RE: Why Children Must Learn Their Times Tables
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When I was at M.I.T (1974-1978) it was basically the dawn of the era of calculators. My dad got me an HP 35 my freshman year. (You know what reverse polish notation is?). Anyway - while this transition from the slide rule to the calculator was happening a professor at M.I.T. wrote a passionate essay about the benefits of the slide rule. His claim was that when you are faced with a calculation like "7.48 * 3.14159 * 19,700" on a slide rule you must first make some kind of order of magnitude estimate of the answer. The slide rule only gives you the digits of the answer. Something like "463". You have to use your estimate for example the result is between 400,000 and 500,000 to know this means the answer is "463,000".
By comparison many students today will type this calculation exactly as written and report the result as 462932.13604. This is wildly off in terms of the actual accuracy you have in the computation. At most you only have three significant digits in the "7.48" term. So here you should only report the answer as "463,000".
There is one other thing to be said for the slide rule. When you mistype something into a calculator and you have no sense whatever of what the magnitude of the answer should be, you tend to just accept the result. Any mistakes in the typing are not detected.
Which brings me to yet another pet peeve. When I was acting as a grad student at Duke and doing work as a teacher assistant I had to correct many students homework and exams. Many times I saw students turn in answers that could not possibly be correct. Answers off by many orders of magnitude, answers given in units that were wrong. I wish I had done more to really teach those kids to learn to review their own work before they turn it in.
Alas - the slide rule has gone the way of the dinosaur. But nevertheless it is worth remembering it's virtues today.
That's the counter argument - humanity is still here. Calculators didn't destroy it, and the economy is still prospering despite them!
But society isn't. And no, that's not the calculators fault. It's one little thing among the many that make us too comfortable and restrict us from thinking things through. From having that experience, that challenge, that blockade we need to get through. Life as surviving is getting easier and easier, thanks to technology. For some, that is necessary still. But for others, who live in over-developed countries, it's slowly destroying life.