examples of math trivias?

Question

examples of math trivias especially more on algebra

Answer 1

I don't understand. Can you be more specific?

Answer 2

One example of a math trivia is this question:

The expression x^2 + 7x + 3 has the same remainder whether divided by x-p or x+p, where p is not equal to -q. Find the value of p-q.

Solution:
Let f(x) = x^2 + 7x + 3
So, f(p) = p^2 + 7p + 3
And, f(-q) = q^2 - 7q + 3
Since f(p) = f(-q), then
p^2 + 7p + 3 = q^2 - 7q + 3
p^2 + 7p = q^2 - 7q
p^2 - q^2 + 7p + 7q = 0
(p+q)(p-q) + 7(p+q) = 0
(p+q)(p-q+7) = 0
Since p + q is not equal to 0, then
p - q + 7 = 0
Therefore p - q = -7

Answer 3

Merrill Algebra 2 With Trigonometry Answers

Answer 4

351

Answer 5

How much does a gallon of water weigh? E+ MCsquared= all of the energy in the universe= all of the mass of the universe x the speed of light squared

Answer 6

log2 simplified examples dummies. math trivia of algebra. new technics in learning algebra ... examples of math trivia. algebra textbook answers ...www.softmath.com/algebra_stats/artin-algebra-solutions.html
Mathematics
Last updated and all links checked July 31, 2002.

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1. Amy's Math Activities
http://teams.lacoe.edu/documentation/classrooms/amy/amy.html

Number concepts, algrbram and geometry activities and Web sites for K-8 grades.

2. Math Explorer and Explorer Plus Activities for Middle School Math
http://www.comcal.net/www.ti.com/calc/docs/actexpmidd.htm

Activities for the Texas Instruments calculator: divisibility rules; number patterns; irrational numbers; place value; improper fractions and mixed numbers, etc.

3. Mathematics Standards of Learning for Virginia Public Schools
http://www.pen.k12.va.us/VDOE/Instruction/wmstds/math.shtml#table

Standards and activities by grade level from kindergarden through high school.

4. House of Math Word Problems for Children
http://www.mathstories.com/

Help grade school children improve their math problem-solving and critical thinking skills. It has over 4000 math word problems for children to enjoy! This site is completely free to all parents, students and teachers.

5. Middle School Geometry interactive Web sites
http://www.ies.co.jp/math/java/geo/index.html

Angles and Pararell Lines;Congruent Figures and Triangles; Quadrilaterals and Conservation of Area; Similar Figures; Circles; Pythagorean Theorem; Miscellaneous.

6. Homework Help
http://www.math.com/students/homeworkhelp.html

Pre-algebra, algrbra, and geometry help and practice quizes.

7. Harcourt Math Glossary
http://www.hbschool.com/menus/math.html

Glossary with illustrated and some animated definitions. Divided into grades 1 - 8.

8. Harcourt Math Manu
http://www.hbschool.com/menus/l_math.html

Web-based examples from their commercial collection of math activities for grades 1 - 8.

9. Learning Planet
http://www.learningplanet.com/

Slick animated K-6 math practice activities and games.

10. Angle Activities
http://www.ambleside.schoolzone.co.uk/ambleweb/numeracy.htm

Interactive activities measuring angles with a virtual protractor.

11. Virtual World Globe and Database
http://www.amiglobe.com/

Shareware interactive world globe and database. Up-to-date world map may displayed as a globe or in several projections. Extensive database on most countries, facilitates graphing to compare data. Measures distance between any two points on map.




12. Change Maker
http://www.funbrain.com/cashreg/

Interactive Web site that uses a game format to practice making change. Students have to figure out how many of each bill or coin that you expect to get back when you pay for something. Shows the money graphically in your choice of national currencies.

13. Gus and Gertie's Graphin' Gadget
http://www.somewareinvt.com/gusandgertie.htm

Simple but versatile program for plotting functions.

14. MathCurve
http://mathcurve.cjb.net/

Nice shareware 2D function plotter with a slick 3D companion program.

15. Interactive math workbook
http://www.inew.com/

Large mathematics database that is useful for practicing and sharpening various skills for the student in Kindergarten through grade 6.

16. Math puzzle games
http://www.sheppardsoftware.com/

Prime Time Math covers prime numbers, factoring, squares, cubes, remainders, fractions, percentages, algebra and most of all logic. Math Function Mania covers functions and predicion of trends. Shareware versions of both programs can be downloaded from this site.

