Why project-based learning fails

Project-based learning is great, if there's few enough gaps - the "shape" of the gap tells you much about the shape of the missing piece. But too many gaps, and you can't tell; perhaps not even the problem is a gap.

It does provide motivation for learning a subject properly. And hopefully some topics in particular, if you've noticed that gap: you'll grab hold of it, rather than wonder what's the point of it.

> [drill] Mathematicians rederive theorems from the book.

Is this at all true?