Here is another book I studied as a graduate student that I found interesting to share.
Small, M. (2012) Good Questions: Great Ways to Differentiate Mathematics Instruction, 2nd Ed., Teachers College Press, NY.
The author suggests 2 different types of math tasks to reach out children with different skills and needs. Makes sense in a classroom, of course, but it makes sense to me at home as I start seeing my son Tom, 4, willing to “do math” with his sister Rosie, 7 (see my previous post here on Doing Math outside, for instance).
The task is “framed in such a way that a variety of responses or approaches are possible” (Blanton, p6). Remember my post on Vygotsky (here) ? Well, the goal is to design the task “in the appropriate zone of proximal development for all students” (Blanton, p6), so that every student can be part of the discussion.
Here is an example of what we did recently:
“Go outside and take a picture of a pattern”.
Rosie came back with a pattern found on a flower, while Tom came back with a pattern he created with rocks and pine cones. Still, we were able to discuss patterns all together.
It is a set of tasks that children can choose from, that are close enough to be discussed at the same time.
For instance, this afternoon, I asked Tom and Rosie to create a story out of:
- Choice 1: 10 dinosaurs
- Choice 2: 3 cars
Again, even if Tom used a number smaller than Rosie to create his story, they still were able to share what they did with each other. Also, Rosie was able to create a math problem, while Tom invented “just” a story involving 3 cars.
Of course, with Tom and Rosie’s difference of age/skills/grade, I may not always be able to provide them with tasks they can explore together, but I really like the idea, and will come back to it regularly.
You may want to check out the book, too ! It includes hundreds of Open Questions and Parallel Tasks organized by math concepts and grade levels.