calculator than that which is used at Kennedy. Whether the Texas Instruments-89 calculator is advantageous to students who choose to use it on standardized tests remains under debate. Many students, parents, and academic officials, however, question the College Board's policy of allowing TI-89 usage on both the SATs and the Advanced Placement examinations.

Each Kennedy student at the pre-calculus level and higher is provided with a Texas Instruments-83 (TI-83) or TI-83 Plus at the beginning of the school year. The calculators cost approximately $90 each. The TI-83 is useful to students in graphing two-dimensional functions, calculating derivatives and integrals (calculus functions) numerically, computing fraction and complex number operations, and performing other basic mathematical operations. The TI-83 also has 24K of memory available for the installation of programs and applications which can help to perform certain mathematical processes.

The TI-89 calculator costs $160. According to the math departments of the schools that distribute it, however, it greatly assists students on standardized exams.

"The students have a definite advantage," said Great Neck North High School's Mathematics Chairperson, Helen Kramer. "[The TI-89] will do derivatives, differential equations, and visualizations."

The TI-89's most unique feature is its Computer Algebra System. The system allows the TI-89 to work with and solve algebraic functions. The TI-89 saves students both time and effort.

Advanced Placement Calculus students often are required to find the derivative and integral equations of a function. These calculations can be performed with the TI-89. The TI- 89, unlike the TI-83, provides users with not only the derivative but also the equation for how to calculate the derivative.

Additionally, the TI-89 has three-dimensional graphing abilities, enabling the calculator to find the roots, factors, and limits of algebraic functions. These capabilities are especially important on the SAT II:Math IIC exam as well as on the AP Calculus examination.

The College Board states that the use of almost "any four-function, scientific, or graphing calculator" is permitted on the SAT I and SAT II tests. It maintains that any of these calculators is sufficient for the SAT II subject tests. The Advanced Placement Examination in Calculus requires a more advanced calculator, but both the TI-83 and the TI-89 meet the College Board's recommended criteria.

When the TI-89 was released by Texas Instruments a few years ago, the Educational Testing Service (College Board's partner organization) redesigned the AP Calculus exams to include a section that permits calculator usage and a section that prohibits calculator usage. Test-makers reportedly worked hard to ensure that all problems, even those in the calculator section, can be solved without the assistance of a calculator. They hoped that these changes would prevent students who belong to wealthier school districts, or who can afford to buy $160 calculators themselves, from obtaining an advantage. The College Board promises that on the AP Examination, "care is taken to ensure that the examination questions do not favor students who use graphing calculators with more extensive built-in features."

The Kennedy Mathematics Department agrees with the Educational Testing Service's claim that the TI-89 does not provide a substantial advantage over the TI-83 or TI-83 Plus. The department has therefore decided to neither purchase this calculator for its students nor request that students purchase it themselves.

In addition to its Computer Algebra System, the TI-89 boasts another important feature that is believed to benefit students. It holds 188K of RAM that can be programmed to solve almost any problem on the SAT I, SAT II, and AP tests. While all problems on the tests can be solved without using a TI-89, the TI-89 is capable of dramatically improving the scores of many students who would otherwise do poorly. Several Long Island private tutoring companies instruct students in programming their calculators.

Many students, parents, and teachers complain about schools' usage of the TI-89, claiming that the calculator inhibits learning.

"The kids don't have to know as much," admitted Ms. Kramer of Great Neck.

A few years ago at Port Washington High School, Math Chairperson Gene Pizzolo and his fellow math teachers decided that their students should be "able to use the greatest technology available to them," and began to supply students with the TI- 89. Mr. Pizzolo admits, however, that there are "a lot of pros and cons" to the TI-89 calculator.

When instructing students in solving derivatives and integrals, Mr. Pizzolo's staff takes care to limit calculator usage.

"We talk to [the students] about why they're doing what they're doing," he said. "They have to know how to do it [without the calculator], so they initially can't use it."

Mr. Pizzolo admits that teachers experience difficulty with homework assignments, as it is nearly impossible to prevent students from completing their work without the use of the calculator.

When questioned about the TI-89's usage on standardized tests, the Educational Testing Service reported that it is well aware of the TI-89's capabilities.

"That is why we leave it up to you to decide [which calculator to use]," explained a supervisor.

The College Board's official website even explicitly states, "Calculator memories will not be cleared. Students are allowed to bring calculators to the examination containing whatever programs they want."

The question still lingers as to whether the College Board is correct in allowing the TI-89 to be used on college-entrance exams. Usage of the calculator is not permitted on tests in some universities' undergraduate math courses.

"Machines that can perform symbolic operations in calculus are not allowed," said Lewis Blake of Duke University's Mathematics Department.
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Math teachers debate the use of high-powered calculators
BY LISA BLACK, Chicago Tribune Mon, Nov. 03, 2003

CHICAGO - (KRT) - A hand-held calculator that can solve brain-numbing algebra equations within seconds has high school math teachers divided over whether it will make algebra more accessible or rob students of basic skills.

