Chapter One

Chapter Two

Chapter Three

Chapter Four

Chapter Five

Chapter Six

Chapter Seven

Chapter Eight

Chapter Nine

Chapter Ten

Chapter Eleven

Chapter Twelve



Donald J. Leu


Deborah D. Leu


Julie Coiro

Chapter Eight

 

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.

   E-MAIL FOR YOU

From: Jodi Moore (jmoore@ms.spotsylvania.k12.va.us)
Subject: Using the Internet for Math

Brain Teasers
The Elementary Problem of the Week
MacTutor History of Mathematics Archive

The Internet is a powerful tool will literally make all the difference in the world with students. I can honestly say I am glad technology has arrived!

Jodi Moore 7th grade
Freedom Middle School
Fredericskburg, VA  22407

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.


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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