26 July 1999 Vol. 4, No. 30
THE MATH FORUM INTERNET NEWS
NCTM Standards on the Web | Prisoners' Dilemma |
Exploring Emergence - MIT
NCTM STANDARDS ON THE WEB
National Council of Teachers of Mathematics
CURRICULUM AND EVALUATION STANDARDS FOR SCHOOL MATHEMATICS
- 1989, Reston, VA
http://standards-e.nctm.org/1.0/89ces/2801.htm
NCTM Standards for grades K-4, 5-8, and 9-12, one facet of
the mathematics education community's response to the call
for reform in the teaching and learning of mathematics. The
document reflects a consensus that all students need to
learn more, and often different, mathematics and that
instruction in mathematics must be significantly revised.
The contents are at:
http://standards-e.nctm.org/1.0/89ces/Table_of_Contents.html
- 1998 Discussion Draft
http://standards-e.nctm.org/1.0/normal/standards/standardsFS.html
Draft of a revision of the 1989 NCTM Standards, organized
into three parts: Guiding Principles for School Mathematics
Instructional Programs; Overview of Standards for Grades
Pre-K-12 Mathematics Education; and Standards for Grades
Pre-K-2, 3-5, 6-8, and 9-12. Readers are invited to submit
responses.
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THE PRISONERS' DILEMMA
A favorite non-zero-sum game theory puzzle, where the best
strategy for a given player is often one that also increases
the payoff for a partner. Many sites, some interactive,
explore the Prisoners' Dilemma on the Web:
- YOU HAVE FOUND THE PRISONERS' DILEMMA - Serendip
http://serendip.brynmawr.edu/playground/pd.html
an interactive game: on each turn, you and your opponent
must choose without knowing the other's choice; following
every turn you will each receive a certain number of gold
coins, depending on the choices made by both of you
- PRISONERS' DILEMMA - Wayne Davis
http://netrunners.mur.csu.edu.au/~osprey/prisoner.html
an interactive game simulation: the payoff is a reduction
in prison sentencing, translated into a point score system
- ITERATED PRISONERS' DILEMMA - Delayaye, Mathieu, Beaufils
http://www.lifl.fr/IPD/ipd.frame.html
a comprehensive source of information about cooperation
between agents, in English and French
- THE PRISONERS' DILEMMA - Principia Cybernetica Web
http://pespmc1.vub.ac.be/PRISDIL.html
cooperation and suboptimization are studied by people in
a variety of disciplines, from biology through sociology
and public policy
- THE PRISONERS' DILEMMA - Walter Korman, Deep Magic
http://www.go2net.com/people/paulp/deep/1997/02/26/
an overview with links to related sites and Java applets
demonstrating different strategies of play. Also SHEEP
MAGIC: http://www.go2net.com/internet/deep/1997/04/02/
- MATHEMATICS AND BIOLOGY - A. Bogomolny
http://www.maa.org/editorial/knot/evolutions.html
a discussion of evolution, inheritance, genes and mutation,
the Prisoners' Dilemma, and how these and other biological
themes relate to mathematics
- A VIRAL DILEMMA - Ivars Peterson (MathTrek)
http://www.maa.org/mathland/mathtrek_4_26_99.html
an article that discusses how, in effect, a virus is caught
up in a version of the prisoners' dilemma
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EXPLORING EMERGENCE - Resnick, Silverman, MIT
http://el.www.media.mit.edu/groups/el/projects/emergence/contents.html
From the Epistemology and Learning Group at the Massachusetts
Institute of Technology, an essay that uses Java applets to
explore the idea of emergence, examining how objects and
patterns can arise from simple interactions in surprising
and counter-intuitive ways. Examples use arrangements of
squares that simply turn on and off, yet give rise to
patterns of motion that offer a new perspective for thinking
about phenomena in the everyday world.
Explorations include rules for Seeds and for John Conway's
Game of Life. Investigations focus on rules that lead to
chaos or to stability; rules on the edge between order and
chaos; spontaneous generation; and instability.
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