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Re: Re: Re: Mathematica and Education
*To*: mathgroup at smc.vnet.net
*Subject*: [mg65082] Re: [mg65014] Re: [mg64957] Re: [mg64934] Mathematica and Education
*From*: János <janos.lobb at yale.edu>
*Date*: Tue, 14 Mar 2006 05:59:58 -0500 (EST)
*References*: <200603111015.FAA15986@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
I agree with all that David said. Addition to it I started yesterday
a small experiment.
I have two boys with age 13 and 9. Both are good students and good
piano players. They compete with each other in as many way they can
think of. The older one is doing only those activities which are his
interest. I bought Mathematica Student edition for him a year ago
but he used it only once or twice. Whenever I showed him different
calculations - like Solve and Simplify to check his school homework,
he listened, looked interested, but he never went back to use it on
his own. The 9 year old is an explorer. If I am not finding
something - because my wife did some re-arrangement - I am just
asking him and he knows exactly where things are. I also bought
Mathematica Teachers Edition and yesterday I installed it on the
younger one's computer. I showed him how to calculate 2/3 + 5/8 ,
how to ListPlot a bunch of random integers, and similar 4th grade
things. One hour after I left him alone he was still ListPlotting
interesting set of numbers and used Play to hear them - with older
brother watching over his shoulder :)
So the experiment will be that I will teach the younger one for any
kind of neat tricks from week to week and watch how much will trickle
down to the older one through pride, envy and competition.
I am also looking for good educational notebooks/packages for their
levels in all areas. Any good suggestions ? /Unfortunately Wolfram
Tunes is out because at home I do not have Internet connection./
János
On Mar 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
>
----------------------------------------------
Trying to argue with a politician is like lifting up the head of a
corpse.
(S. Lem: His Master Voice)
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