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MATH:
THINKING MATHEMATICALLY ON THE INTERNET
Teaching With the Internet:
Elissa Morgan's Class
• On the evening of Open House, Clarissa showed her
mom several sites in the Math classroom:
• Clarissa's mom was thinking that math had certainly
changed since she went to school. She had a conversation with Ms. Morgan
about this because she wasn't certain how she could help Clarissa at home.
Ms. Morgan gave her a copy of an article she had obtained at the US Department
of Education web site and printed out, Helping
Your Child Learn Math.
Central Sites 
for Math Education
• As with science, one of the better central sites
is the Eisenhower
National Center for Mathematics and Science Education.
• Another outstanding central site is the Math Forum,
at Swarthmore College, funded by National Science Foundation. In addition
to links to useful math sites on the web, 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. Dr. Math
is a great resource for homework!
• A third central location you may wish to visit
is
Math Archives. Located at the University of Tennessee,
this site has an especially good collection of interactive math experiences
and free software you may wish to download and use in your classroom.
• The Math section at the Resources
section of Canada's SchoolNet may also be useful as you begin to explore
links to math resources. This location contains a number of links to math
sites you will find useful.
• The Math section of Web Sites and
Resources for Teachers is also a very useful as a jumping off point
into the web for math education. These sites are located at California
State Northridge and maintained by two professors in the School of Education.
• Finally, you may wish to participate in one of
the mailing lists located at the end of this chapter, or view one of several
discussion boards available to math educators. One of the more important
conversations taking place is located in the Teachers
Lounge of the Math Forum. Join in and share your questions, concerns,
and insights or just follow the conversations taking place.
Using Internet Workshop
• Many teachers will develop assignments for Internet
Workshop from one of several locations on the web that provide a weekly
math challenge for students, a math problem that requires careful thinking
to solve. Alternatively, some teachers will just print out this math problem
each week and duplicate copies for their students. One location with weekly
problems for students is Brain Teasers,
a location sponsored by Houghton Mifflin. 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.
• The Little Math Puzzle Contest is another site
with a weekly math problem for students, especially students in Canada.
This site presents a single, ungraded problem for students. There is also
an archive and a winner’s list. You must have a password to access the
answer at this site. Teachers may obtain the password via e-mail.
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Other sites, too, may be used for Internet
Workshop. Here are just a few ideas to get you started with your own
Internet Activity assignments:
• Dr. FreeMath
Dr. FreeMath is an electronic mail project where one mathematics question
per month will be researched and answered from each elementary class.
Past examples of questions include: How much water evaporates in the ocean
each year? Why is any number to the zero power equal to one? Why is pi
not really equal to 22/7? Have individuals bring their best questions to
Internet Workshop and then work together to pick one that is sent to Dr.
FreeMath.
•
Biographies of Women Mathematicians
This site contains a developing set of biographies. The group creating
this site is looking for others to research famous women mathematicians
and submit additional biographies. Invite students to read about one
of these favorite women and bring their story to Internet Workshop.
• MacTutor
History of Mathematics archive
Extensive links to sites with information about the history of math.
A nice location to set up a weekly question related to math history that
will help students develop a richer understanding of math concepts.
• 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
Forget the title. Check this site out! It 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!
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Using Internet Project
• There are several examples of Internet Project
in math that run continuously and have a site on the WWW. The Noon Day Project: Measuring the Circumference of the
Earth is a project in which students recreate the classic experiment
conducted by Eratosthenes over 2,200 years ago to determine the circumference
of the Earth. Collaborating with students from other schools throughout
the world at roughly the same time, 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.
• Another project site for mathematics is The Global Grocery
List Project. This project has your students enter grocery list
data from their location and then conduct a variety of analyses using a
worldwide data base of prices and foods contributed by other classes around
the world. It is an outstanding way in which you can integrate social studies
with mathematics.
