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Re: Cool Math Lessons
Posted:
Feb 29, 2012 12:18 AM
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Well, by my way of thinking any valid way of dividing even small numbers is an algorithm, though at such a primitive stage the "algorithms" and such are fuzzy, sometimes personal, perhaps a bit obscure even to introspection. (Also, by my way of thinking, "lookup in memory" is a very simple algorithm.) I actually remember learning to divide single digits and single into two digit dividends. "Make a guess on the quotient" I was told, followed by words more or less that if the product of guessed quotient and divisor is greater than the dividend the lower the guess. If the remainder is larger than the divisor, guess a higher quotient. That's pretty algorithmic, it presupposes that you can multiply (in your head) single digits, and perhaps more subtly "guess". So what is guessing? Well, one could invent ones own guessing algorithm. But an algorithm nonetheless. I suppose I must have been instructed in "repeated subtraction" as well, especially for single digit division, which I don't have memories of, but I really do remember the "guessing" instruction, and it became an important part of learning LDA a bit later.
Certainly LCD does not "require" a personal strategy, though that may be how it ends up for some folks. I understand what you mean by "personal strategy". A bit of that is good and helpful. I'm pretty sure we were taught LCD from the get-go, I actually found it easier sometimes to cross-multiply and reduce, which I more or less intuited at the time. Which I used was probably based somewhat on the numbers involved in the specific instance.
Certainly a personal strategy.
Joe N
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