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?