• There are also several stock market competitions
that take place between classrooms on the Internet. Good News Bears, a year-long stock market game
for middle school students is one such location. Here, students participate
in a contest using on-line stock market data as they do research and then
buy and sell stocks in an attempt to maximize their portfolio. It is an
excellent experience that brings mathematical thinking to real world problems
and solutions.
E-MAIL FOR YOU
From: Jodi Moore
Jodi prints a problem for my class each week from Brain Teasers
or The Elementary
Problem of the Week. The problems provide an avenue for healthy competition
as well as practice and discussion within the classroom.
Her students also frequent various web sites which provide useful
information for research and reference on mathematicians and related mathematical
topics such as the MacTutor
History of Mathematics Archive. |
• Other projects may be joined by reviewing projects
posted at the traditional locations on the Internet such as Global SchoolNet’s Internet
Project Registry, SchoolNet's Grassroots Project Gallery, and
Intercultural
E-mail Classroom Connections. If you see a project that matches
your instructional needs for an upcoming unit, be certain to join.
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Alternatively, you may wish to work with your
class during Internet Workshop to develop an Internet project in math
that you post and invite others to join. Be certain to plan this far enough
in advance that you can attract enough participants and develop communication
links. 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. The lead class is also responsible for responding
to each class and the solutions they suggested. Each week, another class
becomes the lead class and circulates five new problems or puzzles for
everyone to solve.
• Heads or Tails?
Here is 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 activity was completed by students in grades 2, 4, and 6 classrooms
in Michigan, Minnesota, Canada, Australia, and California. Students in
eight participating classes voted each week on their favorite item in one
category: pets, holidays, sports, school subjects, and food. The data was
calculated separately for boys and for girls. Participating classes sent
their data to the project coordinator who compiled the results each week
and e-mailed 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. Try
the Illuminations
site for teaching graphing with the Internet. The site offers multi-day
lesson plans in which students pose and answer questions using
graphs. Graphing lessons give students an opportunity to apply their
problem-solving and communication skills.
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TEACHING TIP
Here is a project for middle school or high
school students who are exploring statistics. Invite a group of participating
classes to join you in working through the experiences at Statistics Every Writer
Should Know. 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. Then share the reports that
were developed and provide responses to each report. |
Using Internet Inquiry
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Sometimes, it is possible to organize Internet
Inquiry around interesting sites that already exist on the Internet. Some
already existing sites are the following:
• Pi Mathematics
Have students read about the history of pi, 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. Soon,
you will have to have a sign-up list for this site during Internet Inquiry.
• A Fractals
Lesson
Have students explore this site during Internet Inquiry, making a fractal,
learning how fractals are related to chopping broccoli, and viewing fractals
on the WWW. Then have them prepare a poster session on fractals for the
class, including examples they printed out from sites on the WWW.
• Mega Mathematics
There are so many wonderful Internet Inquiry possibilities at this site
it is hard to know where to begin. From a seemingly simple coloring problem
that has 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. Point students
to this site and stand back. Set a bookmark!
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Another approach to Internet Inquiry is to
encourage students to explore sites containing links to many different topics
in mathematics. As students explore these sites, encourage them to explore
and define a project they wish to complete. You could direct them to any
of the central sites described earlier in the chapter or you could direct
them to some of these locations:
• Knot a Braid
Here is a great math location for students searching for an Inquiry
project. 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. It won’t be hard at this location.
• Interactive Mathematics
Miscellany and Puzzles
Have students do Internet Inquiry on one of the puzzles or problems
at this site. Be certain to 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.
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TEACHING TIP
Often each of us has a specific question
about teaching math or the need for new resources to enliven our math
class. When you have a question, be certain to visit the important resources
at Teacher2Teacher in The Math Forum. This resource provides you with access
to some of the best math educators in the country who are ready to answer
any question you might have. Be certain, though, to review their archive
of answers, first, to see if someone has already addressed your question.
