 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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 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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 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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 Problem of the Month  Grovedale Secondary College, Grovedale, Victoria, Australia
Elementary level problems posted monthly for local elementary school students. Examples include: Sums of square numbers; Trial and error spacial arrangement problem; Sums of whole numbers; Jokes/Riddles in code; Order of operations using number cards;
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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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 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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 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 (SMILE)  Marilyn McCree, District 12
A lesson that uses a grocery store in the classroom to teach students to solve word problems using addition, subtraction, multiplication or division. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the
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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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 Professional Development Focus of the Year  National Council of Teachers of Mathematics (NCTM)
The Professional Development Focus of the Year identifies resources from NCTM journals, publications, Web sites, and sessions at the Annual Meeting and Regional Conferences that relate to a key theme from Principles and Standards for School Mathematics.
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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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 Professional Development (NCTM)  National Council of Teachers of Mathematics
NCTM is dedicated to providing professional development for teachers to ensure mathematics learning of the highest quality for all students. Reflection Guides (using NCTM school journals and other publications as a resource for professional development);
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 Professional Development Program: Learning Math Together  the Math Forum @ Drexel
Four types of professional development options: (1) Customized professional development offers opportunities for close collaboration and support over time. (2) Online professional development courses: sixweek courses based around the Problem of the Week
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 Professional Development Programs for Grade K12 Teachers of Mathematics  The State University of New Jersey  Rutgers
Read about and apply for summer institutes such as Institutes for New Teachers of Mathematics and Science, Helping All Students Succeed in Grades 712 Mathematics, the Leadership Program in Discrete Mathematics, and the DIMACS Connect Institute; conferences
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 Professional Development  Texas Instruments, Inc. (TI)
Learn about the T3 Teacher Leader Cadre Program, onsite systemic professional development; T3 Outreach Program, short term, onsite professional development; T3 international and regional conferences; free online courses for professional development;
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 Professor B  Professor B Enterprises, Inc.
Arithmetic CDs, algebra books, and other products and services that aim to structure math ".. so it becomes as connected and flowing as a story."
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 Professors Rethinking Options in Mathematics for Prospective Teachers (PROMPT)  Humboldt State University Mathematics Department
A program funded by the National Science Foundation to bring together mathematics faculty members from across the country to explore the question, "How can we prepare elementary school teachers to teach for the future rather than the past?" The purpose
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 Professor Warwick Sawyer  Mark Alder
Articles by the author of Mathematician's Delight: "Things and Unthings  An approach to negative numbers," "The Contribution of Music to Mathematical Discovery," "Some Thoughts on Education and Mathematics," "Saturday Morning Mathematics in Cambridge,"
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 Progetto Rhoda  Emilio Brengio
"Numeri con qualità." Software (.exe) per la didattica della matematica nella scuola elementare: problemi; operazioni; geometria; logica; procedure e verifiche; poligoni, angoli, perimetri, e aree; e giochi.
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 Program Information Guide Service (NCBE)  The National Clearinghouse for English Language Acquisition and Language (NCELA)
Short monographs that provide schoolbased personnel with information on innovative practices for working with linguistically and culturally diverse students: bilingual and ESL, language minority, immigrants, etc. The National Clearinghouse for English
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 Project 2061: Science Literacy for a Changing Future  American Association for the Advancement of Science (AAAS)
A longterm initiative to reform K12 education nationwide so that all highschool graduates will be literate in science. The project is creating a coordinated set of reform tools and services—books, CDROMS, online resources, and workshops. This site
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 ProjectBased Learning (Learning and Mathematics)  Blumenfeld, Soloway, Marx, Krajcik, Guzdial, & Palincsar; Math Forum
In this 1996 article, "Motivating projectbased learning: Sustaining the doing, supporting the learning," Blumenfeld and her colleagues at the University of Michigan describe projectbased learning and the benefits of using longterm projects as part
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 Project IMPULS  Tokyo Gakugei University
Project IMPULS (Project for International Mathteacher Professionalization Using Lesson Study) offers opportunities and ideas for mathematics teachers using lesson study. The library includes lesson study about positive and negative numbers; division;
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 Project Search: Math  Buck Institute for Education
Dozens of studies and summaries of research on project based learning (PBL) in math. The Buck Institute for Education (BIE) is creates and disseminates products, practices and knowledge for effective PBL.
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 Projects for ProjectBased Learning (PBL)  WestEd Regional Technology Education Consortium (RTEC)
Designed to provide webbased support for teachers, parents, and children who are interested in projectbased learning (PBL), design, and invention. Exemplary Projects has lesson plans, ideas, information, and links to PBL resources, and can be used by
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 Prongo.com
Free online games, such as Batter's Up Baseball and Lemonade Larry, for practicing arithmetic, investing in the stock market with real time stock prices, using logic to guess a number and decipher secret codes, and more. Themes of other games include
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 A Proof of the Pythagorean Theorem  Isaac Reed
One of the most famous theorems in mathematics, the Pythagorean theorem has many proofs. Presented here is one that relies on Euclidean algebraic geometry and is thus beautifully simple.
