When children make meaning of the operations they do so by modeling the action in the problem or situation they are given. Sometimes that action is joining, sometimes it is separating and sometimes it involves comparing.
This week, I worked with students in grades 1 and 2 to explore 2 things – how the structure of the problem posed changes the strategy used, and how students’ strategies evolve depending on their developmental level. All of this is drawn from the work of Fennema and Carpenter, who have written a book called Cognitively Guided Instruction.
The problems we used in grade 1 and 1/2 this week were based on this work, and set in the context of a story- Too many Frogs, by Sandy Asher, and I’m the Biggest Thing in the Ocean by Kevin Sherry.
I read the first book and asked children the following problem, a separate problem:
There are 8 frogs listening to the story.
Some went to the kitchen for snacks.
Five were left listening on the chair.
How many went for snacks?
I told the story problem at the board using simple pictures:
Squid is 8 shells long.
Crab is 2 shells long.
How much longer is squid than crab?
I worked through how we might measure using “shells” – my own invented non-standard unit…! :o) Students modeled their thinking using unifix, having practiced with a similar task done earlier in the lesson… The line master for that task is here: comparing handfuls.
Try these tasks with your children and observe carefully what they do. I am curious what kinds of strategies you’ll see! To read a summary of Fennema and Carpenter’s work, check out the Teaching Student Centered Mathematics grades K-3 book by John Van de Walle – it’s in chapter 3…