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`September 2, 1999
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`Powerful Calculators Throw Teachers a New
`
`Curve
`
`By JENNIFER 8. LEE
`
`352%" mu
`
`Turn ‘jocabulary On: I :
`
`Turn Geography On‘
`
`Like hundreds of thousands of other high school students, Greg Myers,
`16, began using a graphing calculator in freshman algebra. Graphing
`calculators, which bear little resemblance to their 1970's ancestors, 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
`said. "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 H subject tests.
`
`"There is no work involved, you just run the program, plug in the known
`values, and watch your answers appear," says their Web site
`(members.aol.com/highersat). The brothers are charging $35 for the
`programs and guarantee that a student's score will rise by 160 points or
`more. They said they had not had many takers so far. "Right now, we
`don't take credit cards," Greg said. "It's got to be check, money order or
`cash. If things get better, we'll probably start accepting credit cards."
`
`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 adeptness and make
`mathematics 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.
`Even while they solve difficult problems, graphing calculators have
`changed the political equation in the classroom.
`
`http://www.nytimes.com/learning/teachers/featured_artic|es/19990902thursday.htm|
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`Greg contends that his and his brother's programs are not cheating.
`"Cheating is violating regulations unfairly, but our programs do not
`violate any regulations." Graphing calculator programs are allowed on
`College Board examinations. Teachers and test administrators say that
`the arrival of the calculators allow questions to focus more on problem
`solving, rather than plug-and-chug calculations, and they are skeptical
`about claims like the Myers brothers‘.
`
`The two brothers, who attend Princeton Day School, a private school in
`Princeton, N.J., anticipate a potentially large market for their wares.
`
`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 and that nearly all of them take the
`SAT I or SAT II. Hewlett-Packard and Casio have a small share of that
`market.
`
`"These calculators are handheld computers," said Ellen Hook of
`Norfolk, Va., 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."
`
`Since their introduction in high schools in the early 1990's, graphing
`calculators have not only pushed students to expand their mathematical
`reasoning skills but have also fired up their ingenuity.
`
`Charles Sullivan, a 15-year-old student in Georgetown, Tex., used his
`Texas Instruments calculator to explore the structure of triangles in
`trigonometry. The algorithms that computed the intricate relations
`among cosines, angles and lengths gave him an appreciation for the
`elegance of math and programming. "You can understand how math
`comes together more," Sullivan said.
`
`But once Charles 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, you can do it over and over," he
`said. "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 a number of games, like Space Invaders and Tetris, on his
`calculator, and he has no qualms about playing them in class.
`
`Texas Instrument calculators are essentially Nintendo Game Boys in
`disguise -- they have a nearly identical microprocessor with less
`obtrusive packaging. "If some kid brought a Game Boy into class, they'd
`be sent to the office, whereas a graphing calculator can't get you into
`trouble," Charles said.
`
`There are now hundreds of games, including Pac-Man and the Legend of
`Zelda and versions of Mario Brothers, available for graphing calculators.
`The majority of them are written by students and are available free for
`
`http://www.nytimes.com/learning/teachers/featured_artic|es/19990902thursday.htm|
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`downloading on www.ticalc.org and other sites on the Internet. The
`games can then be transferred to the calculators through a cable to the
`calculators. Students can also exchange games with each other by
`connecting their calculators, and it is possible to make the calculators
`communicate through infrared signals.
`
`Games became popular only after the Texas Instruments assembly
`language, the most basic level of programming, became commonly
`available. But that itself came about because of student ingenuity at
`work.
`
`Originally, Texas Instruments had decided not to release the assembly
`language, which provides the most efficient building blocks for
`programming. "We had internal bets to see if people could figure out the
`assembly language," said Richard Schaar, a vice president at Texas
`Instruments. "But then kids figured it out their own. They reverse-
`engineered the assembly language." The engineers at Texas Instruments
`were impressed.
`
`Students like to play games on the graphing calculators because they
`blend into an educational setting. But teachers are not easily fooled. "If
`the kids are moving the keys real fast on the calculator, you know
`something's up," said Sam Powell, a math and computer teacher from
`Middlebury, Ind. "Usually you walk around the class and quietly ask the
`kid not to play on the calculator, and they usually comply."
`
`Teachers are also becoming aware of the power of calculators on tests.
`Many teachers make students erase programs from their calculators
`before exams, and some standardized tests make clear calculator
`memories mandatory. But a number of utilities exist that can make it
`appear that a calculator's memory is clear even though it still has
`programs in memory. The utilities either throw up a screen that mimics
`the real Mem Clear display, or they can make the list of programs
`disappear while leaving them accessible to those who know the specific
`names of the programs.