17. Shapari, shape and pattern exploration
http://www.spelunkcomputing.com/

Produce patterns from very simple shapes and operations. A light exploration of many mathematical concepts including shape, size, count, multiplication, symmetry, transformations, periodicity, convergence, exponential growth, recursion and fractal geometry. Emphasizes abstract thinking, creativity and open-ended exploration. Ages 4 and up. Built-in instructions and demonstrations.

18. Math Worksheets
http://www.edhelper.com/math.htm

Math Worksheets Based on NCTM Standards! Basic math; mathematical sequences; Decimals; Fractions; Ratios; Percents; Measurement ; Probability; Algebra; Statistics; Trigonometry. Every time you click to create a worksheet a New worksheet is created!

19. Awesome Library
http://www.awesomelibrary.org/math.html

Mathematics lesson plans By Grade: Elementary Level; Middle-High School; Lesson Plans; Problem Solving; Multidisciplinary.

20. Math art gallery
http://www-math.sci.kun.nl/math/knopen/art_gallery.html

3D fractals; Singularity knots, Singularity knot animations, Pictures generated by vort.

21. Excel mathematics
http://www.mathtools.net/Excel/Mathematics/index.html

A collections of ideas and downloads for using the Excel spreadsheet in mathematics teaching, mostly at secondary and college level.

22. Graphing and Data Analysis with Technology Across the Curriculum
http://www.mcps.k12.md.us/departments/isa/secondary_team/agendas/Data_Analysis/data_analysis.htm

Use appropriate technologies to analyze and synthesize information to construct knowledge and meaning; Support reading and numeric literacy through data analysis; Identify features essential to constructing and interpreting graphs, charts and maps; Identify the representations and misrepresentations of data; Use a database (Excel) to create a graph.

23. Calculus WIZ
http://www.wolfram.com/wiz

Calculus WIZ is a unique study aid that allows students to concentrate on concepts, not computations. Given the correct parameters, Calculus WIZ can solve homework problems at the click of a button. The new stand-alone edition is the first in Wolfram Research's line of customized kernel products...

24. Chaos, Fractals, and Arcadia
http://math.bu.edu/DYSYS/arcadia/

An animated description of some of the mathematical ideas lurking in the background of Tom Stoppard's play "Arcadia".

25. MathReader
http://www.wolfram.com/products/mathreader

Colleagues without Mathematica can read and print your notebooks using the free MathReader utility. Updated versions of MathReader for Windows and Macintosh, plus a new version for Unix platforms, can now be downloaded...

26. Graph Paper Printer
http://perso.easynet.fr/~philimar/graphpapeng.htm

Graph Paper Printer is a software application designed to print numerous kinds of graph papers, music manuscripts and pattern papers, with user-defined sizes and colors

27. MathDork
http://www.mathdork.com/

Fee-based on-line algebra tutorials, quizzes and games using interactive animation. This self-paced educational tool helps math students in middle school and high school with algebra study and homework. $5.95 per month.

28. The KnotPlot Site
http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html

Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. You can download KnotPlot and try it on your computer.

29. Frequently Asked Questions in Mathematics
http://www.cs.unb.ca/~alopez-o/math-faq/index.html

This is a compilation of Frequently Asked Questions (and their answers) about Mathematics. Topics range from trivia and the trivial to advanced subjects such as Wiles recent proof of Fermat's Last Theorem.

30. Statistics and Statistical Graphics Resources
http://www.math.yorku.ca/SCS/StatResource.html

Annotated, topic-based collection of available resources for statistics, statistical graphics, and computation related to research, data analysis and teaching, now containing over 580 links.

31. Mathematics and its applications in engineering and science
http://links.math.rpi.edu/welcome.html

Cooperative effort by mathematicians, engineers and scientists to develop educational materials that link mathematical topics with applications in engineering and science. The primary product of this effort is a set of interactive, web-based learning modules. Includes Applet Library.

32. Teacher Change
http://change.enc.org/

A collection of resources from the Eisenhower National Clearinghouse to help educators and professional development providers facilitate discussion and reflection on improving K-12 mathematics. The materials include professional development activities, TIMSS publications, articles about teacher change, and teacher narratives.

33. Shape and Space in Geometry
http://www.learner.org/teacherslab/math/geometry/

Geometry and spatial sense, with background on why this is important and how it is addressed in the standards. Interactive web activities are included for both space and shape. For example, students use taxicab geometry in one activity, where they figure out a hidden treasure in a grid based on information given by the site. From the CPB/Annenberg Math and Science Project.

