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This page contains information on Mathematics resources located on the Internet. Our purpose in providing you with information on these resources is simply to draw them to your attention. We are NOT guaranteeing that these particular resources will be valuable and without frustrations.
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His interest in math 'stuff' stimulated by his grandfather, Clay Ford created a web page full of interesting mathematical curiosities. Some of these will be familiar to many of us pre-calculator types, for example some of the quick calculation rules that we were taught by teachers or parents. Others are less practical but still are intriguing to consider and look at - finger math, word roots, Bible numbers are just a few.
Most of the contents are not going to be useful to your students on a regular basis, but they serve as a great way to stimulate interest. For example, introduce your students to the section titled "Scroll Down Slowly". Have each of them complete it on on his/her own and then compare their starting numbers and ending answers. I suspect that almost all of your students with have the same answer no matter what number they started with. The fun part, for the teacher, is explaining why. The next bit of fun then is to challenge your students to create their own mystery so that they can try it on their younger siblings - with suitable warnings against taking bets from them of course.
Curious and Useful Math is hosted by Clay Ford and is suitable for math students in K-12. It is located at:
Cynthia Lanius, a math teacher currently working at Rice University, offers 16 of her lessons on a variety of mathematical topics. High school students will benefit the most from these, but quite a number of the lessons can also be used with students as low as grade 5. The topics covered are: Calculus, Data Collection/Analysis, Exponential Growth, Fractals, Fractions, Geometry, Graphs, Mathematics of Cartography, Pre-Algebra, Puzzles, Series, Slope, and Transformations.
The type and extent of each lesson varies but within the collection you'll find a variety of student activities, teacher guides, exploration or thought questions, links to associated materials on the web, and assignments. There is no one standard approach to the content - you really need to go in and see each lesson. Be sure to look at the link to "Geometry Online" - it's a collection of about 10 lessons/activities and there's enough there to keep you busy for a while.
Mathematics Lessons That Are Fun is hosted by Rice University and is suitable for math students in grades 5-12.
With more than 1,300 mathematicans' biographies accessible either chronologically or alphabetically, this Scottish site sets the standard of comparison for all other math history web resources. In addition to the searchable archive of biographies, you can read the Mathematician of the Day page and/or find the mathematicians who were born on a particular day, access touch sensitive maps of mathematician's birthplaces, see how the lives of mathematicians overlapped each other, learn about the various honours that have been bestowed on famous mathematicians, and print out posters of them.
This site is more than just a set of biographies of mathematicians . If you prefer to study math history in a non-biographical manner, the MacTutor developers have written more than 30 articles on the history of various math topics (e.g., the rise of Calculus, the Quantum age...). They also have given their visitors access to resources which give the history and properties of more than 60 mathematical curves (e.g., Fermat's Spiral, Newton's Parabolas...). If you have a Java capable browser, you can interact with the curves and experiment with them to see how they work.
The MacTutor History of Math Archive site is hosted by John J O'Connor and Edmund F Robertson of the University of St. Andrews in Scotland and is suitable for math students in grades 4-12.
If you're looking for ways to interest students in mathematics, a popular and effective technique is to expose them to math puzzles. These kinds of activities demonstrate that mathematics can be fun and challenging and doesn't have to be confined to traditional arithmetic/algebraic problem sets.
The AIMS Puzzle Corner posts a new puzzle every month. Included in the posting are tips to the teacher on how to use the puzzle as well as student worksheets where appropriate. The solution to the puzzle is posted the following month; however, to discourage casual browsers, they require you to answer a skill testing question to access the solution archives. There's a full set of past puzzles going back to 1995 so there are plenty to offer to your students and you won't have to wait a month to get the answer if you get stumped.
The AIMS Puzzle Corner is hosted by AIMS Education Foundation and is suitable for math students in grades K-9.
Here's a collection of about 30 ideas for activities that all you math teachers might want to take a look at. Organized by grade level (K-6, 7-8, 9-12), they're intended to engage students in real world applications of math. The activities are provided in a lesson plan format complete with rationale, background information, activity materials, instructions, and enrichment.
On the plus side, I liked how the developers tied the activity/problem to the real world. For example, the setting of a new high altitude record by a solar powered aircraft was used to introduce students to the layers of the atmosphere, the relationship between altitude and temperature data, the formulas for converting temperature data (Celsius, Fahrenheit, Kelvin) as well as distance data, and the slope formula. On the cautionary side, the activities don't provide any great depth of content (the teacher would have to supplement that) and the developers use NASA-based examples, products, and problems throughout the activities and, as such, there is an intended, subtle promotion of NASA itself.
The Math Activities for K-12 Teachers site is developed by the California Polytechnic State University and funded by NASA, and is suitable for math students/teachers in grades K-12.
"Word problems, story problems"...whatever you call them, when you are trying to teach math problem solving skills it is nice to be able to have many different examples at your fingertips to use. Well this is the site for you! It contains sample questions for every math topic you need to cover. Some other areas are History and Science , ratio, %, area/volume, critical thinking, number patterns, and 2 step problems (the bane of Gr. 4). Included are interest stories such as Thanksgiving, birthdays, and soccer.