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Using WebQuests
• If you teach at the high school level and are looking
for a WebQuest on statistics, you might find Baseball
Prediction useful. In this experience, students must 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.
• If you teach math in grades 4-8, you might be interested
in using Best Weather, a WebQuest where 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 on Open
House Night.
• If you teach grades 6-12, you might wish students
to 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.
• 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.
Instructional Resources on the
Internet
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• 100th
Day of School Celebration
As you approach the 100th day of school each year in your primary grade
classrooms, here is a series of great activities to celebrate the magic
behind the number 100. Send and receive a hundred e-mails, see how hundreds
of jelly beans can make hundreds of thousands, and many more great, quick
projects for your class.
• About
Today’s Date
Have students visit this page each day to find out interesting information
about each of the numbers from 1 to 31. Your kids will learn a lot by just
reading the information at these pages. Post the information in class,
too, in your math center. Make a bookmark!
• 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. This non-commercial
site challenges you and your students. Set a bookmark and see how much
each student can improve their scores for addition, subtraction, multiplication,
and division during the year. A great location for the elementary grades.
You may even download this software for free.
• Arithmetic Software
Do you 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!!
Blue dog answers all your basic math problems by barking out the answers.
A fun site and especially useful in the primary grades for developing basic
math skills.
• Classroom Links
- Math
Here is a set of great links to wonderful sites for mathematics education.
From a fractal microscope, to a location for Googolplex, to Virtual Polyhedra,
this site has outstanding sites for students and teachers. Set a bookmark!
• 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. If you work with high school students, set a bookmark!
• Flashcards for Kids
This location lets you view 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.
• Geometry Problem
of the Week
Part of the Math Forum at Swarthmore College, this location provides
you and your students with a challenging geometry problem to solve each
week as well as an archive of past problems.
• Interactive Algebra Tutorials
Do your students need additional practice on various types of algebra
problems? Just set a link to this location to provide them with practice,
immediate feedback, and support.
• Jumpin' Jehosaphat
the Counting Sheep
Here is a sheep that will solve addition, subtraction, multiplication,
and division problems for your younger students. It jumps and counts out
the answer, in Sheepese. Much fun! It runs better with Internet Explorer
3.0 or later than with Netscape.
• KidsConnect
Sponsored by the American Library Association, KidsConnect is a question-answering,
homework help and referral service for K-12 students on the Internet. If
your students have questions about math and you are not available, this
is a great resource. The goal of the service is to help students access
and use the information available on the Internet effectively and efficiently.
It is most useful for math, but can service other subjects, too.
• Knot a Braid of Links
Here is a great resource from Canada that announces a best site of the
week via email. It also includes a great collection of best sites from
the past. Many links to very useful resources may be found here.
• 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.
• MacTutor History of Mathematics archive
Interested in the history of mathematics? Here is the URL 4 U. Find
out who the mathematician of the day is, or read the biographies of famous
mathematicians and learn about their accomplishments. It contains many
unique links to sites about the history of mathematics.
• Middle School
Problem of the Week
Great challenges for your middle school math classes, these problems
are brought to you by The Math Forum. Conduct a brief Internet Workshop
each week to solve each puzzle.
• NCTM Standards
This is the document that has had a powerful effect on the way many
people think about mathematics instruction. Reading it can provide you
with useful insights about this area of the curriculum. New standards
for math education will appear in 2000. Be certain to visit the NCTM site to get links
to the new standards when they appear.
• 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.
• 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.
• Statistics Every
Writer Should Know
This is an excellent tutorial for students learning about simple statistics
including means, medians, per cent, per capita, and more. A great interactive
tutorial to help middle school students understand these concepts.
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Listservs/Mailing Lists for Math
Education
• NCTM-L
- listproc@sci-ed.fit.edu
A discussion group on math education sponsored by the National Council
of Teachers of Mathematics. Archives are available at: http://forum.swarthmore.edu/epigone/nctm-l/
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