This year many of our youngest children (primarily 3 year olds) showed strong interests in math, and an opportunity to collaborate on a big mathematical problem came up on our last day of school.

We have been using a rolling calendar all year, marking the number of days we’ve shared at school, and watching the roll of paper get bigger and bigger. Our plan was to unroll the paper on the last day so that we could see how long our school year was. We also planned to cut the paper up afterwards, so that each child could take a part of their school year home.

Rather than lead this process completely, a teacher asked an “I wonder” question once the children marked day number 163 on the calendar:

“I wonder how we could figure out how many days each child can bring home today. We have 163 days and we have 15 children here.”

Many children spontaneously began to share their estimations – (“we’ll each get 2… I think 8…I think 4…. I think more than that…”)

Someone pointed out that we could figure it out if we had something to count. A teacher thought out loud about what we had 163 of in the classroom and remembered that we have many periwinkles, and the children thought we should count out 163 of them. When the teacher pointed out that this would be a very big job, and asked if they really wanted to do all that counting, many children enthusiastically said yes.

At this point, the children needed a bit of guidance, so a teacher suggested that we could count the 163 shells and then make a pile of shells for each child from those 163. Then, if we counted each pile, we’d know how many days could travel home with each child.

Again, teachers asked children to think about how big the job would be. We’d have to find a big enough space for 15 piles, and make sure no one combined piles, or moved them until we had counted out all the shells. About half the group decided they would get the job done.

It took a long time, but we did manage to count out the shells and create 15 piles. And children discovered that some would take home 11 numbers, and some only 10, but that was ok because we only had 163 days.

Before cutting our days, we worked together to unroll the calendar to see how long it was. Too long for the hallway! By this time everyone was working together, since it took all 15 children to hold “our year” in place.

The level of interest and enthusiasm for taking on this counting challenge was quite impressive, as was the children’s capacity to stay on task for the extended time it took for all this counting to happen. Although the children weren’t ready to figure out on their own how to divide 163 into parts, once that suggestion was made, they helped each other stay on track, count accurately, make sure there was a pile for everyone, check their work, and then call on others to help manage the long length of paper representing our year.

Every child was involved in the project – each at his or her own level, each with his or her own approach, some counting by tens, some by ones, listening to and learning from each other. Contrast the learning that comes out of an experience like this to the learning that comes out of drill or worksheets.