When you are tired of the "usual" math problems this is a great resource to have on hand. It is totally text based, free and easy to print out, and best of all contains all the answers - again saving you time.
Math Stories.com is hosted by Highlights and is suitable for Math students in grades K-6.
This site uses a problem solving approach to teaching various Math concepts. At the present time the following areas contain lessons: Understanding Percent, Number Theory, Circumference and Area of Circles, and Perimeter and Area of Polygons. In each of the lessons, various terms are hotlinked to an easy to understand dictionary meaning. Diagrams are included which help clarify the concept. Each group of lessons also contains one set of challenge activities for those students who would benefit from such exercises.
Math Goodies is hosted by Mrs.Glosser and is suitable for Math students in grades 3-8.
Math and Art, what a combination for the two sides of the brain to be developed!! This site explains symmetry and pattern, has a rug gallery of 28 samples (that explain whether the rug is indeed symmetrical), educational resources (ideas for teaching patterns and symmetry, a bibilography with other links), and a section describing oriental carpets (including patterns, and rug knots used).
I had a request for ideas to use with a gifted six year old Math student from Maree Maney in Australia. Here is a site that I think will be just what she wants. It is a series of "teacher submitted" lesson plans. The topics include using the sports page for problem solving (something that a grade 1 teacher I know uses every hockey season), making change, cooking, graphing, and using peanut butter and jelly sandwiches for ratios. The site is nothing fancy but the content is very easy to use and teacher tested!!
"Are you needing ideas for teaching statistics and probability? This is the place to check out. The site is based on the NCTM standards of statistics and probability. There are three main areas on the site: web units, a student center, and the teachersÕ place. In the web unit section are lessons plan topics which include early primary ideas for using picture books and M&MÕs chocolate candies, through intermediate grades and senior secondary (the cereal box problem, NCAA basketball finals, and the Indy 500).
This site is hosted by Urban Systemic Initiative and is suitable for Math students Grades K-12.
Estimating, calculating and evaluating are the concepts behind the collection of links at "Measure 4 Measure'. If you need to deal with numbers related to astronomy, board feet, body surface bowling, budgeting for college, compound interest, daily iron, sun position, water softening, weather or literally dozens of other numeric topics, this is the site to visit.
The "Untangling the Mathematics of Knots" webpage provides a variety of activities for exploring knots made from pieces of rope. Making, classifying and comparing knots are part of the fun, with knot arithmetic, braids, links and others as topics.
For a meta-knot site, with links to dozens of knot-related resources, knot puzzles and even the instructions for tying a necktie knot, try "Knots on the Web".
Knots on the Web:
Finally, I don't know if Celtic Knots are mathematics, history, art, or something else entirely. I just enjoy the beauty and the mystery of them and I found the "how to construct a celtic knot" link to be a fascinating exercise in patterns and symmetry.
"Recently the study of knots has proved to be of great interest to theoretical physicists & molecular biologists. One of the most peculiar things which emerges as you study knots is how a category of objects as simple as a knot could be so rich in profound mathematical connections."
..................from Untangling the Mathematics of Knots.
'Math Homework Help' is an "Ask the Expert" site. You can email your questions directly to "Bram", browse through the links to math formulas, theories and rules, or find information about great mathematicians, math software and more. The emphasis is on secondary level math.
Younger students might enjoy the interactive "Click on Bricks" approach to developing multiplication skills. This site also links to a collection sites appropriate for middle school and younger, with an emphasis on fun. Note that "Click on Bricks" is one of the "ThinkQuest Junior" submissions.
Here's a site where math concepts such as logic and attribute theory can be explored through online and free downloadable games (along with products you can order if you really become hooked).
Visit this web page and learn the rules of the 'Set Game', participate in a daily challenge, find out about the math and brain research related to this type of play and find other Set players to talk to.
The game was developed from the coding system of a genetics researcher who was trying to find out whether German Sherpherd dogs with epilepsy had inherited the disorder or developed it in some other way. Apparently her playful nature crept into the project, and her file cards became a collection of shapes and colours representing various characteristics of the dogs. Ultimately, the shapes and colours took on a life of their own as a game which can challenge players from kindergarten to adult.
"How are rainbows formed? Why do they only occur when the sun is behind the observer? If the sun is low on the horizon, at what angle in the sky should we expect to see a rainbow?"
The Curriculum Initiative Project (University of Minnesota) offers the above online lab where students can find answers to these and other questions by examining a mathematical model of light passing through a water droplet.
Along with a mathematical exploration of rainbows, you might want to consider their poetic and aesthetic aspects. Randy Wang's beautiful photographs are annotated with verse that describes what seems to be an almost inborn fascination with rainbows.
Randy Wang's Rainbow photos: http://www.cs.princeton.edu/~rywang/berkeley/./magic_small/rainbows.html
Fractals and Tesselations are beautiful visual patterns which follow Mathematical rules and illustrate concepts of symmetry, complexity, repetition, iteration, order, chaos, input, output, etc. As well as being educational, they are also fun and can be created using a variety of media.
