# QAMA: The Calculator That Makes You Better At Math

From a post by Alex Knapp on Forbes blog:

QAMA […] is a calculator designed to reverse the last several decades of education by actually improving students’ intuitive understanding and appreciation of math skills.  It does this in a deceptively simple way.

The name itself gives the method away – QAMA stands for “Quick Approximate Mental Arithmetic” (and in Hebrew, it means “How much?”). As with most calculators, to solve a problem with a QAMA, you first do what you’d do with a regular calculator: type in the problem. But rather than just give you the answer right away, QAMA asks you for one more step: you have to estimate the answer. If your estimation demonstrates that you understand the math, the calculator will give you the precise answer. If your estimation isn’t close, then you have to try again before you get the precise answer.

Quick – what’s the square root of 2? What do you mean you don’t have a calculator? Well, you can start guessing, right? So let’s work this through. You know you have an upper bound – it has to be less than 1.5, because 1.5 x 1.5 is 2.25.  And it has to be more than 1, because 1 x 1 is just 1. But 2.25 is pretty close, right? So what if you guess 1.4? Well, then you’d be pretty close. 1.4 x 1.4 is 1.96, and the square root of 2 is about 1.414.

But did you notice something? Without your calculator, you had to estimate. In order to estimate, you had to think about and engage with the math behind exponents and square roots. Which means, hopefully, that you came out of that first paragraph with a bit better understanding of math.

That’s the theory behind QAMA, which is a calculator designed to reverse the last several decades of education by actually improving students’ intuitive understanding and appreciation of math skills.  It does this in a deceptively simple way.

The name itself gives the method away – QAMA stands for “Quick Approximate Mental Arithmetic” (and in Hebrew, it means “How much?”). As with most calculators, to solve a problem with a QAMA, you first do what you’d do with a regular calculator: type in the problem. But rather than just give you the answer right away, QAMA asks you for one more step: you have to estimate the answer. If your estimation demonstrates that you understand the math, the calculator will give you the precise answer. If your estimation isn’t close, then you have to try again before you get the precise answer.

How close is close? Well, that depends on the calculation. If you put in 5×6, you have to estimate 30 – the calculator expects you to know your multiplication tables. For exponent problems, if you have an integer – say something like 23^2, the tolerance is such that you still have to be pretty close, but there’s a wider berth for say, 23^2.1, because non-integer exponents are a tougher problem.

Developing the calculator to have these different tolerances for different types of calculations was the key challenge for QAMA inventor Ilan Samson.