The Internet and Mathematics Education

[Educational] [Student resources] [Teacher resources] [Maths software] [Maths libraries] [Interactive maths]] [Internet maths PD]] [Interactive maths PD]

NOTE: While this page needs to be updated, the final two links above to PD (Professional development) provide suggested ways to explore good potential uses of the Internet for mathematics education, each of which is a bit more likely to be updated than the rest of this page.

This page is mainly designed to try to keep track of some of the possibilities for mathematics education of the Internet, especially of the World Wide Web (WWW). There seems to be several potential uses of the Internet in mathematics and mathematics education. These are still rather severely constrained in many cases by accessibility issues, although time has seen these diminish, a trend that will presumably continue.

Opinions about the Internet appear to lie on a wide continuum from one extreme, reminiscent of a Brave New World:

... to the other Deep Skeptic extreme

As for most issues, neither extreme position is correct. Reality resides somewhere between these two poles, but is constantly changing. It seems important that we keep something of an open mind on the matter.

It is not yet clear how best to classify different uses of the Internet, so that the classification system used here is tentative at best and merely reflects some examples of current uses. I will continue to update this page as I become more familiar with the possibilities, and expect that a better classification system may result. Classification of individual sites is rarely a cut and dried affair, since many could be included under more than one category. Please note that this page does not contain many links to graphics calculator resources, because they are on a separate page on this website.

Sites are briefly annotated, with a view to identifying what is distinctive about them. Many of the annotations include descriptions of the sites based on information provided by the sites themselves, acknowledged at the bottom of this page.

Sites have only been linked from this web page if they appear likely to be of some interest to people interested in mathematics education, as students, parents, teachers, curriculum developers (or, indeed, all of these simultaneously!). In evaluating Internet sites, it seems important to take account of at least:

I would be grateful to be informed of

Please send an email.

Educational web sites

In this category are web sites that have been constructed mainly to provide official information or to provide interesting collections of links to potentially useful sites for mathematics education. These provide starting points for obtaining authoritative information or for some structured browsing. Many of the professional associations also contain good pages of links, which are not repeated here directly.

The Mathematics Forum
A superb US site, well maintained and with links to a vast range of sites. Subscribing to The Math Forum Internet Newsletter (free) is a great way to stay informed of interesting new sites.

Eisenhower National Clearinghouse
A carefully compiled set of links related to mathematics. The ENC evaluates web sites carefully and selects outstanding websites at the beginning of each month to publish their Digital Dozen of thirteen exemplary sites (many of which are for science). (There are links to many of these exemplary sites here on this page.) Worth checking at the start of each month.

BBC Online Education Maths
AS Guru Maths site, designed to help students online.

BBC Education news
A comprehensive and authoritative guide to UK education. Links to important UK sites through How the Education Systems Work. Many interesting issues.

The Department of Education of Western Australia
Official government page, of use to all West Australians and anyone interested in government education in Western Australia. The Technology 2000 project addresses Internet issues. The Graphics Calculator page provides much useful information for mathematics teachers.

Curriculum Council of Western Australia
Official page of the body responsible for WA school curricula. Current senior secondary school courses available for download.

Birmingham site
A good site from the University of Birmingham with links to many interesting mathematics sites, many of which are in the UK. Information for students, mathematical organisations, resources and products are linked.

Southampton resources
From CRIME (Centre for Research in Mathematics Education) at the University of Southampton, this is a annotated list of good web sites of various kinds

Using the Internet for maths (Oundle)
A recent conference on the use of the Internet for senior and college mathematics based at Oundle School in the UK.

Using Internet (Oundle)
A conference on the use of the Internet for senior and college mathematics based at Oundle School in the UK.

Oundle Links
Oundle School web links. Very comprehensive and well-structured

New Scientist Hot Spots
A good collection of mathematically interesting sites with useful annotations.

ThinkQuest
A website related to international competitions to design quality educational materials for educational purposes, some of which have mathematical aspects.

ERIC Digests
ERIC publishes short reviews of recent research in education, many of which deal with mathematics in particular. They are archived and listed on this site and can be searched. A good way of finding out what's happening, although there is still a US bias to the research, understandably.

Resource material for students

This category contains web sites that have been constructed mainly for school students, which is not to say that school students would not find other web sites of mathematical or educational interest. Nor is it t osay that teachers will not find these of interest. What distinguishes the sites is that school students are the primary audience.

The Maths File Game Show
Interactive games and puzzles from the BBC with mathematical and educational punch. Game show hosts are Pythagoras and Hypatia. Needs Shockwave in order to operate.

Pascal's Triangle
A sequence of various interesting activities related to Pascal's Triangle.

