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MATH: THINKING MATHEMATICALLY
ON THE INTERNET
Since 1989, when the National Council of Teachers
of Mathematics (NCTM) first published Curriculum and Evaluation Standards for
School Mathematics, a change in the way that we view mathematics education
has been taking place. These changes continue today in the latest set
of standards developed by the NCTM.
The National Science Foundation has supported the development of several
outstanding directories. In addition, there are sites with intriguing puzzles,
software to download, weekly math challenges, biographies of famous women
in math, mathematicians who answer your students’ questions, lesson plans,
a homework center for students, and even ol’ Blue Dog who will answer
any four-function math problem your primary grade students throw his way...
by barking out the answer!
Teaching with the Internet: Elissa Morgan’s
Class
Numbers
a site located at Nottingham University in England
Math Counts and Math Word
Problems are sites with new math problems each week that really challenged
students to think.
Past Notable
Women of Mathematics
History
of Mathematics
Fractals
What are the Chances
Helping Your
Child Learn Math
Directories for Math Education
We encourage you to begin your explorations at one of the following directories:
• Eisenhower National Clearinghouse for Mathematics
and Science Education There are many great locations in this directory.
We especially like Math Topics
since it is neatly organized around the topics of math education.
Other key locations include:
• Digital Dozen
• Classroom Calendar
• ENC Focus
• Lessons and Activities
The Internet provides many helpful resources that can assist you in developing
an exciting and dynamic science program in your classroom, a program consistent
with the National Science Education Standard’s emphasis on thinking scientifically
through inquiry.
• Math Forum @ Drexel Provides many
useful resources for teachers, students, and others. The Math Forum maintains
chat areas and listservs/mailing lists for students and teachers to share
ideas and questions about math. Dr. Math is also on call
to answer questions from you or your students.
• Math Archives
provides resources for mathematicians at all levels, not just K–12 educators.
This site has an especially good collection of interactive math experiences
and free software to download and use in your classroom. There is also
a nice collection of links to web resources for math in the section Topics in Mathematics.
• Math
Section of Learning Resources This is a section of Canada’s SchoolNet and
is useful as you begin to explore links to math resources. At the present
time, this list is not organized by topic or grade level but SchoolNet is
quickly evolving and it looks like this will be an important resource.
• Mathematics
allows you to browse math resources by topic and grade level. All items are
linked to the standards of Ohio, derived from the national standards. The
grade browser since this saves tremendous amounts of time by organizing links.
All of the sites at this location contain resources you can use immediately
in your classroom.
• Math Virtual Library
This site from Florida State University provides a collection of exceptional
links to math resources. While it is neither topically nor developmentally
organized, it contains highly useful resources for math educators.
Keeping It Simple: Using Internet Workshop
One location with weekly problems for students is Brain Teasers, sponsored by
Houghton Mifflin Publishing. Each week, a new problem is presented by grade
level. If students require it, they may click on a ‘Hint” or a “Solution”
button. There is also an archive of problems used in the past.
If you work at the middle school level, you may wish to use problems that
appear on Japan’s Junior High math tests to see how your students compare.
Visit Japanese Math Challenge. Or, pay a visit to Ole Miss Problems of the
Week , a site featuring a weekly prize.
Here are just a few ideas to get you started with your own Internet workshops:
• Dr. FreeMath
is an electronic mail project where one mathematics question per month is
researched and answered by different classes. A great way to make math
come alive in your classroom.
• Biographies
of Women Mathematicians contains a developing set of biographies. Invite
students to read about one of these favorite women. Or, better yet,
have them do research on a new person, share their work during Internet Workshop,
and then send it to the manager of this site to be posted.
• MacTutor History
of Mathematics archive includes extensive links to sites with information
about the history of math. A nice location to set up a weekly question related
to math history.
• The Fruit Game
A simple interactive game, originally called Nim, with a hidden trick. See
if your students can explain the trick in writing. Share your best guesses
during Internet Workshop.
• Interactive Mathematics
Miscellany and Puzzles has an incredible list of links to games, activities,
and puzzles that will keep your class busy all year with Internet Workshop!
Set a bookmark!
Using Internet Project
In math, Internet Project is important because it encourages students to
work together to develop the ability to think mathematically. Part of thinking
mathematically is being able to communicate problem-solving strategies to
others and to listen as others describe different approaches to proofs.
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Down
the Drain is a project that connects both science and math. It has
students measure the amount of water they use each day and then compare their
use with others around the world.
Graph Goodies
is designed for K–2 students. It provides an early introduction into
the power of numbers and analysis. Take a look and you will find many ideas
that you can use right in your classroom.
The Noon
Day Project: Measuring the Circumference of the Earth is a project also
used in science. Students recreate the classic experiment conducted by Eratosthenes
over 2,200 years ago to determine the circumference of the Earth. Classes
measure the length of a shadow cast by a meter stick, share this data electronically,
use scale drawings and a spreadsheet to make comparisons, and use this information
to estimate the circumference of the earth.