34. THE TITANIC: What Can Numbers Tell Us About Her Fatal Voyage?
http://asterix.ednet.lsu.edu/~edtech/webquest/titanic.html

Using spreadsheets, databases, and graphs, secondary students will learn statistics about the "real" Titanic's passengers and crew, exploring them from a mathematical perspective.

35. CoolMath: An amusement park of mathematics
http://coolmath.com/index.html

Fractals, computation practice, polyhedra, other interesting and fun math topics.

36. MathSurf
http://www.mathsurf.com/

Activities and teaching tips related to Addison Wesley Longman textbooks. A problem of the day for different grade levels.

37. The Perfect Number Journey
http://home1.pacific.net.sg/~novelway/MEW2/lesson1.html

Lessons on number patterns and properties of numbers. Perfect numbers are equal to the sum of all of their factors (not including the number itself).

38. Patterns in Mathematics
http://www.learner.org/teacherslab/math/patterns/index.html

Explore logic patterns, number patterns, and word patterns. In queries about the attributes of things, you'll apply reasoning to answer "what's next?" not with a number but with a description. You'll focus on how to develop "function sense" without simply asking for the next number in the pattern. And through visual and written forms of expressions, you'll connect language and mathematics to develop skills for thinking clearly, strategically, critically, and creatively.

39. Tools for Understanding
http://www.ups.edu/community/tofu/

A resource guide for extending mathematical understanding. Our target audience includes intermediate and middle-grade teachers (particularly those who teach remedial math classes) and secondary special educators. While much of this site focuses on mathematics, there are a number of lessons and activities that are intended to blend mathematics with writing and make use of mathematical reasoning in other content areas such as social studies. Sections on math concepts, integrated lessons, and journaling.

40. Internet Projects for Elementary Statistics
http://hepg.awl.com/weiss/e_iprojects/index.htm

Understand statistics by analyzing real data and interacting with graphical demonstrations of statistical concepts. Simulations, demonstrations, and other activities are useful to anyone interested in statistic

41. Statistics.com
http://www.statistics.com/

Information about statistics software (major packages like SAS, SPSS and S-PLUS, shareware and smaller packages too), as well as about statistics analysis, data analysis and short courses in statistics.

42. Resampling Stats
http://www.resample.com/

Resampling (drawing repeated samples from the given data, or population suggested by the data) is a new method for the solution of confidence limits, hypothesis tests, and other everyday inferential problems. Resampling uses simulations in place of the complicated mathematics, formulas and tables of parametric and non-parametric tests.

43. DIGSTATS
http://www.cvgs.k12.va.us/DIGSTATS/

WWW resource for integrating statistics and data visualization into mathematics and science courses in secondary schools, community colleges and undergraduate programs. Modules cover concepts from descriptive statistics, inferential statistics, two dimensional graphical analysis and three dimensional data visualization.

44. Gallery of Data Visualization: The Best and Worst of Statistical Graphics
http://www.math.yorku.ca/SCS/Gallery/

Some examples of the Best and Worst of Statistical Graphics, with the view that the contrast may be useful, inform current practice, and provide some pointers to both historical and current work. We go from what is arguably the best statistical graphic ever drawn, to the current record-holder for the worst.

45. EggMath
http://chickscope.beckman.uiuc.edu/explore/eggmath/

A collection of Web modules (many with interactive applets) covering different topics in K-12 mathematics related to eggs (that's right, eggs!). Symmetry, exponential growth, etc.

46. Latitude/Longitude Distance Calculation
http://jan.ucc.nau.edu/~cvm/latlongdist.php

Determine the distance between two points on the earth given their latitudes and longitudes. Links to a description to the math behind the calculation.

47. The Golden Ratio
http://www.geom.umn.edu/~demo5337/s97b/

Introduction to the Golden Ratio and Fibonacci Sequence. Instead of simply supplying definitions and asking the student to engage in mindless practice, our idea is to have the student work through several activities to discover the applications of the Golden Ratio and Fibonacci Sequence.

48. Links related to Statistics Education
http://noppa5.pc.helsinki.fi/links.html

Large set of links to online Statistical teaching material, courses , handouts, exercises, articles, datasets.

49. Extend
http://www.imaginethatinc.com/

Powerful simulation software system, used in industry and education.

