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

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.  In addition, the latter could solve more complex or more 
realistic problems than the former.

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 

There have been a number of Mathematica-permeated calculus and 
post-calculus courses taught over the years. Others you might wish to 
look at are:

   Calculus, Keith Stroyan, University of Iowa
   Interactive Multivariable Calculus, Stroyan also
   Differential Equations, Selwyn Hollis,
      Armstrong Atlantic State University
   Abstract Algebra, Al Hibbard and Ken Levasseur, Central College
      and University of Massachusetts/Lowell

There have been presentations about some of these projects at various 
Mathematica conferences.

I've based several courses myself upon Mathematica use. Those of us who 
do so often just grow tired of trying to justify what we're doing to 
those who are dubious or skeptical or just plain ignorant of what's 
possible and how.  My own experience is that those who don't want to 
"believe" simply will not believe.  And often they don't want to make 
the effort to reconceptualize what it is they're teaching (and why) and how.

On 1/19/2010 5:14 AM, Richard Fateman wrote:
> Do you have any evidence that, taken collectively, the students know
> more calculus? Can you show that they do better on the final exam than
> students who haven't used computer systems?
>     Typically the calc teachers I've encountered want to know "what to
> leave out to make room" for computer stuff.  I tell them to leave out
> Logarithmic Derivatives.
> Some students like computers because they are neat, and may be
> enthusiastic about this aspect of the course (though not all...).
> Maybe it is unimportant that they learn calculus at all, and they should
> just learn about computers. This would be an important but divisive
> claim:  i.e. calculus is unimportant; we should require that students
> learn computer skills (Mathematica??) instead. Maybe David Park's point
> is really somewhere along that spectrum, and we should hold students who
> learn Mathematica to a lower standard regarding the traditional
> curriculum.
> To be clear, I don't object to teaching students about computer algebra
> systems.  I do so when I get a chance (in computer science courses).
> I just am unaware of evidence that it makes them better calculus
> students.  I don't doubt that a teacher using a computer to do graphics
> can enliven a calculus class. And even students doing graphics on their
> own (e.g. TI graphing?) can have fun. But can you show they learn more
> calculus if they have Mathematica at hand?
> Helen Read wrote:
>> My students come into university level Calculus I or II with no
>> Mathematica experience, and learn to use it in my calculus class while
>> learning calculus. ...

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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