Anyone who has ever taken a math class (especially at a college level) is aware the calculators are a very contentious topic. Should students be allowed to use them? Are they a crutch? Would they be allowed to use them in the “real world”? Some teachers allow only scientific calculators with the most basic operations. Others have an “anything goes” policy, letting powerful TI-Nspires into the classroom. Others still ban them entirely, requiring everything be done by hand. Since I will have to make the same call some day as a teacher of mathematics, the issue of calculators is one close to my heart.
When I was in high school, I remember being allowed to use calculators and even being required to buy a graphing calculator (I want to say it was the TI-84 that was the most current model at the time). I also distinctly remember resenting these calculators because I had no idea how to use mine. Once I got to college, some of my professors actually took the time to show us how to use calculators and make them do what we needed them to— whether it was manipulating matrices or using Newton’s Method to find zeroes more efficiently and accurately than by hand. I have been attached to my calculator ever since and have ranted tirelessly about how important calculators are.
Consider this: what real world career is going to INSIST their employees do not use calculators? Sure, they will want them to know the math, but certainly calculators will be available to the employees and they would be encouraged and expected to use them. If one of the reasons we teach math is because it is so useful in life, then it seems silly and arbitrary to not allow the most ubiquitous math tool available. I was 100% on this side of the fence for a long time.
The most obvious problem with this train of thought is that it relies on people knowing math before they use a calculator. Too often in my field experience or in my work as a math tutor, I see people relying on calculators for simple operations. “What is 1/3 times 1/3?” or “What is 20 times 1/5?” gets me a blank stare and a hand slowly creeping towards their calculator. Alternatively, and perhaps even more frustrating for the student, people make order of operation mistakes when inputting things into their calculator and don’t realize it is wrong. -3^4 is NOT the same as (-3)^4, but because their mathematical foundation isn’t solid, students don’t realize that the answer they’re getting back doesn’t make sense.
So should all calculators be banned? Should we just make sure that students can do all the mathematics by hand so that they don’t have to turn to a calculator? That seems not only like an extreme overreaction, but frankly not helpful. The further in math you go, the more complicated the calculations get. If I’m trying to find inflection points of a function, I want my mental workbench focused on inflection points— not on arithmetic that I can pass off to my calculator. The question then becomes how do I let students who can appropriately use calculators benefit from them while making sure others don’t use it as a (frequently misleading) crutch?
My current thoughts on the situation would be some form of calculator literacy education. Calculators themselves are here to stay and used so widely that it would be pointless to pretend they don’t exist and ban their presence. Instead of demanding that every student does every problem by hand so that when they get to an instructor who does allow calculators they have no idea how to use one, why not educate students on how to best utilize them? If every math class spent a tiny amount of time showing the right way to use calculators to aid your solution process, we might see fewer mistakes, less resentment towards arithmetic, and better numerical literacy concerning things like PEMDAS and exponents and the like. Learning how to do the math on the calculator would only follow after learning how to do it by hand and the principles the mathematics are founded on.
My goal as a future instructor is to help prepare my students for the rest of their lives, so it seems only logical that I would help them understand how to make their calculator their friend instead of their enemy. However, I still have a lot of mixed feelings on calculators and hear a lot different takes on the issue. How do others handle the issue of calculators?