We spent this morning in self-selected groups, working on Exeter Math 1, Math 2, or Math 3 problems. I worked in the Math 1 group. We agreed to work in a free-form way on the first four pages of the Exeter Math 1 problems, with discussion, collaboration, and analysis in any way we wanted.
I am still digesting and processing my experience, but here are some of the things I noticed.
My general feeling is that the Math 1 problems are all about cultivating independence. The sequence begins with an investigation into rates, but the work requires the learner to actively use what you know.
No spoon-feeding, no spectators.
As a learner, I found I had to focus on reading, interpreting, and decoding problems, listing information (what do I know? what do I need to know?), organizing it, and identifying my objective in the process. I also noticed that everything went more smoothly when I gave names to things and actively identified equivalences. Naming things and identifying parts of the problems gave me a way into organizing my information and my thinking.
I enjoyed working through problems and brainstorming about methods/strategies. I am now wondering, how I can use problems like these to cultivate independence and problem-solving with my students? How much scaffolding would middle-schoolers need to get started?
One of the things I am really interested in is how @k8nowak uses this kind of method to set up some "productive struggle" for a lesson. Oo, I think I'll go over to the other table and ask her!