15 comments Add a comment
How characteristic the paradox of the thought can be - that if a thought process is separated from a seemingly literate person in whom it resides, it can itself become an idea bordering on a contradiction in terms and in fact.
By this, the oldsters belonging in previous generations who think that the calculator ushers in today's generation of math-dumb youngsters who cannot manually do simple arithmetic may be guilty of self-contradiction. The reason given always seems to be as straight-laced as it is boringly repetitious: they have not learned by rote the multiplication tables. They cannot multiply 15 by 9. But they are smart enough, though, to work as a supermart checkout cashier.
Sure, those in the sixties and older have acquired some skills in addition, subtracton, division and multiplication reasonably well; others of the generation do perform ratios, radicals and exponents - to cite these few vital math operations. But, is that IT?
With my calculator having all the built-in facility of mathematical notations, I recently set out to prove a point. Hypothetically, what would I add to my investment account in 3 years at 3% compounded annually if I locked in $9000 in a guaranteed investment certificate as opposed to leaving it in a “power” savings account at 1.35% compounded daily for the same period?
I was deadly curious, since the bank at every turn comes up with newfangled menus of investment and savings intruments; recommending vaguely exotic dishes for our soft, unsuspecting palate.
Co-opting an effective interest rate formula, using first paper and pencil, I plugged in the figures to quantify an algebraic expression that resulted in 9000(1 + 0.03)^3 for the GIC. The interest accrued is roughly $834.54. Easy enough, if it does not call up gut-wrenching numbers like $92,221.34 at 4.75% for 9.5 years compounded, say, 6 times a year, assuming.
For the savings account, it involved a little more than chicken-scratching: 9000(1 + 1.35//365*100)^(365*3). $371.08 will accrue in interest earning in three years, compounded daily, taking straight 365 days into consideration.
But it was at this point that my most berated gizmo came in handy. Why then would any fool sweat his pants off when the donkey work of calculating manually can be undertaken by a donk with a calculator? Or, he could google for an idiot-proof array of selectable calculators to determine the true cost of borrowing, or future and present values due to accrued earnings. No sweat.
I also deliberated over determining the height of a wall panel requiring paint job. My painter knew his math alright – how to multiply, so forth, in his head and when to sleight me with the magic of percentages. But had he been aware, he might have assessed with his long ladder of predetermined length the height of the wall, to work out the wall area slated for a fresh coat of paint. All by initially applying his sharp knowledge for numbers to perfunctorily help himself with available pythagorean theorem calculators. He climbed instead to measure.
Lean the ladder against the fascia board for support, and he'll have a right angle triangle. If the length of the hypotenuse-ladder squared (L^2) is equal to the sum of the squares of the wall height (W^2) plus the distance from the base of the ladder to that of the wall (B^2), then wall height = the square root of (L^2 minus B^2). Let the donkey carry on from here, or punch in your numbers: height of wall equals the square root of (17.5^2 minus 7.25^2).
There is no rocket science involved here to confound, just simple mathematical analogies. Likened to a computer, a $9.00 dedicated electronic contraption simplifies tedious work to free us from the constraints of time to THINK. Understanding, for instance, the concept wrapped in 2 times 8 means that there are 8 twos added in series to produce 16, that sort of analogous thinking might just carry us through the day.
Very few memorize the innumerable scientific and mathematical formulae any more for its own sake; but they know what they mean, where to find them and how and when to apply them. So don't assign blames for our children's deficiency in mathematics. If rote learning has its proper place in learning, so does the calculator have its complementary function, and so indispensable.
By: Sam, the Tiger