World's Largest Math Event
In celebration of Mathematics Education Month, NCTM holds its annual World's Largest Math Event (WLME) promoting the beauty and utility of mathematics in everyday life. Students around the world will engage in rich, problem solving activities using NCTM's WLME activity booklet. Teachers may use activities as presented, or they can tailor the activities to meet specific classroom needs. NCTM's World's Largest Math Event celebrates mathematics and mathematics teaching and is the highlight event of Mathematics Education Month. Begun in 1995 in celebration of NCTM's 75th anniversary, WLME has grown into an annual event with participation estimated at approximately 1 million students.

Australian Mathematics Trust
Information for students about AMT activities, resources and forthcoming competitions

MathsNet
Brian Dye's MathsNet is full of interesting ways of using the Internet with mathematics. Start with the tour suggested on the opening page to get an idea of the range of things available here.

nRich Online Maths Club
After three years NRich, based at Cambridge University, has thousands of members from 50 countries and many more regular users. School students, teachers and those professionally involved in education are welcome to join. On the first of each month (except August) the site provides new magazines for school students of all ages with an emphasis on mathematical activity. NRICH publishes children's solutions to mathematical challenges. NRICH provides an answering service and many special interest discussion groups.

PASS Maths
Public Awareness and Schools Support for Mathematics is a project of the Millennium Mathematics Project, based at Cambridge University (also related to nRich). Contains a wealth of interesting expository mathematical material, with an archive available of earlier publications. Of interest to both teachers and students.

Mega-Mathematics
Assorted activities for students

Homework Help
Resources of many kinds for students, including problems, project information and a question asking facility

Homework Central
Resources of various kinds for students in primary, secondary and college grades.

Pages for students in school
A good list produced by the University of Birmingham

Online journals for high school students
A list of online journals compiled and maintained by SMARD

The Math Den
For students and teachers from upper primary to senior secondary. Contains hundreds of graded skill questions (in groups of 20) for which students can register, work through and have marked by email. They get back an individual report, and their progress is tracked over time. Also includes weekly problems, helpful mathematical tips and much more.

Learning about fractals
Fract-ED is an introductory fractal tutorial intended for high school or college entry-level students. It is an informal discussion of some of the elements of fractal geometry, and includes interactive programs which demonstrate the techniques of fractal generation.

Fractals
A fractals site written for younger students, containing much useful material, including activities, for both students and teachers

Ask Dr Math
An award-winning information service for students who have mathematical questions.

MathMania
Inspired by Paul Erdös, one of the most important mathematicians in the twentieth century. One of his specialties was finding unsolved questions which take mathematics in new directions. He was known for posing problems to students and offering prizes. This site generalizes his activities to a broader and younger audience.

Math in Daily Life
Interactive exhibits from the CPB/Annenburg Foundation's archives regarding the uses of mathematics in everyday life, based on the TV series, For All Practical Purposes. Short video clips from the Foundation's excellent mathematics and science programs are also available, but require some software to be installed first.

International Mathematical Olympiad
Information of various kinds about the annual Olympiad competitions.

Problems of the Week
Based at the Math Forum, POW each week contains problems to which students can submit solutions for assessment. Categories include Elementary (ie Primary school), Middle School, Geometry. Algebra, Discrete Maths and Trigonometry & Calculus. Mentors needed, too (to assess student efforts). The site also contains links to other similar sites.

Figure This! Math Challenge for Families
This is the home page of a US national campaign, sponsored by the Department of Education and the National Science Foundation, is intended to engage middle-school students and their parents by posing mathematical challenges for them to solve together. The goal is to prevent students from moving away from mathematics in the eighth grade, a choice that closes off many significant career options. Fifteen challenges start off the campaign, and another 80 challenges will be developed and distributed over the next two years.

SOS Mathematics
This site provides a great deal of organised help to students studying mathematics at a variety of levels from middle school to the undergraduate years.

MegaPenny Project
This site provides various ways of thinking about large numbers, using US pennies (one cent pieces). Interesting visualisations of millions, billions and beyond!

 

Resource material for teachers

[Reading] [History] [Teaching and assessment] [Electronic mail] [Mathematics]

This category contains web sites that mathematics teachers may find useful for various reasons: devising curriculum, updating or enriching their mathematical backgrounds, planning lessons, finding assessment resources, professional reading, etc.

Mathematics Education Hypertext Encyclopaedic dictionary
As its name suggests, MEHED is first and foremost a dictionary of terms in mathematics education; a dictionary that goes beyond terse definitions and attempts to be more encyclopaedic in its approach; a hypertext document with internal and external links. Biographies of mathematics educators are also included.

