 The Art of Asking Thought Provoking Questions in the Mathematics Classroom  Carmen Bellido, Uroyoan Walker, Keith Wayland
A position paper in PDF format: a "How To" guide for developing higherlevel conceptual questions that provoke students to think. Several techniques for modifying traditional questions are illustrated with examples ranging from elementary to high school
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 The Art of Calculating Real 2D Vectors  Hero van Jindelt
Freeware: Print the text for pupils. Numerical 2Dcalculator. We don't need
words like imaginary, complex number, or Argand Diagram any moresave them
for a history lesson. Ordinary vectorcalculation with a "new" (centuriesold) multiplication,
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 The Art of Renaissance Science: Galileo and Perspective  Joseph W. Dauben, McMurry University
A hypermedia essay devoted to the genius of Galileo and the relation between his role in the Scientific Revolution and the equally remarkable achievements of Renaissance artists reflected, in part, in the discovery and application of mathematical perpective.
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 Art of the Grid  Ivars Peterson (MathTrek)
The idea of transferring information from one grid to another has a long history inboth mathematics and art. When the blank grid differs from the original grid, a drawing can suffer intriguing distortions. In art, the result is sometimes called an anamorphic
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 Art of the Tetrahedron  Ivars Peterson (MathTrek)
"Any four points in space that are not all on the same plane mark the corners of four triangles. The triangles in turn are the faces of a tetrahedron. It's the simplest of all polyhedrasolids bounded by polygons... To sculptor Arthur Silverman of New
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 The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue  Koekoek, Swarttouw; Delft University of Technology
A 1998 report: definition, orthogonality relation, threeterm recurrence relation, second order differential or difference equation, forward and backward shift operator, Rodriguestype formula and generating functions of all classes of orthogonal polynomials;
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 Assessing True Academic Success: The Next Frontier of Reform  Dan Kennedy, Baylor School
Article from Mathematics Teacher 92, 46266, September 1999. "Suppose that your doctor's idea of a successful medical practice is to teach his patients how to pass every diagnostic test that he gives to them. How will you ever know if you are healthy?
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 Assessment  Classroom Compass
The spring 1996 issue of Classroom Compass examines assessment as an integral part of the learning cycle. One activity, Thinking Aloud About Mathematics, provides an innovative idea for assessing student learning in a high school mathematics classroom.
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 Assessment in Mathematics Teaching  Mathematics Education at The Math Forum
The Math Forum's suggested sites on assessment in mathematics education including the NCTM Standards; sessions on assessment at meetings; and selected books and articles on assessment.
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 Association for Advancement of Computers in Education (AACE)
A searchable site, with divisions/societies/chapters; major journals; The AACE listserv, EDUCTECH; Educational Technology Review (the Association member periodical); special publications; and conferences with workshops, and proceedings devoted to advancing
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 Association for Supervision and Curriculum Development (ASCD)
A site designed to provide relevant and current educational resources to members, with an emphasis on ASCD materials and sources of international and federal government information, in particular state and local government sources. Also a forum for worldwide
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 Association for Symbolic Logic
The Association for Symbolic Logic (ASL) is an international organization supporting the presentation, publication, and critical discussion of scholarly work in the field of logic. Its current membership reflects the longstanding important role of logic
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 Astronomy and Astrophysics  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to astronomy and astrophysics: as celestial mechanics is, mathematically, part of Mechanics of Particles, the principal applications in this area appear to concern the structure, evolution, and interaction
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A Supplemental Introduction to Algebra  Rick Garlikov
Some things algebra books don't tend to tell students, but which Garlikov thinks are important for them to know so that they can understand what algebra is about and see, in a sense, how it works. Also The Way Algebra Works.
