In article
<b44d075b-60e7-4894-9a93-b72cdd114efe@[EMAIL PROTECTED]
>,
michalchik@[EMAIL PROTECTED]
<michalchik@[EMAIL PROTECTED]
> wrote:
>
>>
>> But "multiplying out" ->is<- a practical way of checking factoring?
>> How so?
>
>Because it is usually faster and easier than the technique being
>tested and it catches mistakes that occur anywhere in the process, not
>just one step.
I was looking at the simplification (x^2-1)/(x+1) = (x-1). I pointed
out that this consists of a factorization and a cancellation, and
wondered why you could not check it in those terms. You said it was
impractical to that ->that<-. I wonder how can it be impractical to
check a factorization by multiplying out when you are doing
"simplification", but not when you are doing "factorization". You
removed the context, and in any case your reply fails to answer why
this technique that is, apparently, so wonderful in one setting can be
so deficient in another, even though it is the exact same technique
being used to check the exact same process.
[...]
>> >Or sometimes the reverse step is just way too hard for the kid
>> >such as in =A0(2x^2 + x + 2) (x^2-2x+3) =3D3D 2*x^4-3*x^3+6*x^2-x+6.
>>
>> What is the difficulty here that they find so hard, exactly?
>
>Well, when they face this problem they have not yet been taught the
>general method for dividing polynomials.
Huh? You aren't dividing polynomials in the expression above! That's
a multiplication. The "simplifications" that occur above are of the
form "identify equal powers of x and add the corresponding
coefficients", presumably. So why are you bringing up division of
polynomials with regards to this expression?
>> They
>> presumably did not go to this equality directly, but rather went
>> halfway through by first multiplying out and then adding terms with
>> identical powers of x. The step to check is only the last one.
>
>Unless we are misunderstanding eachother, the step to check by
>factoring is longer and more complex than the steps involved in the
>multiplication.
We are indeed misunderstanding each other. Above you a multiplication,
and then go off rhapsodizing about the difficulties of figuring out
how to divide polynomials. I have no idea what you are going on about
now, and I suspect you don't really know what you were going about the
day before either, because you are solidly off in tangential land.
>> >Like I
>> >said, going over the probelm again is not goos since people are prone
>> >to make the same mistake twice.
>>
>> And if they don't know how to add or multiply correctly, which is
>> usually the case with mistakes like the above, how is plugging in -3
>> going to save them?
>>
>
>Well, adding and multiplying numbers most kids find easier than adding
>and multiplying algebraic expressions.
Not in my experience. Anyone who has trouble with x+x=2x has trouble
with (-3)(-2) = 6.
[...]
> Even if they are having
>problems with adding and multiplying numbers, if they make a mistake
>with the minus 3, they will still have a clue that they did somehing
>wrong and they must check thier steps carefully. Sometimes they can
>infer what they did wrong by how thier answers differ.
Ah, yes. The test is so wonderful that even if they mess up the test
they will realize, by sheer inference, that they did something wrong
and figure out the problem. Had I realized this to begin with, I would
have never raised a pip.
Sorry, but that is a silly answer. You are basically saying that the
test is good because if they do it properly they will realize the
problem and if they don't do it properly they will also realize the
problem by "checking their steps." But your objection to other
tests rests on the fact that if they made a mistake and re-check their
steps then they will not discover the mistake because they will repeat
it. Ah, but that doesn't apply to this test. Why not? Wishful
thinking, is about the only thing I can see.
>> >If you can come up with a better
>> >alternative i would be grateful.
>>
>> Ah, but every "alternative" is just not practical. Apparently....
>
>Ok, I think you are being a bit petulant here.
It's called "sarcasm", actually.
>Just because I had
>problems with some of your suggestions does not mean I am not open to
>others. Yes, this was an ad hominum attack ;-)
And it's spelled "hominem", no matter how you insist on misusing the
term. It is ->not<- a synonim for "insult", not should it be misused
as such.
[...]
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
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