Monday, August 15, 2016

Real Mathematicians

   First on my to-do list when I got back from TMC '16 was get a new notebook, because in Minneapolis I learned that real mathematicians go graph ruled.

My old notebook (left). My new notebook (right).

     Day 1 of Tessellation Nation. Michelle Niemi  is hard at work with a folded piece of paper and a scissors.  "I wonder if I could get a snowflake to tesselate?"
     I'm sitting next to her, deep into Christopher Danielson's turtles.  "I don't know," I tell her.  "But someone here probably does."
     Enter Dr. Edmund Harriss.  Co-author of Patterns of the Universe, researcher, professor at the University of Arkansas, and all-around great guy, Edmund would later blow my mind when he explained to me why a square can have wiggly sides and 72 degree angles.  But now he's got a problem to work out.
     I watch him sit down next to Michelle.  After listening to her for a few moments, he takes out a pad of graph ruled paper and a pencil.

     Putting the turtles aside, I turn my attention towards Edmund as he begins to explain to Michelle how he is going to accomplish this task, getting a snowflake to tessellate.  He starts drawing squares.  He's visualizing the folds.  He's marking where to cut.  He sees symmetrical designs in his mind's eye.  Mid-summer, and it's snowing in his head.   Michelle has questions.  She wants to know what he's thinking.   So do I.  Edmund is patient.  What's clear to him isn't clear to us.  He's got to go over it several times.
     And it occurs to me: I am watching a real mathematician solve a problem.  And it's thrilling!   Because I've never been this close before!  I'm not sure I really understand what he's talking about, and I don't care!  I'm just caught up in the excitement of watching him work.  And I think to myself, "This is what mathematicians do.  They solve problems.  On graph paper.  I need a graph ruled notebook.  And I need to stop thinking of myself as only a math teacher.  I need to be more of a math doer."
     Edmund finishes.  He takes a piece of paper, folds it into squares, and makes the cuts.  He's left with the pieces of a snowflake.
     "You could have every child in your class cut one of these out, and put all the pieces together to make a tessellation."    

     That evening: 

Once I started looking, I saw graph-ruled notebooks everywhere.

Henri Piccioto explained how to create a graph ruled notebook.

Megan Schmidt's spiral obsession, inspired by Edmund Harriss, began innocently during a school meeting as she kept herself a graph ruled notebook.

Of course sometimes graph ruled notebooks aren't available, and mathematicians need to improvise:

Jonathan Claydon did calculus on a napkin at dinner one night.

I love my new notebook:

I'm using it to solve problems for an informal summer book club...

...and it really came in handy for helping me understand the tessellation in my uniform tiling with curvature problem.

Up until last month, the closest I'd ever come to watching real mathematicians at work was at the movies.  Both real...

He helped defeat the Nazis!

...and otherwise.

Nice use of a vertical non-permanent surface, Will Hunting!

One of the great thrills of TMC is getting to watch real mathematicians do their thing live and unplugged.

John Golden (left) and Henri Piccioto (right).

So, nearly a month after it ended, I've finally found my #TMC1thing.  It's to put as much effort into doing math as I do into teaching math.  On a vertical non-permanent surface when I can, on a napkin if I have to, but mostly in a graph ruled notebook.  Like real mathematicians do.


  1. When I taught eighth graders, I gave every student a spiral-bound notebook with paper ruled in 1/4-inch squares. I think it was a terrific enhancement and worth the personal expense. I remember having them first number each page in the bottom outside corner. This discouraged them from tearing out pages and gave me full access to their thinking. I hope your graph ruled notebook gives you many mathematical meanderings.

    1. Thanks Marilyn, it already has. And I've found there's a psychological component too, if that makes sense; working in it makes me feel more mathematical somehow.
      The notebooks we order for our students to use for their math work have always been lined marble composition books. Graph paper is made available, but not widely used. I'm thinking now about experimenting with having kids do their work in graph ruled notebooks.