Addition and subtraction will remain important parts of the arithmetic curriculum no matter what technology may devise. But when computers and calculators truly come of age in the schools, paper-and-pencil long division will probably be “as dead as a dodo bird.”
Those, at any rate, are the predictions of one mathematics expert, Richard D. Anderson, president of the Mathematical Association of America and professor of mathematics at Louisiana State University. He offered them to colleagues at a symposium on “The Changing Role of the Mathematical and Computer Sciences in Precollege Education” at the annual meeting of the American Association for the Advancement of Science, held here recently.
‘Essentially Misdirected’
“My own guess is,” Mr. Anderson said at one point, “that one-half of what kids study is essentially misdirected in terms of what they’re going to need and should be replaced.”
The advent of hand calculators and small computers 15 years ago has had “greater consequences for the nature of arithmetic than anything in the last 1,000 years,” Mr. Anderson said.
Traditionally, he continued, arithmetic has largely been a matter of drilling students to improve their skill at doing paper-and-pencil computations. But calculators--fast, efficient, and nearly omnipresent--eliminate the need for those laborious calculations, he said; they are “changing the nature of what is important in arithmetic.”
As examples, he cited these changes:
Multi-digit multiplication and the addition of fractions will be far less important than they are now. Computers and calculators require knowledge of decimals, not fractions.
Square-root computations (although not the square roots themselves) will be “largely out-of-date,” since calculators can perform them far more efficiently.
Estimation and approximation skills will assume more importance, as will the notion of “sense” of numbers.
“Single-digit number facts"--addition, subtraction--will remain important; the concepts are part of the foundation for further learning of mathematics.
Although it may be some time before long division and other “outmoded” techniques vanish from arithmetic classes, the dramatic impact of computers has made some change inevitable, according to Mr. Anderson and other panelists.
Change, however, will be neither instant nor easy, the panelists agreed. Many teachers resist the introduction of calculators into the classroom, preferring to stick to traditional methods they themselves learned, Mr. Anderson said.
“The arithmetic that people have studied tends to become the arithmetic they’re attached to--if it was good enough for them, it’s good enough for everyone.”
‘Subliminal’ Beliefs
And elementary-school teachers hold other, sometimes “subliminal,” beliefs about the value of learning arithmetic, according to Alphonse Buccino, director of the office of program integration at the National Science Foundation’s (nsf) office of science and engineering education. In conversations with teachers, he said, he found that they “believed, sometimes implicitly, that what they were doing was character-building.”
But as technology becomes more common in the arithmetic classes, teachers will probably have to adjust both their methods and their attitudes, he suggested.
Changes in the arithmetic texts used in teacher-education programs would ease the transition, Mr. Anderson said. These texts adopt a very traditional point of view, he noted, and teach neither estimation and approximation, nor a “feel for numbers.”
Opposition to change is likely, Mr. Anderson said. “It will be hard to convince people to make a virtue of inexactitude. It will have to be done gradually, not as an all-or-nothing proposition.”
