Mathcircles.org

This is the website for the National Association of Math Circles:

http://www.mathcircles.org/

A Math Circle can be many things, but essentially it is a group of people who get together to have fun with mathematics.  Math Circles exist for young children, older students, teachers, and professionals, and some groups involve all of the above!

There are Math Circles all over the world, and this website aims to create a directory of such circles and provide resources for students and teachers alike.  Use this resource to find a Math Circle in your area; or, start one of your own!

Math Teachers and Twitter

Twitter is a robust and adaptable social-networking platform that makes it easy to exchange ideas and resources with others who share your interests.  Twitter has dramatically affected how I think about teaching, how I plan for teaching, and what I do when I need ideas, inspiration, or assistance.

What follows is a brief introduction to Twitter, how I use it, and why other math teachers might want to use it, too.

The philosophy that underlies Twitter is very simple.  Every user on Twitter is essentially their own broadcast channel.  You decide which users to listen to by following them.  If you follow a user, you will see every message they publish.  If you like what they say, great:  you can re-broadcast their message to your followers (a re-tweet), you can start a discussion, or you can just listen.

What if you don’t like what someone has to say?  Well, remember, you can always just listen.  Or, perhaps you want to see what other people might say in response.  In the end, if you’re not interested in what someone is broadcasting, you simply un-follow them.  You’ll no longer receive their messages.

One feature that makes Twitter unique is message length:  all messages must be less than 140 characters.  This is a hold-over from Twitter’s beginnings as a text-message-based platform; it forces users to be concise, and it keeps conversations moving quickly.

But what really makes Twitter so powerful are the many communities that use it to share and discuss ideas.  At any given time, there are millions of conversations happening between passionate and knowledgeable people on Twitter.  The key is to find people who are talking about what interests you.  When you find them, listen to them, and find out whom they listen to.  And when you are ready, start participating.

For example, there are thousands of math teachers on Twitter from all over the world, from all different backgrounds, with different perspectives on math and teaching.  Through Twitter, we share ideas, ask each other questions, brainstorm project ideas, pass great around resources, and actively discuss math and teaching in a highly positive and constructive way.

Here are just a few examples of how Twitter has affected me, as both a teacher and a professional.

  • I enjoy taking math photos and posting them here on www.MrHonner.com.  A teacher 1,000 miles away saw them, shared them with his students, and now they are taking their own math photos!
  • Alex Bogomolny, creator of Cut The Knot Math, frequently tweets about great math proofs, paradoxes, and puzzles.  He shared a question about a curious geometric limit and asked if anyone had a different solution; I quickly became obsessed and spent a Saturday morning coming up with this trigonometric approach.
  • After many Twitter-based conversations about the NY Math Regents exams, I wrote a short series on the quality of the tests.  This connected me to other teachers around the city and state who read the articles and shared their thoughts with me through Twitter, email, and blogging.

To get started on Twitter, register for an account and start following some people who might interest you.  For math teachers, here’s a short list of recommendations:  follow these folks, see whom they follow, see who follows them, and pretty soon you’ll have your own personal learning network!

  • @CutTheKnotMath — The creator of Cut-the-knot.org who frequently shares great links and great ideas.
  • @TimChartier — Math professor at Davidson college interested in teaching, technology, and mime.
  • @StevenStrogatz — A well-known mathematician and author at Cornell.
  • @JohnDCook — Applied mathematician, statistician and consultant John Cook.
  • @divbyzero — Dave Richeson, professor of mathematics at Dickinson College, and a great blogger.
  • @evelynjlamb — Evelyn Lamb, a mathematician and writer for Scientific American and other sites.
  • @RepublicofMath — A mathematician and math educator who is actively involved in many Twitter-based math communities.
  • @DavidWees — Canadian educator focusing on math and technology.  A tireless tweeter.
  • @monsoon0 — Applied mathematician at the University of Sydney
  • @MathBloggingEds — Editors picks from MathBlogging.org, a math-blog aggregator site.
  • @mathematicsprof — Math professor sharing an endless stream of interesting ideas and links
  • @maanow — Official Twitter account of the Mathematical Association of America
  • @amermathsoc — Official Twitter account of the American Mathematical Society
  • @MathforAmerica — Official Twtter acccount of Math for America, an outstanding professional organization devoted to recruiting, training, and retaining great math teachers.
  • @MrHonner — My Twitter account.  You can find everyone above, and many others, on my “Following” list.

So sign up, start following, and start listening!  Before you know it, you’ll find yourself thinking, teaching, and learning a lot differently!

Breeding a Better Wind Turbine

This is a truly mind-blowing idea:  using the principle of natural selection to “evolve” a more efficient wind turbine blade.

http://www.youtube.com/watch?v=YZUNRmwoijw

Looking to see if he could somehow improve upon the standard blade design, a designer created a virtual world populated by blades of different shapes.  He then “played god” by defining rules for reproduction between two blades.

Rules like “the most efficient blade gets first pick of mate”, and “the least efficient blades die” created a virtual world governed by the principle of natural selection, and after many generations, only the fittest, or most efficient blades. survived!

An unconventional blade emerged from the virtual world, but it passed the designers tests with flying colors, beating out the standard blade-design in efficiency.  The blade looks strange, but it’s probably not the first odd-looking result of natural selection.  After all, the camel is a weird-looking animal, but it gets the job done!

Fun With Sliceforms

I was recently inspired to make my first sliceform.

With a handful of index cards, a marker, and some scissors, I was able to make this fun representation of a surface in 3D!

Sliceform Front 1

Turn it to the side, and see the surface from a different perspective.

Sliceform Side

The inspiration was timely, as my Calculus class has been discussing cross-sections, traces, and level curves of surfaces in space.  What a perfect way to demonstrate how to understand a surface by looking at representative slices!

A great, simple tool, and you can see some examples of the sliceforms my students created, like the one seen below, here.

fun with sliceforms

A Geometry Challenge

I recently had some fun with one of my favorite triangles.  It all started with this innocent NY State Regents Exam question:

In triangle ABC, we have a = 15, b = 14, and c = 13.  Find the measure of angle C.

This problem is designed to test the student’s knowledge of the Law of Cosines, but because of the special nature of the 13-14-15 triangle, it’s easy to find angle C without it.

And since it was a multiple choice question, I considered another approach.  I constructed an equilateral triangle with side AB and produced the following diagram:

Before I actually performed the construction, I assumed that third vertex of the equilateral triangle would lie in the interior of the original triangle ABC.  By the construction above, it appears to be outside triangle ABC.

So here’s the challenge:  prove that the third vertex of the equilateral triangle lies inside triangle ABC without using the Law of Cosines!

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