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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>
  • 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
> 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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