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

On May 3, 6:32=C2=A0pm, Mensanator <mensana...@[EMAIL PROTECTED]
> wrote:
> On May 3, 7:57=EF=BF=BDpm, "michalc...@[EMAIL PROTECTED]
" <michalc...@[EMAIL PROTECTED]
>
wrote=
:
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> > 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.

> > 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.

> - 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.