 What is Mathematics: Goedel's Theorem and Around  Karlis Podnieks
An extended translation of Podnieks' book, published in 1992 in Russian. Contents include: Platonism, intuition and the nature of mathematics; Axiomatic set theory; First order arithmetic; Hilbert's Tenth problem; Incompleteness theorems; Around Goedel's
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 What Is Mathematics?  John M. Lawler, Dept. of Linguistics, Univ. of Michigan
Listings of links on Godel, Escher, and Bach, and other material related to Hofstadter's book by that name, from a math appreciation course.
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 What is Mathematics?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about what mathematics is, such as "Is math a science, an art, or some other anomaly?" and "Is there a difference between arithmetic and mathematics, and what is it?" and "Is math a science or an art?"
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 What is Math?  Field Cady
Blog of "miniessays about the history and nature of math, and how it fits into the spectrum of human activity," by an applied mathematician and algorithm developer who specializes in statistics and "big data" analytics and statistical modeling. Posts,
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 What is Mod?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about modular arithmetic, including the method of casting out nines.
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 What Is Scientific Notation And How Is It Used?  R. H. Logan, Instructor of Chemistry, El Centro College
A scientific notation lesson that explains how to use scientific notation for: Numbers Greater Than 10; Numbers Less Than One; Numbers between 1 and 10; Division of Exponentially Notated Numbers; Addition and Subtraction Using Exponential Notation. Includes
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 What is the best way to lace your shoes?  Burkard Polster, Nature
"The two most popular ways to lace shoes have historically been to use 'crisscross' or 'straight' lacing  but are these the most efficient? Here we demonstrate mathematically that the shortest lacing is neither of these, but instead is a rarely used
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 What Is the Collaborative Classroom? (NCREL)  M.B. Tinzmann, B.F. Jones, T.F. Fennimore, J. Bakker, C. Fine, and J. Pierce
New learning and thinking curricula require collaboration. An article that addresses shared knowledge and authority among teachers and students; teachers as mediators; heterogeneous groupings of students; teacher and student roles; interactions; challenges
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 What Is Your Answer to That Question?  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
The question  Why study mathematics?  appears in a multitude of guises and a plethora of variants... Mathematics is often compared to art. Like literature, mathematics has metaphor, ambiguity, paradox, and mystery. It has history. Mathematics has contributed
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 What kind of math? Photo Challenge  Kathryn Mann
Pictures of math graduate students with wordbubbles showing "the kind of math that's right" for them. Submit your own group snapshots and subfields. Inspired by an observation that a flyer from the American Mathematical Society (AMS) reinforced sexist
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 What Moves U Campaign  American Heart Association; National Football League (NFL)
A national campaign to inspire middle school students to become more physically active. What Moves U provides curriculumbased activity sheets that can be incorporated into lesson plans for 5 core subjects: math, science, social studies, language arts,
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 What on Earth is a Logarithm?  Peter Alfeld, University of Utah
An understandingbased approach to powers and logarithms, with a link to a special example: how to convert a logarithm with respect to one base to a logarithm with respect to another base; and a Java applet logarithm calculator.
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 What's Going On During Mathematics Awareness Month  Keith Devlin (Devlin's Angle)
"This year's theme is mathematics and biology. Two important examples of how mathematics is used in biology are: in developing computer models of the human heart, which are helping us to understand how the heart works and, more importantly, how it goes
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 What Should I Look For in a Math Classroom?  Mathematical Sciences Education Board (MSEB)
A set of practical guidelines, with explanations of their relevance. From the Mathematical Sciences Education Board of the National Research Council.
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 What's My Area? (SMILE)  Karen L. Mickel, William Carter Elementary School
An elementary lesson designed to teach students to cover an area with uniform tiles and count the number of tiles needed; recognize rectangles, triangles and squares; and review basic colors. From the Geometry and Measurement section of a collection of
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 What's New at the Zoo?  Suzanne Slade, Joan Waites (ill.)
