 The Role of Examples in Learning Mathematics  Annie and John Selden; Mathematical Association of America
"Examining examples and nonexamples can help students understand definitions.... Is the provision of examples always desirable? Would it perhaps be better to ask undergraduate students to provide their own examples and nonexamples? Would they be able
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 Roles of calculators in the classroom  Pedro Gómez and Bert Waits
The site contains the extended papers of the conferences presented in the Topic Group 18 of the International Congress of Mathematics Education held in Seville in July, 1996. Papers are presented both as web pages and as PDF files.
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 The Roles of Interest and Mathematical Beliefs in Preservice Teachers' Learning to Mentor Online [PDF]  Ray & Renninger
Paper presented as part of a symposium, American Educational Research Association, Chicago, IL. A study of preservice teachers working with the Math Forum's Online Mentoring Guide.
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 Rolling a Die Until Every Face Has Appeared (Math Chat)  Frank Morgan, MAA Online
How many times do you think you need to roll a normal die to be 90% sure that each of the six faces has appeared at least once? Why? Answer: It takes 23 rolls, as Al Zimmerman discovered in a computer experiment rolling 5000 dice until 90% of them had
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 Rolling with Reuleaux  Ivars Peterson (MathLand)
Why is the cover of a manhole round? The usual answer is that a circular lid, unlike a square or hexagonal cover, won't fall through the opening. The circle works because it has a constant width, defined as the distance between a pair of parallel lines
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 A Romance With Numbers  K. Venkatasubramanian
Biographical information and thoughts about Srinivasa Ramanujan, from The Hindu, December 24, 1993.
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 Ronald Brown's Home Page  Ronald Brown, Department of Mathematics, University of Wales, Bangor (UK)
An explanatory paper on higher dimensional group theory; Brown's publications list; preprints/reprints (PostScript); articles on popularisation and teaching, such as "What is mathematics?" and "What should be the output of mathematical education?"; course
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 Ross Geoghegan
A mathematician at the State University of New York at Binghamton interested in topology, geometric group theory, fixed point theory, and dynamics. Curriculum vitae and list of publications (some articles and preprints may be downloaded in PostScript
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 ROSSMANCHANCE.COM  Allan J. Rossman & Beth L. Chance
Workshops and presentations, publications, and current projects by the authors of the Workshop Mathematics Project textbooks. See tables of contents, instructor guides, sample syllabi and exams, and answers to activities from books in the Workshop Statistics
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 Rough math: Focusing on rogue waves at sea  Ivars Peterson  Science News Online
Ocean currents and large fields of random eddies can focus a steady ocean swell to create unusually large waves. A current or eddy field acts like an optical lens to focus the wave action, says applied mathematician Bengt Fornberg of the University of
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 Row Your Boat  Ivars Peterson (MathTrek)
Although a rowing shell with eight rowers is much larger than one with a single rower, all shells have roughly the same proportions (at least for the surface area over which the shell makes contact with water). Data from 2000meter world and Olympic championship
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 Sabermetrics  The Baseball Archive
"The search for objective knowledge about baseball." Read a primer of Bill James' findings, or David Grabiner's manifesto on Sabermetrics. Studies address minor league equivalencies ("Are minor league stats a good precictor of major league performance?"),
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 Sabernomics: Economic Thinking about Baseball  JohnCharles Bradbury
A blog on the economics in, and of, the game of baseball. Original tools and studies includes salary estimators, research on age and hitting and pitching, antitrust and Major League Baseball, attendance and winning, Barry Bonds and walks, competition
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 SABER  The World Bank Group
An open data tool that provides comparative data on education policies around the world. The Systems Approach for Better Education Results (SABER) web tool aims to help countries collect and analyze information on their education policies, benchmark themselves
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 Sampling and the Census  Ivars Peterson  Science News Online
Despite strong support from statisticians, the Census Bureau's plan to increase the use of sampling in the next census has met resistance in Congress.
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 Samuel Arbesman
Research and writings by the author of The HalfLife of Facts. As an applied mathematician and network scientist, Arbesman's delves into the science of science, nature of productivity and prosocial behavior within cities, the structure and function of
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 The Sands of Time  Troy Jones
The author uses ridges in piles of salt to model geometric concepts. This page features an article (PDF format), PowerPoint presentation, Geometer's Sketchpad file, and textbook reference for a classroom exploration of such concepts.