The Computer Algebra Systems calculator, or CAS, which sells for about $150 and performs more than 250 algebraic functions, can spit out the answers to even the most difficult equations with the punch of a few keys.

The very idea troubles many higher-math teachers, who argue that students will not learn how to solve problems on their own, leaving them unprepared for college.

"This is just another excuse for letting people go forward without a conceptual understanding," said Wayne Bishop, a mathematics education professor at the California State University who will not let his students use calculators. "The kids become absolutely helpless and yet they are given credit for algebra, as if this opens doors."

Others say it's more important to learn the theory behind the problems than to perform the actual calculations.

"It gives lots of people new life in mathematics," said James Schultz, a math professor at Ohio University who helped organize an international conference on CAS last summer at Glenbrook South High School that drew 150 educators. "It lets them focus more on the problem-solving aspects rather than the tedious computations."

Teachers have used CAS calculators for more than a decade in Austria and other European countries with little criticism. But it's a different story in the United States, where the often passionate arguments pro and con mark the latest skirmish in the calculator wars that began more than 20 years ago when basic calculators were introduced in elementary schools.

Most high schools discourage CAS calculators, fearing students will not learn how to work algebra problems on their own.

Only a handful of Chicago-area high schools - including New Trier in Winnetka, Ill., Glenbrook South in Glenview, Ill., Schaumburg, Glenbard West in Glen Ellyn, Ill., and the Illinois Mathematics and Science Academy in Aurora - use them in some algebra and calculus classes.

Historically, math teachers have drilled students on the skills needed to solve problems, but the CAS calculator shifts the focus toward teaching them how to apply those skills to real-life problems, said Natalie Jakucyn, a Glenbrook South High School teacher who organized the CAS conference.

As much emphasis is put on setting up the problem as solving it.

Students set up the problem by punching numbers, variables and algebra symbols into the calculator, and it instantly performs the mathematical grunt work that can fill worksheets and blackboards. The device even shows them how it reaches its conclusion.

Math teachers at Glenbard West High School teach students the fundamentals with paper and pencil, as well as with the calculator.

Kyle Smith, 15, a sophomore using the calculator for the first time this fall, said he still needs to understand basic algebra to set up the problems.

"I do the problem by myself and check with the calculator to make sure it's right," he said.

On tests, students are allowed to use the calculator on half of the problems but must go without it on the other half.

Teachers use the calculators in different ways. Some pose a problem through text - asking students, for example, to calculate how much a car would depreciate in 10 years. The class translates the question into the appropriate algebraic equation.

Students also might be asked to view a series of problems on the calculator and identify a pattern or general rule.

"If you don't understand, (the calculator) has a special program that helps you know how to work a problem out," said Alyssa Boburka, 16, a junior in an intermediate algebra class at Glenbard West. "The calculator does make it a lot easier. It's not as much writing and not as much of a hassle."

Richard Askey, a retired math professor from the University of Wisconsin at Madison, said the growing acceptance of CAS in high schools reflects broader disagreement about how math should be taught.

Critics complain, for instance, about a new style of math instruction in elementary grades. Instead of rote memorization of math facts, pupils are encouraged to estimate answers or use calculators.

"This is madness," said Askey, who opposes letting students use the calculators. "They won't learn algebra. It will cut off careers in many fields."

Twenty years ago, similar outrage surfaced when teachers introduced basic calculators in elementary school classrooms. Letting the youngest pupils use calculators still remains controversial, although the National Council of Teachers of Mathematics embraces their "appropriate use" in all grade levels. In California, the debate grew so heated that the legislature banned calculators in Grades 1 through 6.

A comparable discussion took place about a decade ago when high school teachers began requiring students to use graphing calculators, a practice that proved less divisive. Widely accepted in high school calculus courses today, these calculators produce a visual display of the student's work, such as plotting numbers on a graph.

The debate over CAS carries into the testing arena.

The college-entrance Scholastic Assessment Tests and calculus advanced placement tests allow students to use CAS calculators. The American College Test, a different type of exam that measures knowledge of content rather than reasoning skills, does not.

"College teachers are telling us it's important for students to come in able to do those algebraic equations," said Ed Colby, a spokesman for ACT, based in Iowa City, Iowa. "It's not as important for them to come in knowing how to use a calculator that can do that for them."

As teachers discuss CAS at national math conferences, a big question remains unanswered: How much basic algebra skill do students need to master before they start using CAS?

Teachers are eagerly watching the classroom experiments with CAS to see if they provide answers.

"People are frightened of it," Jakucyn said. "Not just because they don't know how to use it, but they see it can do all of algebra and they are afraid of what they'll have left to teach."

(Chicago Tribune correspondent Robert Channick contributed to this report.)
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Pricey Calculators Give Some Edge In Math Tests
By Nedra Rhone, Newsday, November 23, 2003
Staff Writer

LINK

Staples office supply store was a madhouse during the late summer back-to-school shopping crush. There was a ruckus in small electronics. "I heard everybody complaining," said John Azzara of Deer Park. "Mothers were screaming, 'I didn't know the calculator was $90!'"

