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