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Discussion: Traffic Jam Applet tool
Topic: Traffic Jam Activity
Related Item: http://mathforum.org/mathtools/tool/10/


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Subject:   RE: Traffic Jam Activity: Math Forum's Applet
Author: Alan Cooper
Date: Aug 5 2004
I had fun with this and with the other versions cited.
Unfortunately I couldn't see anything in the 'History' window in either Netscape
or MSIE - which is a pity since it might have answered a question raised by some
people earlier in the discussion re what the use of a simulation adds over just
playing the game with coins or other markers.

The curricular connections - eg to algebra for discussing how different answers
to the number-of-steps question may in fact be equivalent, and to  the idea
of proof for dealing with the question of whether a proposed traffic cop
strategy is guaranteed to always achieve a minimum, are real and well motivated,
but it takes discipline or strength of will to find the time for activities that
don't address exclusively and immediately the "topic of the day". Perhaps we
should all try to devote a regular part of our class time to such things (if
only students will let us do it without asking "is this going to be on the
exam?" )

P.S. With regard to the "proof-of-strategy" issue, did any of the
discussions get to that stage? I haven't yet convinced myself that my strategy
of "any piece who jumps should be immediately replaced by a team member from
behind" is sufficient, but I suspect that Alex Bogolmony's essay does contain an
answer for if and when I give up.

P.P.S Still with regard to proof, I think that the question of proving
effectiveness of a game strategy may help to give the concept of proof some real
immediacy for students - and may well increase their appreciation of subsequent
proofs in other contexts. In this connection, it might be especially effective
to find games for which some strategy does appear to work for the first few
simple cases but then breaks down at higher levels. Does anyone know of examples
of this?

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