San Diego, Calif., June 27, 2012 — Many students in American high schools graduate knowing thousands of words in a foreign language and yet can’t explain what “sin,” “cos” and “log” mean.
“That’s because, whenever they need the values of these entities, they get them by just punching ‘sin,’ ‘cos’ or ‘log’ into a calculator,” says Ilan Samson, an "inventor-in-residence" at the California Institute for Telecommunications and Information Technology (Calit2) at the University of California, San Diego. “Ideally, we would want them to have to think for themselves in order to solve mathematical problems, but there’s no way of doing that if they just perform rather than understand what they’re doing.”
So how do math and science educators go about getting students to think for themselves and actually understand the functions they’re performing?
That’s easy, Samson says. Give them a calculator.
But not just any calculator. Samson is the creator of the QAMA, or Quick Approximate Mental Arithmetic, a new kind of calculator that is commercially available for the first time — and has already started to have a measurably positive impact on school math classrooms around the world.
Rather than providing an instantaneous result at the stroke of the "equal" sign, QAMA (pronounced “kaama”) requires the user to provide a reasonable estimation of the answer. If the calculator's sophisticated adaptive algorithms approve the approximation as reasonable for the given task, QAMA provides the exact answer as confirmation.
The calculator is being manufactured in China and can be purchased at qamacalculator.com for a mere $19.60 -- a price Samson made purposely low so that he could “see this calculator in the hand of every student, with the hope of making a fundamental change in this badly wanting area.” A typical graphing calculator, by contrast, costs between $80 and $130.
“I want to see every student using the QAMA calculator routinely — not as an occasional aid for estimation sessions, but routinely and everywhere,” adds Samson. “Also, schools are inundated by endless companies who try to sell them products and equipment. I was determined not to be seen by the schools as an organization trying to make money off them, so I set a price which everybody is amazed by — and vociferously.”
In fact, when it came time to determine what the price of the calculator should be, Samson took a tack not common among entrepreneurs: he asked his potential clients what they would pay for the device. The most common response was $50. “The calculators are worth a lot more,” adds Samson, “but schools would have difficulty paying anything more than that.”
Samson says that one headmaster, when told the actual price, shouted “You are kidding!” so loudly into the phone that Samson’s wife could hear him from an adjoining room.
The QAMA has already been tested in three San Diego schools and at one school in The Netherlands (BC Broekhin, Roermond) resulting in remarkable improvements in test scores among math students who have used it.
At the UC San Diego Preuss School, for example, a class of 28 students approximately 16 years in age was randomly split into two groups, with one group using the QAMA calculator and the other group using a traditional calculator. Both groups were tested at the beginning and end of a four-week period. The group using the QAMA calculator scored 42 percent higher overall than control group, and performed twice as well on the material most recently learned.
An additional highlight, says Samson, is that 13 out of 14 users in the QAMA group opted to use the QAMA when given a choice of calculators on a subsequent exam.
Students at San Diego’s Chabad School demonstrated similar improvements after using the QAMA, but math teacher Charlene Stanley says she was most impressed with their increased engagement with the material:
“I can tell you that when we took the first test, students worked for about three minutes and then were done — they basically gave up,” she notes. “When taking it this time students worked longer and were trying the whole time. This is already a huge improvement, I think.”
Programming the calculator was no easy feat. Explains Samson: “The ‘strictness’ of the calculator must always appear reasonable, and by ‘reasonable’ I mean it should reflect the difficulty of the task but not be so strict that it frustrates the user.”
For example: An ‘easy’ calculation such as five multiplied by six, would have zero tolerance for any incorrect answer. Calculating 23 to the power 2.1 (answer: 723.81) would ‘tolerate’ an estimate of 550.
“As there are infinitely many types of calculations, each requiring respective tolerance, it wasn’t clear if it could be done at all with a finite program, let alone one that could fit on calculator chip. This was something that was on the verge of insurmountable. This is why it took fourteen years to develop QAMA.”
Prior to developing the handheld calculator, the software had to be classroom-tested. To facilitate this Samson worked with Calit2 programmer Ricky Huang to install the software (programmed in the C), into existing hand-held hardware.
The QAMA (which, when pronounced phonetically, also means "how much" in Samson's native Hebrew) boasts many features that make it ideal for classroom use, Samson notes. The estimation function, for example, can be switched off so the QAMA can be used like a traditional scientific calculator, making it unnecessary to equip students with two different versions. But to prevent students from switching out of estimation mode during exams, the calculator has a built-in ‘alert’ system that flashes red lights when in the ‘non thinking’ mode (and the lights continue flashing even if the student tries to power the calculator off).
But more importantly, QAMA gets students “switched on and engaged with the problem,” Samson emphasizes. “They actually enjoy it too: Getting an estimate accepted is pleasing.”
Samson says his calculator proves “there’s a case for suggesting that no information, which is at least in part deducible, should be provided without first prompting the student to think about what he expects it to be.”
“The purpose of QAMA is not to compete with calculators on accuracy, but to make sure the student knows what he is doing, to make sure he or she also learns not to accept results without knowing where they come from,” he adds. “What is special here is this is something that exercises your brain while you do what you need to do anyway.”
Samson says he hopes the QAMA will eventually improve education in all of the science, technology, engineering and mathematics (STEM) fields by training students not to fear math, but to understand it. It’s something he’s so passionate about, he used the royalty income from his other successful inventions to fund the development, tooling and patenting of the calculator.
“However, delicate plants wilt in the wilderness” Samson says. “QAMA could not bloom in a better nursery than the encouraging supporting environment of UCSD’s Calit2 and its Jacobs School of Engineering.”
by Tiffany Fox, (858) 246-0353, email@example.com