Hand-Held Calculators' Milestone Number
Monday, October 1, 2007
In a darkened Algebra II classroom, all eyes were on an illuminated graphing calculator projected three feet high on the white board as students studied a series of graphs and talked about absolute value functions.
The weightless image of a TI-84 Plus Silver Edition graphing calculator is a far cry from early typewriter-size calculators that weighed 55 pounds and plugged into an outlet. This year marks the 40th anniversary of the moment that revolutionized not only the calculator but also the way students learn math. It was 40 years ago that three Texas Instruments scientists shrank that monstrosity and created the hand-held calculator.
To mark the milestone, the Texas company donated some historic hand-helds to the Smithsonian's National Museum of American History last week as symbols of change in the United States. The devices will go alongside the table Thomas Jefferson used when he wrote the Declaration of Independence and the top hat Abraham Lincoln wore when he was assassinated.
In math classrooms, calculators mechanized finger counting, pencil-and-paper calculations and slide rules. Elementary students weaned on Little Professor calculators that can add, subtract, multiply and divide move on to graphing calculators in later grades. Future students will use programmable devices that show algebraic formulas, graphs and word problems on the same screen.
But as the technology continues to advance, a question remains: Are the devices helping or hurting students? Educators are deadlocked over whether calculators are helping create a more numerate society capable of claiming the next technological breakthrough or making students technology-dependent and mathematically insecure.
The United States lags in international math exams. Top performers, including Singapore and China, put more emphasis on mental math and memorization and introduce calculators to the curriculum later than the United States does, said Tom Loveless, director of the Brown Center on Education Policy at the Brookings Institution, who has researched how calculators affect student achievement.
Today's students "maybe are not so great at computing numbers on the back of a notebook," said Jerry Merryman, 75, a co-inventor of the hand-held calculator, as he stood before a velvet-encased 1967 prototype during a ceremony at the Smithsonian Castle last week. But he said calculators have expanded "their reach and grasp" of mathematics.
Given a shortcut, Americans embraced it. Educators pride themselves on circumventing repetitive, drill-based learning and instilling creativity and curiosity in students. These are lessons calculators help facilitate, many say.
"We can jump past the grunt work and get to more sophisticated levels of analysis," said James M. Rubillo, executive director of the National Council of Teachers of Mathematics.
The teachers group was instrumental in making calculators ubiquitous in math classrooms by recommending their use as early as kindergarten in the 1980s. The group emphasizes the importance of teaching mental math and estimating skills in its most recent position paper.
Some teachers say calculators make it possible for students who struggle with basic math concepts to explore higher math.
"Kids whose arithmetic skills may be weak can rely on calculators to do that work, and they can still do algebra," said John Mahoney, a math teacher at Benjamin Banneker Academic High School in the District and a consultant for Texas Instruments. "It's just like word processing. There are people who can't spell . . . but word processing can allow them to express things well and be creative," he said.
But the concern is that students rely on calculators too much.
Elizabeth Korte, a math teacher at Stone Bridge High School in Loudoun County who used the oversize graphing calculator to teach about absolute value, said calculators can be a huge help to understanding math trends and principles. But they have to be used "in their place," she said.
"You should memorize your basic math facts. Period. The end," she said. If she sees one of her students reaching for the calculator for a basic multiplication or subtraction problems, she stops them short.
"I believe if you are comfortable with mental math, it's easier to do higher math," she said.
To keep her students' computing skills sharp, she gave them a multivariable algebra problem to solve early in the class. What would probably take 30 seconds to solve on the calculator, she went through -- step by step -- with her class by hand.
Ten minutes in, with just one more variable to solve, the class paused at some double-digit multiplication problems, and she relented. "Go on and get out your calculator," she said.