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 Discussion: All Topics for Patterns and sequences Topic: Order of Operations (BOMDAS)

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 Subject: RE: BOMDAS and PEMDAS Author: MarcJL Date: Apr 15 2007
On Apr 14 2007, rbednarski wrote:

Thank
> goodness someone finally addressed the real problem.

The
> various devices used to teach Order of Operations are among the most
> destructive to math learning, in my opinion.  If you put six letters
> to indicate 6 operations there is nothing in there to cue the
> students that some of them are sequential and some of them are not.
> So you need ancillary explanations and they are not remembered -
> particularly by exactly the low functioning students that need
> clarity the most.

I teach order of operations as 4 categories.
> Category 1: grouping symbols

Categotey 2: exponents

Category
> 3:  Division and multilication, left to right.  They are together
> because they are inverse operations of each other.

Category 4:
> Subtraction and addition, left to right.  They are together because
> they are inverse operations of each other.

We need to be much
> more careful than we are in not teaching things in ways that greatly
> enhances the likelihood of confusion, particularly in the low
> functioning students.  Some memory aids are wonderful.  But there
> are some areas where the memory aide is positively harmful. In that
> regard, PEMDAS, BOMDAS and its variants are an abomination and
> should be completely banned.  Little tricks that have no grounding
> in the underlying mathematical concepts have no place in the
> classroom, IMO.

Amen.

I have similar revulsion to FOIL.  Kids have to be able to use the distributive
property.  Most of these tricks and rules are misremembered and/or misapplied.
How would your students FOIL two  trinomials?

Worse still, teaching tricks and special cases gives the mistaken impression
that "math" is a succession of tricks and procedures to memorize.