A picture book featuring counting and animal facts. Book available in hardcover, paperback, and eBook. Free educational resources on the Sylvan Dell website include Teaching Activities, Math/Reading Comprehension Quizzes, Related Website Links, and English
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 What's New  Terence Tao, UCLA
Updates on Tao's research and expository papers, discussion of open problems, and other mathsrelated topics. Blog posts, which date to February, 2007, have included "Riemannian manifolds and curvature" and "Sailing into the wind, or faster than the wind"
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 What's Noteworthy on Learners, Learning & Schooling  Midcontinent Regional Educational Laboratory (McREL)
"The major challenges for educational reform today are putting the pieces together to create sustainable systemic change and scaling up systemic reform to encompass all schools, all programmatic areas, all levels of schooling and diverse social contexts."
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 What's Sophisticated about Elementary Mathematics?  HungHsi Wu
"The characteristics of coherence, precision, and reasoning are not just niceties; they are a prerequisite to making school mathematics learnable." In this American Educator article originally published Fall, 2009, the author goes on to unpack whole number
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 What's Special About This Number?  Erich's Puzzle Palace; Erich Friedman
A list of the integers from zero to 9,999, each annotated with one significant mathematical property and colorcoordinated by that property's category.
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 What's the City Mileage of a Typical American Car? (MSTE)  Ed Malczewski; University of Illinois at UrbanaChampaign (UIUC)
Analyze the data and find an average for the mileages of American cars. A
problem like this can sometimes involve difficult and timeconsuming statistical analyses, but in this lesson you will explore a method of analysis called the bootstrap that will
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 What's the Problem? Geometry & Art through the Ages  Indianapolis Museum of Art
An exhibit exploring how some artists have used geometry as a creative tool. The site is divided into three topics: lines, polygons, and volume. Also provided as links from the left sidebar are a glossary and a list of references for further reading.
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 what's your favourite number?  Alex Bellos
Enter your favorite number and the reasons for your choice. Part of a research project concerning how humans relate to numbers, this international survey is being conducted by Alex Bellos, author of Alex's Adventures in Numberland and Here's Looking At
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 What the Heck are Logarithms?  William Park
A paper designed to help college freshmen develop an intuitive understanding of what logarithms are and how to use them. Problems to be worked without using a calculator.
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 What the Media Look for in a Math Story  Kathleen Holmay
A summary of comments by Shirish Date, Reporter, Orlando Sentinel; Samantha Eaddy, Public Information Officer, U. of Central Florida; and Keith Devlin, Saint Mary's College, Moraga, CA. A discussion organized by Richard H. Herman and Kathleen Holmay of
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 What Will Be the Effect of a Standardsbased Education on College Students?  Judith Roitman
This article, by Judith Roitman of the University of Kansas, appeared in the April 1995 FOCUS, the newsletter of the MAA. Among other things, Roitman discusses the need for dialog between K12 teachers and their college counterparts, and difficulties
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 What Work Requires of Schools  Secretary's Commission on Achieving Necessary Skills (SCANS)
The Secretary's Commission on Achieving Necessary Skills (SCANS) was asked to examine the demands of the workplace and whether today's young people are capable of meeting those demands as they enter employment. In carrying out this charge, the Commission
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 What Works Better than Traditional Math Instruction  Alfie Kohn
Chapter 9 from Kohn's 1999 book The Schools Our Children Deserve contains the subsections "Why the Basics Just Don’t Add Up," "Math Worth Doing," and "Inventing Facts," as well as an appendix entitled "The Hard Evidence: Math Results."
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 What Works Clearinghouse
Reviews of the effectiveness of educational intervention programs, products, practices, and policies. Among other curricula, the WWC has reviewed studies of the Middle School Math Curricula interventions Cognitive Tutor, Compass Learning, Connected Mathematics
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 When Am I Going to Use This?  Column Five Media
This graphic plots popular career choices on axes of "number of math concepts" and "median average salary" to illustrate the basic math, algebra, geometry, or trigonometry required of athletes, cosmetologists, carpenters, pilots, psychologists, lawyers,
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 When mathematics has to be theater  Keith Devlin (Devlin's Angle)
A mathematician's entry into the world of commercial multimedia  the creation of an interactive calculus textbook on CDROM.
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 When mathematics is plain sailing  Keith Devlin (Devlin's Angle)
In the ocean waters off New Zealand, an intense mathematical olympiad has just begun: The America's Cup  a yacht race, the premier international event in
ocean sailing. Competition is fierce. The technical challenges are enormous. And the costs are
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 When The Counting Gets Tough, The Tough Count On Mathematics  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A discussion by William A. McWorter, Jr. of the application of the recursion formula for the Fibonacci sequence to counting and vector problems.
