🚀 go-pugleaf

This is true.  The graphing calculator makes it easier to look at
*concepts* in higher mathematics without getting dragged down by the
sheer complexity of the calculations involved.  I am a high school
student in a precalculus class where a graphing calculator is required.
I believe the calculator is a useful tool which can clarify concepts and
aid in exploration and 'what-if' type of thinking.  Without the
calculator, the student is less likely to 'play around' and change a
coefficient here and there just to 'see what happens'.  We still learn
the manual methods and do mental math, so the calculator does not become
a crutch.  Technology is good.  With the right tools, the drudgery is
removed or greatly reduced, and you focus on concepts, rather than
calculations.

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On Tue, 22 Nov 1994, Mark Howell wrote:

>
> In response to the interesting questions brought up by rww taylor
> regarding how technology affects our perceptions about what
> problems are "difficult" (and perhaps bends our interests
> towards solving certain types of problems)...
>
> I think that certainly we perceive some problems as newly-"doable"
> with technology that earlier we'd never have thought of
> tackling.  Imagine having students calculate Riemann sums
> with partitions of size 5, 10, 20, 60, etc to see the
> convergence even with a *scientific* calculator.  Never.
> Or finding arclengths that before were unyielding because
> we ran head-on into integrals for which there is no closed-
> form antiderivative.  Today, for instance, I asked my BC
> calculus students to determine which of y=x^3, y=2^x-1,
> y=sin(pi*x/2), y=tan(pi*x/4) or y=log3(2*x+1) traced the
> shortest path from (0,0) to (1,1).  They had a lab
> assignment recently to define a function on [0,1] whose
> actual arclength differed from that produced by adding the
> lengths of 100 line segments by at least a factor of 10.
>
> None of these activities would've been possible without
> some fancy tools.  The other isue is whether some other
> types of problems are supplanted by technology.  Again, I'd say
> yes.  And probably, the loss of some of that is a shame.
>
> What we need are clever teachers to devise ways to bring out some of
> those clever and beautiful methods of great mathematicians, with
> or without the use of technology.
>
> I've often wondered what calculus would be like today if Newton or Leibniz
> had had a graphing calculator.
>
> Mark Howell
> mhowell@jacks.gsfc.nasa.gov
>
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