Functional MRI is still fairly limited in terms of what questions it can examine, but in response to mark's question below, we think that while it might be that successful problem solvers in complex scenarios start off in story and context mode - relying on similarities in experiences and situations to help make decisions about unknowns- this usually changes with time - so that experiences become grouped and linked into patterns and rules. Ultimately this results in simplification, but requires different processes of selection and comparison, so we expect to see a shift to more conventionally analytical areas.
In the grammar learning paradigm below, the figure shows how brain activation patterns change when test subjects develop new rules about how words should be organized. It's not a perfect analogy, but it's probably a start for sorting out how real life problem solving is done.
There is a lot of interest in this more inductive pattern of learning from artificial intelligence people and engineers, but it often can't be taught well in conventional schools because it either takes too long (it's much easier to just tell students what to think) or kids just don't seem to get it. It helps to have a tweaker personality to work with - because tweakers are tenacious about problems that don't completely make sense.
Last night, I was just reading an excerpt from Ben Franklin's autobiography, and was impressed that when he was a teenager, he also found it necessary to take notes from great works he had read, then rewrite them in simplified (and at times more colorful) terms. It's probably no accident that this practice pops up in many other biographies of innovative thinkers (Robert Hooke also comes to mind) - it can be a more creative or synthetic process than we might think.
Rule-Based versus Similarity-Based Learning
Eide Neurolearning Blog: Critical Thinking - Inductive and Deductive Reasoning
Eide Neurolearning Blog: Training Tweakers