One Point of View: Making RoomAuthor(s): Jane SwaffordSource: The Arithmetic Teacher, Vol. 31, No. 7 (March 1984), p. 2Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192314 .

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One Point OF '7iGCO

Making Room

By Jane Swafford Northern Michigan University, Marquette, MI 49855

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Computers and calculators are here to stay. The challenge facing us, as stated in An Agenda for Action, is to "take full advantage of the power of calculators and computers at all grade levels." Much has been written and said about how this goal might be accomplished, about what we should add to the curriculum or how we can enhance the existing curriculum. But where will we find the room?

Let me hasten to add that the pres- ence of a computer need not change the mathematics classroom into a computer class. Many excellent ex- amples show how computers and cal- culators can enhance the existing mathematics curriculum without transforming it into a computer curric- ulum. Computers can be used for drill and practice, tutorial, simulation, demonstration, concept development, and problem solving. Calculators can be used within the current syllabus in many of the same ways.

This is not to say that the mathe- matics curriculum is unaffected by computers and calculators, nor is it to argue that we should continue to each what we have always taught but with embellishments that computers and calculators can give.

We must recognize that computers and calculators have changed the type of mathematics that the average per- son uses and needs to know. For example, unless forced, adults no longer do long division. Instead, they use a calculator. Similarly, who among us completes our income tax returns or balances a checkbook with- out a calculator? What teacher aver- ages grades with pencil and paper?

When have you seen a clerk figure the price of more than five items without a cash register or a calculator?

The Agenda recommends that "changes in priority and emphasis in the instructional program should be made in order to reflect the expanded concept of basic skills." At the same time, our concept of what is basic needs to contract to reflect the changes brought about by new tech- nology.

From my point of view, the first thing to eliminate to make room for the new is long division, that is, divi- sion by a two-digit divisor. Facts about division should be retained and emphasized. Short division, that is, division by a one-digit divisor without writing anything under the dividend, should become the goal for computa- tional instruction about division in el- ementary school. A strong emphasis should be placed on division by multi- ples of powers of 10, such as 50, 700, or 3000, using short division. We cur- rently spend an inordinate amount of time in the intermediate grades in helping students master the algorithm for long division. Like telling time by the sun, this skill has become obso- lete. If people want to know the time and don't have a watch, they will either guess or wait until they find a clock. This phenomenon is true of long division and calculators.

Some people argue that we should at least require the skills to do long division with two-digit divisors but none any larger. I say no, not in the elementary school. Long division wastes too much time regardless of the digits in the divisor. Short division

is sufficient. What would be more useful would be the ability not to divide by a two-digit divisor but to round it to a multiple of ten and esti- mate. Machines give us quick exact answers - humans need only be in the ballpark.

The ubiquitous presence of calcula- tors and computers should also change how we teach some mathe- matical concepts, for example, frac- tions and decimals. In the pencil-and- paper curriculum, much is made of converting fractions to decimals by first writing the fraction as an equiva- lent fraction with a denominator that is a power of ten. Conversion by division, especially long division, is the last resort. In a society replete with calculators, division is the first approach, provided the operation is done with a calculator.

Many other changes must be made in the curriculum to fit the needs of today and tomorrow. We all hope tc see a mathematics curriculum in the future filled with exciting problem- solving opportunities, broadened to include an expanded notion of basic skills and enhanced with appropriate applications of computers and calcu- lators. To accomplish these goals, we must make room. Some old friends will have to go, like house guests, before they overstay their welcome.

The Editorial Panel encourages readers to send their reactions to the author with copies to NCTM (1906 Association Drive, Reston, VA 22091) for consideration in "Readers' Dialo- gue." m

2 Arithmetic Teacher

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