Re: LOGO-L> tossing dice

[neuwirth <neuwirth@smc.univie.ac.at>]

i did not say that you should not use random.
but random numbers calculated by a computer are just pseudo random 
numbers.
and intuition for randomness and statistical phenomena is
not developed very well in may people.

if you are starting with a computer simulation,
you never show how this corresponds to reality.

usually, when i do things of that kind with my students
i start with a galton board
(a mechanical device)
producing binomial distributions.

then we "translate" the model into a spreadsheet,
and use random numbers to model the mechanical device,
and then we compare the graph produced by the computer
with the real galton board.

this is the key moment:
usually, the graph and the physical device
look very similar, but not identical,
and so wee see that the computer model 
can be used to model certain aspects of reality.

after that, we can start calculating the
theoretical distribution and compare the physical device,
the random simulation, and the mathematical probability model.

so i agree that random numbers are important.
but it always should be very clear
that a computer simulation is a simulation.

if you don't connect computer models to
reality, that danger is that the message you send is

computer generated models behave like
"theory predicts"

this is especially true with the law of large numbers.
it is important that this law is experienced with "real
data" not just with computer generated simulations.


--
Erich Neuwirth <neuwirth@smc.univie.ac.at>
Computer Supported Didactics Working Group, Univ. Vienna
Visit our SunSITE at http://sunsite.univie.ac.at



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