The Global Grocery
List Project invites your students to enter grocery list data from their
location and conduct a variety of analyses using a worldwide database of
prices and foods contributed by other classes around the world. It is an
outstanding way to integrate social studies with mathematics.
Other projects may be joined by reviewing projects posted at the traditional
locations on the Internet such as:
Global SchoolNet’s Internet Project
Registry
Oz Projects
SchoolNet’s Grassroots Project Gallery
Intercultural Email Classroom Connections
Examples of projects that you may wish to post for others to join include:
• Problems for Problem Solvers Invite other classrooms to join
you in exchanging interesting math problems to solve together. Appoint one
class each week to be the lead class on a rotating basis. The lead class
is responsible for developing five problems or puzzles that are sent to participating
classes who then have a week to return the answers. Each week, another class
becomes the lead class and circulates five new problems or puzzles for everyone
to solve.
• Heads or Tails? A simple probability project for younger students.
Invite other classes to flip a coin from their country ten times and record
the number of times that heads turn up. Repeat this ten times. Then have them
send the results to your class. Record the data, write up the results, and
send back a report with the percentage of times heads turns up during a coin
toss. You may wish to invite participating schools to exchange the coins
they flipped so that young children become familiar with different currency
systems.
• Graph your Favorite This project was completed by students
in Grades 2, 4, and 6 classrooms in Michigan, Minnesota, Canada, Australia,
and California. Classes voted each week on their favorite item in one
category: pets, holidays, sports, school subjects, and food. Participating
classes sent their data to the project coordinator who compiled the results
each week and emailed it to everyone for further analysis. Students used
the data in raw form to make their own spreadsheets, both manually and by
computer. They also made computer bar graphs and pie graphs as well as manually
drawn bar graphs. Then they analyzed the graphs and drew conclusions using
the graphing website Create
a Graph.
 TEACHING TIP
Invite a group of participating classes to join you in working through the
experiences at Statistics Every
Writer Should Know and What
Are the Odds . After completing these experiences, have each class develop
group projects to analyze and report comparative statistics from their country,
state, or nation on some category where numerical data is kept. Use the site
Finding Data on the Internet
to obtain these data. Share the reports and provide responses to each report.
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Using Internet Inquiry
It is possible to organize Internet Inquiry around interesting sites that
already exist on the Internet. Examples include the very rich sites that
exist for the following:
• Kids Count Data Book
lets students explore all types of demographic information. Their explorations
will lead to important questions. The site includes exceptional tools for
displaying results in graphs, maps, rankings as well as raw data files. Use
this in your social studies classroom, too!
•NationMaster provides students
with important demographic statistics by nation, allowing them to compare
countries around the world on a number of different variables (over 900!).
It also provides graphing and presentation tools. Set a bookmark for Internet
Inquiry!
• Pi
Mathematics provides a history of pi. Students can view a video,
complete several different activities, calculate the best deal on several
pizzas, and share their favorite pizza topping with students around the world.
Have them write up a report on their experiences and share them with others.
• A Fractals Lesson Make
a fractal, learn how fractals are related to chopping broccoli, and view
fractals on the Web. Have students prepare a poster session on fractals for
the class including examples they printed out from sites on the Web.
• Mega Mathematics From
seemingly simple coloring problems that have perplexed cartographers for
centuries, to the mathematics of knots, to issues of infinity, to graphs
and games, this site has enough intriguing issues to keep any student thinking
mathematically for a year.
Another approach to Internet Inquiry is to encourage students to explore
sites containing links to many different topics in mathematics. Direct students
to any of the central sites described earlier in the chapter or explore some
of these locations:
• Knot a Braid of
Links is a great math location for students. Each week a new site
is selected in math. Previous links are available so that you can go down
the list until you find something really interesting.
• Interactive Mathematics
Miscellany and Puzzles Have students explore this site. Encourage
them to report on the history behind the problem as well as the problem itself.
They may wish to visit some of the history sites mentioned earlier to gather
information.
Using
WebQuest
If you teach middle grade math students, explore A Creative
Encounter of A Numerical Kind. This humorous webquest will send your students
on a voyage of number systems, determining which system would be best.
Perhaps you would like your students to calculate the current cost of building
a pyramid using modern materials and ancient methods. Take a look at Mr. Pitonyak’s Pyramid Puzzle.
If you teach math in Grades 4–8, explore Best Weather ,
a webquest for which you must develop a definition of good weather and then
evaluate the weather statistics in several cities, making graphs for each,
as you present the case for which city has the best weather. Student presentations
are then displayed for Open House Night.
If you teach Grades 6–12, complete World Shopping Spree. In this webquest, you find four common objects for sale in four different
countries. Then, converting each cost into dollars, you determine which country
has the best buy for each item.
