Math Forum Internet News

Volume 4, Number 30

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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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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 -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- 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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/pow/ Mathematics Library http://mathforum.org/library/ Teacher2Teacher http://mathforum.org/t2t/ Discussion Groups http://mathforum.org/discussions/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \

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