50. The Mathematical Miseducation Of America's Youth
http://www.pdkintl.org/kappan/kbat9902.htm

Illustrated article from the Phi Beta Kappa magazine, Feb. 1999, by a professor of mathematics education at Kent State University.

51. Parrot Math
http://www.pdkintl.org/kappan/kobr9902.htm

We cannot go back to basics as the critics demand, because we've been there all along. And the fact is that the back-to-basics approach, not the activity-based approach the critics abhor, has failed us badly. Article from the Phi Beta Kappa magazine, Feb. 1999, by a professor in the Department of Curriculum and Instruction at Southern Illinois University.

52. Some disasters attributable to bad numerical computing
http://www.math.psu.edu/dna/disasters/disasters.html

The Patriot Missile failure, in Dharan, Saudi Arabia, on February 25, 1991 which resulted in 28 deaths, is ultimately attributable to poor handling of rounding errors. The explosion of the Ariane 5 rocket just after lift-off on its maiden voyage off French Guiana, on June 4, 1996, was ultimately the consequence of a simple overflow. The sinking of the Sleipner A offshore platform in Gandsfjorden near Stavanger, Norway, on August 23, 1991, resulted in a loss of nearly one billion dollars. It was found to be the result of inaccurate finite element analysis.

53. Circles of Light: The Mathematics of Rainbows
http://www.geom.umn.edu/education/calc-init/rainbow/

How are rainbows formed? Why do they only occur when the sun is behind the observer? If the sun is low on the horizon, at what angle in the sky should we expect to see a rainbow? This lab helps to answer these and other questions by examining a mathematical model of light passing through a water droplet.

54. The University of Minnesota Calculus Initiative
http://www.geom.umn.edu/education/calc-init/

Interactive technology-based modules for the engineering calculus sequence. These modules emphasize geometric concepts of calculus while examining applications of mathematics to the physical and life sciences.

55. Biographies of Women Mathematicians
http://www.agnesscott.edu/lriddle/women/women.htm

These pages are part of an on-going project by students in mathematics classes at Agnes Scott College, in Atlanta, Georgia, to illustrate the numerous achievements of women in the field of mathematics. There are biographical essays or comments on most of the women mathematicians and some photos.

56. Teach/Me - Data Analysis
http://www.vias.org/teachme/

Teach/Me - Data Analysis is a software system for networked environments that has been developed to support the teaching and learning of the statistical analysis of data. Teach/Me is an open system which is based on internet standards (HTML, and VRML) enabling the teacher to provide students with additional material via the web. In addition, a special client delivers full power and support for teaching and learning.

57. Tessel version 2
http://www.uniovi.es/~quimica.fisica/qcg/tessel/tessel.html

Tessel2 is a 3D "compiler" to produce crystal and molecular models, parametric surfaces and several forms of sphere tesselations. Molecular models combine balls-and-sticks, arrows and coordination polyhedra representations of pure and defective crystals, finite molecules or clusters. Several methods for tesselating the sphere are currently implemented, including: recursively subdividing a inscribed cube, tetrahedron or octahedron; geodesic division based on a number of meridians and parallels; and minimization of the electrostatic repulsion of a set of points lying on the sphere surface. The program produces output to be rendered with POV-Ray 2 or 3, Geomview (OFF format), or any Virtual Reality renderer (VRML V1.0 format). In addition, a very simple output (POINTS) is provided for those applications in which a list of points is best suited.

58. The Connected Curriculum Project
http://www.math.montana.edu/~frankw/ccp/home.htm

The Connected Curriculum Project uses the usual three perspectives -- numeric, visual (graphic), and algebraic -- to help understand phenomena involving mathematics. In addition, we use hands-on experimentation. We chose this module as the starting point for our tour because it illustrates the use of hands-on experimentation and our emphasis on using mathematics as a language to express, communicate, and reason about real-world phenomena. One of the central themes of this modeling course is Newton's Model of Cooling. As with all models, the limitations of Newton's Model are as important as its successes in describing real-world phenomena. We begin with an experiment, described in this module, intended for high school or middle school science or mathematics classes.

59. SCORE Mathematics Lessons
http://score.kings.k12.ca.us

These SCORE Mathematics Lessons have been written by teachers selected to participate in SCORE Mathematics workshops. This page is designed especially for mathematics teachers and students in California. Its contents and links reflect our state's Mathematics Framework and the NCTM Standards.

60. Fermi Questions Library
http://mathforum.org/workshops/sum96/interdisc/sheila3.html

Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. Students often believe that "word problems" have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage multiple approaches, emphasize process rather than "the answer", and promote non-traditional problem solving strategies.

