**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*:

- A global classroom is now a desirable possibility; we should think of ourselves as residents of the global village and take advantage of the possibilities offered by email and the WWW
- Students are more likely to engage fruitfully with Internet-based materials than traditional media
- Education can and should be restructured to take advantage of online learning. This seems to be especially so in tertiary education.
- The penetration of the Internet into homes is happening so fast that home learning via the Internet TV is not far away and a serious alternative to formal schooling; already very many Australian students have better access to the Internet at home than at school.
- The classroom as an isolated box and perhaps even the book will shortly disappear; the role of the teacher will need to be redefined as a consequence.
- Professional connections will be mainly electronic and not restricted to one's local geographical environment
- The amount of useful material on the WWW is already very large and there are many people around who will continue to improve it and provide more material of high educational quality without necessarily seeking commercial gain

... to the other *Deep Skeptic*
extreme

- Access is a critical issue; many students and teachers do not really have significant personal access to the Internet. School use is generally occasional, constrained, brief and peripheral to the curriculum. Much Internet access requires movement to a special room outside the normal classroom.
- Cost/benefit ratios are grossly disproportionate; very high school investments have relatively low educational returns for most students
- Signal/noise ratios are disturbing; there is a great deal of useless information on the Internet that is easily located and much less really useful information that is harder to find
- Information is unfiltered, unlike traditional media such as books and journals which are edited and scrutinized by people other than the authors; many students in particular seem to think that information on the Internet is as reliable as information elsewhere
- Most of the Internet is about advertising and commerce and must be interpreted in those terms
- Who reads anyway? Many schools provide meager resources for student (or teacher) reading in mathematics. Web information that relies on reading seems premised on an assumption that reading will suddenly become more popular
- Surfing the net is about as intellectually productive as surfing the waves at the beach; a great deal of time can be wasted browsing that could have been used productively for learning
- Does WWW stand for the
*World Wide Wait*? At present, many Internet connections are very slow, particularly on older machines, slower (home and school) phone lines and over-graphicised web pages - Is it really the Information Super Hypeway after all?

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:

- What is the significant advantage of the site for students over other media?
- What is available or accessible for teachers that is not otherwise as readily available or accessible?
- What is the significance for curriculum development of the existence of the site?

I would be grateful to be informed of

- any errors, such as links to non-existent or hopelessly out of date pages
- any suggested deletions, mainly pages of little educational or mathematical value
- any suggested improvements to the annotations
- particularly interesting sites for mathematics and mathematics education that are not represented here
- suggestions for improving the classification scheme

Please send an email.

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.

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!

[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.

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,

*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.

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.

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.)

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.

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.

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.

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.

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.

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