Dan Meyer wrote a nice post about suggested restructuring of a Geometry assignment recently. It got me thinking about how I could guide my students through this involving, but rich, task.
First, if you have not tried the problem yourself (and read through Dan's post on this), you should do it. It's a great problem, I think. At first glance it seems fairly obvious, but upon further examination, it isn't. I'm still not sure if I took the "easiest" approach or not, and I'd be curious if you solved it an entirely different way.
But, solving the problem and creating opportunities for students to solve the problem are two entirely different beasts. I think if I were to use this problem, it could be "taught" in steps by breaking it down as shown below, but it's not clear 1. whether all students (or most students) would understand this problem, and 2. what I hope the students would gain or retain from this problem. I guess the latter bothers me more.
(In the picture below, "All Students" means all students would be encouraged to independently explore/figure out the important relationships. "Teacher guided" is more like places where I would intervene and provide hints.)
How would you present this problem? Would you scaffold more than what I propose above? The idea is that, in my class, I would give kids a few hints, one at a time, and see how many of them can run with it. If they can't, I'd guide them more heavily and hope that I can stop a bit further down the line for them to re-gain independence on the problem. But that's a fine line, because at that point, are they doing the thinking or have I stripped them of that opportunity?
Do you find the process of maintaining a cognitively demanding task challenging? How do you manage it to balance the need to make the task accessible to students (not just upon the entry point, but throughout the task) and still not over-simplifying the cognitively demanding parts for them?