The amazing thing to keep in mind is that in almost every class, you've got kids on all levels of this ladder, except maybe the very bottom and the very top. (Most kids are accustomed / brain-washed into thinking that all problems are possible, and few kids are ready to prove everything they think is true.) How do we inspire all of them to learn?
This ladder made me think of a couple of things:
ReplyDelete1. The teacher must aim high and go ahead and prove things - because there is no way the students will climb higher than the goal set for them by the teacher. Many students (most who have achieved the "how to" stage) don't even see that there is any higher to go than where they are currently at.
2. Showing this ladder may make learning more explicit and together with student reflection it may stimulate to advancement up the ladder.
3. I'm thinking of an exercise where I choose a method, say using the formula for geometric series, and ask students in groups to choose a step on the ladder and write a paragraph (which they present to class) about that particular stage of learning. I'll let you know how that goes. We're onto logarithms next and I suppose that concept and associated methods will be perfect for using this ladder.
I agree that most kids are stuck at the "how to" and "why" stages. I think my job is to keep nudging them in the upwards direction. If I can mentally identify which rung each kid sort of belongs to most of the time, I can more consistently work on getting that kid to the next level (although it's also possible for a kid still learning the "how" to have a partial illumination of proofs and "what info is missing").
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