What I wrote about measure of progress is also a way to guide us to think about problem solving. What is the progress towards a problem solved? If the problem is to fell a tree, what amount of sharpening the axe is considered to constitute progress or does the progress only begin when the axe first strikes the tree. If you look at progress from that kind of visible, hole-in-tree kind of basis, then you obscure an important component of the solution which is to sharpen the axe.
If I had 1 hour to solve a problem, I’d spend 55 minutes thinking about the problem and 5 minutes thinking about the solutions.Albert Einstein
Psychologically, and also our training in schools, at exams does not impart this sort of wisdom to us because we are expected to know the solution at the snap of our fingers and get on to work it out. There’s also this tendency in teaching scientific enquiry to dwell on just designing and performing experiments to test different hypotheses rather than get into the thick of how a hypothesis comes about in the first place.