How many different ways could the dogs be on and off of the bed?
We put the book and some different math materials out as a provocation to engage the children during learning centres. We also worked in small groups with children who were both invited or interested.
We were amazed by the many different ways that the children solved the problem:
1) Acted it Out: We sang the song and one at a time "fell" out of the bed. We captured pictures of all of the stages and have made our own book. This was a great way to engage all of the children in the problem solving process and to make our thinking visible.
2) Using 10 Frames: Some children used 10 frames and different coloured cubes to represent the number of dogs on and off of the bed. This was difficult for some of the children and was easy for others.
3) Cubes and a Bed: We drew a bed and the children used manipulatives to show their thinking.
4) Abacus: After beginning to explore ways to solve this problem, I found this abacus at Ikea. I simply set it out with the problem provocation. Some of the children were drawn to it while trying to solve the problem.
5) Drawing Solutions: Some children wanted to draw their solutions. Even while drawing they represented their ideas very differently.
What I learned through problem solving...
We learned that children are naturally curious and excited to solve problems, especially when the problem posed is connected to their lives or interests.
All children solve problems in different ways and showing them only one way will not help all children in their learning. The way that children learn ... kinesthetic, visually, orally ... really begins to come out in their problem solving strategies.
You can often learn a lot about children's mathematical thinking. I have also had to tell myself that you can gather assessment information about things that may not have been intended. Keeping a very open mind while watching children to solve problems allows you to really see their mathematical thinking process rather than just looking for a quick assessment snap shot.