The calculator, a graphing handheld listed among the necessary class materials for Deer Park High School and others on Long Island, earned a place in the great Regents Math A debate. While the issues of content and grading dominated educators' discussions after an estimated one-third of students in the state failed the exam last June, the use of the pricey calculator that sent some parents into a frenzy raised questions of equity and stirred age-old debates about the use of technology in math instruction.

Students who are able to afford graphing calculators, or who live in districts that provide the tools, have a distinct advantage over other students if permitted to use the calculator on a Regents exam, reported an independent panel of educators last month. The panel, convened by the state Department of Education to evaluate the Math A exam, recommended that the calculator not be allowed during testing until the state can be sure that all children have access to one.

State officials announced early this month that they would continue to look at the issue, while allowing students to use calculators through next August.

The recommendation that calculator use be standardized was "an equity issue," said panel member Alan Tucker, distinguished teaching professor of applied mathematics at Stony Brook University. "There is definitely a problem there."

Tucker said some inner-city districts reported having so few calculators that during the Math A exam, teachers had to pass them from student to student, pausing between each use to clear the memory.

Azzara, who left Staples without buying the recommended TI83 Plus by Texas Instruments, said his son, Joseph, reported only two or three calculators available in his class. "When he needs to do his work he has to wait until one of them is freed," Azzara said.

Deer Park director of mathematics Eva Demyen said there may have been battery problems early in the year so some teachers may have had to share, but that each class now has a set of functional calculators.

Joseph, a sophomore at Deer Park High School, who will take the Regents exam this year, said having a calculator "would help me do math better." He said using a calculator during the test may be hard for him because he is not as adept at using it as the students who use them regularly.

"It was hard to learn," said Tommy Piccione, 15, a student at Levittown High School, "but once you learn, it makes math easier." Piccione, who has his own graphing handheld, said he uses the device for "all the big stuff" and to check his work.

Some educators said the state should be responsible for making calculators available to all students at the appropriate grade levels. "Everybody agrees that equity is important," said Caryl Lorandini, president of the Nassau County Math Teachers Association, "but to deny access to something that kids should be using is not the way to create equity."

The effect of calculators on student achievement has been an issue of contentious debate among math educators for many years.

The National Council of Teachers of Mathematics officially recommends that calculators be integrated into math programs at all grade levels.

But some in the math community caution that there is the potential for misuse. The classic example is the student who does not understand the basics of mathematics and keys any number multiplied by zero into the calculator. "There are a lot of benefits to teaching math with technology, but inappropriate use can negatively affect the learning of a fundamental skill," said Neil Portnoy, director of math education at Stony Brook.

With only about 35 percent of the nation's high school students owning graphing calculators, according to industry experts, school districts must often bridge the remaining divide.

After searching eBay and finding that a used model of the calculator was selling for $80, Azzara gave up. "I said, I refuse to do this. My family cannot afford a $90 calculator."

Some parents said the decision to make the purchase is less a matter of poverty than priority. "I know it was expensive, but I was all for it," said Deborah Bruno of Levittown. "Parents can go out and buy their kids a $100 pair of sneakers, so why can't you buy a calculator?"

Some districts, particularly those in socio-economically diverse areas, generally write the cost of the calculators into their budgets. "We cannot require our parents or students to buy their own calculator, so we do the next best thing by providing class sets," said Robert Wayne Harris, executive director for curriculum for Freeport schools.

But even though all students have access to the device in class, Freeport teachers feared that the lack of continuity at home could negatively impact student performance, Harris said.

Dave Santucci, director of education for Texas Instruments, said the company is aware that the calculators are a big purchase for some parents, but that they try to add value to the product over time.

Teachers at General Douglas MacArthur High School in Levittown have already implemented another use for the graphing handhelds, even as the calculator's future in Math A hangs in the balance.

During a recent class, students sitting in groups of two or three hooked their calculators up to a wireless box. They tapped in numerical answers to questions and moments later the data was beamed to the teacher's terminal showing how many students got the correct answer.

If Rosemary Kaste, who teaches Math A in the district, sees too many wrong answers, "I'll reach for a different perspective. It's always surprising to me what the kids find confusing." Teachers in other curriculum areas, including foreign language, also use a similar system.

Though the district provided calculators this year, a number of Levittown students have owned their own since eighth grade. Over the years, they have learned to plot graphs, calculate exponents, check their computations as well as download games from the Internet.

If the state decides to prohibit optional use of graphing calculators on the Regents Math A exam, these are the students who may suffer. Experts generally agree that the mismatch of allowing students to use a calculator in class, but not letting them use it on the exam, could put them at a disadvantage.

Students seem to be the only ones at ease with either outcome. "I don't think it makes a difference," Piccione said. "A calculator just makes it easier."

Copyright © 2003, Newsday, Inc.

Illinois Loop on Calculators and their use in math classes.