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Why The QAMA Calculator Is A Game-Changer 

(It Requires An Estimation Each Time!)
Richard Andrew  
Estimation is a skill we should all possess. Being able to estimate is advantageous. Imagine, for example, having poor estimation skills, travelling overseas and spending foreign currency without really knowing how much things really cost! Being numerate means, in part, that we can estimate. It is especially important, therefore, that estimation is taught as part of maths education.
As Siegler, & Ramani state, ‘Learning how to estimate is important… because proficiency at estimation is substantially correlated with many aspects of numerical understanding and with overall maths-achievement-test scores (Siegler, & Ramani, 2006)’ 

The use of calculators

Estimation is also a skill that should be employed when using calculators. A simple google search will bring up many voices arguing the pros and cons of using calculators in classrooms. One concern of some educators is that ‘when students pick up a calculator, they stop thinking’. Although clearly an over-statement, I have witnessed first-hand, many occasions where a student is oblivious to the fact that his calculator answer is incorrect - to the extreme - yet is happy to use it in his solution.
As is pertinently asked by Walen, ‘Do students see the calculator as a ‘doing tool rather than as a teaching tool?’ (Walen, et al., 2003). 
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Of course, we could teach estimation simultaneously with calculator use via a teacher-centric activity where students estimate an answer and then use the calculator to check their estimation.
However, will such an activity transfer, for students, the habit of estimating when using a calculator unsupervised?
What if there was a calculator that required an estimation before the correct answer was delivered?
Well, there is! It is called the QAMA calculator! 

The QAMA Backstory

Back in June 2019, I was stopped in my tracks when I read something about a calculator that requires an estimation before issuing an answer. Hey, what? This sounded a bit too good to be true. I had to investigate. The creator of the QAMA is Ilan Samson, a 70+ year-old physicist and inventor originally from Israel and now living in San Diego, USA. I emailed Ilan, and we set up a Skype chat. I describe Ilan as an incredibly intelligent gentleman and somewhat befitting of the ‘mad scientist’ stereotype - very eccentric, very brilliant, very driven. During the chat, we discovered a great deal of common ground in regard to our views on mathematics education.
Referring to the importance of estimation in maths, Ilan says:  ‘One can not estimate by rote. One needs to first 'see' something in one's mind rather than just obey dogmatic instructions.’
​Amen to that!

What does QAMA stand for?

QAMA stands for Quick Approximate Mental Arithmetic. However, very quaintly, and related to Ilan's Israeli background, Qama is a Hebrew word meaning 'How much?'

The QAMA calculator - Three aspects that are ‘ridiculously’ brilliant

ONE - ‘Your estimation please!’

The simple requirement of the user to enter an estimation BEFORE receiving the correct answer is, without a doubt, brilliant. Think about it! What a great way to learn tables! What a great way to practice converting fractions to decimals. What better way to have students THINKING about the meaning of a trigonometric ratio BEFORE they reach for the calculator? The potential upside is astounding.

TWO - Estimation range varies with difficulty! ​

If we have a calculator that requires an initial estimation and allows passage to the correct answer depending on the adequacy of that estimation, then the accuracy range of the permissible estimation needs to vary according to the difficulty of the problem! Think about that for a moment. If we are entering a multiplication table question or a simple addition question, for example, 7 x 8 or 11 + 4 then what should the estimation range be? It has to be zero! The only acceptable estimation for these types of simple questions must be the exact answer. However, for questions like 5.9 x sqrt 23 the QAMA requires a reasonable estimate (e.g.30) but for questions like 3.4 x Tan 70 the QAMA becomes even more lenient. 
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How does one build a calculator that 1) requires and estimation in the first place and 2) varies the range of permissible entries according to the infinite types of complexity of question?  With great difficulty, so it turns out. To quote IIan, “It took years off my life!” 
Read how and why the QAMA is an extremely complicated device.
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THREE - Hard and soft versions

The QAMA is both in the form of a calculator and an App. The App is called ‘QAMA calculator’ for both IOS and Android.

How powerful is the QAMA?

The QAMA is roughly equivalent in power to a scientific calculator. It is, therefore, ideal for students up to middle school. However, the real ‘power’ of the QAMA clearly lies with the requirement to enter an estimation for each problem.

How could the QAMA be used in schools?

Ideally, the QAMA could become the standard classroom calculator for your middle-school students. 
Another idea would be to have one or two class sets of QAMAs to be used for specific lessons where estimation is the focus? At the very least, and in a more student-centred way, students could be encouraged to download the phone app and use it at home to develop their estimation skills. ​

Why write this article?

The QAMA fits nicely with the Learn Implement Share mantra that maths students need to be understanding what they are working on as much as is possible. Furthermore, the QAMA is so impressive that, in my humble (!) view, maths teachers need to know about it. Oh, and by the way, in case you are wondering, no I am not receiving kickbacks for sales nor for penning this article!

QAMA Cost

At the time of writing, the cost per calculator is $19.60 USD. Granted, this is more expensive than a scientific calculator (an unfair comparison).
The iOS and Android App cost approx $3 USD each.