Discussion:  All Topics 
Topic:  Traffic Jam Activity 
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Subject:  RE: Traffic Jam Activity: Math Forum's Applet 
Author:  Alan Cooper 
Date:  Aug 5 2004 
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 numberofsteps 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 "proofofstrategy" 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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