Re: Checking simplified algebraic expressions (the -3 test)

In article
<67bf4bbd-9ae0-4e9c-9e93-5763534a471f@[EMAIL PROTECTED]
>,
michalchik@[EMAIL PROTECTED]
 <michalchik@[EMAIL PROTECTED]
> wrote:
>On May 3, 11:42=A0pm, Arturo Magidin <magi...@[EMAIL PROTECTED]
> wrote:

>> > Solve you check by plugging the answers back in.
>>
>> > Factor you check by multiplying things back together.
>>
>> > Simplify... Well neither my students nor I were ever taught a
reliable
>> > and simple check for simplified expressions. Example "Simplify (x^2
>> > -1) / (x+1)" this becomes "x-1".
>>
>> And if "factor" you check by multiplying things back together, why is
>> it that "simplify" cannot be checked similarly? You go from (x^2-1)/(x
>> +1) to x-1 by either long division (which can be checked through
>> multiplication), or by factoring and cancelling; the factoring can be
>> checked, and the cancelling can be checked simply by multiplying and
>> dividing again. So how is this different from 'factor" and "solve"?

You did not address this.

>I always teach them that there are cases when this won't work and your
>would need to test with all numbers to be sure. The remultiplying
>before cancelling allwos them to check one step in a simplification
>but not the whole process. You might be right that -2 would be a good
>choice but I will have to think about it. As for the ad hominum attack
>that I must think I am really clever for thinking of this, 

An "ad hominem" is a kind of fallacious argument. It is predicated on
using the (lack of) qualities of the person advancing the argument in
order to reject the argument being advanced. "Ad hominem" is not a
synonym for "insult", in any case. And while I ->was<- making fun, I
was not engaging in an ad hominem argument.

Just so you know.

>I do not
>and never pretended to be so. I posted here to hear if people had
>better suggestions and get an idea of what reasonable objections
>people had.

It is misleading to encourage students to test a universal proposition
by checking a single test case. It is misleading to encourage students
to test a universal proposition that is to hold for ALL numbers by
testing INTEGERS. It puts them in the rut of thinking that the only
"numbers" are the integers; they never bother with fractions, or real
numbers. I cannot tell you how many students I have to flunk because
they apparently don't know that there are a few numbers strictly
between 0 and 1. In my humble opinion, your test is both misleading
and likely to create false impressions on the students. If you
encourage them to multiply out to test factoring, then it should be
just as hard/easy for them to test "simplifications" in a similar
manner: through long division or through multiplication. 

-- 
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"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org