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 Where to Start?  Cut the Knot!, Alexander Bogomolny
A discussion of math education: the intent of the NCTM Standards, reflections on the history of constructivism, classroom practices (with a link to Marilyn Burns' Math Solutions page), and a simple applet for solving linear equations. An interactive column
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 Where Will the New Millennium Begin? (Math Chat)  Frank Morgan; Christian Science Monitor
Assuming the third millennium arrives on January 1, 2001, where on Earth should the celebration begin?
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 Which Countries Are Most Like Stars? (Math Chat)  Frank Morgan, MAA Online
Which countries in the world have a point such that the shortest line from
every other point in the country stays inside the country? (ignore mountains and valleys). Mathematicians call such countries starlike. Are there any countries such that the shortest
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 Which One Doesn't Belong?  Mary Bourassa
Also known as Imposter Sets, "Which One Doesn't Belong?" provides thoughtprovoking puzzles, each with many different, correct ways of identifying the exceptional shape, number, graph, or equation from the colorful 2 × 2 grid of similar ones.
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 Which One Is Older? (Math Chat)  Frank Morgan, MAA Online
Creative solutions to the challenge: how can two people determine which is older without revealing their ages? Math videos available from the Mathematical Sciences Research Institute via the MAA. "Mathematics in Arcadia," "Fermat's Last Theorem," as seen
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 Which Polygon Sides are Parallel?  NASA Lewis Learning Technologies Project
Which of these line segments are parallel? Two adjacent sides of a triangle; Two adjacent sides of a pentagon; Two opposite sides of a rectangle; Two radii of a circle. A diagram and a detailed answer are provided. From NASA's 9th Grade Math Proficiency
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 Which Problem Equals 25 Percent?  NASA Lewis Learning Technologies Project
Which problem has an answer of 25 percent? 1) 10 is what percent of 50? 2) 25 is what percent of 75? 3) 25 is what percent of 125? 4) 20 is what percent of 80? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Whips and Dinosaur Tails  Ivars Peterson (MathTrek)
The loud crack of a deftly flicked bullwhip is a small sonic boom, generated when the whip’s thin, highly flexible tip exceeds the speed of sound. Sauropod dinosaurs of the family Diplodocidae have enormous tails that gradually narrow to thin, delicate
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 Whistler Alley Mathematics  Paul Kunkel
Kunkel's Geometer's Sketchpad lessons convey a conceptual understanding, usually without rigorous proof, with questions and suggestions for extensions: Buffon's Needle (an old probability exercise); Chinese Handcuffs (questions with applications for geometry,
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 White Group H2 Maths Tuition  Koh Y.S. Frederick
This Singaporean tutor offers examination advice and recommendations ("A level H2 maths question spotting thoughts"), a section for those "pursuing mathematics beyond the Singapore H2 9740 standard," and a "question locker" for students who "wish to challenge
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 White Narcissus  Ivars Peterson (MathTrek)
The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical
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 WhizGraph  a program for data analysis and graphic presentation on your Mac  Hans Timm
WhizGraph is a data analysis and graphic presentation shareware program for the Macintosh. It combines professional graphing and versatile layout options with clear data management and comfortable macro calculation. The website provides more specifications,
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 Whole Language Approach in Solving Word Problems (SMILE)  Barbara Thomas, Langston Hughes School
A lesson that uses the story of the Three Little Pigs to teach students to formulate addition and subtraction problems of whole numbers; relate everyday language to mathematics meaningfully; use problemsolving approaches to investigate and understand
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 Wholemovement  Bradford HansenSmith
Bradford HansenSmith presents the art and geometry of folding circles. As he explains, "Everything we know about geometry, mathematics, and all spatial arrangement and organization of matter is demonstrated by cutting into the wholeness of the sphere.
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 Whole number arithmetic  Martin Selditch
A tutorial that covers basic arithmetic with whole numbers. Exercises allow students to practice arithmetic skills.
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 Who Likes Homework
Tutors and homework helpers in math, chemistry, physics and more.
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 Who's Counting  John Allen Paulos
Columns by Prof. John Allen Paulos, the author of Innumeracy, Mathematician Reads a Newspaper, and other popular books. Humorous and enjoyable articles by a keen observer of the world around him whose mind has been sharpened by mathematical practice.
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