Eric Weisstein's World of Mathematics
A vast resource of mathematics, hosted by Wolfram Research Inc., makers of Mathematica. Self-described as 'The Web's most extensive mathematics resource', not obviously an exaggeration. Many cross-references (including many to published books), animated graphics, live Java applets, images, etc. All is searchable, although there is much here that is beyond secondary school level. Animations etc require Java and a recent browser. This site is often a bit slow, but usually worth the wait.

 

Mathematics Education reading

Most of the sites here refer to mathematics education journals, some of them published electronically.

Journals
A list of journals in mathematics education, maintained by the University of Nottingham, Useful for contacting editors and, in some cases, seeing copies of the journal.

Maths-Science Online Newsletter
The Newsletter is devoted to the issues surrounding online science and mathematics for high school students, undergraduates, and graduate students. In the interest of seeing as many techniques as possible the editors are interested in almost all online experiments that our readers have tried or are trying. Success stories are especially welcome. However, as most of us that work in the sciences and mathematics know well, what is tried first often does not work. We know that the ongoing worldwide experiment in online course delivery is itself (or will be) a science that needs years of patient research. The potential seems to be there for all to see; it is the reality we seek.

The Australian Mathematics Teacher
Published by the Australian Association of Mathematics Teachers for teachers of students aged 11-16 years. The website contains ordering information as well as recent contents and sample articles.

The Australian Primary Mathematics Classroom
Published by the Australian Association of Mathematics Teachers for teachers of primary (elementary) students. The website contains ordering information as well as recent contents and sample articles.

The Australian Senior Mathematics Journal
Published by the Australian Association of Mathematics Teachers for teachers of senior high school and early post-secondary students. The website contains ordering information.

Teaching Statistics
An excellent journal of interest to teachers of statistics across a wide range. The website contains recent tables of contents and allows for some previous articles to be downloaded. Especially interesting is The Best of Teaching Statistics, a compilation of the best 41 articles from the first 5 years of the journal. .

Journal of Statistics Education
An electronic journal in which papers are refereed. From 1993 to 1998, subscriptions were free, but now involve a small charge.

Teaching Mathematics and its Applications
Published by the Institute of Mathematics and its Applications in the UK, this is always an interesting journal. The website has abstracts of articles and a search facility.

Chreods
Chreods is an electronic journal devoted to exploratory writing about education to provide a forum for practising teachers of pupils and students of all ages engaged in research into their own practice.

POME
Paul Ernest's electronic journal, The Philosophy of Mathematics Education

Micromath
A journal of ATM focused on the use of computers and calculators in school mathematics. Always good reading. The website contains information and tables of contents.

Mathematical Thought
A peer-reviewed and reflective journal on mathematics education, published by CRIME at the University of Southampton

International Newsletter on the Teaching and Learning of Mathematical Proof
A French publication, edited by Nicholas Balacheff. Deals with a range of aspects of proof, including the use of Cabri Geometre and similar dynamic geometry software.

Mathematically Correct
Writings of various conservative groups opposed to changing US mathematics curricula. Much of it is in the public domain and much of it appears to have been written by people without extensive personal experience of mathematics education in schools.

HOLD
Another conservative US group, based in California and opposed to recent US curriculum changes. More heat than light.

ICTCM Proceedings
Electronic Proceedings of the International Conference on Technology in Collegiate Mathematics (EPICTCM), an annual conference sponsored by Addison-Wesley. These Proceedings are published on the World Wide Web by the Math Archives.

ERME Proceedings
Proceedings of the First Conference of the European Society for Research in Mathematics Education (August 1998).Vol. 1 + 2, Editor: Inge Schwank, 1999, Publishing House: Forschungsinstitut fuer Mathematikdidaktik, Osnabrueck. Papers can be downloaded as pdf files.

International Journal for Mathematics Teaching and Learning
This journal, which is published only in electronic form, aims to enhance mathematics teaching for all ages (and abilities) up to 18 years, through relevant articles, reviews and information from around the world. It is aimed at practitioners and educationalists, providing a medium for stimulating and challenging ideas, innovation and practice in all aspects of mathematics teaching and learning.

 

History of Mathematics

These links are mainly likely to be used for reference purposes, to find out something about a particular person or piece of mathematics. They can also be fruitfully browsed.

St Andrews' History of Mathematics
Produced by the University of Saint Andrews in Scotland, this is a wonderful and rich archive related to the history of mathematics. The site has deservedly won very many international awards for excellence.

History of Mathematics
Produced by David Joyce of Clark University, this site contains an interactive and annotated version of Euclid's Elements (using geometric applets). It also contains David Hilbert's famous 1900 address in which he posed the 23 problems.

Biographies of women mathematicians
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. Comprehensive and well-organised.

