by Lee V. Stiff, NCTM President 2000-2002

*NCTM News Bulletin*, April 2001

A recent newspaper article critical of calculator use reported that calculators harm students' ability to learn mathematics. An example similar to the following was cited: A fifth grader, Tamika, age 10, says she likes to buy potato chips for 60 cents and chocolate chip cookies for $1.15. When asked to find the sum, she enters the numbers in her calculator--but forgets a decimal point. "Sixty-one dollars and 15 cents," she says. The article concludes that this and similar examples demonstrate that calculator use among elementary school students is bad.

What's bad are classrooms in which students do not employ their estimation skills in concert with their calculator use to decide about the reasonableness of answers. The rote use of calculators is no more appropriate than the rote memorization of basic facts. In each situation, students should acquire an understanding of the tools and concepts they employ.

It's not surprising that critics of calculator use in the elementary grades present the worst-case examples as standard practice to convince their audience that back to basics is the best educational path to take. Our response should not be to ban calculators from elementary grades, as some critics suggest, but to continue our efforts to make sure teachers are well prepared to teach, and as part of that, well prepared to teach using calculators.

Why calculators? And more to the point, why calculators in elementary school? First and foremost, the research shows that calculators have their place. Hembree and Dessart's (1992) analyses of research on calculator use revealed that appropriately using calculators during instruction improves paper-and-pencil skills for low-, average-, and high-ability students. They found that in the early grades, calculators are frequently used for exposure to the tool itself, for checking work, and for problem solving. From the evidence available, appropriate calculator use enhances the learning and performance of arithmetic concepts and skills, problem solving, and the attitudes of students. Research indicates that students perform better when using calculators to supplement strong programs of computation (Carnine et al. 1998).

Research has also shown that calculators can aid in "stimulating problem solving, in widening children's number sense, and in strengthening understanding of arithmetic operations" (Campbell and Stewart 1993). Calculators can help students learn basics, such as numbers, counting, and the meaning of arithmetic operations. Students show greater ease in problem solving when using calculators because they focus less on computational recall and algorithmic routines and more on the other aspects of the problem-solving process. Appropriate calculator use promotes enthusiasm and confidence while fostering greater persistence in problem solving.

Furthermore, our best teachers strongly support calculator use. In a study of Presidential Award–winning teachers (Weiss and Raphael 1996), 84 percent of the elementary-level awardees said that students should be allowed to use calculators most of the time.

It is important for all students to become flexible and resourceful problem solvers. Helping students acquire a better understanding of the underlying concepts and relationships of computational algorithms is essential if we are to accomplish that result. Developing the ability to appropriately use relevant technologies to solve problems is also essential.

Recently, the Brookings Institution (Loveless and Diperna, 2000) raised concerns about minority students' use of calculators. It reported that 50 percent of Black and 44 percent of Hispanic fourth graders nationwide use calculators every day, compared to 27 percent of White students. Analyzing data from the National Assessment of Educational Progress (NAEP), the Brookings Institution report noted that the everyday calculator users scored lower than less frequent users, both overall and within each racial group. It was also reported that the same test data indicate that poor students and students whose parents have little education are more likely to use calculators more frequently.

Critics of calculator use cite the findings above to make their case. However, the amount of calculator use that they cite is student-reported data. What they don't say is that teacher-reported data tells a different story. Fourth-grade teachers who reported on the 1996 NAEP that their students used calculators daily or weekly had students with the highest test scores, whereas fourth-grade teachers who reported that their students never used calculators had students with the lowest test scores (NAEP did not permit calculator use on the assessment). I believe the discrepancy in the reported data lies in students' and teachers' differing views of whether or not calculators have been used in well-designed lessons.

As indicated in the discussion of NCTM's Technology Principle, "Technology should not be used as a replacement for basic understandings and intuitions." The proper implementation of the Technology Principle depends on teachers' creating approaches to classroom instruction that appropriately integrate uses of technology into lessons focused on the learning of mathematics.

Calculators can and should be used to promote higher-order thinking--the kind of thinking students need to be able to function in our information- and technology-based society. The depth of problem solving that students can pursue with proper use of calculators is astounding--and it's something for which every teacher should strive from the time students enter school until they graduate.

For more information about NCTM's perspectives on technology and calculators, please see the Technology Principle of *Principles and Standards for School Mathematics*.

**References**

Campbell, Patricia F., and Elsie L. Stewart. "Calculators and Computers." In Early Childhood Mathematics: NCTM Research Interpretation Project, edited by Robert Jensen, pp. 251–68. New York: Macmillan Publishing Co., 1993.

Carnine, Douglas W., David Chard, Robert C. Dixon, Dae-Sik Lee, and Joshua Wallin. Report to the California State Board of Education and Addendum to Principal Report: Review of High Quality Experimental Mathematics Research. Eugene, Oreg.: National Center to Improve the Tools of Educators, 1998.

Hembree, Ray, and Donald J. Dessart. "Research on Calculators in Mathematics Education." In Calculators in Mathematics Education, 1992 Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by James T. Fey, pp. 22–31, Reston, Va.: NCTM, 1992.

Loveless, Tom, and Paul Diperna. The Brown Center Report on American Education: How Well Are American Students Learning? Focus on Math Achievement. Washington, D.C.: Brookings Institution, 2000.

Weiss, I. R., and J. B. Raphael. Characteristics of Presidential Awardees: How Do They Compare with Science and Mathematics Teachers Nationally? Chapel Hill, N.C.: Horizon Research, 1996.