Re: Re: learning calculus through mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg108109] Re: [mg108035] Re: learning calculus through mathematica
- From: Canopus56 <canopus56 at yahoo.com>
- Date: Mon, 8 Mar 2010 06:16:23 -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> <201003070901.EAA00305@smc.vnet.net>
Richard wrote: > 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". Perhaps recent graduates could weigh in on this. Is industry expecting competence in CAS (e.g. Mathematica, etc.) as an assumed productivity tool skill? If so, in which fields? Just wondering. - Kurt ----- Original Message ---- From: Richard Fateman <fateman at cs.berkeley.edu> To: mathgroup at smc.vnet.net Sent: Sun, March 7, 2010 2:01:58 AM Subject: [mg108109] [mg108035] Re: learning calculus through mathematica 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".
- References:
- Re: learning calculus through mathematica
- From: Richard Fateman <fateman@cs.berkeley.edu>
- Re: learning calculus through mathematica
- From: Richard Fateman <fateman@cs.berkeley.edu>
- Re: learning calculus through mathematica