61. Project SkyMath: Making Mathematical Connections Using the Science and Language of Patterns to Explore the Weather
http://www.unidata.ucar.edu/staff/blynds/Skymath.html

This Web Page is designed for middle school mathematics teachers. It contains all of the information needed for teachers to use the 15 classroom activities of SkyMath, including the module itself. We believe that it is an effective and innovative way to present elements of the middle school mathematics curriculum.

62. Math Connections
http://www.mathconnections.com/index3.html

HS math curriculum that seeks to connect math to the real world.

63. HTML Math Overview
http://www.w3.org/Math/

Various ways to present math expressions on Web pages.

64. Mathematics Information Servers
http://www.math.psu.edu/MathLists/Contents.html

Comprehensive set of links to mathematics-related Internet servers all over the world.

65. Numerical methods
http://www.math.psu.edu/dna/num_methods.html

Database of Numerical methods

66. Macsyma
http://www.Macsyma.com

Macsyma, one of the three large symbolic and numeric mathematical software packages in the world, is now available in Version 2.2 which sets an unequaled standard for friendliness and ease in mathematical computing. The new Natural Language Query feature allows users to type in a request (such as, for instance, "provide the sum of trig functions").

67. InvestSmart
http://library.advanced.org/10326/

Developed by students for the ThinkQuest competition, this site includes basics, lessons, a simulation, and examples. In the interactive stock market simulation, each "player" is given $100,000 to invest in over 5,000 companies. Other features include easy setup for classes or investment clubs, a "Group Directory" view of each student portfolio, research capability of stocks, benchmark of each portfolio, and helpful set up tips for classes from 20 to100 students.

68. Gordon's Games: Simple Math, Not So Simple Math, and Not Just Math
http://www3.telus.net/public/m.games/welcome.html

Simple arithmetic games (math games) and variations, made up by the author over a number of years in teaching young children, which are contained in a 24 page booklet. As well there are suggestions for similar games using number, letter, and word cards. There is also a spelling game, and an arithmetic game, for the whole class. The games deal with number recognition, order, comparison of value, place value, addition, subtraction, multiplication, division, multiples, factors, and even fractions and decimals if you want to carry them that far. There are games that cover the basic skills for each of the grades from K-3, ages 5-8. Most games can be used at home, and played in any language.

69. Scilab, a free scientific software package for numerical computations
http://www-rocq.inria.fr/scilab/

Scilab is a scientific software package for numerical computations in a user-friendly environment. It features: Elaborate data structures (polynomial, rational and string matrices, lists, multivariable linear systems,...). Sophisticated interpreter and programming language with Matlab-like syntax. Hundreds of built-in math functions (new primitives can easily be added). Stunning graphics (2d, 3d, animation). Open structure (easy interfacing with Fortran and C via online dynamic link). Many built-in libraries: Linear Algebra (including sparse matrices, Kronecker form, ordered Schur,...). Control (Classical, LQG, H-infinity,...). Package for LMI (Linear Matrix Inequalities) optimization. Signal processing. Simulation (various ode's, dassl,...). Optimization (differentiable and non-differentiable, LQ solver). Scicos, an interactive environment for modeling and simulation of hybrid systems. Metanet (network analysis and optimization). Symbolic capabilities through Maple interface.

70. UCALC: A Windows Multi-purpose Calculator
http://www.ucalc.com

Whether you need to compute compound interest, convert from miles to kilometers, solve a quadratic equation, plot a 3D surface, or simply add up bills, you will find a tool in UCALC 4.0 which performs the task. UCALC for Windows 95: Ê$40; Ultimate Calculator (DOS): Ê$25

71. Statistics Every Writer Should Know
http://nilesonline.com/stats/

This easy-to-understand guide offers short lessons (with examples!) in basic mathematics for journalists and other writers

72. Ask Dr. Math
http://mathforum.org/dr.math/dr-math.html

You can submit your K-12 math question using the above link or by sending e-mail to [e-mail]. Tell us what you know about your problem, and where you're stuck and think we might be able to help you. Dr. Math will reply to you via e-mail, so please be sure to send us the right address. K-12 questions usually include what people learn in the U.S. from the time they're five years old through when they're about eighteen. Elementary School Level, Middle School Level, High School Level, College Level and Beyond.

