 What do we know about mathematics curricula?  Alan Schoenfeld, Journal of Mathematical Behavior
In the absence of either largescale 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
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 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
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 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,
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 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.
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 What is Chaos?  Matthew A. Trump; University of Texas at Austin
An interactive online physics course for everyone: a 5part 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);
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 whatis?com  Glossary of Internet Terms
An annotated glossary of Internet terminology, from abacus, aliasing, Altavista, and avator to zcoordinates 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,
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 What is Go?  Mindy McAdams
An introducation to the 4,000 year old Chinese board game called Go in Japan, Baduk in Korea, and Weichi in China. Teaching materials and links to many of the most popular Go websites are included. Contents: brief history of the game; professional players,
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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 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 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 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 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 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 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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 Wheeler's Thoughts on Teaching  Laura Wheeler
Blog by a Canadian high school teacher in Ottawa, Ontario. Posts, which date back to October, 2012, have included "Assessment & Evaluation in the OCDSB"; "BYOD Classroom Management"; "Quadratic Visual Patterns #3actmath #MFM2P with Linking Cubes"; "When
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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 Math Happens  Dane Ehlert
A Texas high school teacher's blog of 3 Act Math, estimation, and other lessons, each with alignments to the Common Core and TEKS. Posts, which date back to May, 2012, have included "How To Praise Students," "Exponential Functions ReEngage," "Paul Sturgess,"
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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 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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 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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 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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 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 onehalf a game
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 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
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 Who Wants to Be a Mathematician  American Mathematical Society
In the game show "Who Wants to Be a Mathematician," high school students compete for cash and prizes by answering multiple choice mathematics questions. Read about past performances of the game; view videos of games played in Danvers, MA, at Danvers High
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 Who Wants to be a Millionaire? (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: On ABC TV's "Who Wants to be a Millionaire," to maximize your expected winnings how sure should you be of your answer to the $500,000 question to answer? Somewhere from about 22.5% to about 46.5%, probably closer to the latter.
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 Who was Marin Mersenne?  Luther Welsh
It was not until the mid 20th century that Mersenne became known primarily for his Prime Number Conjecture. Historically, he was much better known for his correspondence with leading scientists of the day. Interested in optics, he also been called the
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