Mathematics and the Liberal Arts
The Mathematics and the Liberal Arts pages at Truman State University are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. This is a large collection, referenced to a rich source of books and journals, but it is fairly easy to navigate from any starting point to other points of interest. (The link above starts at Arithmetic). In most cases, you will need to locate the original article, rather than relying on the web description given here.

Teaching and Assessment

The category here is especially fuzzy, since almost anything on this page might have value for mathematics teachers planning lessons or courses. What distinguishes the sites here is that their main purpose is to support teaching and learning activities.

PlanetQHE
The Probabilistic Learning Activities Network (PlaNet) is located here. David Harris has assembled some very interesting perspectives of teaching and learning probability and some associated resources. The 'essential questions' aspect is particulartly interesting, as is the focus on counter-intuitive questions. His project invites contributions and comment.

National Math Trail
This site describes a collaborative project concerned with making and using mathematics trails in the classroom. Includes an intersting video of one NY teacher's experiences and her students' reactions.

Gallery of Data Visualisation
This wonderful site contains a number of examples of the best and worst of statistical graphics, following in the footsteps of John Tukey and Edward Tufte. A truly wonderful collection of examples, good and bad.

Data and Story Library
DASL (pronounced "dazzle") is an online library of datafiles and stories that illustrate the use of basic statistics methods. Data from a wide variety of topics is provided so that statistics teachers can find real-world examples that will be interesting to their students. You can use DASL's powerful search engine to locate the story or datafile of interest. (Data can be imported directly into Fathom from this site.)

Fathom
Fathom is a new piece of statistical software developed and marketed by key Curriculum Press. This site allows you to find out more abouyt it and to download a demonstration copy. There is an active email list community for this superb software package, which is likely to be very popular in educational settings. Fathom uses dynamic statistics, a term coined by and trademarked to the developers, to analyse data in visually powerful ways. Data can be imported directly from a URL (See DASL site above, eg.). Certainly worth a look.

Maths posters in the London underground
During World Mathematical Year 2000, a sequence of posters designed at the Isaac Newton Institute for Mathematical Sciences was displayed month by month in the trains of the London Underground. The project hoped that these would stimulate, fascinate - even infuriate! But most importantly that they would bring maths to life, illustrating the wide applications of modern mathematics in all branches of science - physical, biological, technological and financial. Posters can be seen online, and can also be ordered for purcahse.

PBS TeacherSource
TeacherSource is a large collection of information of various kinds for mathematics tecahers (and others) in the USA. There is a searchable data base of ideas for lessons and activities, monthly articles on topical matters and, most recently, Mathline, a searchable data base of classroom video clips linked to the new NCTM Standards. Material of interest to preschool teachers, primary school, middle school and high school mathematics teachers is included. PBS is the Public Broadcasting System, a major producer of quality television in the US (not unlike the ABC in Australia in some respects). This is a major resource. Certainly worth a look.

Show-Me Center
The Show-Me Center, in partnership with five NSF-sponsored middle grades curriculum development satellites and their publishers, provides information and resources needed to support selection and implementation of standards-based middle grades mathematic curricula in the USA. These curricula showcase the vision of the National Council of Teachers of Mathematics as outlined in their Standards documents. The five curricula are The Connected Mathematics Project, Mathematics in Context, Mathscape, Math Thematics, Middle School mathematics through Applications Project.These documents call for major reform of school mathematics to support the goal of improving mathematics learning. Emphasis is on important mathematics that is explored by middle school students through active engagement.

SMARD
SMARD is the Secondary Mathematics Assessment and Resource Database, owned and managed by the Queensland Association of Mathematics Teachers and sponsored by Sharp Corporation. SMARD provides an opportunity for secondary mathematics teachers to share quality assessment and resources. Most of the assessment and resources available from this site have been classroom-tested, and much of it is non-traditional.

SMARD Lesson plan database
Maintained by SMARD (see previous entry)

Numbers Count
Information, including Teachers' Notes, for the Australian Broadcasting Commission Television Programme for middle primary students

Sketchpad for Little Ones
Experiences and ideas for using Geometer's SketchPad with young middle school students

Mathematics of Change
A site that presents calculus as the mathematics of change, in order to make the subject an essential part of the general education of the population and an accessible and relevant domain of mathematics. TERC envisions calculus as one of the important contexts for students' learning of arithmetic, algebra, and geometry starting in the elementary grades.

ABC Learn Online
Mathematics resources from the Australian Broadcasting Commission for a range of ages and subjects

Mathematics Assessment Resource Service
Describes the Balanced Assessment Project conducted by Michigan State, Berkeley and the Shell Centre. Sample tasks are included.

Mathematics Teacher Education Resource Place
A website dedicated to supporting and improving the preparation of mathematics teachers (pre K-16) by providing on-line resources, hot links, and a professional forum for those engaged in the teaching of mathematics content and methods courses, or in the field supervision of beginning teachers.