73. Web sites and resources for teaching math
http://www.sitesforteachers.com/

Lesson Plans For A Variety Of Math Topics; Ideas And Activities; Bits & Blurbs; Online Strategy And Board Games For Math; Other Resources For Teaching Math; Major Math Education Organizations. (Drs. Vicki F. Sharp and Richard M. Sharp, Professors of Elementary Education at California State University, Northridge.)

74. MATLab Programs and Activities
http://isaac.williamsport.wa.k12.md.us/~ctrout/sciproj/MATLAB/index.html

MATLab programs, worksheets and activities developed at a high school Often sample data files are included. The programs are barely beta versions and require thorough testing.

75. Sound of Trigonometry
http://www.math.montana.edu/~frankw/ccp/before-calculus/trigonometry/soundtrg/learn.htm

When you think trigonometry you should think triangles -- not just geometric triangles but musical triangles -- because trigonometry is the mathematics of sound and music.

76. MLAB software for mathematical and statistical exploration
http://www.civilized.com

Advanced mathematical and statistical modeling system for mathematical and statistical exploration, and for solving simulation and modeling problems such as chemical kinetics, pharmacological compartmental models, multiple site ligand binding, neurophysiological modeling, and ultracentrifuge models, wetc. Runs on PC, Mac, SUN, RS6000, DEC-Alpha, Convex, SGI, NeXT (Motorola, Intel, and HP. Descriptive material plus a collection of technical reports showing the application of MLAB are available.

77. A Brief History of Algebra and Computing: An Eclectic Oxonian View
http://www.comlab.ox.ac.uk/oucl/users/jonathan.bowen/algebra/algebra.html

An interesting paper on the origins of algebra and its history. There is also a discussion of how algrbra and computing go together

78. Dave's Math Tables
http://www.sisweb.com/math/tables.htm

One expects just tables, but gets more - lots of formulas, identities, tables, series, etc. For example, surface areas for geometric figures, trig identities - a great reference for college math students.

79. Mathematical Quotation Server
http://math.furman.edu/~mwoodard/mquot.html

Comprehensive collection of math-related quotes, organized by author or quote. You may browse, search by keyword, etc.

80. Mandelbrot Explorer
http://www.softlab.ece.ntua.gr/miscellaneous/mandel/

A graphical exploratwin of the Mandelbrot set that is interactive - zoom in and out at user-selected points, plus a gallery of colorful fractal designs.

81. Tessellation Tutorials
http://mathforum.org/sum95/suzanne/tess.intro.html

What Is a Tessellation? Investigating Tessellations Using Activity Pattern Blocks; HyperCard: Black & White Tessellations. HyperStudio: Color Tessellations. Step-by-step instructions and illustrated tutorials on The Four Types of Symmetry in the Plane, Glide Reflections, Rotations, and Repeated Reflections of an "R" . Very nicely done.

82. MegaMathematics
http://www.c3.lanl.gov/mega-math/menu.html

MegaMath offers a number of mathematical concepts which would supplement curriculum documents. There are a number of activities which allow students to explore and understand some different, yet interesting math topics. For example, students can learn all about logic, graphs, infinity, algorithms, and mathematical knots through games, activities, plays and problem solving stories.

Applications and Misapplications of Cognitive Psychology to Mathematics Education.

John R. Anderson, Lynne M. Reder, Herbert A. Simon

We show that cognitivism does not imply outright rejection of decomposition and decontextualization. We critically analyze two movements which are based in part on this rejection--situated learning and constructivism. Situated learning commonly advocates practices that lead to overly specific learning outcomes while constructivism advocates very inefficient learning and assessment procedures. The modern information-processing approach in cognitive psychology would recommend careful analysis of the goals of instruction and thorough empirical study of the efficacy of instructional approaches.

On Growth & Form: Learning Probability Concepts By "Doing Science"
http://cps-www.bu.edu/~trunfio/cps-ogaf.html
Analyzing fractal patterns in nature. In each module, students typically start with a hands-on activity in which they flip coins or roll dice to mimic the randomness involved in forming structures such as lightning bolts, coastlines, neurons, termite tunnels, bacterial colonies, root systems, forest growth, soil cracking, galactic distributions, mountain ranges, deltas, tides, clouds, DNA nucleotide sequencing, coral formations, and body organs. As repetitive coin flipping becomes tedious, students turn to computer simulations, which demonstrate how fundamentally random microscopic events can give rise to fractal macroscopic patterns. The programs can be downloaded right from this page.

