Posted by: lboudreau | August 20, 2011

Fractal Day

I’ve wanted to do this for years.  For the first day of school, no syllabus.  Instead, we do math.  We’re making a big old fractal.

In each of five classes, we start by looking at images of all sorts of fractals, and how complex and lovely they can be.  Specifically, we look at the Koch Curve, and how each iteration builds toward infinite length bounded by a finite distance (which seems a metaphor for a person’s life, and rather profound, but that’s a blog for another day).  We guess what’ll happen next.  We explore self-similarity a while.  We apply the word “iteration” to sports practice.  Some students mention that it looked like the side of a snowflake, which moves us into the Koch Snowflake (smart students).

Next, we move to Sierpinski’s Carpet (related to the Triangle, but easier to draw on graph paper).  We guess what comes next.  We imagine end behaviors.  We admire it’s filigree state.

Finally, we break out the markers.  Life is so often about the arts and crafts. (Sorry for the fuzziness– camera’s acting up.)


Tables of students get large sheets of graph paper, off the presentation pad.  They choose their colors, and duplicate the Carpet on the third iteration.  That level is essentially a 27X27 block square and the paper is (conveniently enough) a 27X34 block sheet (something I didn’t count out until the morning we started, which caused a momentary panic flash, but all was well).  No table finished its fractal, so we’ll resume Monday.

But we won’t be done even then.  I teach girls, who are generally relational learners, so why not connect all my classes together in some sort of uber project?  Each sheet will be connected in a larger fractal; I think we’ll have three 3X3 sheet fractals when all is completed, and we’ll have to find some place to hang them.  Can’t wait.

Now this would be fine if it were simply a hook into the math, something for our first day together.  But it was better than that.  Sure, we learned math, but I learned a great deal about my students.  It turns out that there are numerous ways to look at that fractal and to get it onto paper.  It was enlightening to see how each student created patterns within patterns, how she counted and checked work, how she placed her body around the table to orient her thinking to the projected image.  Or how she didn’t.  We broke out the White Out a few times.  It was a very kinesthetic, very spatial kind of day and I had a chance to see a number of strategies at play.  (It would have been better if I’d known all these students already and could link learning approaches to individuals.  As it is, I only have a general sense for each class.)

I also plan to come back to this day at points during the year.  These two simple fractals are rich in topics: probability, sequences, area and length.  I’m looking forward to seeing what we do.


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