MathDI
Contains information about a database for accessing literature in mathematics education

The Chance Data Base Project
This data base contains materials designed help teach a Chance course or a more standard introductory probability or statistics course. The Chance course is a case study quantitative literacy course developed cooperatively by Middlebury, Grinnell, Spelman, University of California San Diego, University of Minnesota, and Dartmouth.

Chance and Data in the News
An excellent website maintained by Jane Watson and colleagues at The University of Tasmania, highlighting the role of chance and data in news media.

Australian Bureau of Statistics
Access to authoritative statistical data (Australia Now) and information about education products and services.

SimCalc
An innovative approach to the ideas of the calculus developed at the University of Massachusetts by Jim Kaput and colleagues. Computers are used to simulate various kinds of motion and to explore it dynamically for young students.

Exploring Data
A rich resource created by Rex Boggs of Queensland. This website contains activities, worksheets, overhead transparency masters, data sets and assessment to support data exploration. It also contains an extensive collection of articles designed to enhance the statistics knowledge of the teacher. There is a resources page that gives a select list of the finest resources available to support introductory statistics, including texts, web sites, data sets, java applets and mailing lists.

Life by the Numbers
Home page of the recent PBS television show, devised to present a modern view of mathematics to the general public. A version of the series is also published as an excellent book by Keith Devlin.

Tools for Understanding
A resource guide for extending mathematical understanding in secondary schools. This site is intended for educators who teach mathematics and are interested in integrating common technologies into their daily instruction. Examples of common technologies are spreadsheets, word processors, journals, calculators.

Mathematical Games
Some information about their place in school and some examples of suitable games from the Centre for Innovation in Mathematics Teaching at the University of Exeter

Statistics Every Writer Should Know
Basic statistical concepts written about for a general audience

Web-based lessons
A collection of mathematics lessons from Cynthia Lanius of Rice University. See also here recent presentation on web-based teaching at the NCTM 1999 conference.

Symmetry and Tessellations
A large collection of activities of various kinds and many WWW links related to symmetry and tessellations

Mathematics and the WWW
An early paper by Gene Klotz on the relationships between mathematics education and the web.

Millennium Mathematics Project
The Millennium Mathematics Project is an excellent UK initiative based at Cambridge University which aims to make people of all ages and interests more aware of the importance and excitement of mathematics - and its many applications - to their everyday lives. The Project builds on the existing successes of both PASS Maths and its sister online publication, nRICH, in reaching schoolchildren and teachers with interesting articles and puzzles about mathematics.

NOVA
Maintained by the Australian Academy of Science, this site contains some interesting material concerned with how mathematics is used. Well-structured self-contained articles contain activities, a glossary, information and links to other related sites. The goal of NOVA is to provide reliable and up-to-date information for senior secondary school teachers to use in class (although they also hope that anyone with an interest in topical issues will find it useful). The information on Nova has been checked for accuracy by experts in the field and is updated regularly. Of interest to students as well as their teachers.

Internet projects for elementary statistics
Addison Wesley Longman have produced this site, with a wealth of material for an introductory one-semester statistics course, based on data (mainly US in origin) of various kinds. The site is intended to supplement an AWL statistics textbook written by Neil Weiss, but seems to stand alone as well. Each chapter is based around actual real-world situations, with sections on Background, Data Views, Analysis and Reference. Although the course by its nature deals with many inferential ideas, it would still serve as a useful resource to teachers and students of statistics courses that did not involve inferential statistics. An innovative and very impressive use of the web for teaching and learning.

CAST
Computer Assisted Statistics Teaching (CAST) is a complete web-based course on introductory statistics produced by Massey University in New Zealand. It incorporates a number of interactive elements and is data-focused. This is a pre-release version. It is not freeware or shareware, and the final version of CAST will be sold commercially. Full copyright is retained by the author. If you are interested in using this pre-release version for teaching, please contact the author, Doug Stirling, at d.stirling@massey.ac.nz.

The Cereal Box problem
This is a nice example of using simulation to tackle a problem when you don't have enough theoretical mathematics to do otherwise. This website includes a Java applet for simulating the purchase of successive cereal boxes in order to collect a complete set of cards. A good elementary introduction to Monte Carlo procedures.

NCTM Illuminations
This website is intended to help 'illuminate' the new NCTM Principles and Standards for School Mathematics by focusing on Internet-based teaching and learning, including online, interactive, multimedia mathematical investigations
. Links to good practice are provided as well as material of direct use for various age groups. The site also contains a searchable electronic version of the new standards-based document.


