The debate over calculator use (and overuse) hinges on the notion that an over-reliance on the calculator will prevent students from mastering math for themselves. But why agonize over long division when we can solve problems with the touch of a button nearly wherever we are? The calculator is a valuable tool, and one that can be especially helpful for students who struggle with math sense. However, it can’t become a replacement for showing work or understanding the logic behind each problem.
Just yesterday, I was reviewing a diagnostic SAT result with a bright student who has a tendency to leap for his calculator on every problem, but seldom writes anything on the page. What we discovered, revealingly, was that while he had missed several questions on the calculator section, he had aced the section of the test where no calculators were allowed. We reasoned that he should be more cautious about giving up his thought process to the machine. On the other hand, I have another student who is so frustrated by frequent errors in adding up when she works by hand that every assignment is anxiety-inducing—and using a calculator once she’s set everything up on paper helps her to balance accurate calculations with an accurate understanding of what she’s actually calculating.
Being able to master procedures and concepts in math is crucial, but showing that mastery is just as important. Lots of people (especially students!) misunderstand why teachers ask students to show their work. Students are asked to show their work because it helps them think. With their thought process on paper, kids are able to review and check their work. They can see their calculations and the steps they took to find an answer. They can identify simple mistakes if their final answer seems off. And even if the student doesn't catch them, the teacher will. With work on paper, instructors can understand a child's thinking and provide more targeted support. Plus, with calculations on paper, there is the chance to earn partial credit in most classes! Mastering this skill is crucial for students who struggle with executive function skills. And working on graph paper can make a world of difference for students. If kids learn to put just one number in a box, they can effortlessly organize problems and place value.
The morale of the story is that no one should be shamed for using a calculator, so long as it’s not turning into a means of avoiding the work of understanding how things fit together. Math often involves some level of fruitful struggle as we grow, absorbing new ideas that challenge what we knew before. Calculators can help in that struggle, but the goal should not be to erase the struggle entirely: it’s how we learn!