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The Calculator Question


People have been debating the proper place of calculators in math classes almost as long as those hand-held devices have been around.

Those disagreements boil down to this: Are calculators necessary tools to help students cut through tedious procedural steps they already know on the way to performing more challenging math? Or are they crutches that keep students from mastering the basic steps they need to master in that subject?

A new study takes up that issue once again. Researchers at Vanderbilt University found that elementary students' pre-existing knowledge of basic multiplication facts was the factor that determined whether calculators benefit or have no impact on their learning. That work, conducted by Bethany Rittle-Johnson and Alexander Kmicikewycz, looks at the performance of students after they had spent a class period working on multiplication problems.

The researchers found that the calculator's effect on subsequent performance depended on how much the students knew to begin with. For students who already had some multiplication know-how, using the calculator before taking the test had no impact. But for those who struggled at multiplying, use of the calculator had a negative effect on their performance, according to a summary of the study provided by Vanderbilt. Another effect: Students using calculators were able to practice more problems and had fewer errors, the researchers found.

"These findings suggest that it is important children first learn how to calculate answers on their own, but after that initial phase, using calculators is a fine thing to do, even for basic multiplication facts," Rittle-Johnson said in a statement released by the university.

A link to the study, titled "When Generating Answers Benefits Arithmetic Skill: The Importance of Prior Knowledge," can be found from this link. It has been published in the Journal of Experimental Child Psychology.


As someone who has always found math to be easy, I always thought that giving a calculator to student was a form of “cheating.” I grew up in a family that stressed the mastery of math and has always prided myself on this achievement. Reading you article, I was surprised to learn that the results were the reverse.

I used to believe that students should be allowed to use calculators to free them from "tedious procedural steps". I have come to realize that the fluent use of basic math facts is not a matter of rote memory but is a reflection of basic number sense. If you look at this study more carefully, the supposed benefits of using calculators are trivial at best. The students are able to do more problems and have fewer errors, so what? A major problem in American math instruction is that students are given too many problems to plow through, often with little real understanding of what they are doing. Students shouldn't be given more than 5 problems. 1 or 2 challenging problems is the ideal. Students need to be taught to anticipate making errors on their way to solving more difficult problems. If a student makes a makes a procedural error, just hand the paper back and say that answer is way too big (or small), can you tell me why? Better yet, encourage the students to catch their own mistakes by trying to find the answer by working a problem in two different ways. If the answers don't agree, then the students needs to think the problem through more carefully.

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