If you teach at the high school level Baseball Prediction
is useful. Students analyze statistical correlations between a team’s winning
percentage and several performance indicators in order to make a recommendation
to management about which type of player to acquire: a home-run hitter, a
high-average hitter, a hitter who bats in more runs, a base stealer, or a
pitcher with a low earned-run average. If you have any baseball fans, this
would be a big hit.
A final example of a math webquest is Titanic:
What Can Numbers Tell Us About Her Fatal Voyage . In this activity students
evaluate several data bases containing statistical information on survivors
and deaths from this tragedy. Students use these data in the construction
of spreadsheet tables, with appropriate graphics, to illustrate specific statistical
conclusions.
Visiting the Classroom: Rob Hetzel’s
Math Classes in Wisconsin
"Life is good for only two things, discovering mathematics and teaching
mathematics.” You can see the true meaning of this quote by paying a visit
to his excellent homepage .
New Literacies in Math
The Internet is an exceptional tool for helping our students to think mathematically
as they develop the new literacies that are quickly becoming part of our evolving
definition of mathematics in a world in which math, information, critical
thinking, problem solving, communication, and the Internet are all converging.
Additional Math Resources on the Internet
100th Day of School Celebration Here is a series of great activities
to celebrate the magic behind the number 100. Send and receive a hundred emails,
see how hundreds of jellybeans can make hundreds of thousands, and many more
great, quick projects for your class.
Additional Resources
This is a teacher friendly collection of great math resources for your classroom.
Many useful links for teaching and learning. Set a bookmark!
ArithmAttack How
many basic math problems can you solve in one minute. Set a bookmark and
see how much each student can improve his or her scores for addition, subtraction,
multiplication, and division during the year.
Arithmetic
Software Do your students need new and fun ways to master basic arithmetic?
Here is a central site for great freeware and shareware you can download right
to your classroom computer. Set a bookmark!
Blue Dog Can Count!! A
classic! Blue dog answers all your basic math problems by barking out the
answers. A fun site and especially useful in the primary grades for practicing
basic math skills.
Explorer:
Mathematics The Explorer is a collection of educational resources including
instructional software, lab activities, and lesson plans for K–12 mathematics
and science education. A nice collection for busy teachers to obtain very
useful resources. Set a bookmark!
Finding Data on the Internet
Here is the place to get nearly every piece of statistical data on states,
countries, cities, and other geographical and political units. A treasure
trove for data snoopers and a great place for older students to explore during
Internet Inquiry.
Flashcards for Kids This
location offers a set of flashcard experiences for your students for addition,
subtraction, multiplication, and division at several different levels of difficulty.
It also lets you run flashcards in a timed or untimed mode and keeps your
score for you. A great resource for students learning their basic facts.
Geometry Classroom
Materials Are you looking for a range of Internet resources for your course
in geometry? Here is your answer, a great collection of teaching tools from
The Math Forum.
Great Graph Match If you work with graphs, here is a great location
for an Internet Workshop assignment. It may be set to make it harder or easier
for your students as they work to solve the problems.
Macalester College Problem
of the Week If you are looking for math challenges for your high school
classes, here is a wonderful site. Use each week’s problem to run a brief
Internet Workshop on Fridays to see if anyone has come up with the solution.
Math Hunt Have
your students complete a series of treasure hunts that help them to solve
a math problem. A great Internet Workshop resource.
Numbers in Search
of a Problem Looking for real-world statistics for problems in your class?
Here is a great site with statistics on everything from sports to population
to the stock market.
Practical Algebra
Lessons from Purplemath A series of wonderful tutorials and then interactive
Try-Its. A great set of assignments for Internet Workshop.
Statistics Learn
about central statistical concepts as you follow a fictional race between
two candidates by reading news bulletins. Discover what a random sample is,
what “margin of error” means, and why polls aren’t always right.
Online Communities for Math
Math Forum Newsletter An electronic newsletter from Drexel University.
Homepage: http://mathforum.org/electronic.newsletter/
Subscription address: majordomo@mathforum.org
Mailing Lists and Newsgroups list: http://mathforum.org/discussions/
Mathedcc This list is intended for anyone interested in technology in
math education.
Subscription address: listserv@vm1.mcgill.ca
Archives: http://archives.math.utk.edu/hypermail/mathedcc/
Mathsed-L A discussion on mathematics in education.
Subscription address: listserv@deakin.edu.au
MATHWEB-L A general math discussion area.
Subscription address: mailserv@hcca.ohio.gov
NCTM-L National Council of Teachers of Mathematics. Discussion of
mathematics teaching and the national standards.
Subscription address: majordomo@mathforum.org
Archives: http://mathforum.org/epigone/nctm-l
Math and Science Board from ProTeacher
Homepage: http://www.proteacher.net/cgi-bin/dcforum/dcboard.
cgi?az=list&forum=science
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