Counting Collections

Today I had the great pleasure of working with a group of first graders on their very first counting collection.  As I sat at the alphabet carpet with 22 smiling faces looking at me to provide some meaningful and fun learning, I knew that what I had prepared was going to be perfect!

What, exactly, is a counting collection?  Put simply, it is a collection of objects (popsicle sticks, cotton balls, etc.) that students count collaboratively with a partner.  Why should we spend our precious and limited classroom minutes engaging in counting collections?  “Research shows that although counting is one of the best ways we know to help children develop number sense and other important mathematical ideas, we do not do nearly enough of it in elementary schools.” (Schwerdtfeger and Chan, 2007)  Why else should we do it?  Because it is fun and the kids love it!

I began our morning by showing students my bag of connecting cubes and telling them that I didn’t know how many I had.

cubes

I then asked what we could do to determine the number of cubes I had.  Students immediately suggested counting them.  AWESOME! As students in Kindergarten, they had a heavy focus on the Common Core State Standards – Math (CCSS-M) domain of Counting and Cardinality, so I was not surprised when this was their first response.  My next question was met with less immediate enthusiasm.  When I asked, “How should I count them?”, answers varied greatly.  As a group we agreed to count them by ones and discovered that we had 89.  Having successfully counted our first collection together, I knew they were ready to count their own collections with a partner.

For our first day, we had to begin by discussing what our goal was and the norms we would use during our collection counting. We focused on what it meant to use the collections as “tools and not toys” and also noted what it meant to work cooperatively.

Poster 2

This poster was displayed during our discussion and throughout the length of our counting.  It served as a reminder of our purpose and expectations.

Another important decision that had to be made was how many objects to have the students count.  I decided to give each partnership a collection of 100 objects.  However, each group received a different collection of items.

collections 2

I selected 100 objects to begin because the CCSS-M Kindergarten standards state that students will leave Kindergarten knowing the skills of rote counting to 100 and counting objects of up to 20.  I knew that these collections were going to be challenging.  In fact, not one group counted the collection accurately.  This was not the goal of today’s count.  My goal was to help students see a need for more efficient ways of counting.

And away they went!  Students immediately began negotiating the way to count their collections with their partner.  Overwhelmingly, students focused on counting by ones.

For many groups, the count look a lot like this:

scattered paperclips

While this lacks strong organization, I noticed that these students were engaging in powerful conversation about what and how to count.  A great place to start!

As I walked around observing the counting and collaborating (a powerful side effect of counting collections!), I began to notice a few students engaging in some strategic counting.  One group explored with sorting their objects by color and counting each of the color groups.  It was only when they were left with four different totals and no means for combining them that they abandoned ship and counted by ones.  What a noble effort at efficiency.

The next group I observed had organized their count this way:

Beans - by 2s

When I asked how they organized their count, they stated that they thought counting by twos would be a faster way to count so many objects.  I left them to do that count, but returned when I observed them dropping beans in their bag, one by one, while counting.  When I inquired about their current strategy, they shared that they couldn’t count by twos “that high” and reverted back to counting by ones.  Also a noble effort.

Finally, I stumbled upon this group:

Counter Array 3

The holy grail!  Hooray!  When I asked how they were counting, the stated that they were counting by ones.  With them arranging their objects into arrays, this was a perfect opportunity to prompt these students to think more strategically.  I asked them how many were in the bottom row of yellow disks.  After counting, the student proudly informed me it was five.  I then asked how many were in the yellow row above and, without counting, his quick response was five.  For good measure, I asked about the row above that, to which both partners answered with “5!”.  I then asked if there was another way they could think of to count these objects.  This questions was met with crickets.  So much wait time…to no avail.

So I further prompted them by asking about this grouping:

Counter Array 2

“What do these look like to you?”, I asked.

“Ten frames”, they said.

I asked how many are in a ten frame and they responded with “ten”.   Now we were getting somewhere!

“How many are there in both these ten frames?” I asked the partners.  After counting by tens, the boy answered, “twenty” as his partner nodded in agreement.  Victory!  When I asked if they could use that information to count the whole collection, they nodded and began the task of making groups of ten.  I left the group knowing that this was a huge breakthrough that needed to be shared with the group.

As the groups all finished their counts, I had them return to the carpet and proceeded to have the following groups share their counting strategies in this order:

  1. The sorting group
  2. The counting by twos with beans group
  3. The counting by tens with disks group

Taking a note from the work of Smith and Stein in the book Five Practices for Orchestrating Productive Mathematics Discussions, I selected this order because I wanted our math discussion to unfold like the plot of a good book.  As the final group shared their strategy of counting by tens, light bulbs began sparking above the heads of several children around that very same alphabet carpet.  Just a short 60 minutes before, those faces were looking to me with hope and wonder.  Now these same faces were filled with ideas and questions.  If that isn’t a homerun, I don’t know what is.

Advertisements

Published by: jgarner05

I am a math consultant with the Stanislaus County Office of Education and a preservice math content instructor at California State University, Stanislaus. It is my passion to work with teachers to improve math content understanding and instruction.

2 Comments

2 thoughts on “Counting Collections”

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s