Re: Can TI-85 calcs FOIL?
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Re: Can TI-85 calcs FOIL?
Ms. Rachels:
My concern here is one that has been brought up before, and
(believe it or not) Goatboy actually started out a while ago. How much
math should students know before letting the calculator do the work for
you.
Goatboy hasn't completed Algebra II yet and wants someone, or
something, to do his homework for him. He didn't know enough about
factoring techniques to recognize that x^2 + 25 does not factor as
(x-5)(x+5), nor did he recognize that x^3 + 5x + 25 does not "factor" in
the traditional sense (implying a search for rational roots). He doesn't
have the prerequisite knowledge to understand what the calculator is doing
as it determines the roots. This in my mind is a poor use of the
technology because as a result, he isn't learning anything from it.
This seems to be what the "trolls" in the inferior category seem
to be arguing back and forth about. What is important that students
learn? In my mind, it is when it is appropriate to use a calculator over
pencil and paper, but also understanding what the calculator is doing as
it does it. I knew (thanks to an older brother's experimental prank) in
Grade 3 that the square root of ten to fifteen decimal places was
3.162277660168379. It certainly impressed my seventh grade teacher when
we first learned square roots that I could rattle off such a ridiculous
decimal so quickly; however, she was more unimpressed by the fact that I
couldn't figure out the square root of 9, the square root of 4, or the
square root of anything other than 10. Why? Because I didn't know what
a square root was.
My advice to Goatboy was to try to have him learn how to do things
on his own with pencil and paper. then once he learns that method, to
try to figure out not only how the calculator does it, but if it doesn't
directly give you the answer you want (i.e., how can one do factoring on
the TI-85) to learn how to program the calculator to do it for you. That
is how one becomes the better mathematician. At this point, Goatboy
doesn't know much about factoring. I question whether he would have even
known what "i" was if one told him the true factoring method was
(x + 5i)(x - 5i) had someone not mentioned it. We have to remember that
this is the same Goatboy that wanted to put a 486 processor and a hard
drive into a TI-8x calculator.
On a side note, I, as a teacher, would have a difficult time
accepting your decimal expansion for the factoring of x^3 + 5x + 25. It
is clear that the roots are irrational, possibly imaginary, and a decimal
expansion, in my mind, does not do them justice.
That's my two cents. Let's end this discussion here.
-- J. Big Dog
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| --------- | John M.H. Miyares (aka "Johnny Big Dog") |
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On Mon, 25 Nov 1996, Daniel A. Rachels wrote:
> No, the TI85 can not do symbolic solutions unless you have an additional software program for it that adds that capability.
>
> x^2 + 25 does have factors, but they are (x + 5i)(x - 5i), not what's listed below.
>
> x^3 + 5x + 25 also has factors too:
> (x + 2.3625656590074)(x^2 - 2.3625656590074x + 10.581716493121)
> (the numbers are rounded off at 12 digits)
>
> Anyone who wants to do symbolic solutions and doesn't have a TI92 but
has a PC running windows, you can get a FREE math program call ed
"Solutions" at: http://www.qbc.clic.net/Elan
> Solutions can give symbolic or numeric answers. It also will work in
RPN mode and graphs in color.
>
> ----------
> From: Johnny "Big Dog" Miyares[SMTP:jmiyares@mdihs.u98.k12.me.us]
> Sent: Monday, November 25, 1996 7:42 AM
> To: CALC-TI@LISTS.PPP.TI.COM
> Subject: Re: Can TI-85 calcs FOIL?
>
> On Fri, 22 Nov 1996, Goatboy wrote:
>
> > Can the 85 do:
> >
> > from this: x^2+25
> > to this?: (x+5)(x-5)
> >
> > or more complicated like this?: x^3+5x+25
> >
> > ...or do I have to find a seperate prog online?
> >
>
> Goatboy,
>
> Try finishing Algebra before asking questions like this. x^2 + 25
> does not factor as you suggest, and x^3 + 5x + 25 does not factor at all.
> I've tried to tell you what it does. It can find roots, but not
> factors directly...I've tried to tell you this on the side, you haven't
> either understood, or listened. For algebra questions, learn algebra
> first. Then consult either the manual or your high school teachers.
>
> -- JBD
>
>
>
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