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 Sangaku, Japanese Temple Geometry  Tony Rothman, Princeton University
For centuries in Buddhist and Shinto shrines, Japanese have hung wooden tablets containing mathematical problems. Read PDF or PS downloads of a tutorial on the inversion method for solving Sangaku, or of the article "Japanese Temple Geometry," which first
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 Sangaku: Reflections on the Phenomenon  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of sangaku problems with Java simulations and complete solutions, preceded by an introductory article that promotes an unorthodox view point on the wonderful phenomenon of Temple Geometry.
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 The Saqquara Ostrakon  A. D. Conner
An article with background history and a new analysis: A unique 3rd Dynasty (~2600 B.C.) Egyptian artefact thought to be an architect's drawing has heen reevaluated by the author and the geometry reveals surprising results.
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 Sara Billey
Sara Billey researches combinatorics, algebra, Lie theory, algebraic geometry and probability. Her papers on these topics may be downloaded in PostScript or gzipped PostScript format. The syllabi and problem sets for her undergraduate courses, i.e.
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 Sarah Glaz
Teaching, research, books, and articles by the algebraist, ring theorist, and poet. See, in particular, the math poems of undergraduate students and Glaz's own poetry, which includes "Mathematical Modeling," "A Pantoum for the Power of Theorems," "I am
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 The SAT: Aptitude or Demographics?  Glenn Elert
A paper discussing the SAT's validity, coachability, biases, and implications, especially with respect to race and socioeconomic status.
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 Scales of Measurement  Niel Brandt
An extensive list of physical and mathematical events and objects in ascending values and orders of magnitude.
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 Scaling Up Innovative Practices in Mathematics and Science  Carpenter et al.
Download a PDF of a research report that clarifies the meaning of the phrase "learning with understanding," describes the nature of successful professional development, and outlines how to scale successful practices. The research by Thomas P. Carpenter,
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 Scheduling Random Walks  Ivars Peterson (MathTrek)
Among networked computers, some sort of software scheduler must regulate data flow, but proving that a given scheduler not only prevents conflicts but also performs its duties efficiently can be surprisingly difficult. Computer scientists have found that
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 School Wise Press
California publishers of school profiles for use in choosing schools for your children. The site also provides: educationoriented news, articles, and books; online school comparisons; an askanexpert service with a parent advocate; and editorial responses
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 Schroedinger's Cash Register  Oliver Baker  Science News Online
A discussion of the application of physics (particle physics, quantum theory, and statistical mechanics) to finance theory, with econophysicists attempting to break ground in Wall Street, and the possible underlying mathematical structure of market behavior.
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 Science Access Project  Oregon State University
A group dedicated to developing methods for making science, math, and engineering information accessible to people with print disabilities. Includes braille representations of mathematical notation, and other resources for blind students.
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 Science and Mathematics Education: Similarities and Differences  Lynn Arthur Steen; St. Olaf College
Lynn Steen writes on the similarities and differences between the NCTM Standards and those of the National Research Council. Intellectually, the two communities agree on virtually all comparable aspects of their respective standards. But the nature of
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 Science Daily: Research Shows Homework Does Boost Academic Achievement; but Overemphasizing Grades and Performance May Lead to Cheating  American Psychological Association
This article, from the ScienceDaily Magazine site, describes an investigation into the effect of homework and grade emphasis on academic achievement of students and selfreported rates of cheating.
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 Science, Engineering, and Technology for Youth  eXtension
Lessons, news, articles, answers from experts, a glossary, and other science resources for young people. See especially Math in Child Care, which organizes suggestions for developing children's mathematical foundations into topics such as onetoone correspondence
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 Science News for Kids  Science Service
Science articles written for kids, along with activities for kids to try on their own and ways for kids to comment, ask questions, or submit their own work through the site. Also includes: brain teasers and Javabased games; science fiction discussions
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 Scientific American
The online version of the technology magazine, with interlinked articles, interviews with scientists, Ask the Experts, and Explorations, guided tours across the Web of recent technological developments. An archive of past articles is included.
