So although I was busy presenting at the Northwest Math Conference, I did get to attend a few sessions from speakers from the US that I typically wouldn’t get to hear. The Saturday session I went to was presented by Elham Kazemi from the University of Washington and focused on the importance of counting routines, not just for our youngest children but for all elementary-aged students. She shared her work in the areas of counting collections and choral counting and many wonderful resources to support teachers can be found on tedd.org
We have been talking about the NCTM book High Yield Routines in our district, routines that can be used regularly across grades and topics to develop mathematical thinking, reasoning and communication. I think the routine of “counting collections” is another high-yield routine, one that engages in the concepts and skills of counting, understanding our number system, grouping, multiples, etc as well as providing openings for inquiry and problem-solving. Students work in partners which allows for a social component that nurtures thinking and communication.
On Thursday afternoon I visited Michelle Hikida’s grades 2&3 class at Diefenbaker Elementary to give “counting collections” a go. We presented the students will a tray of bags of collections to choose from as well as a collection of materials to organize the materials into groups if the students wanted to.
We asked the students to choose a collection, count all of it (more on this later), and then record on the whiteboard what they counted it, how they counted it and what the total count was.
One of the things that became very clear was that collections of items with different colours caused a distraction mathematically. The students instinctively “sorted” these items into colour groups. In the example below, the students noticed most of the groups had 8 in them, so challenged themselves to count by 8s to #countall – the focus of the task.
Another pair of students poured out a large quantity of coloured beads and began counting the pink beads by 2s into a cup. There were 22 and then they started another colour, starting at 0 again. I asked them how they were going to #countall and they said they would add up the groups, which is different than counting up by equal multiples.
Part way through our hour together, I shared the idea of using a referent for estimating, using the book Great Estimations by Bruce Goldstone as an inspiration. We then asked students to add the layer of estimating before they started counting and including this in their record.
The students really enjoyed recording on the whiteboard and they created quite the “math graffiti” wall.
Before I left, we scanned our data on the board and I asked the students what they thought the most common way of counting was. One student commented that it was hard to tell because the data wasn’t organized and that maybe we should create a graph! It was the end of the afternoon, so that task was left for the next day.
On Monday, I spent the afternoon in Kelly Hinks’ K&1 classroom at Diefenbaker. Some routine, I just took out a few bags that had really large quantities (over 100 – although I missed a few) and added a few more that were 30 or less. I quickly summarized the story Too Many Pumpkins and showed the students the illustration with all the pumpkins growing in the woman’s yard. One of the students exclaimed, “So many pumpkins!”
I asked how the woman could count the pumpkins and the students suggested by 2’s, by 5’s and by 10’s. I wondered how the woman might keep track of her count and a student suggested she would move the pumpkins together, so she could see them in groups. Such a perfect segue…from a 6 year old.
The students then chose their collections and began their counting. Counting by 2’s, 5’s and 10’s isn’t yet fluent for these students and it was fascinating to listen in to the partners trying to figure some of this out together. I was able to capture some amazing conversation on video.
The students used little individual clipboards to record what they counted, how they counted and the total count.
As I listened to this pair of girls count to 54 by 2’s, I noticed that they hesitated slightly as they approached each decade – 36, 38…..40, 42, 44 etc.
This pair of boys wasn’t distracted by the colours of the pompoms and grouped them by 5s onto plates. They struggled to count by 5s past 20 though and negotiated between them what to do. They ended up putting two plates together and counting by 10s to 40. For their next collection, they applied the same counting strategy as seen in the photo below – first grouping by 5s and then combining to make 10s as they are more fluent in counting by 10s.
Another pair of boys used the same strategy across the classroom – grouping by 5s first and then counting by 10s. In both cases, counting on the “extra” 1s was a bit of a challenge.
At the end of the afternoon, we had pairs of students share their counts.
Both Kelly and I noted how much mathematical thinking we were able to listen to during this routine and Kelly mentioned she would have likely limited the size of the collections but realized how rich an opportunity it was for students to problem solve and figure out ways to count their collections of quantities that might typically be considered out of their range.