On May 4, 11:14=A0am, magi...@[EMAIL PROTECTED]
(Arturo Magidin) wrote:
> In article
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> michalc...@[EMAIL PROTECTED]
<michalc...@[EMAIL PROTECTED]
> wrote:
> >On May 3, 11:42=3DA0pm, 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
reliabl=
e
> >> > 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
> =A0what I accept as reality."
> =A0 =A0 --- Calvin ("Calvin and Hobbes" by Bill Watterson)
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> Arturo Magidin
> magidin-at-member-ams-org- Hide quoted text -
>
> - Show quoted text -
You may be right about at least some kids getting mislead by this
technique. My main problems is that wwhat you suggest is really not
practical. For example a common mistake kids make is accidently or
mistakenly cancelling part of a numerator or denominator as in a^2/(a
+1) --> a/1 --> a. There is no reversable step that they can use to
test. Or sometimes the reverse step is just way too hard for the kid
such as in (2x^2 + x + 2) (x^2-2x+3) =3D 2*x^4-3*x^3+6*x^2-x+6. Like I
said, going over the probelm again is not goos since people are prone
to make the same mistake twice. If you can come up with a better
alternative i would be grateful.
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