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 Automated Deduction  William McCune
Research on applications of automated deduction to problems in abstract algebra and algebraic geometry, algorithms and strategies for searching for proofs and for counterexamples, highperformance implementation of automated deduction algorithms, and
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 "Average" Temperature (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: The National Weather Service approximates the daily average temperature by the average of the daily high and low temperatures. Why is this such a good approximation? Mathematically, the approximation is good because Earth's warming
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 Averting Instant Insanity  Ivars Peterson (MathTrek)
Once called "The Great Tantalizer," the puzzle looks innocuous and sounds quite simple. It consists of a set of four cubes with one of four colors on each of their six faces. Your goal is to arrange the four cubes in a row so that all four colors appear
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 Aviezri Fraenkel
Aviezri Fraenkel is an Israeli mathematician investigating combinatorial game theory. This page offers preprints and recent reprints in postscript format; a comprehensive bibliography on combinatorial games; and links to information on conferences and
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 Axiom (Encarta Encyclopedia 2000)  Robert M. Baird; Microsoft Encarta Online
Axiom, in logic and mathematics, a basic principle that is assumed to be true without proof. The use of axioms in mathematics stems from the ancient Greeks, most probably during the 5th century BC, and represents the beginnings of pure mathematics as
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 The Aztec Calendar: Math, Geometry, and Design  Charles William Johnson
A site that explores the relation between the mathematics of ancient reckoning systems, expressed in historically significant numbers (cited in the historical record), and designs within the geometry of ancient artwork. The complexity of design within
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 Azulejos Que Ensinam  Museu Nacional de Machado de Castro
Catálago sobre uma coleção de azulejos que mostram Os Elementos de Euclides e otras figuras de matemáticas.
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 Babylonian and Egyptian Mathematics  MacTutor Math History Archives
Linked essay describing the character and accomplishments of these two early mathematical systems, with references and other related web sites.
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 Babylonian numerals  MacTutor Math History Archives
Linked essay exploring the development of the Babylonians' number system, with ideas inherited from the Sumerians and the Akkadians. From them came base 60, or the sexagesimal system, but neither the Sumerian nor the Akkadian system was a positional system
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 The Bakhshali manuscript  MacTutor Math History Archives
Linked essay on the discovery and history of an early mathematical manuscript. The Bakhshali Manuscript is a mathematical work written on birch bark, found in the summer of 1881 near the village Bakhshali in Mardan tahsil, 50 miles from the city of Peshawar
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 Balanced Assessment in Mathematics  The Concord Consortium
From 1993 to 2003, the Balanced Assessment in Mathematics Program existed at the Harvard Graduate School of Education. The project group developed a large collection of innovative mathematics assessment tasks for grades K to 12, and trained teachers to
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 Balducci's Actuarial Home Page  David P.M. Scollnik; Dept. of Mathematics and Statistics, Univ. of Calgary
Links to popular actuarial resources: Balducci's List of Actuarial, Risk, and Insurance Links; Actuaries ( with Home Pages ) on the Web; Actuarial Programs in Academia; Actuarial ( Statistical ) Research Papers. Also information relating to actuarial
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 Barcode Encoding  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Barcodes are used with various encodings all over the world to simplify product identification, especially in retail. The site explains the most popular encodings, like UPC (Universal Product Code), ISBN (Intenational Standard Book Number), and EAN13
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 Barry Garelick, Author at Education News  EducationNews
Articles by Garelick, who teaches middle and high school math in California, have included "The Myth About Traditional Math Education," "Fran, Henderson & Pingry, and Me: A Tale of Problems vs Exercises," "Mathematics Education: Being Outwitted by Stupidity,"
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 Bartlett Corrections  F. CribariNeto
Introduction to and compilation of resources on Bartlett corrections: scalar transformations "applied to the likelihood ratio (LR) statistic that yields a new, improved test statistic which has a chisquared null distribution to order O(1/n). This represents
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 Base Considerations  Keith Devlin (Devlin's Angle)
A discussion of base systems, including negative bases, used in computers. "We are so used to computers nowadays that it seems obvious that computer arithmetic should be performed in a binary fashion. After all, this is the most natural form for a computer,
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 BaseGroup Labs  data analysis, forecasting, free analytical components
A commercial software company that creates systems for information analysis and forecasting, and develops custom integrated circuits. The site offers scientific articles concerning data analysisneural nets, selforganizing maps, filtration, decision
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 The Battle of The Frog and The Mouse  John Hays
In the 1920s, Albert Einstein heard of a Foundational debate between Formalist
David Hilbert and Intuitionist L.E.J. Brouwer, and asked: "What is this frog and mouse battle between the mathematicians?" This fable presents Brouwer as the frog, Hilbert
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 Beeneet Kothari Wins First $1000 National High School Calculus Student Award (Math Chat)  Frank Morgan, MAA Online
Beeneet Kothari of Half Hollow Hills High School West, Long Island, has been awarded the first $1000 National High School Calculus Student Award by ecalculus.org, based at the University of California at Davis and Williams College. In ninth grade he wrote
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 ... Before This Decade Is Out ...  Keith Devlin (Devlin's Angle)
With four thousand professionally active mathematicians gathered together, the January Joint Meeting provides an opportunity to check the pulse of the US mathematical community and to look for any significant new trends... "Make the preparation of K12
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 The Beginnings of Set Theory  MacTutor Math History Archives
Linked essay describing the rise of set theory from Cantor (with discussion of earlier contributions) through the first half of the 20th century, with another web site and 25 references (books/articles).
