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Topic: Order of Operations (BOMDAS)


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Subject:   RE: BOMDAS and PEMDAS
Author: hemili
Date: Apr 16 2007
Completely agree with rbednarski. We tend to reduce Algebra to a bunch of
processes and mechanisms that students repeat without thinking why they work.

Algebra is a language. A powerful one, a universal one, and independent of the
language you speak at home. That is part of its beauty.
Any language will have some rules, some "grammar" that everybody will respect in
order to be able to communicate to each other. That's all. I like the idea of
four categories. And I can't stand FOIL. There is not any operation or property
in Math called FOIL, as you know. And the order that you choose to multiply out
the terms of two binomials or polynomials in general doesn't matter. Remember
that multiplication in the set of the real numbers is commutative. All you need
to do is make sure that you multiply every term in one with every term in the
other one. So you need to understand what "term" means. Which takes you back to
the basic grammar rules of Algebra. So you go back and think about it. Terms in
Algebra are like cells in biology, or moleculae in chemistry, or words in any
language. So you start to make deeper connections between ideas, that go beyond
PEMDAS or FOIL or SOHCAHTOA or ...
Plus, when we use those stupid letters, we forget that they only make some kind
of sense in English (SOHCAHTOA also works in Spanish). I'm a bilingual Math
teacher. The universal concept is the distributive property, not the FOIL. We
should stop with all the nonsense. Think about it. If students need some kind of
mnemonic rule, they should develop their own, don't you agree?.

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