Re: Re: learning calculus through mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg108015] Re: [mg107971] Re: learning calculus through mathematica
- From: "David Park" <djmpark at comcast.net>
- Date: Fri, 5 Mar 2010 04:33:23 -0500 (EST)
- References: <hmiiop$3v3$1@smc.vnet.net> <hmlf25$jsp$1@smc.vnet.net> <3434740.1267699632618.JavaMail.root@n11>
Certainly not every student should be learning Mathematica at the earliest possible age. But maybe those who are seriously interested in a technical career and are motivated should. Maybe it wouldn't be a part of regular secondary school education, but be done on their own, or in math clubs, or via mentoring over the Internet. Maybe it's true that CAS have not made a significant positive impact in technical education. Does that mean people should give up? Maybe we haven't properly learned how to use them yet. When new technologies come in they are often used to just make the old approaches more efficient. Usually what is needed is entirely new approaches. Instead of mass lectures and mass exams, maybe there should be more self study, more mentoring and more mathematical essay writing. As things stand now I have the sneaky suspicion that students just don't know Mathematica well enough and it is another obstacle to getting through the course. So, why should they do better? Also, Mathematica off the shelf is not a great educational tool. It does too much at a high level with commands like Solve, Integrate or Limit. That's all fine, but students need something I call "hierarchical depth", the ability to do mathematics at different levels and see how things work. It is somewhat ironic that as a computer algebra system, Mathematica (and I suspect most systems) are poor at providing the kind of algebraic manipulations that students need to work with. They are hierarchically thin. This all could be provided, but it takes more work. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Richard Fateman [mailto:fateman at cs.berkeley.edu] There is a substantial list of links to calculus resources at http://www.calculus.org/ This includes complete on-line courses. I have searched in vain for objective evidence that students who learn calculus with a computer algebra system at hand learn it better than students without such a tool. (e.g. higher exam grades.) This is disappointing to people who would like every student to learn how to use a CAS at the earliest opportunity. Historically, the big success for calc students was using computers to plot functions. Handy to understand slopes and areas. Very easy to use. Not so prone to arithmetic mistakes, though with problems of their own.
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