Monday, August 29, 2016

Talking Math With Your Kid: End of Summer Edition

    Having aged out of camp, and unable to subsist on the cash received from her intermittent babysitting gigs, my daughter faced the same prospect her brother had faced two summers before: get a job. That's how, on a warm, late June afternoon, with her dad in tow for moral support and a folder full of very skimpy resumes, she found herself pounding the pavement in downtown Princeton, New Jersey.

Nassau St.

Throughout the spring, she had deflected every conversation on the subject of summer employment.  There was school, and dance, and a busy social calendar.  She expressed ambivalence about working at a day camp, and anxiety about working retail.  Never a good math student (and that's putting it kindly), she was afraid, she explained, of working the cash register.
   "I don't really know how to make change!  And I'm afraid that there will be a long line of customers and they'll all get mad at me!"
   "You don't have to make change," I answered.  "You just punch in the numbers, and the machine figures out the change for you."
   Variations of this conversation, and others concerning the urgency of looking for work while there were still positions available for teens, continued up through the final day of her high school sophomore year.   Finally, she ran out of time and excuses.   School ended on a Thursday; on Friday we were on the hunt.  I could sense her unease, and knew that the entire project could end up in tears, raised voices, slammed doors, and recrimination.  This was going to be a delicate operation; with a ticking time bomb of a soon-to-be 16 year old, it would test all my fatherly skills and powers.
    The plan was to walk around town, looking for businesses with Help Wanted signs in the window.  But she had her own, difficult-to-verbalize litmus test: regardless of whether or not they were hiring, some stores were simply off-limits.  We fell into a rhythm: JaZams toy store: No. Thomas Sweet: Absolutely not.  Nina's Waffles: A half-hearted yes.  Hulit's Shoes: Heck no! As frustrated as I was by her refusal to jump on every opportunity, I kept my cool as we trudged on.

Here was one that passed the test.

    We stopped for lunch at PJ's Pancake House (they were looking for help; another defiant no.)  She had left her resume at four stores.  It was a start.  We were emotionally exhausted.  We would go home and regroup, but not before making one more stop on our way out of town.

Bon Appetit.  A gourmet food store in the Princeton Shopping Center.  Her older cousin had worked there when he was in high school.

  She protested, but I put my foot down.  Sensing I wouldn't budge, she walked in reluctantly, asking for the manager as I browsed the shelves.  Several minutes later she found me.
   Panic and barely concealed tears.  "Dad!  They want to interview me!  I don't want to work here!  What do I do!  You made me come in here!"
  "Calm down.  Let them interview you.  It will be good practice.  Why don't you want to work here?  Ben worked here and he liked it."
   "I just don't want to work here!"
  "You might not even get the job.  Sit down with the manager.  It will be a good experience either way.  Ask him what he might want you to do."
   "But I don't want to work here!"
   Back and forth, our voices rising, then lowering so as not to make a scene, until she gave in.
   I waited outside, peering in the window, pacing up and down the outdoor patio.  I knew she was mad at me for having forced her into the store, and I hadn't thought things would proceed so far so fast.  But I  hoped that all would be forgotten in the afterglow of a successful interview.  Boy, was I wrong.
   When she came out to meet me, all the pent-up emotion came flooding out.
  "Dad!" she cried, fear and anger mixing together.  "They want to hire me!  Right now!!  I don't want to work here!  What do I do?"
  "That's great, honey!" I was proud she had made such a good impression.  "Why don't you try it out?  Did you ask what they wanted you to do?"
  She unfolded a piece of paper.  On it were the words: cash register.  Of course.
  "We've been over this a million times!"  I was exasperated.  She had a job offer in hand.  She could start tomorrow.   "You don't have to make change.  If someone gives you cash, the register will tell you how much change to give the customer."
  "I know that," she quavered, voice rising through the tears.  "It's that I don't know what coins to give back!"
   There it was.
   It had been there all along, but I didn't hear it.  Her fear wasn't about figuring out how much change was due.  True, she would have a lot of trouble doing that, but she knew the register acted as a calculator.  It was about finding the right combination of coins.  Not only that, she knew that a customer would expect the combination be comprised of the least number of coins possible.  She was unsure she would be able to do that, especially under pressure, with a line of impatient customers backing up out the door and onto the street.   Her litmus test, which had seemed so arbitrary, finally made sense: the store had to have as little foot traffic as possible, and at least the potential of non-register related work.
    I told this story one evening at Twitter Math Camp, along with what I had taken away:
  • It was possible for a student to go through elementary school, middle school, and Algebra 1 and Geometry in high school without mastering the ability to make change with the least number of coins;
  • That this was less a reflection on her than it was on a system of math education that, from early on, left her feeling inadequate, disconnected, and disaffected;
  • That math anxiety is real, that it interferes with performance, and that bad things happen when we put undue pressure and time constraints on kids.
And bless Andy Gael for his response: "I love how your daughter advocated for herself."

     She went back in and told the manager she'd get back to him.
     She eventually found a job:

JerZJump: A family entertainment center.  Birthday parties, open play, camp field trips.  No cash register.

Her first paycheck.

Here's how the story ends:
     Summer is over, and the novelty of the job has worn off.  The smile you see above hasn't been seen in quite a while.  There's no air-conditioning, the hours are irregular, the pay stinks, and the kids are uncooperative and unruly.  Lately she's taken to spending time with her babysitting loot and the contents of the house change collection:

"Make 38 cents with the fewest possible coins."

Nothing like a little intellectual need.


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.