`
`Calculators have even had educational impacts beyond quantitative
`subjects. A few years ago, French and history teachers approached Ms.
`Hook because they were curious about why students were using their
`graphing calculators during their tests. Mrs. Hook quickly deduced that
`students were storing information for the tests as text in the memory of
`the calculator. Now calculators are forbidden for such tests.
`
`Teachers are wising up. "A teacher that is smart enough to use
`technology is smart enough to know what students are doing," Ms. Hook
`said. "Physically clear the calculator yourself. Don't just accept a blank
`screen." At her school, some teachers get together after school to have a
`calculator-clearing session.
`
`Rather than fighting students‘ programs, some teachers are redesigning
`their exams to take the programs into account. "My level of
`sophistication has changed in What we ask the kids to do," Ms. Hook
`
`http://www.nytimes.com/learning/teachers/featured_articIes/19990902thursday.html
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`said. "I never ask a question that just depends on calculator use. You
`want to mix the question with analysis." Occasionally she will even
`distribute programs for the graphing calculators for students to use 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, said Kevin Gonzalez, a spokesman for the service. Calculator
`programs like the Myers brothers’ will not help on the tests, the testing
`service said. "There is nothing about the test that is geared to the
`calculator," Gonzalez said. "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."
`
`Then what about the Myers brothers’ programs? Douglas Myers said he
`had raised his score on a SAT math subject test by 90 points, to 700, in
`part because he used his programs -- only about a third of them were
`available at the time. On his first try, Greg scored a 640 on a similar test,
`but he said he planned to use the graphing calculator again. "There are a
`lot of common formulas and stuff that you have to use," Greg said. "To
`have programs to do them faster without mistakes for a long problem
`really helps, especially the speed thing."
`
`Others are skeptical about the brothers‘ contentions. "Their claims are
`logically implausible," said Robert Schaeffer, public education director
`of Fairtest, a nonprofit testing watchdog organization based in
`Cambridge, Mass. "It's hard to believe that it would be a significant
`boost to anybody's scores since so few questions involve calculators of
`any form. The basic formulas are supplied on the test booklets."
`
`But he gives the brothers credit for their ingenuity. "It's creative
`marketing," he said. "And it's creative programming to get the power of
`that handheld to get that kind of information."
`
`Other students have used graphing calculators to show their flair for
`engineering. Charles Sullivan is constructing a pair of infrared links
`based on designs he found on the Internet. He plans to keeping lending
`an infrared accessory to friends so their calculators can communicate
`using invisible signals. "During the test, I can be giving answers across
`the room or getting answers across the room," he said.
`
`Sami Khawam, 19, an engineering student at the University of
`Edinburgh in Scotland, began the design for the infrared accessory for
`the Texas Instrument calculators while he was in high school. The
`infrared link can act as a universal remote control that can send
`commands to televisions and VCR's. "The calculator is also able to
`receive I.R. data, thus making it controllable by any remote control
`device," Khawam said.
`
`The infrared devices have raised some eyebrows, but some doubt that
`
`http://www.nytimes.com/Iearning/teachers/featured_articles/19990902thursday.html
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`Powerful Calculators Throw Teachers a New curve
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`they can be used effectively to cheat. "The concern with calculators is
`that there are some schools who are afraid that students can use this I.R.
`feature to cheat on exams," said Whit Hickman, a technical sales
`manager at Hewlett-Packard. "The reality of that happening is that you
`have to be within two inches of each other." Nonetheless, in response to
`the criticism, HeWlett—Packard pulled the infrared feature from one of its
`latest models of graphing calculators.
`
`The cat-and-mouse game between teachers and students will probably
`accelerate as calculators grow even more sophisticated. The latest
`generation of Texas Instrument calculators now have what is known as
`flash memory, which gives the calculator the flexibility to offer functions
`beyond mathematics. A calculator could, for example, act as a handheld
`digital organizer.
`
`"I can see the handheld devices getting pretty close to the Apple Ile
`functionality from the early l980's," predicted Jim Kaput, a professor at
`the University of Massachusetts at Dartmouth.
`
`Ms. Hook said the increasing power of calculators was a positive trend.
`
`The more power in the hands of her students, the better, she said. "I
`think that is exactly what we need for this generation," she explained.
`"They need to be in control."
`
`Score Raising Programs
`
`ticalc.org
`
`_C_gpy_r_ight 2005 The New York Times Com1g_ny
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`Children's Privacy Notice
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`http://www.nytimes.com]Iearning/teachers/featured_artic|es/19990902thursday.html
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