I got a call months ago from someone with what sounded like like a bizarre idea: he claimed he’d invented a special calculator to use as a pedagogical device in the classroom. I was about to dismiss the call as being a crank, when I realized that what he was describing, if it worked, was potentially a brilliant idea.
I bought myself a calculator, and began to check it out. It’s called QAMA, and it’s now available as an app, which is a much better deal, and you won’t accidentally kill the batteries if you leave the calculator on, as I did after the first time I used it. Nevertheless, I’m blown away by QAMA, since it elegantly solves one of the central problems of using calculators in the classroom: the problem of students handing all the thinking to the calculator.
Here’s how it works.
You plug in whatever equation you want to solve. For example, I entered “65.86 x 21.”
Then you hit the equals button. And the calculator doesn’t give you an answer. And therein lies its genius, its usefulness, and also, according to my conversation with the designer, the great technical difficulty in creating it in the first place.
To get an answer, you have to enter an estimate. If it’s just an arbitrary number, the calculator won’t accept it. Your estimate must prove that you were thinking. And the calculator expects that you can work at a pretty decent level. It requires perfect answers for single digit multiplication for example—it is no help with memorizing your multiplication tables. For this particular problem, I figured that 1300 would be a decent estimate. I entered it, and the calculator showed me the real answer: 1383.06.
It can be fun to play around with how good the estimates need to be. I tried 13/21. First estimate: 1.6, and this turned out to be an excellent guess. Second estimate: 1.5. QAMA wouldn’t accept it. Third estimate: 1.55. That was acceptable. The promise of this innovation is no doubt obvious to middle and high school teachers. QAMA has reinforced in its architecture the process of thoughtful calculator use, by making the tool that much more difficult to use mindlessly. Here’s what students should do when they use a calculator:
- Decide if the problem actually requires a calculator.
- If it does, get a rough sense of what a reasonable answer might be, then enter the problem on the calculator.
- Pay attention to whether the answer the calculator gave you makes sense.
Here’s what students too often do once they have easy access to calculators:
- Grab a calculator whenever they have an arithmetic problem to do.
- Take whatever comes out as fact, and move on.
I’ve seen eighth graders reach for a calculator to solve 100 – 98. I’ve seen college students accept total gibberish from their calculator after mis-keying, without considering whether the answer makes sense on a gut level. (“The swimming pool costs… 53 billion dollars.”) Any teacher who gives their students access to calculators knows who pervasive these problems can become. “Does your answer make sense?” we ask, repeatedly, and often to no avail. But QAMA prevents students from having the option to be lazy. Their motto is: “The calculator that thinks only if you think too.” And that seems true.
Personally, I’ve come down against having students use calculators until middle school (except for occasional use in 4th-5th grade). But I think QAMA could take all the worst parts (mindlessness, laziness, etc.) of calculator use out of the middle and high school classroom. I think they’re on to something.