Re: Why the FOIL Method is a failed method

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You speak the truth.

Shoot me, but I use mnemonics like PEMA (not PEMDAS) and FOIL all the
time.

I tell them to flip and multiply. I do explain the concept of dividing
fractions. I get that one should truly understand the concept, especially
if one is ever going to be successful with simplifying complex rational
expressions in Algebra 2. But I'm teaching high school here. While I can
go over the concept a few times, at some point we need to move on and
just FLIP AND MULTIPLY when two fractions are hanging around needing to
be divided.

As for FOIL, sure, it's a very special case of distribution only for
binomial times binomial. That needs to be explained. Examples of
distribution of higher term polys need to be done. But later on, it's
factoring of trinomials that's a big deal in algebra and calculus (even
though that's just all textbook and in real life the expressions are
rarely factorable). When I teach trinomial factoring I like to talk
about/ show how the leading term and the constant of the trinomial come
from the First and Last terms of the binomials and how the middle term is
the combined form of the Outer and Inner products. I've had a lot of
success teaching kids to factor trinomials this way; FOIL is not the
devil!

On 10/15/11, Not being a devil's advocate--being quite serious. wrote:
> I absolutely agree with you that teaching "flip and multiply" and other
> things that don't reflect understanding of why something is happening
> is a poor substitute for understanding.
>
> However, I have found that there are students whose abilities to
> understand abstract ideas are so bad that no matter how many ways or
> how often you try to explain to them the concepts, they are just
> unable to understand it. Finally, you just end up telling them "flip
> and multiply" to just get them through.
>
> Are you saying that you don't have students like this? Warning: If you
> say you don't, I am not going to believe you. Because there is a
> pretty standard bell curve of intelligence in most schools. Frankly,
> some students just aren't going to understand some concepts because
> they were never equipped from birth to understand them.
>
> Ok. Go ahead liberal educators.... Yell at me. Call me elitist. Say
> that if I can't teach all math concepts to all of them that I'm a bad
> teacher. Say water is made of helium and silicone too while you are at
> it. And fish swim in the air and birds fly in the sea. Whatever.
>
> But, really, for everybody with a clue, isn't what I said true? Have we
> gone so far down progressive fantasy land that even reasoning and
> reasonable people all really believe that all students are endowed
> with equal ability to understand math as each other?
>
> Isn't believing such a thing as silly as believing we were all born
> with an equal ability to sprint 10 yards as fast as anybody else?
> Aren't we born differently abled in different areas?
>
> What do you do with the students who just don't get the idea? In a
> perfect world, you could keep working with them until they do get it
> or else when they reach 18, just stop at whatever they have mastered.
> But, some of them, let's be honest, would never ever get through even
> pre-algebra. And that just is not allowed. They are pushed into our
> math classes ready or not. And we have a curriculum to get through
> like it or not because there are students who are getting it who have
> the right not to be held back for years because of the others. If we
> don't pass the struggling ones so they can see the math again, then too
> often, we are evil monsters who don't care about them. "If you fail
> them, then you don't care," so I've been told.
>
> So what are we as teachers supposed to do? We're really between a rock
> and a hard place. So, finally, you just say, "flip and multiply" to
> some of them. What else are you supposed to do?
>
>
> On 10/14/11, Rich/CA/Math wrote:
>> On 10/14/11, John wrote:
>>> You can toss PEMDAS, "cross multiplication", "flip and multiply"
>>> into the same heap of garbage.
>>
>> Yup.
>>
>>>
>>> On 9/21/11, Rich/CA/Math wrote:
>>>> On 9/18/11, David Ginsburg wrote:
>>>>> The case for math teachers forgoing catchy but confusing
>>>>> mnemonics like FOIL, and instead stress the mathematics
>>>>> behind various concepts and procedures.
>>>>
>>>> Excellent^3

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