84. SimCalc: Simulations for Calculus Learning
http://tango.mth.umassd.edu/

The SimCalc Project aims to democratize access to the Mathematics of Change for mainstream students by combining advanced simulation technology with innovative curricular solutions that begin in the early grades and includes powerful ideas extending beyond classical calculus.

85. "Measuring Up": Prototypes for Mathematics Assessment (1993)
http://www.nap.edu/books/0309048451/html/index.html

An electronic version of "Measuring Up," a popular book by the National Research Council on assessing students in accordance with the National Council of Teachers of Mathematics (NCTM) math standards, is now available. "Measuring Up" provides examples of problems that students should be able to solve at a fourth grade level as well as insights on how to evaluate their responses.

86. The FAMILY MATH Home Page
http://theory.lcs.mit.edu/~emjordan/famMath.html

FAMILY MATH is a program developed by EQUALS, at the Lawrence Hall of Science, University of California, Berkeley, California. The goal of FAMILY MATH is to encourage underrepresented groups (especially girls and minority students) to enter careers that use mathematics. FAMILY MATH is, of course, family-based. Includes back Issues of The FAMILY MATH Newsletter

87. Graphics for the calculus classroom
http://www.ima.umn.edu/~arnold/graphics.html

Excerpts from a collection of graphical demonstrations developed for first year calculus by Douglas N. Arnold at Penn. State. Includes mpeg animations and Mathematica notebooks. Topics include: Derivatives and differentials; Computing the volume of water in a tipped glass; Archimedes' calculation of ¹; How the ball bounces; Secants and tangents; Zooming in on a tangent line; A trigonometric limit; A nowhere differentiable function; The intersection of two cylinders

88. The Geometry Forum
http://mathforum.org

A Virtual Center for Math Education on the Internet Funded by the National Science Foundation

89. K-12 Teaching Materials
http://archives.math.utk.edu/k12.html

The following are Internet sites which contain significant collections of materials which can be used in the teaching of mathematics at the K-12 level. We have organized these materials into the following categories: Lesson Plan, Schools, Software.

90. Guide to Available Mathematical Software
http://gams.nist.gov/

This is a gateway to the NIST Guide to Available Mathematical Software, a cross-index and virtual repository of mathematical and statistical software components of use in computational science and engineering.

91. Mathematics Archive at the University of Kentucky
http://archives.math.utk.edu/

Materials available on the Mathematics Archives are classified into five main categories: Topics in Mathematics:Teaching materials, software, WWW links organized by Mathematical Topics. Searchable database. Software: Public domain and shareware software, links to other software sites. Teaching Materials: Calculus Resources On-line, Emerging Scholars Program, Graphing Calculators, JAVA and Other Interactive WWW Pages, K-12 Teaching Materials, Lessons, Tutorials and Lecture Notes, Visual Calculus, etc. Other Math Archives Features: Electronic Proceedings of the CTM and the ICTCM, POPMathematics, Project NEXT, UTK Mathematical Life Sciences Archives, etc.

92. Galaxy's list of Math Sites
http://www.galaxy.com/cgi-bin/dirlist?node=23651

Algebra, Applied Math, Calculus, Geometry, Number Theory, Statistics, Topology.

93. Complexity On-line
http://complex.csu.edu.au/complex/

Complexity On-line is a scientific information network about complex systems. You will find access to sites, publications (including the Complexity On-line Journal ) and other sources of interest.

94. Fractal pictures & animations
http://graffiti.u-bordeaux.fr/MAPBX/roussel/

FRACTAL images & animations of CNAM Paris. A french version of these web pages is available Some very nice Mandelbrot pictures & zooming animations are available

95. The Fractal Microscope: A Distributed Computing Approach to Mathematics in Education
http://archive.ncsa.uiuc.edu/Edu/Fractal/Fractal_Home.html

The Fractal Microscope is an interactive tool designed by the Education Group at the National Center for Supercomputing Applications (NCSA) for exploring the Mandelbrot set and other fractal patterns. By combining supercomputing and networks with the simple interface of a Macintosh or X-Windows workstation, students and teachers from all grade levels can engage in discovery-based exploration. The program is designed to run in conjunction with NCSA imaging tools such as DataScope and Collage. With this program students can enjoy the art of mathematics as they master the science of mathematics. This focus can help one address a wide variety of topics in the K-12 curriculum including scientific notation, coordinate systems and graphing, number systems, convergence, divergence, and self-similarity.