Electronic mail

The Internet includes electronic mail (email) as well as the WWW. Use of email is much less demanding on resources than is the WWW and is an increasingly important means of professional communication, especially as schools get better access to it. Apart from person-to-person communication, email lists have become a useful way to communicate efficiently and inexpensively to a wide audience.


Maths Email Centre
A good overview of the (many) kinds of ways in which email might be used productively for mathematics education purposes, including links to relevant sites and lists.

Mathematics Education International Directory
Email list of many mathematics educators. Very handy as the first place to look to contact someone.

MAWA List
Mailing list of the Mathematical Association of Western Australia

AAMT List
Mailing list of the Australian Association of Mathematics Teachers.

INTERACT!
This AAMT initiative is designed to inform and promote debate on key issues in mathematics teaching and learning in Australia. Debating the hot topics in Australian mathematics education, it will focus on contentious issues in mathematics education. Each issue consists of stimulus papers that argue the case for either side of a hot topic and reactions to these papers from prominent educators including practitioners. The discussion will then be thrown open for interaction via the AAMT email list. All the traffic will be archived so participants can 'jump-in' at any time. It is anticipated that a summary and collection of the best/most useful commentary will be published on the website and maybe in hard copy or summarised in the newsletter.

Teaching Statistics List
Contains information about the list available for interested readers of the journal and an excellent collection of links to statistical sites on the WWW.

 

 

Mathematics

This category contains sites that are included primarily because of their mathematical interest. Teachers may well find them of value for curriculum planning and development purposes, or to update and enrich their mathematical background in some sense. However, the main reason for their inclusion is that they deal with an interesting aspect of mathematics or do so in a particularly interesting way.

Powers of Ten
This was a great film some years ago by Charles and Ray Eames and the website captures the essence of it beautifully. A wonderful demonstration of the significance of powers of ten in representing large and small numbers ... the Internet at its best.

The World Of Escher
All about the wonderful art work of Maurits Escher and its connections with mathematics. Many Escher drawings online.

Mazes
A website devoted to the mathematics of mazes

The Fibonacci Home Page
A wonderful collection of things related to the Fibonacci Sequence and the Golden ratio from Dr Ron Knott of the University of Surrey

The Fibonacci Series
A multimedia version of many aspects of the Fibonacci Series and its links with other things, such as the Golden Ratio.

The Great Internet Mersenne Prime Search
A website devoted to finding Mersenne primes. Join in the search!

World Population Clock
A dynamic counter showing the world population at various times, including now. Select a time in the past or future and obtain an estimate of the population of the world at that time.

Mathematical quotations
A searchable data base of quotations about mathematics produced by Furman University, South Carolina. Includes a random quotation generator, too!

The Beauty of Chaos
Contains many images and exploration opportunities for fractals and chaos

The Chaos Experience
Many aspects of chaos, its history and uses are accessible through this site

Chaotic Attractors
Contains graphics of many strange attractors and chaotic images, together with information on their generation.

Benford's Law
A nice article from the New Scientist about this remarkable law about the prevalence of the numeral 1 as the first digit in various kinds of data, and its unexpected applications to the detection of fraud.

Mathematics of Cartography
Many interesting aspects of map-making

Wallpaper Groups
David Joyce provides extensive information about the 17 symmetry groups in the plane, as observed in wallpaper patterns.

Glossary of Mathematical Mistakes
Paul Cox's collection of mathematical mistakes made over and over by advertisers, the media, reporters, politicians, activists, and other non-mathematical people. Lots of information about the many ways of making mistakes.

Largest Known Primes
Contains up to date information about large prime numbers

Prime Numbers
Just about everything you are likely to want to know about prime numbers

Erdös Numbers
Paul Erdös, the late widely-traveled and incredibly prolific Hungarian mathematician of the highest caliber, wrote hundreds of mathematical research papers in many different areas, many in collaboration with others. His Erdös number is 0. His co-authors have Erdos number 1. People other than Erdös who have written a joint paper with someone with Erdös number 1 but not with Erdös have Erdös number 2, and so on. If there is no chain of co-authorships connecting someone with Erdös, then that person's Erdös number is said to be infinite. This web site explores these numbers and the whole issue of collaboration in mathematics.

The uselessness of pi
Dedicated to those fascinated in finding yet more digits of the decimal expansion of pi. Many opportunities here to explore widely.

 

Mathematical software sources

One of the advantages of the Internet is the possibility of providing access to mathematical shareware and freeware relatively easily. In this category are some sources of software that I have found useful from time to time. Some of this can be downloaded for local use, either as shareware, freeware or as demonstration copies. In other cases, software is described and can be ordered via the website in some sense.

University of Tennessee Archives
There is a large number of links to downloadable software for mathematics and mathematics education here. This is usually the best place to start looking for a particular piece of software.

