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MathGroup Archive 2006

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Re: Re: Mathematica and Education

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65090] Re: [mg65042] Re: Mathematica and Education
  • From: "David Park" <djmp at earthlink.net>
  • Date: Tue, 14 Mar 2006 06:00:09 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

What an excellent and encouraging response! Here we have:

1) A skilled teacher who has given much thought on how to use Mathematica in
an educational setting and has gained a lot of experience.
2) An institution that has given her serious support.
3) All the students have access to Mathematica all of the time.
4) The students learn Mathematica early in their college career so they will
have easy use of it in their more advanced courses.

I hope people flock to the University of Vermont to see how it's done.

I'm sure there are others also and I hope we hear from some of them.

It was especially interesting that students do better on the Mathematica
assisted portion of their tests than the non-Mathematica portion. And it's
because they can actually try things and see whether or not they actually
work.

The response by G. Raymond Brown was also interesting but here there was
much less support from the institution. It must be much more difficult to
'do Mathematica' halfway, or when only some of the students have it.

The Theodore Gray, Jerry Glynn essay that Matt points us to is priceless.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/




From: Helen Read [mailto:hpr at together.net]
To: mathgroup at smc.vnet.net

[parts snipped.]


At my institution, we have a university wide site license allowing us to
install Mathematica on all of our computers, not just those owned by the
university, but also laptops and desktops owned by faculty, staff, and
students. Mathematica is available to everyone literally 24/7.

I have been teaching calculus with Mathematica for 10 years, for the
last 6 of those years in a classroom equipped with 31 networked PCs (one
for each student, plus one for the instructor), and a printer. We now
have two such rooms. The instructor's machine is connected to the
overhead projector, and we have software allowing easy communication
between the student PCs and the instructor. I can, for example,
broadcast my screen or any of the students' onto the projector or onto
everyone's monitor. Unlike the computer labs on campus, these rooms are
designed for teaching, with clear lines of sight from every student to
the teacher and whiteboard, enough space for the instructor to walk
around and interact with the students, etc.

My students use Mathematica routinely.


I give two-part tests. Part I is done with pencil and paper...

When a student finishes Part I of the test, s/he turns it in and picks
up Part II, which is done with the use of Mathematica.


All of my students, even the weakest among them, are quite comfortable
using Mathematica by the end of the semester.

The students almost always do better on Part II (the Mathematica
portion) of the test than Part I, despite the fact that the problems on
Part II are usually what I consider more difficult. Often they can catch
mistakes when working on Part II, things they would have done
incorrectly on a pencil and paper test without realizing it was wrong.
For example, they will set up an arclength integral incorrectly, and get
an answer from NIntegrate (of course with Mathematica, we are not
limited to the small number of examples whose arclength can be
calculated exactly)--and they can see the answer is off by an order of
magnitude when they estimate the length of the curve that they plotted.
Or, they'll find the equation of a tangent line and plot it with f(x),
only to find that they messed something up -- the line is not tangent!
On a pencil and paper test, they'd have done these things wrong, not
known it was wrong, and moved on to the next question. With the use of
Mathematica they can *see* something is wrong, and can very often fix
it. They are much better at checking whether an answer is reasonable
with all the graphical / numerical feedback that they get from
Mathematica than without it.

--
Helen Read
University of Vermont



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