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Re: Re: More /.{I->-1} craziness

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  • Subject: [mg106731] Re: [mg106680] Re: More /.{I->-1} craziness
  • From: Murray Eisenberg <murray at>
  • Date: Fri, 22 Jan 2010 05:37:15 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <> <hhhmn8$o9t$> <hhpl28$9lf$> <hip8gf$t4d$> <8304354.1263643340634.JavaMail.root@n11> <hiuur1$919$> <hj130e$bcn$> <> <hj6qf0$8qo$> <>
  • Reply-to: murray at

Comments inserted below.

On 1/21/2010 4:50 AM, Richard Fateman wrote:
> Murray Eisenberg wrote:
>> It's been some years since I've seen studies comparing performance of
>> students taking a traditional calculus course, on the one hand, and
>> those taking a Mathematica-using course, on the other hand.  As I
>> recall, the studies showed the latter group performing at least as well
>> as the former, and sometimes better, at traditional pen-and-paper
>> skills.
> Rather than looking at all the material you suggest, I will take your
> word for it, since it generally agrees with what I recall.  What I
> recall is that, essentially, the group of students using computers did,
> on the whole, substantially the same as the students not doing so.

In the case of Calculus & Mathematica, the "treated" (Mathematica-using) 
group distinctly performing better than students in the control 
(standard course). Before even imagining the possibility of bias on the 
part of those who conducted the study, one might begin by looking at 
what the study found and how it was conducted.

For example, see:

(on the University of Illinois Mathematics Department's "Calculus & 
Mathematica") web site).

One thing you'll learn about was the concomitant change for the 
treatment group from lecture to hands-on, lab-based approach.  So yes, 
it was not simply that computing was used per se.  Rather, the use of a 
computing-base course made the hands-on approach possible.
>> ... You might want to take a look, e.g., at the link to "A guide to the
>> studies done on the Mathematica-based courses" at
>> This concerns the "Calculus&  Mathematica" project created by Jerry Uhl,
>> Horacio Porta, and Bill Davis, at University of Illinois and Ohio State
>> University.
> The success of such courses obviously depend on the enthusiasm, energy,
> and charisma of the teachers. To what extent does it depend on the
> computing aspect?
> In the case of this particular link, this leads to a business, where the
> professors are apparently selling courseware.  I'm not saying this is a
> bad thing. Just that I would not expect statements on that web site to
> present nuanced opinions on pro/con teaching math with computers :)

I don't recall for sure whether the Calculus & Mathematica project was 
one of quite a number of pedagogical innovations backed by NSF funding. 
  But one of the NSF program's objectives was dissemination of 
successful projects, and this included commercial dissemination as one 

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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