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MathGroup Archive 2006

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Re: Re: Re: Mathematica and Education

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65045] Re: [mg65014] Re: [mg64957] Re: [mg64934] Mathematica and Education
  • From: ggroup at sarj.ca
  • Date: Sun, 12 Mar 2006 23:58:35 -0500 (EST)
  • References: <200603111015.FAA15986@smc.vnet.net>
  • Reply-to: ggroup at sarj.ca
  • Sender: owner-wri-mathgroup at wolfram.com

David,

I agree largely that Mathematica (or any math software) can be used to
great benefit.

One point that I believe your argument takes too lightly is the
availability of the technology. Your example of spinning wheels
becoming obsolete is not really valid. Manufactured clothing is
available everywhere, and there is sufficient variety that it is
available at prices that are accessible to pretty well everyone.

Mathematica and even computers are not.  There is a large cost to buy
and maintain both a computer and a license.  You can argue that
computers are starting to become cheap and common enough that we can
drop computers as a significant cost.  Fine, but a Mathematica license
is not cheap.  Overall value doesn't always win the day when there are
many other financial obligations to consider.

So what is the student to do when they go to work for such a company?
Or even if the company does buy a license, it may not provide a home
license for the employee to use.  Even if they do provide a home
license, you suddenly run into a whole bunch of other issues, like who
owns the IP of anything you might produce.  No such barrier exists
with the pencil and paper model.

I think the crux of the argument is that if you are taught well, it
doesn't matter much how you were taught. There are benefits of all
approaches. The problem lies in the fact that in reality, regardless
of the system, students will not be taught nor learn optimally. With
course loads and all the other pressures of student life, there is no
way that most students can devote enough time to get the most out of
any teaching system. Similarly, with all their other obligations, few
professors have the time to devote to being truly excellent
instructors. So you have to fall to a compromise; knowing that the
average student is only going to absorb a fraction of what you're
teaching in the time that is available, what is important?

From my experience, all technology, no matter how reliable, has some
sort of failure in a teaching environment (how many times have you
seen the projector not work correctly?).  Dealing with these problems
has merit, but it robs valuable time from instruction of other
concepts.  How many times have you seen a university/college level
student go to their professor to figure out how to sharpen their
pencil?

Do these problems with technology outweigh the potential gain by
systems like Mathematica? I don't know. I do know that the
effectiveness of any teaching system boils down to the quality and
motivation of the instructors and students and sadly, even the
administrators.


On Saturday, March 11, 2006 at 5:15 AM, David Park wrote:

> Peter,

> I find your remarks very interesting and I think you state the principal
> reasons for NOT making the maximum use of Mathematica in education. It
> certainly helps to get the objections and perceived limitations on the
> table. However, I would like to try, to the best of my ability, to make the
> counter arguments.

> If I may summarize the reasons you, and others, have put forward.

> 1) Mathematica allows a student to get an answer without truly understanding
> the underlying theory and reasons. Pencil and paper forces the student to
> understand things more deeply and provides additional experience.

> 2) We have to preserve the old skills. In emergencies we may be forced to
> fall back on them, such as in the field, in exams without computers and
> after the next nuclear war. Good penmanship and mental arithmetic will save
> us.

> 3) Mathematica will automatically make choices for us that we do not
> understand. I would like to state this in a more general sense. Students
> haven't mastered Mathematica well enough to use it as a reliable tool.

> I have often argued here that students should be taught to think of
> Mathematica as 'pencil and paper'. They should use it just like they would
> use pencil and paper. Theodore Gray has provided us with the wonderful
> notebook interface. You can have titles, sections, text cells, equations and
> diagrams. It's the style of textbooks, reports and research papers. It goes
> back at least to Euclid. So, I don't understand specifically what advantage
> real pencil and paper have over a Mathematica notebook, except perhaps that
> it is far easier to get away with writing nonsense.

> In fact, let's look at the advantages that a Mathematica notebook has over
> real pencil and paper.

