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  1. What are Fractals?
    A short description of fractals, with illustrations. ...more>>

  2. What Can Mathematics Do For The Businessperson? - Keith Devlin (Devlin's Angle)
    In business, the ability to dig beneath the surface of a problem to see what the real underlying issues are, and the capacity for clear and logical thought, can be extremely valuable. And learning mathematics provides an excellent way to develop that ...more>>

  3. What Color Is My Hat? - Math Forum, Ask Dr. Math Common Question
    A selection of answers to questions about which person wears which hat, such as "Three students close their eyes, and the teacher puts a hat on each of their heads (hiding the other two hats)...." ...more>>

  4. What Does It Take to Be an Expert Problem Solver? - Annie and John Selden; Mathematical Association of America
    Organized into five sections: Expert-Novice Studies Have Often Concentrated on Textbook Problems; Solving Nonroutine Problems; Are Mathematicians Expert Problem Solvers? How Might One Teach Problem Solving? and The Importance of Affect. From the MAA's ...more>>

  5. What do we know about mathematics curricula? - Alan Schoenfeld, Journal of Mathematical Behavior
    In the absence of either large-scale empirical proof of success or the existence of compelling and documentable standards, there is reason to be cautious. The traditionalists are nervous for good reason. It should be noted, however, that the resistance ...more>>

  6. What, How, and the Web - Cut the Knot!, Alexander Bogomolny
    More on place value. "There is an obvious confusion there between two questions, what to teach and how to teach it. Does the failure of the New Math to present a specific topic necessarily imply that teaching this topic has no merit? The New Math has ...more>>

  7. What is a Fractal? - Alan Beck; Glyphs
    The word "fractal" was coined less than twenty years ago by Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision. Mandelbrot derived the term "fractal" from the Latin verb frangere, ...more>>

  8. What is a Fractal? - Sarah Seastone, Math Forum
    A short description (with illustrations of the Mandelbrot Set) of fractals, paraphrased from Chapter 1, "A Mathematical and Historical Tour," of Robert Devaney's book, A First Course in Chaotic Dynamic Systems. ...more>>

  9. What is Chaos? - Matthew A. Trump; University of Texas at Austin
    An interactive online physics course for everyone: a 5-part nontechnical introduction to physics and chaotic motion in classical and quantum mechanics. Contents include: The Philosophy of Determinism (every cause has a unique effect, and vice versa); ...more>>

  10. whatis?com - Glossary of Internet Terms
    An annotated glossary of Internet terminology, from abacus, aliasing, Altavista, and avator to z-coordinates and zipping. Also The Top Twenty (last week's most frequently consulted words); Books you like; phone numbers; and Every file format in the world, ...more>>

  11. What is Go? - Mindy McAdams
    An introducation to the 4,000 year old Chinese board game called Go in Japan, Baduk in Korea, and Wei-chi in China. Teaching materials and links to many of the most popular Go websites are included. Contents: brief history of the game; professional players, ...more>>

  12. 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. ...more>>

  13. 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?" ...more>>

  14. What is Math? - Field Cady
    Blog of "mini-essays 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, ...more>>

  15. 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. ...more>>

  16. 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 ...more>>

  17. 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 ...more>>

  18. 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 ...more>>

  19. What on Earth is a Logarithm? - Peter Alfeld, University of Utah
    An understanding-based 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. ...more>>

  20. 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 ...more>>

  21. 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. ...more>>

  22. What's Noteworthy on Learners, Learning & Schooling - Mid-continent 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." ...more>>

  23. 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 color-coordinated by that property's category. ...more>>

  24. What's the City Mileage of a Typical American Car? (MSTE) - Ed Malczewski; University of Illinois at Urbana-Champaign (UIUC)
    Analyze the data and find an average for the mileages of American cars. A problem like this can sometimes involve difficult and time-consuming statistical analyses, but in this lesson you will explore a method of analysis called the bootstrap that will ...more>>

  25. 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. ...more>>

  26. 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 ...more>>

  27. 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 ...more>>

  28. 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 ...more>>

  29. 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 Donít Add Up," "Math Worth Doing," and "Inventing Facts," as well as an appendix entitled "The Hard Evidence: Math Results." ...more>>

  30. 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 ...more>>

  31. Whelk-Come to Mathematics: Using Rational Functions to Investigate the Behavior of Northwestern Crows (i-Math Investigations) - Illuminations; National Council of Teachers of Mathematics (NCTM)
    An online, interactive, multimedia math investigation in which students use rational functions to explore the possible reasons behind the observation that northwestern crows consistently drop a type of mollusk called a whelk from a height of 5 meters. ...more>>

  32. 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, ...more>>

  33. When Is Easter? - Jim Loy
    "Easter is my favorite holiday, because of the bizarre way in which its date is determined. When is Easter? Here is how you can answer that question..." (Easter is the next Sunday, after the Paschal Moon date.) ...more>>

  34. 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 CD-ROM. ...more>>

  35. 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 ...more>>

  36. 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. ...more>>

  37. 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 ...more>>

  38. 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? ...more>>

  39. 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 ...more>>

  40. 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 ...more>>

  41. 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 ...more>>

  42. 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. ...more>>

  43. Whips and Dinosaur Tails - Ivars Peterson (MathTrek)
    The loud crack of a deftly flicked bullwhip is a small sonic boom, generated when the whipís thin, highly flexible tip exceeds the speed of sound. Sauropod dinosaurs of the family Diplodocidae have enormous tails that gradually narrow to thin, delicate ...more>>

  44. 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, ...more>>

  45. 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 ...more>>

  46. Wholemovement - Bradford Hansen-Smith
    Bradford Hansen-Smith 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. ...more>>

  47. Who Likes Homework
    Tutors and homework helpers in math, chemistry, physics and more. ...more>>

  48. 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. ...more>>

  49. Who's Really Ahead? - Ivars Peterson (MathTrek)
    The winding down of the current baseball season seems an appropriate time to take a look at a curious inconsistency that sometimes appears in team standings... Once in a while the team with the higher winning percentage may be at least one-half a game ...more>>

  50. Who's Really No. 1? - Ivars Peterson (MathTrek)
    It happens every fall. Fierce arguments erupt over which U.S. college football team is the best in the nation. As the season progresses, this frenzy of head scratching and navel gazing mounts until the climactic bowl games at the end of the year (more ...more>>

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