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Re: learning calculus through mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108035] Re: learning calculus through mathematica
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Sun, 7 Mar 2010 04:01:58 -0500 (EST)
  • References: <hmiiop$3v3$1@smc.vnet.net> <hmlf25$jsp$1@smc.vnet.net> <201003041028.FAA26665@smc.vnet.net> <hmqj02$shk$1@smc.vnet.net>

Murray Eisenberg wrote:
> Try contacting the folks at the Calculus & Mathematica project at 
> University of Illinois and Ohio State.  They should be able to point you 
> to, or provide, the objective studies they did on performance in their 
> Calculus & Mathematica program vs. standard courses.
> 
> As I recall, one of their methods was to compare grades of the two 
> groups in subsequent courses.
> 
> Unless I recall incorrectly, I posted about that very project to this 
> group before.  Whether or not I did, please do try to follow up on my 
> suggestion above.
> 
  I recall this too.  So I did look up online ... Here's what I found.
[[executive summary: Very thin evidence of sometimes positive results]]

In
http://library.wolfram.com/infocenter/Articles/3227/
a thesis at Southern Illinois Univ,
entitled

The Effects of a Calculus Course Based on the Computer Algebra System 
Mathematica  on Subsequent Calculus Dependent Undergraduate Course 
Performance

A key result is
"The two groups were compared by means of final grades in a physics 
course that had calculus or concurrent enrollment as a prerequisite. It 
found a nonsignificant difference in the mean grades of the two groups 
in this case. "

(there were differences when students learned calculus first and then 
mathematica.  I think there is a problem with self-selection here, but 
hard to say. I could not get the thesis to read.)

Then there is this, from the atelier of Jerry Uhl ..

http://www-cm.math.uiuc.edu/studies
which suggests that Mathematica helps, but looking at more info at
https://cm.math.uiuc.edu/?q=node/30
suggests it helps not much.

See the sales-brochure-style info at

http://cm.math.uiuc.edu/faq

which suggests that people who takes these courses go to excellent
graduates schools like Cal-Berkeley and get jobs at great places like 
Wolfram Research.(pardon the snark).

It also suggests that significant differences between the 
calculus+mathematica  (C+M) vs
calculus-mathematica courses may also include substantial extra staff
and hand-holding associated with C+M.

See also the discussions
http://www.iiuedu.eu/press/journals/sds/sds1_july_2008/11_SECC_07.pdf


The principal thesis by Alwasaie at UI in 2000 which Uhl claims contains 
the positive results appears to be unpublished and not available on the 
internet. Unusual in this day and age to be so hard to find.

A paper that can be read, thanks to Google Books is here

http://books.google.com/books?hl=en&lr=&id=e2CxhUABjeAC&oi=fnd&pg=PA155&ots=0QQVjzfVWl&sig=jJokgjwRTGzaEskHFXh00d3suK0#v=onepage&q=&f=false

(skip the first page indexed -- it is blank or missing).

This seems to reflect slightly positively on C+M, but this does not take 
into account the strong possibility that students who enroll in the C+M
sections vs. conventional sections are better to start with, or again) 
that they may respond to many of the non-mathematica aspects, such as 
working in groups, using an open laboratory model rather than lectures, etc.

None of this mostly unpublished material is, I think, terribly 
convincing.  Over the past 50 years or so there have been many 
experiments in improving calculus, and probably any of them can be shown 
to have some positive effect -- if for no other reason than the persons 
studied are aware they are the subjects of a study and want to respond 
to the extra attention.

This does not necessarily affect the views of advocates of CAS as part 
of a technical education who are seeking some justification for the 
expenditure of time and money in the undergraduate curriculum for 
introducing this technology. And I am not personally saying it is a bad
thing. Just not proven.  And I can personally attest to the possibility
that people will find a CAS quite difficult and puzzling -- an 
additional burden to the course that was already difficult for them.

My own personal view is that students in technical areas should be made 
aware of CAS as part of their education the way they (used to be?) 
taught drafting, technical drawing, use of a slide rule...   However, 
engineering curricula are all filled up, so much so that a 5-year rather 
than 4-year set of courses is advocated in many places.  So I am told 
there is "no room".





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