Graph Paper Printer
Shareware software for Windows plaform that allows you to print your own graph papers of various kinds.

Logo
The Logo programming language has been much discussed in educational circles. The MSWLogo site from Softronix has various downloadable versions of MSWLogo for Windows computers, together with some nice educational resources. UCBLogo is available on various platforms, including Windows and Macintosh from Brian Harvey's site; this site also includes resources for thinking about Logo and its significance.

The Logo Foundation
The Foundation is an excellent source for most aspects of Logo and probably the best place to go to if you want to explore its significance.

Statistics
NCSS 6.0 Junior is a stripped-down version of NCSS 6.0, an older version of NCSS that was developed for Windows 3.1. It includes data entry, descriptive statistics, t-tests, multiple regression, tests on proportions, cross tabs, one-way ANOVA, exponential smoothing, histograms, scatter plots, and box plots. It can be downloaded free of charge to use in statistical classes.

Java applets
Here is a guide to the use of Java applets in mathematics and mathematics education, with links to lots of examples.

Peanuts
The Peanuts software for PC's from Rick Parris of Phillip's Exeter Academy is especially good, with the added advantage that it's free.

GASP
The Globally Available Statistical Procedures initiative is designed to make statistical routines easily available via the WWW. The routines currently available have been divided into two categories, data analysis and educational. For the data analysis procedures, users need only choose the routine of interest and then enter the data as well as any other necessary information into a form or a Java applet. It's that simple. Results will be returned to the user's browser window or to a Java applet window. The educational procedures are all written in Java and feature interactive graphics. A wide range of statistical topics are covered.
An article describes this.

Dr Geo
A dynamic geometry program, available free for the PC.

SMARD
SMARD is the Secondary Mathematics Assessment and Resource Database, owned and managed by the Queensland Association of Mathematics Teachers and sponsored by Sharp Corporation. Contains many links to software sites, organised by subject area.

 

Mathematical libraries

This category contains libraries of reference material for mathematics itself.

Earliest known uses of the words of mathematics
A large indexed collection of references maintained by Jeff Miller, a high school teacher. Also links to a similar collection for mathematical symbols.

Mathematical library
This is the library from the Math Forum, containing a wide and searchable range of resources on many topics and at many levels.

Math Search
A very wide Internet search facility for mathematical terms, based at the University of Sydney

Mathematical Sources
A well-organised collection of links to mathematics departments, organisations, etc, mainly focused at the tertiary level.

Mathematical Resources on the WWW and the Internet
A vast catalogue of sites related to mathematics or mathematics education. Lacks descriptive help, but an excellent place to look for things nonetheless.

StatLib
Maintained by the Department of Statistics at Carnegie-Mellon University, this is a system for distributing statistical software, data sets, and information by electronic mail, FTP and WWW. StatLib started out as an e-mail service and some of the organization still reflects that heritage. A very rich archive.

WWW Virtual Library of Statistics
Brought to you by the University of Florida Department of Statistics, this is an archive of many kinds, including links to departments, organisations, software, data sets, lists associated with statistics.

Chance
An extensive database constructed by Dartmouth College, focused on the teaching and learning of chance.

SOS Tables
A set of mathematical tables, formulas, prime factorisations, constants, integrals, etc.

Interactive mathematics

This category contains interactive sites, which rely on the remote user sending requests to a computer program and then seeing the results. Results are of course dependent on access speeds, machine speeds and the nature of the software. In most cases, you will need to ensure that your browser is Java-enabled.

Project Interactivate
The goals of Project Interactivate are the creation, collection, evaluation, and dissemination of java-based courseware for middle school mathematics explorations. "Interactivated" lessons, discussions, and activities enable the teacher to extend hands-on activities and to teach new content areas with professional competence and confidence, incorporating technology in appropriate ways. The project includes many resources designed specifically for students or teachers, including the java-based activities, sample lesson plans, background materials, and hyperlinked textbook tables of contents. This site contains many interesting Java applets in geometry & measurement, algebra and probability & Statistics. A US project, Project Interactivate is funded, in part, by the Office of Dependent Education of the Department of Defense. Well worth a look.

Journal of Online Mathematics and its Applications (JOMA)
This is a new journal, sponsored by the MAA. JOMA will publish innovative, class-tested, web-based learning materials, articles on design and use of online materials, original research articles on student learning via online materials and other technology-rich environments, surveys of existing online materials and high-quality "mathlets" (self-contained, dynamic, single-purpose learning tools).

National Library of Virtual Manipulatives for Interactive Mathematics
The goal of this project is to provide (eventually) a large collection of interactive Java applets for learning mathematics, especially K-8. Ultimately the authors will make all materials available at several sources on the Internet, creating a national library from which teachers may freely draw to enrich their mathematics classrooms. The materials will also be of importance for the mathematical training of both in-service and pre-service elementary teachers. These require Java and a fair bit of memory at the moment. Many are still under development, but watch this space!

