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

On May 4, 1:23=C2=A0am, "michalc...@[EMAIL PROTECTED]
" <michalc...@[EMAIL PROTECTED]
> wrote:
> On May 3, 6:32=C2=A0pm, Mensanator <mensana...@[EMAIL PROTECTED]
> wrote:
>
>
>
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> > On May 3, 7:57=EF=BF=BDpm, "michalc...@[EMAIL PROTECTED]
" <michalc...@[EMAIL PROTECTED]
>
wro=
te:
>
> > > I tutor a lot of algebra and as you know there are three basic types
> > > of problems that algebra students are given. The ones that say
> > > "Solve", "Factor" and the ones that say "Simplify".
>
> > > 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".
>
> > > The best check I have thought of I call the -3 check. You plug in
the
> > > number -3 into the unsimplfied expression and the simplified
> > > expression and see if you get the same answer. This technique is not
> > > perfect. Sometime you will get the same answer even if the
expressions=

> > > are not equivalent such as -3x and x^2 and the test blows up for
> > > expressions like 1/(x+3). Still these problems come up seldomly.
>
> > > -3 is the smallest and easiest to use number that rarely gives a
false=

> > > check.
>
> > > 0 fails in multiplication x=3D2x
> > > 1 fails in exponentiation x=3Dx^2
> > > 2 has some weird properties x+x =3D x*x =3D x^x
> > > 3 has a problem with abs(x) =3D x and some other minor ones
>
> > > -3 distinguishes all the above situations and is easier to computer
> > > than larger numbers.
>
> > > So, I want to get your opinion on this test and ask if you can think
> > > of anything better.
>
> > How hard is it to check 0,1,2,3 & -3?
>
> Actually pretty hard when they have 25 problems to complete in 50
> minutes. Most students only have at most 25% of total test time left
> to check problems and then correct them.

Then maybe the test should have fewer questions.

Are you running a quiz show or trying to educate?

>
> > > I encourage my students to review their
> > > calculations but many times they will make the same mistake more
than
> > > once if they don't know that their answer is wrong. Remember, in
> > > general I am teaching this to 8th and 9th graders. They are not very
> > > sophisticated or abtract thinkers yet and thier ability to keep
track
> > > of multiple things is quite limited.
>
> > That's why they invented paper & pencil. Put your
> > calculator aside and try it sometime.- Hide quoted text -
>
> These kids are all working on paper, but approaching problems on paper
> in an organized fa****on is a skill that takes years to develope and
> changes with each new type of problem it is not trivial.

Years? Aren't you teaching them how to do that?

>
> > - Show quoted text -
>
> I think you are out of touch with what it is like to be a kid trying
> to learn new math concepts.

No argument there. I'm not a teacher and haven't been
a student for a long time. But I tinker with math as a
hobby, where there's no teacher involved, no book to
fall back on and you can't simply dismiss anything you
get wrong. So I think I'm pretty in touch with how to
keep track of multiple things.

Go have a look at

<http://members.aol.com/mensanator/cycle/ultimate_cycle.htm>

for an example.