Re: HELP!! (implied multiplication)

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Re: HELP!! (implied multiplication)

Both TI and HP have made poor choices in this. Expressions such as 10/2x
should be undefined because it is ambiguous. Neither TI nor HP seem to have
had talented people in numerical analysis when they put their software
together, and hence this sort of problem occurs frequently, due in large part
to the desire of programers for a "friendly" calculator. It is a shame, since
both companies produce devices that should be an adjunct to teaching:
something that instructors ought to  able to reference in general without
having to check the
specifics themselves.  This is just the tip of the iceberg. When one gets into
the algorithms involved in integration, differential equations, linear
algebra, etc. the situation is bad indeed. There is no excuse for this, since
the calculators  have the capacity to do things both correctly and faster..

--
Bob Wheeler --- (Reply to: bwheeler@echip.com)
        ECHIP, Inc.


Nester, Darryl wrote:

> >I am a high school teacher at Northern HS in MD.  Our faculty has been
> >recently debating an issue that up until yesterday seemed quite simple.
> >We would like your help in resolving the issue.
> >
> >The problem:  Evaluate   10/2x when x=4.
> >
> >Some of our faculty seems to think that 2x is like an understood group.
> >Therefore, 10/8=1.25. ...
> >
> >On the other hand, according to the order of operations, mult and div go
> >left to right, so 5*4=20. ...
>
> I'm not sure this issue can really be "resolved" -- it's just one of those
> bits of mathematics that is open to debate!
>
> I think the breakdown is that the 80, 81, 82, and 85 all treat implied
> multiplcation as having a higher precedence than "ordinary" (explicit)
> multiplication (and division).  The newer calculators (83, 86, 92, and [I
> assume] 89) all treat implicit multiplication the same as explicit, and
> therefore follow the "usual" order of operations.
>
> The scheme followed by the earlier calculators has its merits (and
> devotees); for example, one might argue that 10/2x is a fairly natural (if
> somewhat casual) way to write what might be typeset as
>
>      10
>      -- .
>      2x
>
> As I understand the story, TI abandoned this scheme because teachers
> complained that it was confusing their students.  I can recall several
> instances where I asked students to graph (e.g.)
>
>      1
>      - x + 2
>      2
>
> and then found students who got a hyperbola instead of a line.  (I would
> have hoped that they would have known something was wrong when they looked
> at the graph, but ....)
>
> Now on tests and quizzes I make sure to ask students to graph 0.5x+2
> instead, just to avoid the potential snags that those with older
> calculators might encounter.  (I save the discussion of such snags for
> class time.)
>
> Darryl K. Nester                E-mail: mailto:nesterd@bluffton.edu
> Assoc. Prof. of Mathematics        WWW: http://www.bluffton.edu/~nesterd
> Bluffton College                 Phone: 419-358-3483
> Bluffton, OH  45817-1704           Fax: 419-358-3232
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