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Re: Mathematica-assisted learning was .. Re: Speak errors
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*Subject*: [mg130638] Re: Mathematica-assisted learning was .. Re: Speak errors
*From*: Helen Read <readhpr at gmail.com>
*Date*: Sun, 28 Apr 2013 00:59:39 -0400 (EDT)
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On 4/26/2013 4:24 AM, Richard Fateman wrote:
>
>
> I note that the MIT regular calculus, 18.01
> http://math.mit.edu/classes/18.01/Spring2013/
> apparently uses a computer algebra system, but not Mathematica.
> I do not see how it is used or how it could be used on the exams.
I teach calculus in a classroom (we have two such rooms) equipped with a
computer for each student. We use Mathematica routinely throughout the
semester, in and out of class, and most of the students like having it
and using it. We have a site license that allows the students to install
Mathematica on their own laptops so they can use it outside of class.
I try to present things with the "rule of three" when possible, looking
at things from the numerical, graphical, and analytic points of view.
Obviously Mathematica is a big help for the numerical and graphical
approaches. One of my favorite examples is introducing series, where
give the students some examples and have them make tables and plots of
partial sums and try to guess whether or not the series converges (of
course I give them some examples where it's difficult to tell), and
after a bit of this they practically beg to be taught analytic tests of
convergence. We continue with the numerical/graphical/analytic approach
throughout the chapter, using analytic tests to prove that a series
converges and then using numerical methods (with the help of
Mathematica) to approximate the limit of partial sums. I find that
overall they seem to end up with a better understanding of series than
my students did years ago when all we did was paper-and-pencil
convergence (which the students found to be terribly abstract).
My students do use Mathematica on exams, but not for everything. I make
up exams in two parts. Part 1 is paper and pencil only, and I keep the
computers "locked" (using monitoring software installed on all the
student computers). When a student finishes Part 1, s/he hands it in and
I unlock that particular computer (which I can do remotely from the
instructor's desk), and the student has full use of Mathematica for Part
2. I can monitor what the students are doing on their computers from the
instructor's station (and of course I get up and walk around and answer
questions if they get stuck on something like a missing comma). We have
a printer in the room so that the students can print their work and
staple it to their test paper when they hand it in.
I've been teaching this way since the late 1990s, and wouldn't dream of
going back to doing it without technology.
Helen Read
University of Vermont
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