Archive for the ‘Resources’ Category

Guest Post for Moebius Noodles: Mathematical Weaving

It was an honor to contribute a guest post to Moebius Noodles, a wonderful project focused on creating resources that provide rich mathematical experiences for young children.

After seeing my TED Talk on Creativity and Mathematics, Maria Droujkova, one of the authors of Moebius Noodles, contacted me and asked if I would put together a piece about how I use weaving to explore mathematical ideas.

My piece is titled “Weaving Your Way Through Mathematics,” and can be found on the Moebius Noodles website.

More resources on mathematics and weaving can be found here.

Cool Milk Experiment

This video demonstrates a really cool and simple experiment that can be conducted with milk, food coloring, and dish soap.

Watching this pattern change and evolve made me think of chaotic dynamical systems, and their representations like the Mandelbrot set.

I wonder if there is mathematics that models systems like this and describe how they behave?

Click here to see more in Resources.

Unsolved Math Problems

June 9, 2012 1 comment

This is a nice list of famous unsolved math problems from Wolfram MathWorld:

There are some well-known problems here, like the Goldbach Conjecture and the Collatz Conjecture, and some lesser-known open problems like finding an Euler Brick with an integral space diagonal.

It’s especially nice that several of these challenges are easy to explain to non-mathematicians.  For example, the Goldbach Conjecture asks “Can every even number be written as the sum of two prime numbers?”  Somewhat surprisingly, after nearly 300 years, the best answer we have is probably.

I think I’ll make this page next year’s summer homework assignment.

Click here to see more in Challenge.

Catalog of Mathematical Knots

This is an amazing collection of interactive diagrams of mathematical knots:

Click on any of the hundred or so knots here to go to a flash-based interactive diagram of the knot that can be rotated and manipulated.

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Mathematical Image Galleries

This is an great website full of galleries of mathematical images:

There hundreds of beautiful images in many categories, like fractals, knots, spirals, and tesselations.

There’s even a gallery inspired by the techniques of  M.C. Escher!

Click here to see more in Resources.

TEDxNYED: Creativity and Mathematics

June 5, 2012 1 comment

Here is the video of my talk at this year’s TEDxNYED conference.  My talk was on Creativity and Mathematics.

Mathematics is an inherently creative activity.  Students and teachers alike often fail to appreciate just how creative math really is, so I wanted to share some of the simple ways that students and I create with mathematics in our classroom.

Speaking at this year’s TEDxNYED conference was a professional highlight for me.  Getting to share ideas with so many interesting and passionate people was an honor, and the unique experience created by the speakers, attendees, and conference organizers was a true inspiration.

Click here to see more in Teaching.

Fun With Self-Referential Tests

May 29, 2012 1 comment

A few years ago, I discovered a “self-referential test” online.  I was immediately hooked, and spent hours navigating the interconnected logic puzzle that posed questions like “The answer to number 8 is ” and “The first question whose answer is C is “.

The experience was so challenging, frustrating, and ultimately rewarding, that it didn’t take long to realize it was a perfect exercise for students.

I ended up creating some simpler examples that gently introduce the student to the idea of a self-referential test, a test where questions and answers refer to other questions and answers.  By playing around with these easier versions, students develop a sense of how to reason their way through using various problem-solving strategies.

After working through the more challenging versions, the final project for students is to create their own self-referential tests, which we then all enjoy solving.  This is the perfect kind of project, in that it allows students to exercise their creativity while pondering substantial and significant mathematical questions like “What constitutes a solution to this test?” and “Are we sure that this puzzle has a solution?”, as well as fundamental mathematical ideas like logical consistency.

To get you started, I offer two simple versions of the test.

Five Question version:  Simple Self-Referential Test 1

Ten Question version:  Simple Self-Referential Test 2

If you need the answers, you can click here, although I strongly encourage you to play around with the tests for a while before you look at the them.  The fun of this activity is in the struggle!

Click here to see more in Teaching.

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