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Re: The instructional Roles of Mathematics Lectures
Posted:
Apr 29, 2011 6:12 PM


On Apr 28, 2011, at 10:39 PM, R. Wright wrote:
>> The order of operations, as we >> know, is an algorithm that must be followed exactly. > > I'm not sure whether you really mean what you're saying here. I > would like to believe that you don't, because taken literally, what > you've said is misleading. > > The order of operations is merely a convention that makes it easier > for people to communicate in mathematical writing. There is no > fundamental property of numbers that demands that 3 + 4 * 5  1 is > equal to 22, rather than 59, 48, or 19. But agreeing to the > conventional order of operations allows us to avoid having to use > parentheses for clarification. As with any convention or definition > in mathematics, the order of operations is an organizational tool > and should serve to make things simpler. It would be nice if we > could help students to see it this way. > > If we began by telling our students something like "This is how > numbers work: You have to do exponentiation before multiplication, > multiplication before addition, etc. etc., otherwise you get the > wrong answer," then we would be, from the beginning, teaching them > that mathematics is a set of arbitrary rules handed down from above.
And, as I said, there are many ways of coding. One I forgot to mention, by the way, was Reverse Polish Notation: No parentheses whatsoever (e.g, the "reverse" of The product of the sum of 3 and 5 and 2) and quite nice in many other ways. But of course, even HP had to give it up. Well, it was nice while it lasted.
Regards schremmer
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