At the end of each trial, subjects reported whether or not they had a strong "Aha!" moment. Interestingly, researchers found that subjects who were aware that they had found a new way to tackle the problem (and so, had consciously restructured their thinking) were less likely to feel as if they'd had eureka moment compared to more clueless candidates.
People who are better aware of their problem-solving strategies are less likely to experience surprise at the moment of discovery. I've seen it over and over again in invention workshops. Clueless people have a lot of "wonderful discoveries" during brainstorming sessions, but the end result often is not that interesting.