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 Behind the Numbers  Jonathan Sills; ESPN SportsZone
A monthly column that explores the gray area between math and sports and what happens when exact calculations meet the human, unpredictable factors that make sports so entertaining. A combinatoric and probabilistic analysis of changes in World Cup soccer
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 Benchmarks for Optimization Software  Mittelmann, Spellucci
I: Several codes, one computer  linear and quadratic programming; quadratically constrained quadratic programming; geometric programming; boundconstrained nonlinear programming; nonlinear programming; largescale nonlinear system benchmark; benchmarks
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 The Benefits of MixedAge Grouping (ERIC Digest)  Lilian G. Katz
"Goodlad and Anderson, who introduced the modern notion of the nongraded elementary school in 1959, raised our awareness of the fact that age is a crude indicator of what learning experiences children are ready for... The terms 'ungraded' and 'nongraded'
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 The Benezet Centre  Richard Hake & Sanjoy Mahajan
In 1929, Louis Benezet tried an experiment, "abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite." The experiment was successful; this site includes Benezet's
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 Bernhard Kutzler's Collection: Technology in Mathematics Education  Bernhard Kutzler
Read or download the author's articles: "Algebraic Calculators as Pedagogical Tools for Teaching Mathematics"; "Indispensable Manual Calculation Skills in a CAS Environment"; "TwoTier Exams as a Way to Let Technology in"; and "Interconnectivity  Derive
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 The Bertrand Russell Editorial Project  McMaster University
These archives, at McMaster University, house the complete papers of Bertrand Russell (18721970), British Philosopher, logician, essayist and renowned peace advocate. His Collected Papers include logical and philosophical works, Toward the "Principles
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 Bessel, Friedrich Wilhelm (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
A short biography of Friedrich Wilhelm Bessel (17841846), the German astronomer and mathematician, best known for making the first accurate measurement of the distance to a star.
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 The Best Two Points in a Square (Math Chat)  Frank Morgan, MAA Online
Solution to the challenge: Where do you think you should you place two points in a unit square to minimize the average distance in the square to the nearest of the two points? Computer calculations by Al Zimmermann yield configurations of 211 points
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 The Better File Cabinet  Eric Hsu
A database of nonroutine calculus problems used in college workshops for Uri Treisman's Emerging Scholars Programs. It was originally a highly searchable database of calculus problems, comments and solutions. It will eventually will be a database crossreferencing
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 Between Arithmetic and Algebra  Cut the Knot!, Alexander Bogomolny
What is the difference between the arithmetic 3+5 = 5+3 and the algebraic a+b = b+c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives expression
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 Between Arithmetic and Algebra  Cut the Knot!, Alexander Bogomolny
What is the difference between the arithmetic 3 + 5 = 5 + 3 and the algebraic a + b = b + c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives
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 Beyond Extra Large (and Ultra Small)  Ivars Peterson (MathTrek)
Metric prefixes come in handy for expressing both large and small quantities. So we have megawatt power systems and gigabyte hard drives at the high end, and we have nanoscale electronics and femtosecond lasers at the low end. Advances in scientific research
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 Beyond the Block: Tessellating Patterns  Linda Hampton Schiffer
An article about using tessellations in quilt design.
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 Beyond the Ellipse  Ivars Peterson (MathLand)
There's a simple trick one can use to draw an ellipse. Tie the ends of a length of string to two pins (or thumbtacks) stuck in a sheet of paper on a drawing board. Then, keeping the string taut with the point of a pencil, allow the pencil to trace a path
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 Beyond the IndividualSocial Antimony in Discussions of Piaget and Vygotsky  Cole, Wertsch
A discussion of the ongoing debate about the relation between the ideas of Vygotsky and Piaget, emphasizing a cardinal difference between them: their views concerning the importance of culture, in particular, the role of mediation of action through artifacts,
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