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Topic: Order of Operations (BOMDAS)


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Subject:   RE: BOMDAS and PEMDAS
Author: cfriesen
Date: Apr 15 2007
I like the thinking by rbednarski.

I would add LEFT TO RIGHT for steps 1 and 2 as well.
Everything is left to right!!  (or can be thought of that way)

2^3^2 = ???  64 or 512???

and there may be multiple symbols of inclusion, thus left to right is a
convenient way to help students adopt a consistent methodology.

Choosing appropriate problems can quickly help break bad habits.  Getting
problems incorrect on a test or quiz, with opportunities for the student to
demonstrate they learned from their errors is one of the best ways to make
progress in this area.

And, especially when there are multiple symbols of inclusion, it is good for
students to realize that you ALWAYS restart the list (#1-6) at the top and
work your way down.  Over time this added caveat can receive less emphasis as
they gain experience.  But it helps make an important point.

Chuck Friesen

___________________________
On Apr 14 2007, rbednarski wrote:
> I've been reading this thread in growing disbelief.  

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.

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