Diane Hunsaker
1 I sigh inwardly as I watch yet another student, this one a ninth grader, struggle with an advanced math problem that requires simple multiplication. He mentally battles with 5x6, looks longingly at the off-limits calculator on the corner of my desk and finally guesses the answer: "35."
2 The growth in the use of calculators in the classroom amazes me. The students I tutor tell me regularly that their teachers allow unlimited access to this tool. The National Council of Teachers of Mathematics actively encourages its use. Recently I attended a math seminar where the instructor casually stated that teachers were no longer reluctant to permit calculators in the classroom. Now "everyone" agrees on their importance, she said. The more I hear from the education establishment about the benefits of these devices in schools, the less surprised I am when middle- and high-school students who have difficulty with arithmetic call for tutoring in algebra and geometry. Having worked six years as an electrical engineer before switching to teaching, I often suggest to my students that they consider technical and scientific careers, but I'm discouraged when I see an increasing number of kids who lack simple math skills.
3 Educators have many arguments in defense of calculators, but each one ignores the reason that we teach math in the first place. Math trains the mind. By this I mean that students learn to think logically and rationally, to proceed from known information to desired information and to become competent with both numbers and ideas. These skills are something that math and science teach and are essential for adolescents to become thinking, intelligent members of society.
4 Some teachers argue that calculators let students concentrate on how to solve problems instead of getting tied up with tedious computations. Having a calculator doesn't make it any easier for a student to decide how to attack a math problem. Rather, it only encourages him to try every combination of addition, subtraction, multiplication or division without any thought about which would be more appropriate. Some of my elementary-school children look at a word problem and instantly guess that adding is the correct approach. When I suggest that they solve the problem this way without a calculator, they usually pause and think before continuing. A student is much more likely to cut down his work by reflecting on the problem first if he doesn't have a calculator in his hand. Learning effective methods for approaching confusing problems is essential, not just for math but for life.
5 A middle-school teacher once said to me, "So what if a student can't do long division? Give him a calculator, and he'll be fine." I doubt it. I don't know when learning by heart and repetitious problem solving fell to such a low priority in education circles. How could we possibly communicate with each other, much less create new ideas, without the immense store of information in our brains?
6 Math is as much about knowing why the rules work as knowing what the rules are. A student who cannot do long division obviously does not comprehend the principles on which it is based. A true understanding of why often makes learning by rote unnecessary, because the student can figure out the rules himself. My students who view the multiplication tables as a list of unrelated numbers have much more difficulty in math than those who know that multiplication is simply repeated addition. Calculators prevent students from seeing this kind of natural structure and beauty in math.
7 A student who learns to handle numbers mentally can focus on how to attack a problem and then complete the actual calculations easily. He will also have a much better idea of what the answer should be, since experience has taught him "number sense", or the relationship between numbers.
8 A student who has grown up with a calculator will struggle with both strategies and computations. When youngsters used a calculator to solve 9x4 in third grade, they are still using one to solve the same problem in high school. By then they are also battling with algebra. Because they never felt comfortable working with numbers as children, they are seriously disadvantaged when they attempt the generalized math of algebra. Permitting extensive use of calculators invites a child's mind to stand still. If we don't require students to do the simple problems that calculators can do, how can we expect them to solve the more complex problems that calculators cannot do?
9 Students learn far more when they do the math themselves. I've tutored youngsters on practice SAT exams where they immediately reach for their calculators. If they'd take a few seconds to understand the problem at hand, they most likely would find a simpler solution without needing a stick to lean on. I have also watched students incorrectly enter a problem like 12+32 into their calculators as 112+32 and not bat an eye at the obviously incorrect answer. After all, they used a calculator, so it must be right.
10 Educators also claim that calculators arc so inexpensive and commonplace that students must become competent in using them. New math texts contain whole sections on solving problems with a calculator. Most people, including young children, can learn its basic functions in about five minutes. Calculators do have their place in the world outside school and, to a limited extent, in higher-level math classes, but they are hardly education tools.
11 Many teachers as well as students insist, "Why shouldn't we use calculators? They will always be around, and we'll never do long division in real life." This may be true. It's true of most math. Not many of us need to figure the circumference of a circle or factor a quadratic equation for any practical reason. But that's not the sole purpose of teaching math. We teach it for thinking and discipline, both of which expand the mind and increase the student's ability to function as a contributing individual in society: the ultimate goals of education.