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Re: Re: The audience for Mathematica (Was: Re: Show doesn't work inside

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  • Subject: [mg102130] Re: [mg102084] Re: The audience for Mathematica (Was: Re: Show doesn't work inside
  • From: Andrzej Kozlowski <akoz at>
  • Date: Thu, 30 Jul 2009 05:32:30 -0400 (EDT)
  • References: <32390795.1248259308283.JavaMail.root@n11> <h4951e$q2e$> <> <h4h235$if5$> <h4jti9$3kt$> <h4m4b8$eb9$> <>

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  

>  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.

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