How many ? # 1 – At the coffee shop

Our journey “How many” comes from the presentations and discussions I had at the Cognitively Guided Instruction conference last month, around counting collections of items (e.g. legos® blocks, buttons, etc) with young children (Carpenter et al., 2016) and how the question “how many?” can lead to math discussions deepening the children’s understanding in number sense in upper grades (Schwerdtfeger & Doto, 2017). Depending on their counting skills, children may explore a collection by counting each item. Others may select a specific feature, such as the pegs of the legos® blocks or the holes of the buttons. Children may count by 1s, 2s, 4s, etc, keeping track of their counting on paper, using cups or bags to group items in Tens, or Hundreds, etc. Children can also count items from their environment, or on a picture (see a post from Christopher Danielson here and Brian Bushart here or search #unitchat on Twitter).  It is endless.

I started the journey informally with Tom, 5, and Rosie, 8, a couple of weeks ago. As we were taking a break at the park, I looked around, and asked them: “How many?”. After an expected “How many what?”, they quickly figured out that they could count whatever they wanted: the cars passing by, the trees, the people, etc. Since then, we have been taking our “how many” breaks regularly. Sometimes for just a few minutes, sometimes for a longer period of time. And we take a picture of what we have been counting. I am going to post theses pictures, with the hope that soon, you will, too, put your “how many?” glasses on. Indeed, I sometimes feel like I am wearing new glasses, looking around for things to count wherever we go…

Here is a first picture, taken at my office our nearby Starbucks®.

“How many?”

What I enjoy the most with the activity is that, although Rosie and Tom are at a different stage of development in their counting skills, they can both be fully engaged in the same discussion.

• Tom started counting items by ones: some of the packages of coffee, the shelves, the straws, etc.
• Rosie, who has been quite curious about  multiplication and arrays for a little while, decided to count the bags of coffee on the top shelf, including the ones hidden. So, 7 rows of 4 packages of coffee… Your child may know that 7 x 4 = 28, Rosie solved it with a repeated addition… it would be 28 packages… That’s when Tom mentioned that there were not 1 shelf but 5 shelves, so Rosie kept adding…

We also discussed why people may want to know how many packages can be held on the shelves. When doing math, we always try to keep in mind the purpose of it…

Your turn to look around!  “How many ??”

References

• Thomas P. CarpenterMegan Loef Franke Nicholas C. Johnson, Angela C. Turrou, Anita A. Wager (2016) Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Heinemann: Portsmouth, NH.
• Julie Kern Schwerdtfeger & Darlene Fish Doto (2017) Counting Collections in the Upper Grades (3-5). Cognitively Guided Instruction. 2017 National Conference, Seattle June 26-28.