Tuesday, December 23, 2014

Happy Birthday, Exit 10A

     Exit 10A is one year old today!

Let's celebrate!
     The blog has come a long way from its first post, which featured a video of me peeling a clementine for an estimation180-type activity.  When I started writing, 1 year, 51 posts, and 35,000 pageviews ago, I could never have imagined that it would experience such growth.  I remember the feelings of nervousness and anticipation as I hit the "publish" button for the first time and sent my thoughts hurtling into the internet universe.  Would anyone listen?  Would anyone respond?
     I spent a week obsessively checking, hoping someone would leave a comment.  Nothing. I rationalized by telling myself that teachers were on winter break, and had better things to do then read math blogs, but as the days wore on I grew increasingly despondent.  And then, finally, it happened:

     A comment!  Someone named George Broklaw had taken the time to respond to the clementine post.  Who was he?  A teacher?  Maybe from the UK?  No matter.  I was ecstatic.  It wasn't until several days had gone by that I found out (from my wife) that "George Broklaw" was actually my son, Sam, commenting under a pseudonym.  He felt sorry for me.  What a good boy!
    Comment number 2 came about a week later:

     Andrew Stadel had been the inspiration behind the estimation task that I had described in that first post, and his work, both at estimation180 and his blog, Divisible by Three, was a major catalyst for starting a blog of my own.  His comment, along with Mr. Broklaw's, was all the encouragement I needed.
     Of course it takes a village to raise a child, and I need to take a moment to thank those who have been instrumental in helping make Exit10A a reality.  I have written about the tremendous influence those in the MTBoS have had on my work.  Special thanks to Dan Meyer, who was an early supporter, and brought word of my blog to the attention of his wide audience with this post.  I am blessed to work with an incredible group of teachers.  They have given me their time, their classrooms, and their trust.  Nothing could happen without the support of my principal.  A shout-out to my partner-in-crime and "work wife", Theresa.  And to Barbara, Kay, and Mr. Broklaw: love you guys!
  OK, enough yappin'.  Time to eat!

How many people can this cake feed?
Give me a too low, a too high, and a just right.  On an open number line, of course.

Saturday, December 13, 2014

The Most Important Period of My Week

   What's the most important period of my week?

Monday morning, first period.  
     Every Monday morning, beginning at about 9:20 and ending around 10:00, Rich and I sit down at his back table.  There's no formal agenda.  Just two teachers talking, and we cover the waterfront.  For example, during the the past several Mondays we:

  • Looked over the next unit assessment and made some decisions about what concepts to give priority focus;
  • Checked the calendar and the curriculum guide to make sure we were on schedule, and determined how to arrange and organize the week's lessons;
  • Previewed a fraction project we had found on the Georgia Frameworks and started brainstorming how it might be adapted for the class;
  • Discussed the most effective way to provide meaningful feedback for an open response problem we had given the kids to work on the previous week;
  • Analyzed the work of some at-risk students and began re-formulating intervention plans;
  • Debated what to assign for homework;
  • Reorganized the room to accommodate the new 4 ft. by 8 ft. whiteboard we had secured to mount on his back wall;
  • Commiserated on the woeful seasons our two favorite football teams were suffering through, the Redskins (him) and the Giants (me).
We're very busy, and there's lots to accomplish.
     It may seem counter-intuitive to claim that the most important period of my week is spent sitting at a table with a teacher and not standing up in front of a class.  But everything good that happens during the time we spend with our fifth grade class has its origin in our Monday morning meeting.
     I wish I could do this with every teacher in my building, but there are many obstacles to making this wish a reality.  Teachers are very possessive of their "prep periods", and for good reason.  They don't have many of them, and it's the one time during the day where they can catch their breath: check homework assignments, clean up from lessons just completed and set up for lessons that will follow, touch base with grade-level colleagues, meet with administrators or school support staff, mark classwork, contact parents, fix bulletin boards, catch up on clerical work, and the myriad of other tasks, both important and mundane, that  must be done but cannot be done while the kids are in the room.  And of course there's the issue of finding a time in my schedule that might coordinate with a time in theirs.  So we talk wherever and whenever we can.  Before school (if you happen to come in early), after school (if you happen to stay late), in the hallway while you're walking your class to gym or back from music, in the copy room, by the laminator, in the all-purpose room during morning line-up, in the parking lot.  Small moments, and, yes, they're helpful, but they feel rushed and incomplete.  Not like my Monday morning meeting with Rich.
     Clearly this is a problem, and it's illustrated in a graphic I saw on my twitter feed this past October:

     I found these statistics astonishing.  It's clear we need more time during the day to engage in meaningful collaboration with our colleagues.  If we use it wisely, it will make the time we spend in class more meaningful to our students.
     What's the most important period of my week?  Monday morning, first period.
     What's the most important period of  your week?

Saturday, December 6, 2014

Kindergarten Interlude

    Out of all the grade levels I visit, kindergarten holds the most surprises.  I never fail to be astonished by something I see or hear during the hour a week I split between two kindergarten classrooms in my school.
     Case in point: Several weeks ago I stopped by a room on my regular Thursday morning rounds.  The kids were working at centers while their teacher called students over to her desk one at a time for some individualized reteaching.  I sat down at a table where some students were working with a basket of bears and some number cards.

The activity called for the kids to pull a number card out of the basket and then count out a corresponding set of bears.  
     I watched for a while, paying close attention to their counting strategies.  Were they counting with one-to-one correspondence as they took each bear out of the basket?  When I asked them to recount, were they actually touching each bear as it was counted, or did they point with a finger in the air?  Did they use a finger at all?  Were they moving bears from one set to another as they counted?  Did they keep them in a jumbled pile, or did they arrange them in a row or array?  What did they do if they lost count?  As they counted up from 1, did they encounter trouble with the "tricky teens"?  The diversity of technique and strategy was both fascinating and informative.    After several minutes, I had an idea.
         "Next time you count out a set of bears, try arranging them in a pattern," I told them.  I was curious to see how they would execute two different skills, counting accurately and patterning, at the same time.

The fact that they had to pattern led many to arrange the bears in a single file row.

I challenged them to come up with 8 bears in a different pattern.  No sweat.

No prompting necessary.

Of course not everyone prefers single file.  Here's a 6 by 3 array.

This child made a line of 20 bears (18 are visible in the picture).  
Here's a close-up of part of the row.  Not only did the student alternate color, the bears also alternated sitting and lying on their backs!  Then, instead of putting the 20 back and starting over, he pulled another card from the pile.  It was a 6.  "I'm going to add a 6 and a 20!" he exclaimed proudly.

Now we've got problems! 
     Can you make a pattern with just one bear?  What about 2 bears?  What's the least number of bears you need to make a pattern?  I left them to ponder these questions,  questions they had earned.
     I wasn't always able to work kindergarten visits into my schedule.  Until recently, our district had a half-day kindergarten program.  By the time the little guys and girls had taken off their coats, found their seats, eaten a snack, and gone to the bathroom, it was time for them to go home.  But now we have a full-day kindergarten program, and the teachers have more time to spend on math.  And since Theresa has joined the staff, adding another math specialist to our building, it has freed up some time in my schedule, time I have dedicated to kindergarten.
     Working in our kindergarten classrooms has made Theresa and I much more effective and knowledgeable specialists.  It is important for us to understand what is happening in these classrooms; to observe how our youngest students interact with and create mathematics, to help their teachers find appropriate resources and continue their professional development as math educators, to model lessons, to assist with assessments, to poke, push, and experiment.
     Yes, kindergarten is a wonderland full of surprises.  Plus they have the best snacks, and some really cool things to play with!

Who doesn't love big dice?