"If a problem seems too hard, the formulation is probably wrong." -David Chapman
Often when working our way through a problem we become stuck. Getting unstuck can just be a matter of applying the right tool/concept/idea to it, but sometimes this gets us nowhere. In these cases it is worth examining the structure of the problem formulation itself.
Some common issues with problem formulation:
The problem formulation makes different distinctions than a useful answer would make. Some examples might be: Trying to explain a phenomena with no separation between leading and lagging indicators.
Compressing relevant and irrelevant details into a single word or concept. A concrete example of a failure mode might be in medical studies, where one might draw conclusions about the population as a whole based on results obtained on a few students at a particular university, or results based exclusively on diabetic Swedish twins etc.
The problem is scoped poorly. In extreme cases this means you don't even know what an answer would look like. Models like SMART goals point to this with every single one of their terms. The idea being that by the time you know exactly what an answer would look like, when it would show up, and what you would do with it, you're most of the way there.
The problem formulation is thought of as 'true' rather than 'useful.' Forgetting that a particular problem formulation is just a leaky abstraction of the actual problem. This prevents open mode curiosity and play.
The language used in the problem formulation imports unseen assumptions/connotations about the problem. These assumptions may be true or false, but the important part is that you don't know that until they are made explicit. This effect can be explored by tabooing words. E.g. "How are we going to get our sales numbers up this quarter?" makes locus of control, measurement resolution, and time lag assumptions that may not be true.
One general technique for exploring problem formulation is brainstorming questions rather than answers.