Virtual laboratory in probability and statistics
The goal of this project is to provide interactive, web-based resources for students and teachers of probability and statistics.

Maths Online
This Austrian site contains many excellent multimedia lwearning materials oin the form of Java applets.

Java Applets on Mathematics
This set of applets was written and published by Walter Fendt and includes some nice examples.

Coin Flipping
A page devoted to flipping coins and seeing how many heads and tails occur. Check the past results and add to them!

Live Mathematics on the Web (AAMT)
A good place to start exploring the idea of doing mathematics on the web, which also contains some information about configuring your computer software for this purpose.

Cut the Knot
A rich collection of diverse resources, many of them interactive in nature.

Virtual Polyhedra
George Hart's collection of over 1000 virtual reality polyhedra for to explore, requiring appropriate VRML software to be downloaded first.

Moebius Strip
An animated Moebius strip, together with extensive detailed information about them. From Eric Weisstein's World of Mathematics.

Klein Bottle
An animated Klein Bottle, a one-sided surface, together with extensive detailed information about such objects. From Eric Weisstein's World of Mathematics.

The Geometry Center
A large repository of many interesting geometric projects.

Uses of Java Applets in Mathematics Education
A good overview of the topic, consisting of an interactive paper by Chris Mawata of the University of Tennessee. The paper was presented at the Tsukuba, Japan ATCM conference in 1998. The paper contains many examples of Java applets. Here are some more examples from Chris.

Java applets
A large collection of Java web sites to support mathematics education, collected by SMARD.

Inverse Symbolic Calculator
A set of programs and specialized tables of mathematical constants dedicated to the identification of real numbers. It also serves as a way to produce identities. An ongoing project of the Centre for Experimental and Constructive Mathematics (CECM). Enter a decimal number and let the site decide what it is symbolically.

The Integrator
Enter an integration exercise and Mathematica will complete it for you.

Statistical Tools
An article from The Amnerican Statistician describing the use of the WWW as a powerful tool for furthering the development and practice of statistics using GASP (Globally Accessible Statistical Procedures). The GASP website has been set up as a primary listing of statistical procedures which can be used over the WWW. Applying the methods discussed, any statistical technique can be made available to anyone with a forms- or Java-capable WWW browser.

WebStat
A statistical software package written in the form of a Java applet which provides routines for statistical analysis via the WWW.

SISA
Simple Interactive Statistical Analysis (SISA) allows you to do statistical analysis directly on the Internet. Click on one of the procedure names provided, fill in the form, click the button, and the analysis will take place on the spot.

Calculators on line
Contains over 9330 calculators of various kinds created by over 1870 people.

Combinatorial Object Server
Specify a type of combinatorial object, together with specific parameter values, and COS will return to you a list of all such objects. COS can generate permutations, combinations, various types of trees, unlabelled graphs, linear extensions of posets, pentomino puzzle solutions, numerical partitions, and a host of other combinatorial objects.

Maths Online
Interactive multimedia learning materials for mathematics in schools from a project based at the University of Vienna, Austria, running since March 1998. Its goal is the construction of a modern mathematics learning site on the web.

Non-Euclidean Geometry
Interactive experience using Java scripts.

ExploreMath.Com
Interactive multimedia mathematics actiuvities from Millennium Press. This site is best viewed with a version 4 or higher web browser with the latest Shockwave Plugin from Macromedia installed. Lots of really interesting activities involving algebra and coordinate geometry. Many activities use slide-bars for varying parameters and values of variables, many use the coordinate plane well and msot also allow screen snapshots.

Platonic Solids
This entry is from Eric Weisstein's World of Mathematics, and contains interactive images of the Platonic solids as well as lots of related information. Following the various links to solids allows other aspects (such as duality) to be explored.

QuickMath
This site is available to perform mathematical computations of various kinds, using Mathematica as the engine. Algebra, equations, inequalities, calculus, matrices, graphing and numbers are all accessible. Very powerful, easy to use, good help accessible and even shows the working for some operations (such as algebraic expansions).

Centre for Technology and Teacher Education
This centre at the University of Virginia offers a number of activities for secondary mathematics teachers, incluing various interactive aspects (some of which are downloadable Excel worksheets.

Explore graphs of polar equations
This page contains a neat Java applet for graphing functions in polar coordinates. The site is located on the larger Experiment and explore mathematics site, which has many other interesting applets on it as well.

Acknowledgment: Many of the descriptions of the sites given above are abstracted from information provided by the sites.

Last Updated: 3 February 2001