> 1) Neatness. And a student can correct and rewrite more easily.
> 2) An active document. The definitions students write can actively be used
> in further derivations. In fact, the student is forced to make these
> definitions and assumptions explicit.
> 3) Permanent record. Not only a permanent record but also a repository of
> resources that the student may have developed.
> 4) Proofing. With a Mathematica notebook you can actually evaluate things
> and verify that they work. One can't get away with sloppiness.
> 5) MORE and DEEPER experience. With a Mathematica notebook a student can
> actually do many more, and more difficult, exercises and examples. Many
> times, while working through textbooks, I have seen cases where the author
> either skipped the demonstration or simplified the case for no other reason
> than the difficulty of hand calculations.
> 6) A literate style. Conventional exercises and tests are usually skimpy
> throw away documents. Mathematica notebooks provide a perfect opportunity
> for 'essay' style work and develop the skills for technical communication.

> Of course, we have to have teachers and students who know how to take
> advantage of these features.

> As for preserving old skills, I'm not too sympathetic. Are students to be
> taught how to sharpen spears (no advanced bow and arrow technology allowed!)
> track animals and identify eatable grubs and berries, just in case we get
> thrown back into a hunter-gatherer society? It wasn't that many generations
> ago when almost all women knew how to weave or operate a spinning wheel.
> Should these skills be preserved? Like it or not, we are dependent on
> civilization and modern technology. Rather than teaching 'survival skills'
> we should make sure that civilization is preserved and advanced. That's the
> best chance. If worse comes to worst, some people will learn the
> multiplication tables fast enough (and also how to sharpen spears).

> The problem of using Mathematica intelligently, and not blindly, is serious.
> Most students are not well enough prepared with Mathematica to use it to
> anywhere near its capability. Mathematica is not wide spread enough and
> students do not learn it early enough. Any student interested in a technical
> career could do nothing better than start learning it in high school.
> Furthermore, Mathematica is not optimized for students and researchers. When
> it comes to ease of use there are many gaps. I believe that Mathematica can
> truly effect a revolution in technical education. But it is not as simple as
> just installing it on a departmental server. A lot of preparation is needed.
> Additional packages geared to student use are needed. Educators have to
> learn how to take advantage of the resource. (For example how to shift from
> quick calculations to essay type questions.)

> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/


> From: King, Peter R [mailto:peter.king at imperial.ac.uk]
To: mathgroup at smc.vnet.net

> I should like to say that as an educator of science students in a
> (predominantly) non-mathematical branch of science (earth sciences) I am
> very concerned about this approach. Sure Mathematica is a wonderful
> tool. As a professional researcher I use it all the time for doing
> tedious calculations to save time, or to check claculations where I may
> have got things wrong and so on and so on. If I didn't think Mathematica
> was useful I wouldn't have it and wouldn't subscribe to this list.

> But it is still a tool. IT can't know what calculations to do, what
> approximations to make and sometimes when there are mathematical choices
> to be made. For example there are times when Mathematica's choice of
> branch cut doesn't correspond to the one I want to make. Not a problem I
> can tell it what I really want. There are times when its choice of
> simplification doesn't suite my purpose. Again not a problem I can tell
> it what to do or simply carry on by hand if that's easier. But how do I
> know when the defaults don't suite my purpose, because I have spent many
> years doing things by hand and gaining that experience to know what I
> want. I am not convinced that if I had done all my mathematics within
> Mathematica I would have gained the same experience. But I am open to
> discussion on this if anyone wants to put the counter case. However, I
> would need very strong convincing that it is good for students never to
> have to do old fashioned calculations on paper. In the same way I think
> it is important for children to learn multiplication rather than rely on
> a calculator or to learn to write rather than use a word processor.

> In particular for practicing engineers they may be out in the field,
> away from a computer and be required to do a back of the envelope
> calculation by hand. If you have never done it before you will be stuck
> and I don't think you could consider yourself a "real" engineer.

> So yes Mathematica is great. Yes students should be taught to use it and
> use it properly. But please make sure you could have done your homework
> by hand (it is often not as bad as you might think!). Perhaps I am a
> dinosaur but I have been in meetings which required moderately difficult
> numerical calculations which I could do by hand whereas other (younger)
> people present were stuck without calculators.

> I was once told a quote and I can't remember who it was from "A fool
> with a tool is still a fool"

> (Incidentally please don't take this personally. I don't know you and so
> I have no reason to doubt that you are a perfectly good scientist I am
> simply commenting on a current trend for people to run to software
> rather than doing it by hand - which in some cases is actually easier).

> Peter King





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