Re: The audience for Mathematica (Was: Re: Show doesn't work inside
- To: mathgroup at smc.vnet.net
- Subject: [mg102168] Re: The audience for Mathematica (Was: Re: Show doesn't work inside
- From: AES <siegman at stanford.edu>
- Date: Fri, 31 Jul 2009 05:55:52 -0400 (EDT)
- Organization: Stanford University
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FWIW, I agree with essentially all of this post. There is nothing like taking a textbook formula, or the results of some complex derivation or expansion in a journal article, and actually _calculating_ and _plotting_ the results for a real case, using the extraordinarily powerful and useful capabilities of Mathematica, to provide understanding, physical insight, and intuition. That's why Mathematica's design and interface should be focused on making it as accessible as possible to "ordinary users". In article <h4rpb5$l36$1 at smc.vnet.net>, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > On 29 Jul 2009, at 18:08, Richard Fateman wrote: > > > Helen Read wrote: > > > >> > >> It *is* useful to average college students. Every one of my calculus > >> students learns to use Mathematica successfully, even the below > >> average > >> students. The Classroom Assistant palette has made the learning curve > >> even easier for them. > > > > By what measure is it useful to these students? What most observers > > would consider a mark of success is that the students learned the > > subject matter (calculus) more effectively with Mathematica than > > without. > > I cannot answer for Helen (and I am sure that she would not need my > help to answer this) but anyone who has taught almost any mathematics > courses at almost any level (not just calculus) should find the answer > to this obvious. In short, Mathematica makes it possible for an > average or slightly above average students to *discover for himself* > mathematical phenomena that otherwise he would simply be told about. > In other words, an average student with the help of Mathematica can do > some of the things that would only be done by a far above average > student without Mathematica. And I am sure I don't need to convince > anyone of the value of discovering things for oneself. > > If you really wish I can provide lots of concrete examples, but I am > sure you can easily come up with them yourself, if you were only so > inclined. > > > > I recognize that this may be hard to measure without a control > > group, but do you have some evidence that Mathematica helped them > > learn > > calculus? Being introduced to Mathematica per se may be useful to > > some > > of them who have a career that involves continued access to > > Mathematica > > or perhaps similar programs, but this is somewhat unlikely to be the > > case for "average" math students. > > What is useful is to be able to observe interactively mathematical > phenomena, perform experiments and deduce general principles etc, etc, > really too obvious to have to state it here. > > Of course Mathematica is not the only tool that makes this possible > but I dare say, since version 6 it is by far the simplest to master > and the most powerful. I have been using Mathematica in almost the > courses that I have taught for many years at levels ranging from first > year undergraduate to graduate, in Japan and in Poland, and I can > confirm the same thing that Helen observed - which is that it takes an > average student roughly about 3 weeks to learn more about Mathematica > that a certain distinguished Stanford professor learned in a decade or > so (just to avoid any misunderstanding, note that I wrote "Stanford > professor" and not "Berkeley professor". The Berkley professor knows > or at least used to know Mathematica a lot better than that.) > > Andrzej Kozlowski > > > > > > >> > >> My students use Mathematica on some of their quizzes, which I give > >> them > >> daily during the accelerated summer session. The students are > >> permitted > >> to raise their hands and ask me for help if they run into issues with > >> Mathematica during the quiz. By the end of the second week of my > >> summer > >> class, they were rarely asking for help with Mathematica on the > >> quizzes. > >> We are now three weeks in, and today *nobody* asked for help during > >> the > >> quiz. All of them were able to do what they needed to do without any > >> help from me. Nobody was perplexed. > > > > I am curious as to what kinds of questions you had on your quizzes > > that > > required or even suggested the use of Mathematica for obtaining the > > answers. Derivatives and integrals? Numerical evaluations? Plotting? > > To what extent were the computations uniquely symbolic as opposed to > > (say) something that could be done with a numeric hand-held > > calculator? > > > > While Mathematica as a computational engine may serve many > > audiences, it > > seems that different views of the program, tailored to each audience, > > ease the learning. This is a fairly common phenomenon for complex > > systems, not just software. > > > > RJF > >
- References:
- Re: Show doesn't work inside Do loop ?
- From: AES <siegman@stanford.edu>
- Re: The audience for Mathematica (Was: Re: Show doesn't work inside
- From: Richard Fateman <fateman@cs.berkeley.edu>
- Re: Show doesn't work inside Do loop ?