The need to teach creativity in mathematics + FRACTALS!

I really resonated with Sam's most recent post about building time and space into curriculum to let students play with math. Mathematics is incredibly creative and innovative and I know that I (and I'm guessing others?) don't take enough time to let kids tinker. It's only when we sit there and tinker (preferably with something that intrigues us) that we become really good at something. This is a truth I constantly try to convince both kids and adults of: a mathematician wasn't miraculously born a "math person"; she found some kind of math that interested her and played with it for a very long time.  I.e., she had to work for it, but she most likely enjoyed the work.

And I am convinced every person can find some kind of math that he enjoys.

And I'm certainly convinced I can do more to be an advocate of the CREATIVITY needed to be successful in mathematics.

So here's a small first attempt! We're currently in our chapter of sequences and series in Precalc (which also includes the Binomial Theorem and hence Pascal's Triangle !!), so I thought it'd be fun to talk about fractals:

Fractals

(Email me if you would like the SMART Notebook file.)

I was able to find a decent video of the Mandelbrot Set (I muted the audio and played it on 2x speed).  We watched this as we talked about what they noticed/wondered.  They were very quick to point out possible fractals found in nature.

And we also watched one of Vi Hart's fabulous clips to motivate drawing fractals by hand (which is pretty darn addicting, no matter who you are):

After this video, we went over how to draw Sierpinski's Triangle (and how it's related to Pascal's Triangle!) and the Koch Snowflake. Then I let them research other fractals (there's a QR code to a Google doc I made with various good links for instructions on how to draw some fractals). Their assignment was to submit a fractal that they've drawn before spring break (either their own fractal or one that's already been "invented"). They are also to include both a recursive and explicit formula that models their iterations.

The types of things I saw as I walked around and the kinds of questions they were asking and the stuff they were pulling up on their phones made me so very happy. I felt completely justified in taking this time to breathe and to play and to create. I think I've said this before, but when you combine teenagers, art, and mathematics, you're bound to be continually impressed. I need to do this more.  

With that said, hopefully I'll have some good pictures to share next week!