 The Prisoners' Dilemma  F. Heylighen, Principia Cybernetica Web
Cooperation in game theory: the principle of suboptimization. A game that has been and continues to be studied by people in a variety of disciplines, ranging from biology through sociology and public policy. It is a "nonzerosum" game: the best strategy
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 Prisoners' Dilemma  Wayne Davis
An interactive game simulation inspired by Prisoners' Dilemma game theory as described in the book The Selfish Gene by Richard Dawkins. The payoff is a reduction in prison sentencing of very good, fairly good, fairly bad or very bad, which is translated
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 Prisoners of Time  U.S. Dept. of Education
Report of the National Education Commission on Time and Learning, April 1994, established as an independent advisory body to study the relation between time and learning in American schools. "The degree to which today's American school is controlled by
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 The Private Eye  Kerry Ruef
A handson, investigative teaching approach that attempts to stimulate the wonder of looking closely at the world, thinking by analogy, changing scale, and theorizing. It uses everyday objects, a jeweler's loupe, and a series of simple questions, which
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 Prized Geometric Logic  Ivars Peterson (MathTrek)
Computer programs can handle all sorts of data [such as] a set of discrete
elements, such as temperatures. Some elements of a set may be larger in value than others, or they may exhibit some other relationship that allows you to rank them or put them
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 Prize offered for solving number conundrum  Ivars Peterson  Science News Online
A proof of a conjecture related to Fermat's last theorem would earn $50,000.
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 Prizes and Perils of Popularizing  Keith Devlin
A series of vignettes abouut some of the leading popularizers of mathematics. Sections include: Casti's Tale; Devlin's Tale; Stewart's Tale; Paulos's Tale; Dunham's Tale; and Why Do We Do It? Previously published in Focus.
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 Probabilistic Thinking  Richard Jeffrey, Princeton University
A 1995 book. Chapters include: Probability; Methodology; Expectation; Decision; Probabilism and Induction. Solutions to problems are included.
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 Probability Abstract Service  University of Washington, Seattle, WA
Latest abstracts, with some preprints and information about authors; all abstract titles (old and new titles and authors, a large file); old abstracts; submission and subscription information; and related WWW servers.
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 Probability and Quantile Applets  Balasubramanian Narasimhan
The Probability Applet calculates areas under the standard normal density curves. You are presented with two fields and three buttons on top of a normal density curve. The buttons allow you to calculate areas to the left or to the right or between. The
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 Probability and Statistics  Math Forum
Links to some of the best Internet resources for probability and statistics: classroom materials, software, Internet projects, and public forums for discussion.
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 Probability and Statistics (MathPages)  Kevin Brown
More than 40 "informal notes" by Kevin Brown on probability and statistics: evaluating probabilities of Boolean events, area under the bell curve, N items distributed in M bins, dice rolling a given sum, a better lottery, meetings and birthdays, on random
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 Probability by Surprise  Susan P. Holmes et al.
Experimenting Paradoxes  browsersensitive Java applets (try Internet Explorer first) to try out: The Birthday Problem; Say Red; The Collector; Banach's Matchbox Problem; The Matching Problem; The IID Sequence; Polya's Urn as a restaurant choice; Random
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 Probability Explorer  Hollylynne Stohl
An openended learning environment for Windows for representing data in multiple ways, engaging students in designing, simulating, and analyzing results of probability experiments. The software environment can be used for activities from upper elementary
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 Probability  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A short essay on probability theory, with links to some wellknown problems: Monty Hall Dilemma; Three pancakes problem; Lewis Carroll's problem; Bertrand's Paradox; Bear cubs problem; Misuse and Misconception of Statistics; Pauling's joke; Probability
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 Probability in the Real World  Math Forum, Ask Dr. Math FAQ
An introduction to the uses of probability in everyday life, including: weather forecasting, flipping coins, batting averages, lightning strikes, and the lottery.
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 Probability  Math Forum, Ask Dr. Math FAQ
An introduction to basic concepts.