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 A Proof that e is Irrational  Isaac Reed
A proof by contradiction that relies on the expression of e as a power series.
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 Properties Glossary  Math Forum, Ask Dr. Math FAQ
What is an operation? What is an identity? What are the associative, commutative, and distributive properties? What is the property of closure? What is the inverse of something?
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 The Pros and Cons of Technology in the Classroom  Roy Pea, Larry Cuban, Bay Area School Reform Collaborative, TAPPED IN
Nationally recognized experts on the subject, Dr. Roy Pea and Dr. Larry Cuban offer their insights in this transcript of speeches each gave to a gathering of organizations that fund school reform projects. A transcript of questions and answers from the
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 ProTeacher  ProTeacher
A teachercreated resource site for elementary schoolteachers, offering lessons and materials, education news, links for finding schools, news and weather, and a reference desk. An index of links to information on various academic subjects includes Mathematics
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 Providing HandsOn, MindsOn, and Authentic Learning Experiences in Mathematics (NCREL)  Cathy Cook; Pathways to School Improvement
A linked essay giving overview, background, and issues around constructivist theory and its implementation. "When educators begin to see learning as knowledge construction, they change their thinking about curriculum, instruction, and assessment, developing
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 Proving Pi (SMILE)  Gwendolyn D. Williams, Paul Robeson High School
A lesson designed to show the ratio of pi by revolving a circle one complete time, and to teach students why the ratio is true. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and Mathematics
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 Psychosemiotic Theory and Educational Practice  Alice Leonard
Walkerdine and Corran's (1979) paper showed how psychosemiology may account for developmental data as a potentially fruitful alternative to the better known stage theories, like that of Piaget. They argued that learning mathematics is an ideal activity
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 Publishing or Programming? A Framework for the Development and Presentation of Work by Children on the World Wide Web  Judy Keiner
A paper to be presented at SIGGRAPH97, Los Angeles, August 8th 1997, involving process writing approaches, and including three criteria for evaluating Web pages. Also links to example sites.
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 Purplemath  Your Algebra Resource  Elizabeth Stapel
Algebra modules provide lessons, practical tips, hints, worked examples, and point out common mistakes in basic triangle length (trigonometry) values, calculators (what model to buy), canceling units, domain and range, exponents, factoring quadratics,
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 Puzzlemaker  Discovery Education
A puzzle generation tool for teachers, students and parents. Create and print customized puzzles, including math squares and number blocks, online, or buy a CD with editing tools and other extras.
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 Puzzle Page  The Black Stump Ltd.
More than 150 links to puzzle sites on the Web. A new site is added each week.
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 Puzzler  Franklin Institute Online
Puzzles from the inQuiry Almanack Puzzle Archive: e.g. Cryptograms, January, 1998. Coded messages hide famous quotations. A clue is offered to begin breaking the code, and an answer key is provided. One puzzle a month from March of 1995 through July of
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 Puzzlers  Bryan Clair, University of Chicago
A collection of Clair's favorite puzzles (no discussion or answers are provided): The Nine Dots; Weighing Coins; The Dollar Hotel, Planning an Orchard; The Math Department; Tea and Cream; Bugs on a Square; River Crossing; More Crawling Bugs; The Unexpected
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 Puzzles, & Riddles  The Contest Center  Frank Rubin
Hundreds of puzzles and mathematical problems ranging from kindergarten through postdoctoral levels. For the easier puzzles, answers are provided on the site; names of those who submit correct solutions to harder problems are posted. See also Puzzles
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 Puzzle Up  Binary Arts Corporation
A collection of others' Java puzzles, baffler and logic questions, "for serious puzzlers," best of the week, and mazes and mysteries, each organized into the three different skill levels of young, brisk, and expert. Also, information on the company's
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 PuzzleWise  Test Best International, Inc.
A supplemental program consisting of math crossword puzzles, each clue of which links directly to state and national gradelevel math skill expectations. The site offers samples, testimonials, prices, and a free newsletter.
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 Puzzle Workshop  maths online  University of Vienna, Austria
Make your own interactive "jigsaw," or multiple choice puzzles, to save and run on your own computer or to publish on the web. The Applet puzzle creation page requires Java; the Test puzzle creation page allows greater use of mathematical symbols.
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 Puzzling Primes  Isaac Reed
To fully comprehend our number system, mathematicians need to understand the properties of the prime numbers  but even finding them isn't so easy.
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 Pythagoras: Music and Space  J. BoydBrent
A brief introduction to Pythagoras' observations on the relation between music and number. Graphics show music intervals expressed as mathematical ratios. Pythagoras observed that when the blacksmith struck his anvil, different notes were produced according
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 Pythagorean Puzzle (SMILE)  Earl Zwicker, Illinois Institute of Technology
A lesson that models the phenomenological approach to enable students to prove the Pythagorean Theorem on their own using puzzle pieces and working together.
From the Geometry and Measurement and Algebra and Trigonometry sections of a collection of almost
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