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Re: Mathematica as a New Approach to Teaching Maths
*To*: mathgroup at smc.vnet.net
*Subject*: [mg127512] Re: Mathematica as a New Approach to Teaching Maths
*From*: W Craig Carter <ccarter at MIT.EDU>
*Date*: Mon, 30 Jul 2012 22:15:37 -0400 (EDT)
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I teach a class on the subject of mathematics applied to materials science and engineering. I use mathematica as a tool to emphasize the application of mathematics, visualization, simulation, and programming. http://pruffle.mit.edu/3.016/
I find that it serves as excellent reinforcement to concepts that they have only learned once in their mathematics curriculum. Furthermore, believe mathematica is an excellent vehicle for doing a broad survey of many maths topics and encourages students to browse, explore, and experiment with "untaught" mathematics material.
I felt strongly that the "M"-like programs will play fundamental part in the students' future professions. Of the several choices, I picked mathematica because I felt that the mathematica skills were more natural with regard to mathematics. I believe that the learning curve being steeper was a net benefit as the students pick up other languages.
As a final observation, I note that students who have taken my class do use mathematica as a tool in their subsequent classes, and I do hear from graduated students that they appreciated the skills that they have learned.
W Craig Carter
Professor of Materials Science, MIT
On Jul 30, , at Mon Jul 30, 12 @3:45 AM, Richard Fateman wrote:
> On 7/27/2012 11:43 PM, Ralph Dratman wrote:
>> David,
>>
>> I agree that Mathematica is quite difficult to learn, but I also think
>> a good teacher could make the learning process significantly easier by
>> going carefully over certain key points which are not emphasized in
>> the documentation.
>
> I think the point that is easy for enthusiasts to miss (and this
> pertains not only to Mathematica but its competitors) is that students,
> by and large, will (mostly correctly) view the introduction of
> Mathematica into their courses as "extra work", "more homework" and
> irrelevant to testing (will there be a computer on exams?).
>
> In point of fact, the difficulties of Mathematica are orthogonal to the
> material in courses in numerical analysis, calculus, and probably other
> topics. I have, for a number of years, been the "go-to" person for
> instructors teaching calculus at UC Berkeley, when students using a
> computer algebra system get what appear to be wrong answers from such
> systems. While the number of such instances has decreased, they have
> not disappeared, and some are "features".
>
> It is also important for enthusiasts to realize that many students do
> not want their classes to be "enriched" by the introduction of a
> peculiar computer program which they are forced to learn. Many students
> simply want to get a passing grade so they never have to take another
> math class.
>
> There are, of course, some set of students who are interested and
> curious and enthusiastic. For example, students who ask, "How do
> you write a computer program that does integrals?" These are perhaps
> the same students who realize that the calculus textbook fails to
> describe an algorithm for doing integrals, and may even understand
> that there are some integrals whose closed form does not exist.
>
> Publications which address the question of "how does the introduction
> of computer labs (etc) affect the student learning level" rather
> consistently come up with a conclusion that is roughly, "they learn
> about the same."
>>
>> For example, one of the most fascinating features of the language --
>> its ability to mix symbolic and numeric quantities -- can also be a
>> source of great confusion for the neophyte.
>
> This is confusing only because they have learned another, more
> restricted, language first. Ab initio, why can't
> the mixture of symbolic and numeric calculations work? To a
> mathematical sophisticate totally unaware of programming, it is
> a big disappointment that BASIC (etc) cannot deal with uninitialized
> variable x by computing x+x resulting in 2*x.
>
>
>
>
>>
>> I would also go very carefully over what one must do to keep the front
>> end and/or kernel from going out of control, and how to recover when
>> that does happen.
>>
>
> This is of course totally irrelevant to the subject matter at hand, and
> disappointing in the extreme that one must spend any time on this.
>
>> I have a number of related ideas to help students get the feel of the
>> Mathematica environment before plunging in to accomplish serious work.
>
> Unfortunately, serious work encounters, fairly often, serious barriers.
>>
>> I would love an opportunity to teach Mathematica to a small group of
>> smart high schoolers or beginning undergraduates.
>
> Tell us when you figure out how to market such a course.
>
>
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