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 Probability of Getting Doughnuts  NASA Lewis Learning Technologies Project
A box of doughnuts contains 4 glazed, 3 creamfilled, and 2 jelly doughnuts. What is the probability of getting a creamfilled doughnut, eating it, and then getting a glazed doughnut? A detailed answer is provided. From NASA's 9th Grade Math Proficiency
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 Probability: Rolling Dice  NASA Lewis Learning Technologies Project
Probability: If a die is rolled 18 times, how many times is the number 2 expected to come up? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Probability (S.M.A.R.T.)  Math Share Shop
Counting principle; Probability reference sheet. By students at Theodore Roosevelt H.S., Bronx, & Edward R. Murrow High School, Brooklyn.
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 Probability (SMILE)  Laura Willis Moss, South Shore Community Academy
A lesson designed to teach students to derive a general formula for the probability of a given event when each possible outcome is equally likely. From the Probability and Statistics section of a collection of almost 200 single concept lessons by the
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 Probability/Statistics and Calculus Problems of the Week (PCPOW)  Kentridge High School, Kent, WA
Probability, statistics, and calculus problems and solutions, some of which date back to 1999.
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 Probability/Statistics: First Semester Project  Lisa Stanfill; Math Forum Teacher Exchange
A culminating project developed as part of a probability and statistics class, designed to help students put the topics of data collection, organization, presentation and interpretation together to see how and why learning that content is important.
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 The Probability Web  Bob Dobrow; Department of Mathematics and Computer Science, Carleton College
A collection of pages to serve people with interests in probability theory and its applications. Information is presented under the following headings: Probability links, Abstracts, Listservers, Newsgroups, People, Jobs, Journals, Software, Books, Booksellers,
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 Problem at the Art Gallery  Ivars Peterson (MathLand)
The Crystal Art Gallery was being readied for its grand opening, and I had to figure out how many guards were needed to make sure that every wall of paintings was under scrutiny. I was also ordered to keep costs as low as possible. The trouble was that
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 ProblemAttic  EducAide Software
Thousands of questions from New York State Regents exams, the National Assessment of Educational Progress (NAEP), the Trends in International Mathematics and Science Study (TIMSS), academic competitions, and other test banks. Sign up for a free account
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 Problem Corner  Les Reid; Southwest Missouri State University (SMSU)
High School, Advanced, and Challenge problems, updated monthly (approximately). High School: solutions are not solicited, although feedback (generalizations, suggestions for future problems, etc.) is appreciated. Each month, the solution to the previous
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 The Problem of Points  Isaac Reed
An ageold gambling problem led to the development of probability by French mathematicians Pascal and Fermat in the 17th century.
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 The Problem of the Knight: A Fast and Simple Algorithm  Arnd Roth
Download a Mathematica notebook that discusses different algorithms for solving the Knight's Tour problem, finding a path for the chess knight that visits every square once. For an Introduction, Implementation, and Examples, visit Roth's MaxPlanckInstitut
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 Problem of the Week Articles  the Math Forum @ Drexel
These three published articles give context to using the Math Forum's Problems of the Week with students: Writing to Develop Understanding: The Math Forum @ Drexel's PoWs; Problems of the Week Engage Students with Special Needs; and The Impact of the
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 ProblemoftheWeek  David Poole; Department of Mathematics, Trent University, Canada
Most of these problems can be done using only high school mathematics and logical reasoning. Eight problems with solutions and one without, from the fall of 1997, at Trent University, Canada. An email contact is listed, for those outside the university
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 Problem of the Week  Dr. Annalisa Crannell; Franklin & Marshall College
Puzzles to solve in number theory, geometry, probability, cryptography, and the like. See problems from 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, and 1997.
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 Problem of the Week  Duc Huynh
A new math problem each week, with an archive of past problems.
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 Problem of the week  Stephen Sproule
An index of sites offering Problems of the Week, organized by level: elementary, middle grades, high school, and advanced. Sproule appraises PoW sites according to whether or not they include solutions and archive past puzzles.