96. Gallery of Interactive Geometry
http://www.geom.umn.edu/apps/gallery.html

In order to enjoy this exhibit, you will need a Web browser that understands graphical Fill-Out Forms.

97. Data Powers of Ten
http://www.ccsf.caltech.edu/~roy/dataquan/

The following list is a collection of estimates of the quantities of data contained by the various media. Each is rounded to be a power of 10 times 1, 2 or 5. Most of the links are to small images. Suggestions and contributions are welcomed, especially picture files or pointers to pictures, and disagreements are accepted at [e-mail]. The numbers quoted are approximate. In fact a kilobyte is 1024 bytes not 1000 bytes but this fact does not keep me awake at night.

98. Annotated Internet Resource Collection
http://mathforum.org/library/

A well-developed, annotated, searchable collection of Web resources for teachers and mathematicians. Everything from math departments and graphics to lesson plans and software. All sorts of general education resources from education departments and virtual field trips to lesson plan archives, professional organizations, and software.

99. MathMagic
http://mathforum.org/mathmagic/

MathMagic is a K-12 telecommunications project developed in El Paso, Texas. It provides strong motivation for students to use computer technology while increasing problem-solving strategies and communications skills. MathMagic posts challenges in each of four categories (k-3, 4-6, 7-9 and 10-12) to trigger each registered team to pair up with another team and engage in a problem-solving dialog. When an agreement has been reached, one solution is posted for every pair.

100. MathMol (Mathematics and Molecules)
http://www.nyu.edu/pages/mathmol/

An introductory starting point for those interested in the field of molecular modeling.




101. Learning Through Collaborative Visualization Project (CoVis).
http://www.covis.nwu.edu/

This is the web site of the Learning Through Collaborative Visualization Project (CoVis). Today, CoVis is a community of thousands of students, over one hundred teachers, and dozens of researchers all working together to find new ways to think about and practice science in the classroom.

102. MAPLE home page
http://www.maplesoft.com/

Maple V, a leading interactive mathematical problem-solving and programming environment featuring symbolic, numeric, and visualization facilities. Maple V is used worldwide by more than 100,000 users in research, education, and industry.

103. Authentic Assessment in Mathematics
http://mathforum.org/sum94/project2.html

The goal of this project was to collect and organize available INTERNET resources on Authentic Mathematical Assessment applicable to Secondary Schools. What is it? Are there examples? Where can I find additional information?

104. MatLab home page
http://www.mathworks.com/

Software via FTP; User contributed M-files; MathWorks contributed M-files

105. Mathematica
http://www.wri.com/

Home page of the famous mathematics software program. "[Mathematica 4] is an extremely powerful tool with which to understand and solve a variety of problems." --Science, December 1999

106. STELLA Models
http://isaac.williamsport.wa.k12.md.us/~ctrout/sciproj/STELLA/index.html

Library of STELLA models in the Physics and Chemistry high schoolClassroom




107. Netlib Repository
http://netlib2.cs.utk.edu/

Netlib is a collection of mathematical software, papers, and databases.

108. The Little Gallery of Roulettes
http://aleph0.clarku.edu/~djoyce/roulettes/roulettes.html

Roulettes are produced when circles revolve around or inside other circles. More precisely, they are the locus of a point on, inside, or outside the revolving circle. When the drawing point is right on the rotating circle, an epicycloid or hypercycloid is produced.
http://falcon.jmu.edu/~ramseyil/math.htm
Math Help & Learning Resources
Is math your favorite subject or your most hated topic in school? Here's plenty of math help, math fun and other useful resources for you! Find interesting quizzes, practice, homework help and other materials to keep you occupied; or fun facts, games, puzzles and other cool stuff to make this subject something to be enjoyed rather than dreaded. Have some fun while learning some key skills to improve your grades.
Are you preparing for the SAT test? Check out our pages here for additonal math help and useful tips for SAT. You can also download our FREE SAT practice test by registering on this form.

For parents, teachers and educators, there are loads of materials here for teaching and learning. Find interesting and fun stuff to help your kids, students and children to enjoy, appreciate and learn numbers, counting, arithmetic, fractions, computation, geometry, trigonometry, tessellations, and even algebra and calculus!

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Arithmetic - Lessons In Numerical Computation
Arithmetic - Lessons & Resources In Numerical Computation.


Algebra Help - Lessons in Algebra
Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra.


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Geometry Help - Definitions, lessons, examples, practice questions and other resources in geometry for learning and teaching geometry.


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Statistics - collection, analysis, presentation and interpretation of data.


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