Re: Why are TI Calcs so inferior?
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> Mark -- Very Good Post, I (of course) agree whole-heartedly.
>
> Person who wrote the "Churning Butter Post" -- I'm afraid that your
> Calculus class IS Taught with a Ti-graphing-calculator because anyone
> who compares butter churning, which is a _Process_ to an abstract set of
> ideas, is being Taught A Process.
>
> Everyone knows that:
>
> y(x) = x^n
> y'(x) = n * x^(n - 1)
>
>
> Something my ti-92 can symbolically show me. I'm sure you could even
> program it into a ti8x. Now, can any of you soft-minded HS students
> PROVE it? Qualitativly and Quantitativly?
>
> OR is it simply a PROCESS which you have come to memorize?
>
> Can you tell me what e is withouth thinking about it?
>
> How about the logarithm?
>
> Sadly, a lot of _good_ students I know, who have done well on AP exams
> (4s and 5s), don't have this drilled into their head like they have 6*6.
> Why is that? Because they learned it ONCE in Algebra, or precalc, or
> whatever, and ever since then they have been using their calculators.
>
> Are graphing calculators nice? Sure, they can show a few things which
> would be very hard to show w/ just chalk. But they don't teach you
> calculus, they teach you how to plug equations in.
>
> We don't need any more hands-on-training in school folks. People have
> to learn to use their Brains. It's _FAR_ More usefull.
>
> Wish you all the best
> -nick
>
I agree, I am a college student and I love programing but it would be imposable
to write a good program knowing just the procces, I must know how and why a
problem comes to a particular solution.
I am not saying that TI's are not wonderful tools, I have used them on every
math exam I have taken even when I have had access to Mathmatica but before you
use them you should have at least a pretty good Idea what you are doing
for example how many of you have just used the solve command and written down
the result, if you have read the manual, and after reading som of the posts on
this listserv I begin to doubt that, you may know that the calc uses somthing
known as newton's method to find the solution.
I know that those of you who have had calc have probably covered newtons
method but for the rest let me clear somthing up, solve does not solve an
equation, it aproximates a root. that's why you have to guess at a solution.
the basic method is this
the calc finds the derivitiv of the equation, how it does this is still unclear
to me but I think that it is simply taking the limit of the secants as h -> 0
then it finds the tangent line where x=your guess
then it finds the x-intercept drops a vertical line there and starts the whole
proccess again from F(x1) it repeats this proccess probbably untill the last
digit and all before it have repeated themselves 3 times in a row, this is
common aproximation, if you did not already know this then I would not use
solve or root on your calculators untill you do
same with many other functions, I just used Solve as an example. some
functions like sin^-1 etc. make life a lot simpler, all most people did before
calcs was memorize tables and look up values, I say most I know there is
probably some who will read this and remember learning all sorts of formulas
for finding sin, cos and there arc-s, but for many functions it a working
knowledge of the principals by which they work shuld be gaind before ever using
the calc's shortcuts.
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