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 Problem Pictures  Richard Phillips
A CDROM of 184 attractive, unusual, or puzzling color photographs accompanied by activities for mathematics teaching. Images may defy explanation, motivate investigation, or inspire the viewer to answer a question. Other pictures may be the starting
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 Problem Problems  Michael Pershan
Blog by a New York City math teacher trying "to better understand the connections between problem solving, learning, and teaching." Posts, which date back to May, 2015, have included "Getting Stuck on a Geometry Problem," "Minimalistic Hints Are Still
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 Problems  Bojan Mohar
Conjectures in graph theory ranging from paths to colorings to matchings to crossings. With references, links to other collections of open problems, and chapters of the book that Mohar authored with Carsten Thomassen, Graphs on Surfaces.
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 The Problem Site  Douglas Twitchell
Math puzzles, brainteasers, strategy games, web quizzes, and informational pages. Flashpowered math games include Adders, Zap (slide tiles to move digits and add up to a specified sum), Side By Side (number rearrangement), One To Ten (given four numbers,
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 Problems of the Week  Math Forum @ Drexel
Our goal with the Problems of the Week is to engage students in nonroutine, constructedresponse mathematics investigations that integrate writing with problem solving in the math classroom. In addition to the Current PoWs and the Problems of the Week
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 Problem Solving in Mathematics  Jim Wilson; Univ. of Georgia
Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links
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 Problem Solving Island  Samuel A. Rebelsky
Challenging openended word problems on the topics of games, such as Blockade, Finger Multiplication, and The Word Pyramid; puzzles such as Error Correction, Error Detection, The Fake Coin, Friday the 13th, and Leap Birthdays; and problems based on figures,
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 Problem Solving
(SMILE)  Patricia Rogers, Edward Hartigan School
A lesson designed to demonstrate some common ways problems can be solved; to list some basic steps in problem solving; and to suggest some useful strategies for solving word problems. From the Practical and Applied Math section of a collection of almost
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 ProblemSolving: Steps and Strategies (SMILE)  Sarah G. Barrett, Mars Hill School
A lesson designed to teach and reinforce strategies for problemsolving. Sample problems are included. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning
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 Problem Solving Strategies  Finlay McQuade, Boğaziçi University (Turkey)
Strategies for solving problems, each illustrated with sample math challenges and worked solutions: draw a diagram; make a list; guess and check; divide and conquer; look for a pattern; start at the end. Also available in Turkish.
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 Problem Solving with Heron's Formula  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
A paper on the development and demonstration of Heron's formula for the area of a triangle given the lengths of its three sides. Problems and explorations are included for using Heron's formula.
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 The Problem with Algebraic Models of Marriage Structure  James M. Cargal; The Math Forum
Algebraic models of marriage systems have been in use for nearly fifty years. These models continue to be a matter of controversy. Most anthropologists have found algebraic models abstract and unnecessary. Mathematical scientists have tended to consider
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 Procon Technology  Maths Tips and Tricks  Peter King
Math tricks, divisibility rules, and mental math tricks, many from a book by Kjartan Poskitt called Numbers  the key to the universe, one of the books in the Murderous Maths series published by Scholastic.
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 Productive Struggle
Group blog, with most contributions by secondary math and science teachers, that aims to "push teachers to learn in the same way that we push our students to learn" and "work together to make our struggles productive." Posts, which date back to March,
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 Professional Development Center (PDC)  Key Curriculum Press
Professional development opportunities from summer institutes to weekend workshops for teachers across the United States, with scheduled 1day, 3day, and 7day courses, as well as opportunities for custom offerings specific to district needs. In particular,
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 Professional Development in a Technological Age: New Definitions, Old Challenges, New Resources  Cathy Miles Grant
This paper looks broadly at the field of professional development and the underlying principles that guide current approaches. The paper suggests specific issues that come with the process of supporting teachers in technology use, and concludes with a
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