This video demonstrates a really cool and simple experiment that can be conducted with milk, food coloring, and dish soap.
http://www.youtube.com/watch?v=Rs8masuu5oE
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?
At the end of the term I ask students to write simple reflections on their experiences from the year: what they learned about math, about the world, about themselves. It’s one of the many ways I get students writing in math class.
It’s a great way to model reflection as part of the learning process, and it’s also a good way for me to get feedback about the student experience.
Mostly, it’s fun! I love sharing and discussing the reflections with students, and it always results in great end-of-year conversations.
Here are some of my favorites.
After learning a little more about math, I think math is created rather than discovered. This makes mathematicians and scientists the creators, not merely the seekers.
I learned a lot of things from my classmates that I wouldn’t have learned if I were to just study on my own.
I have learned that I still have very much to learn about myself.
Mathematics is magical; it can lead you to a dead end, but then it can miraculously open up an exit.
Learning how to think of things in three dimensions completely changed the way I saw math.
By seeing algebraic and geometric interpretations, I learned how to communicate math in more ways.
The process which turns a difficult problem into a relatively easy problem is the beauty of math.
One of the best parts of reflection is how much it gets you thinking about the future. Plenty of food for thought here.
For more resources, see my Writing in Math Class page.
Related Posts
This is a nice list of famous unsolved math problems from Wolfram MathWorld:
http://mathworld.wolfram.com/UnsolvedProblems.html
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.
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.
This is an great website full of galleries of mathematical images:
http://www.josleys.com/galleries.php
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!