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!
Thank you so much for posting while you're in the midst! (Wish I could be there, commenting is the next best thing...)
ReplyDelete>everything went more smoothly when I gave names to things
I've been thinking about naming lately. This is intriguing.
I apologize for making anybody feel back with my last paragraph! It was not my intention - I was expressing awe.
ReplyDeleteThe irony, of course, was that as soon as I posted that, I discovered that @k8nowak had left to take a walk!!!
Seriously, thank you for posting while you're there. I absolutely want to hear what goes on, and this was a solid first hand account. More please.
ReplyDelete@lostinrecursion
How much scaffolding does Exeter do with these problems? I am wondering if most of us would have to choose between an Exeter like method or the Exeter problems. Exeter has an elite class of students by almost any measure. If we want to use the problems, would we would need to do so much scaffolding that it is really spoon feeding? If we want to foster independence, we would need a more appropriate set of problems for our students?
ReplyDeleteI think that the Math 1 problems don't need much scaffolding, if you start with ones from the beginning of the packet and work forward since they do build on each other. I don't use them the way that they are used at Exeter though - my understanding of their approach is that students work the problems independently as homework and then explain their thinking to each other in class the next day in a moderated class discussion. I typically use them in class in small group settings where they can work with peers and I can ask questions or help steer students as needed. I think that means my kids aren't pushed as hard to dig deep and figure out what they can do on their own, but it does give them a lower-stress environment to grapple with non-prescriptive problems. If you were worried about your students' ability to handle it, you could use a group/class setting as a scaffold and gradually pull it away as kids got used to working on problems like this.
ReplyDelete