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RE: Re: Re: Mathematica and Education

• To: mathgroup at smc.vnet.net
• Subject: [mg65102] RE: [mg65075] Re: [mg64957] Re: [mg64934] Mathematica and Education
• From: "King, Peter R" <peter.king at imperial.ac.uk>
• Date: Wed, 15 Mar 2006 06:28:14 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

David,

I think actually we are possibly talking at cross purposes. Although I 
also think this leads to some interesting points. I was responding in 
the first instance to a post from a student who had proudly proclaimed 
that he had done all of his assigments without using pen and paper at 
all and only in Mathematica. My view is that this is dangerous for the 
reasons outlined. And in fact my concern is not for the professional 
technical expert (or the prospective ones). In my experience a good 
student who is capable and motivated to understand the material will do 
so and tools like Mathematica can make this an even more exciting 
experience. For them I would agree 100% with what you have said. 
However, poorer students will simply learn how to use the tool as a 
black box. Superficially they will look as skilled as the others because 
they can produce a glossy presentation and they can end up causing alot 
of trouble (I am absolutely serious about this I have seen it - not with 
Mathematica but with other commercial software, which is where my fool 
with a tool quote came from). for weak students they will think that 
learning how to do something substitutes for learning how to understand 
something. As for education for the masses actually I do think there is 
a point. As well as learning about Shakespeare, Bach, Beethoven, 
Michealangelo, Cezanne and so on every civilised person should know 
Newton's laws (with Einstein's amendments), thermodynamics, trigonmetry, 
algebra, calculus and the principles of scientific study.

 My anology with calculators is to show that reliance on using a tool 
can weaken the more traditional skills. Not in itself a problem. As you 
very eloquently pointed out I cannot sharpen a spear and hunt for my own 
food, it is easier to go down to the supermarket. If shops ceased to 
exist I would be stuck! The point being that there are some 
cirucmstances when we don't have calculators about us or when it is 
easier or even better not to use them (I think it is a great skill that 
is underestimated and lost to be able to estimate answers to problems 
without doing an "exact" calculation). I make this analogy, not because 
I think that Mathematica is a glorified calculator (it is much more than 
that) but because I remember the discussions 20-30 years ago when 
calculators were first introduced. Many people in education argued that 
they would enable students to do more calcuations, more quickly and get 
on to the "more interesting stuff" because they weren't being held back 
by "boring" caclulations. In fact I think for weaker students the 
opposite has happened. They do the caclulations but don't understand 
them - as I said they don't really understand the concept of numbers at 
all. This hasn't happened with more advanced mathematics (yet?) because 
the tools haven't really been available for so long but the same 
arguments are being made. My concern is that the same mistakes will be 
made and we will end up with a less mathematically literate population 
then before. Now this is not inevitable and so this is the real 
challenge. How can we ensure that these tools are used appropriately to 
improve mathematical skills and not used lazily to reduce them. There 
have been some excellent and thought provoking examples of how people on 
this list have done this. My fear as that these few sites of excellence 
will be outnumbered by rather lazy teachers (& students) for whom 
Mathematica will used as a black box. I hope I am proved wrong.

I must also confess that I have another sneaking fear. I first learnt 
progamming by writing FORTRAN IV on punched cards on mainframes. I could 
probably still do it tomorrow if such things existed. However, the 
energy barrier to learning more modern languages has meant that I 
haven't bothered. OK so I'm a dinosaur and therefore out of touch. My 
worry is for people who have only learnt how to use MAthematica, when 
that is superceded (and again I am sure that it will) will they have the 
ability to move on to something else if they haven't learnt the 
underlying mathemtics properly. However, the mathematics is much more 
enduring.

Anyway I don't really want to keep batting this around, I am sure 
everyone knows my point of view by now. I hope the message I have got 
across and that I suspect we would agree on is: anyone claiming to use 
mathematics must really understand the basic maths (however they are 
taught it); there is no doubt that modern technologies have an essential 
and deep rooted part to play in education, research and practical 
application in mathematical science; the challenge is to ensure that 
this is done thoughtfully and carefully to ensure best practice and 
maintainence of fundamental skills (rather than erosion as I feel has 
happened in some sectors with numeracy skills). I would be very pleased 
and interested to hear about how this can be done (and perhaps I can 
sneakily take advantage of some of these ideas in my own teaching).

Best wishes,

Peter