What Are Calculators Good For?Author(s): Leroy G. Callahan and Marilyn N. SuydamSource: The Arithmetic Teacher, Vol. 34, No. 6, FOCUS ISSUE: CALCULATORS (February 1987),p. 22Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193090 .

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Research Report

What Are Calculators Good For? Calculators are good for promoting

achievement: their benefit has been shown in reviews by Suydam (1982) and, more recently, by Hembree (1985). Suydam summarized findings and reported that achievement scores were as high or higher when calcula- tors were used for instruction as when they were not. Hembree used a dif- ferent technique to analyze the find- ings of seventy-nine research reports. At only one grade level did calculator use appear questionable: at every other level, he reported that the use of "calculators in concert with tradi- tional instruction . . . can improve the average student's basic skills with pa- per and pencil, both in basic opera- tions and in problem solving." More- over, "students using calculators possess a better attitude toward math- ematics and an especially better self- concept in mathematics than noncalculator students."

What topics do calculators help stu- dents learn? Among the topics on which research has provided evidence are the following:

- Problem solving: Using calcula- tors allows students to focus on prob-

Edited by Leroy G. Callahan ótate University of New York at Buffalo Buffalo, NY 14260 Prepared by Marilyn N. Suydam Ohio State University Columbus, OH 43212

lem-solving situations. Students ap- pear to be able to take their attention off the computational aspects of the problem and to focus on the relevant factors for solving the problem. They have more time to spend analyzing the problem, allowing for clearer under- standing and interpretation.

- Number ideas: Does the commu- tative property apply to 659 x 382 as well as to 6 x 3? Too often we ask children to generalize the property from work with a few simple exam- ples: the calculator allows many ex- amples to be tried - and relatively quickly. Have every child in the room pick two three- or four-digit numbers and multiply them, then reverse the order and multiply them again. Let them summarize their results: you won't have to tell them that the com- mutative property works for all whole numbers. Have them explore the dis- tributive property - and help them to see how useful it is when they're doing multiplication with paper and pencil, or addition "in their heads."

- Counting: What happens when you add 1 or 3 or 10 repeatedly? What patterns can be found? The calculator is a valuable tool in this process.

- Basic facts: Calculators actually seem to help students learn the basic facts: waiting until after the facts are fully mastered before using calcula- tors does not appear to be necessary.

- Addition, subtraction, multiplica- tion, and division with whole numbers and decimals: Try activities in which students find missing numbers, as in the following:

3_ x _2

72 14, 1512

Have them record the number of at- tempts they made before they were successful, and discuss what they learned. Such activities help to strengthen student's understanding of the algorithm, as well as provide ap- plications of other number ideas.

All students can profit from using calculators. When students with phys- ical and mental handicaps use calcu- lators, they score higher, are faster, and attempt more problems. Children who are mentally handicapped learn to operate the calculator with a mini- mal amount of instruction, and blind and partially sighted students can use cassette manuals to learn how to op- erate calculators. Thus, students with a variety of handicaps can use calcu- lators to aid them in mathematics. Similarly, students with learning dis- abilities can use calculators to help them overcome difficulties, both with computing and with the manipulation of symbols on paper.

Many materials are available to help you make use of calculators in teaching mathematics: even your text- book can probably help!

References Hembree, Ray. "Model for Meta- Analysis of

Research in Education, with a Demonstration in Mathematics Education: Effects of Hand- held Calculators." Dissertation Abstracts In- ternational 45A (April 1985):3087.

Suydam, Marilyn N. "The Use of Calculators in Pre-College Education." Columbus, Ohio: Calculator Information Center, 1982. (ERIC Document Reproduction Service No. ED 220 273) m

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22 Arithmetic Teacher

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