The Community Learning Network (CLN) has gathered internet sites and created two theme pages. These K-12 resources for the study of Fractals and Tesselations include samples of student designs, lesson ideas, software approaches and more.
Conspiratorial Coincidences, Number Numbness, Percentage Pumping and Self-Fulfilling Prophecies are among the many topics at the above site. A humourous discussion of the mathematical mistakes that are made with all-too-much regularity by the media, reporters, advertisers, politicians, and others (perhaps even by students), this site opens the door to discussions about whether or not some 'mistakes' might be intentional efforts at deception.
There are enough topics here to generate a new weekly theme in your math class over the course of the full school year. Magazine and newspaper clippings could be collected to demonstrate that the errors described are really out there -- and they're out to get us. What better motivation to learn the 'correct' math?
To find out about new directions in teaching Math, ways for evaluating student learning in Math, using technology in the Mathematics classroom, or, as a place to find out what the current research is saying about Math Ed, you need look no further than the Swarthmore Math Forum.
This site has hundreds of links to the types of information that Math teachers can use in their daily lives. Many of the articles could be very useful to share with parents as well.
A section that was of particular interest to me dealt with constructivism in Math. There were also some intriguing references in the research sections on "Cross-Age Tutoring", "Motivation in Math" and "Girls' Attitudes, Self-Expectations, and Performance in Math."
"...the use of cooperative rather than competitive learning, plays a pivotal role in girls' relationship with math..."
Attitude is an important factor in learning, and "What Good is Math?" (the above website) has ideas designed to promote a more positive attitude towards mathematics. This is the site for kids who might not realize that math can help them plan the chocolate fudge cake for their next party, or get the best deal when buying a new pair of shoes.
Older students, who might be ready to start interpreting statistical information will appreciate the "Statistics every writer should know" page. This site deals with concepts including mean, median, percentage, per capita, margin of error, standard deviation and more. It's all written in plain English. Perhaps an interesting lesson could be built around this site in combination with some current news stories. Just how valid are those numbers we're always reading about? The URL is: http://nilesonline.com/stats/
"Mathematicians have developed an entire field - statistics - dedicated to getting answers out of numbers."
"Pi in the Sky", "Pi through the Ages", "The Pi Trivia Game", and "Pi Poetry", are just a handful of the dozens of Pi-related links at this web site. The people who build Pi pages often have more than mathematics on their minds and you'll find everything from humour to the Bible to some rather bizarre mnemonic devices and puzzles.
I'll stop here, but in 1995, Pi was calculated to 3,221,220,000 decimal places by Yasumasa Kanada. If you consider the fact that "39 decimal places of pi is enough to compute the circumference of a circle around the known universe to within an accuracy of the radius of a hydrogen atom!" then Kanada's calculation is impressively compulsive!
If you're interested in logical puzzles, perhaps as part of a math curriculum, the above web sites offer a range of levels. The first,in the format of a play, allows upper elementary children to act out a variety of parts and discover clues that should lead them to a logical conclusion. The second offers puzzles that will change regularly and from my encounter with this month's 'dinner party' example I am guessing that each one is likely to be a challenge for middle school students and beyond.
Finally, if you want to get into the most formal level of logic, Stefan Waner and Steven R. Costenoble of Hofstra University have created a complete, online textbook on the topic. This information is suitable for senior students and you'll need a graphical browser to view the tables and equations.
The site also includes interactive math quizzes and links to free downloadable
software. What is the "liar's paradox?" Can all truths be expressed using
formal logic? When the Zen master says "If I am Buddha, then I am not Buddha,"
how should you respond? Find out at:
Math Activities for 5-13 year olds are the focus of this web site hosted by the U.S. Department of Education. Topics include things that kids can do at home, at the grocery store, or in transit. Everything is designed with kids and parents in mind, but could be adapted for classroom use.
Note that some of the accompanying materials at this site are geared towards parents as participants in their child's math education experiences. These ideas could be useful discussion starters at parent/teacher meetings.
A few links down on this web page you will find the Swarthmore Math Forum website, which I highly recommend. The purpose of this update is to let you know about a new way to keep informed about the site.
You can subscribe to their weekly newsletter as follows:
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Find out about the interactive math projects, Geometry Problem & Elementary Problem of the Week, suggestions for K-12 teachers and students and much more. Previous newsletters are archived
This web page is designed for math educators, math students, and their parents. Preschoolers to teens are represented in the brain teasers area, there are opportunities to set up projects with other classrooms, links to internet math sites, and software demos.
The Parents' Handbook has ideas such as games, activities and reading lists that could also be useful to people other than parents. Teachers or even kids (especially if you set up pairs of 'math buddies') would probably have fun trying out the suggestions here.
The Math Forum is a centre for teachers, students, researchers, parents and mathematicians at all levels. This site offers "Ask Dr. Math", as well as problem-solving activities, an annotated collection of Internet math sites and sections devoted to math education and key issues of interest to the mathematics community.