You go on to say that the teacher has to be “exceptionally clear about … where [your students are] going.” From this sentence, I don’t think it is at all fanciful to extend my analogy of erecting a tent to saying that the teacher is the “only one who knows why it is being erected”, although, of course, the teacher might share her intentions on the way.

I’m just not sure extending the lines to tents has been all that productive here.

The tension I’m trying to resolve with an open middle is between an underspecified and overspecified task. This tension (and one possible resolution) is nicely illustrated by Sudoku.

Underspecification starts with a blank game board and the instructions to make a game board that satisfies the constraints of Sudoku. This can result in excessive cognitive load and a certain sense that one is flailing. It’s too open.

Overspecification starts with an entirely full game board and the instructions to check its correctness. This can result in a lack of self-determination, a sense that you’re wandering down a narrow path prescribed by others.

Sudoku instead offers a partially-completed game board and invites students to complete the rest. The initial state is clear. The goal state is clear. But the middle is calibrated so that players feel self-determined but not overwhelmed. That task clarity, rather than undermining a student’s curiosity or sense of agency, has enhanced it.