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 Scientific Surfing for Children  Mike May, American Scientist
An early article about the World Wide Web by Mike May in the NovemberDecember issue of American Scientist, pp. 568571, discusses the world of scientific information and activities on the Internet, and forums in which professional scientists are waiting
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 ScottBeall.com  Scott Beall
Professional development programs for mathematics teaching and interdisciplinary curricula, emphasizing the integration of music and mathematics. With examples from his recent publication Functional Melodies  Finding Mathematical Relationships in Music
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 Scrambled Grids  Ivars Peterson (MathTrek)
The socalled baker's map, or transformation, in dynamical systems theory. One special case: Start with a square. Stretch it to twice its original length
while making it half as wide. Cut the result in half, and stack one half on top of the other to
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 Sculpture Generator  Ivars Peterson (MathTrek)
"Judging what a sculpture will look like after it is finished can present many difficulties for an artist just beginning a piece... Computer scientist Carlo Séquin of the University of California, Berkeley, specializes in the
computerassisted
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 Sean's Home Page  Sean Mauch
"For the past few years I have been working on an open source textbook. It contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations...." This former
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 Searching For New Mathematics  Ivars Peterson
Peterson points out that nonmathematicians interested in keeping up with contemporary mathematical research face daunting obstacles: the high level of abstraction, unenlightening notation, and the format of journal papers all conspire to make any foray
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 Search MSRI Library Catalogue  Mathematical Sciences Research Institutes
Fill in the patterns (words or word fragment) you wish to search. The pattern can be from the title, author, subject, publisher, or series.
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 Search Netlib  Netlib Repository at UTK and ORNL
Netlib is a collection of mathematical software, papers, and databases. Another Netlib search interface (which indexes the same material) is available at
http://netlib.belllabs.com/netlib/search.html. Also search the NADigest.
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 Search the UK Mirror Service  Higher Education National Software Archives
Formerly HENSA, this UK service maintains copies of electronic archives from all over the world, providing access to a wide range of uptodate software for those using PC's and microcomputers. The indexes searched allow you to find software held in any
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 Second Moment  Stone Analytics
A meeting place for academia and industry in the fields of applied statistics and analytics, showcasing cutting edge academic research. Also a resource for industry analysts and businesses interested in applying the latest statistical and analytical tools
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 Secrets of the Beehive  Keith Devlin; Guardian Unlimited Archive
The 4th century geometer Pappus was one of several ancient Greek mathematicians who suspected that the elegant shape of the honeycomb was a result not of an innate beesense of geometric beauty but of nature's efficiency. The repeating pattern of sixsided
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 Seeing Red  Keith Devlin (Devlin's Angle)
Though it is fashionable to talk about the mind as a computer, a better description is that it is a pattern former/recognizer... The problem facing the computer scientist trying to equip a computer with vision is how to simulate
this pattern creation/recognition
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 Selected Papers  Louis A. Talman
"An Unfortunate Metaphor" [the assembly line], Notices of the American Mathematical Society, 40 (1993); "Weekly Journal Entries  An Effective Tool for Teaching Mathematics," Using Writing To Teach Mathematics, MAA Notes, No. 16, Mathematical Association
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 Selected Recent Publications  George W. Hart
Areas of Hart's research and pointers to further information, including a bibliography of his publications. Links to pages on: Multidimensional Analysis; Nonintrusive Appliance Load Monitoring; Telecommunications Network Management; Viterbi Algorithm
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 Selected Technical Papers by Title  UAB Graphics and AI Laboratory (GRAIL)
Papers from GRAIL, the University of Alabama at Birmingham Department of Computer and Information Sciences center for research in computer graphics and vision. Includes: The bisector of a point and a plane parametric curve; Computing point/curve and curve/curve
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 Self Portrait at Age 13: Albrecht Durer 1484  Ralph Martel
A paper illustrated by a PowerPoint slide show to demonstrate how Albrecht Durer used geometry in his art work from the age of thirteen. This paper by Martel is one of a series that he is writing on mathematics and art. Suzanne Alejandre wrote a teaching
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