It's math time in Dee Parsons' fourth-grade class, and instead of struggling with workbooks or multiplication tables, the students are using restaurant menus and calculators.
They split into groups of four, and each party pretends that it has left Santa Ana's Hoover Elementary School for a Denny's restaurant, with exactly $25 to spend on a meal.
After discussing the relative merits of patty melts and chicken-fried steak, the students total up their bills on the pocket-size calculators, adding a soda if there is money left, subtracting a chocolate sundae if they come up short. They even total up tax and tip.
Then the first group reports to the class that it has spent a total of $24.78.
"How much change are they going to get back?" asks visiting resource teacher Sally Milton, drawing some blank looks. "Are they going to get a dollar back?"
"No," several students answer in unison.
"Are they going to get 50 cents back?" she prompts.
"How much are they going to get?"
"Two dimes," one student suggests, proving that he has absorbed one point of the lesson by learning to make a workable estimate of the answer to a real-life math problem.
He has also gone far beyond his grade level, Melton points out, handling decimals and percentages to arrive at the tax and tip.
'It frees them to think about how you go about solving the problem.'
That is just one of the reasons Melton and a growing number of teachers nationwide are introducing their elementary school students to calculators.
The best estimates are that 20% to 50% of elementary classes use calculators to some extent, says Marilyn Suydam, an Ohio State University education professor who has studied the matter extensively.
The American educational establishment is urging wider use of the basic hand-held calculator, despite resistance by some parents and teachers who worry that children will become so dependent on the machines that they will never really learn to add, subtract, multiply and divide.
The National Council of Teachers of Mathematics wants calculators in every math class from the first grade up. The National Science Foundation concurs, and in cooperation with school districts and universities, is sponsoring research on how calculators can be used to boost children's test scores and understanding of math.
Enthusiasts list a number of pluses for the devices:
- Students can tackle tougher, multistep problems if they use calculators to do the time-consuming basic math.
For example, Parsons says her fourth-graders would have missed the point of the menu exercise if they had used paper and pencil because they would have gotten hopelessly bogged down in adding up the long list of prices.
"It frees them to think about how you go about solving the problem," Suydam says.
If educators assume that students will have calculators when they graduate--a safe expectation since the devices are available for under $10--they can cut the amount of time spent drilling kids on the basics. This will allow more time to teach pupils to solve real-life math problems or advanced concepts.
"Certainly within one grade level it's not unlikely that six weeks could be spent on one basic (operation)," says David Pagni, an education professor at California State University, Fullerton. "Suppose we take away some of that long division, then we have four weeks to spend on something more valuable, maybe logic, reasoning, statistics."
- Some research shows that students taught with calculators actually learn the basics better.
In 1982, Suydam, former head of the Calculator Information Center, analyzed the results of 75 studies on the subject. She found overwhelming evidence that students taught with the aid of calculators performed as well or better on math tests than did students taught the traditional way.
- The most common argument is that it simply makes sense to prepare students for life in an increasingly technical society where calculators are commonplace.
"Adults use them all the time," Pagni says. "To ban them from the mathematics curriculum just doesn't make any sense."
But there are doubters.
'A Magic Box'
"If they give the kids the calculator too early then some of the kids will say that the calculator is a magic box," argues John Saxon, whose Grassdale Publishers Inc. in Norman, Okla., sells a line of back-to-basics math books. "They will resist the very difficult, arduous 'dog work' that is necessary to give them the number sense that is needed to use the calculator intelligently."
Saxon, whose high-school texts have been credited by some teachers with dramatic improvements in students' standardized test scores, says calculators have their place: In high school, and maybe in junior high.
He insists that the elementary years should be spent drilling the basics until they are second nature.
"If you pick a number out of your head and ask me what three-fourths of it is, I know the answer because I've worked it out over and over," Saxon says. "If we do not teach the child this number sense at the right age . . . they will always be crippled."
Variety of Techniques
Educators maintain that they are not abandoning the teaching of basic, paper-and-pencil arithmetic, just supplementing it.
At Hoover Elementary, for example, teachers use a variety of non-traditional, game-like techniques to teach math. But they also hold a weekly speed test in the basic operations, with prizes for those who score the highest.
"Mathematics in so many people's minds is computation," Suydam says. "So when you say, 'We're not going to spend as much time on computation,' they think we're not going to teach mathematics."
Even the strongest backers of calculators in the classroom acknowledge that they run into resistance from some parents and teachers, many of them harboring bitter memories of the "New Math" flop of the 1960s.
Scarcity Because of Resistance
That resistance accounts for the relative scarcity of calculators in classrooms more than a decade after the price plummeted in 1974 and 1975, says Suydam.
She notes that the same parents who insist that their schools buy computers often oppose calculators out of fear that they will become a crutch their children will not be able to discard.
Beth Andrini, who oversees the updating of the math curriculum at Hoover Elementary and the rest of the Santa Ana Unified School District, says the calculator can help students learn basic math.
Seeing an answer flash on the screen reinforces learning in a way similar to repeated paper-and-pencil exercises, she says. And using the machines seems to spark students' interest in math.
Math educators say the use of calculators goes hand in hand with a new emphasis on teaching students to solve practical problems in math.
Estimating Is Revived
Some say calculators have helped revive teaching of the important but long overlooked practice of estimating an answer to make sure that calculator or paper-and-pencil figures are at least in the ballpark.
Estimating also happens to be a valuable real-life skill, Suydam says: "You go to the grocery store and most of the time you don't have to know exactly how much the bill is going to be, but it's helpful to have an estimate so you know if you have enough money."
Suydam and others suggest that estimating and other problem-solving skills may be more useful than some traditional measures of math prowess, like long division.
Rather than spend a lot of time practicing division with three-digit numbers, they say, students should do enough problems to get the basic idea and then move on to something more important, perhaps some very basic statistics.
"We're spending a lot of energy teaching students to do things that calculators and computers can do better than they can, and not enough time teaching the things that people can do uniquely," says Lynn Arthur Steen, president of the Mathematical Assn. of America.
"Adults estimate, they use calculators, they solve things in quick and dirty methods," he said. "If you go around and look at what people really do, you'll find very little evidence that people use paper and pencil for anything."