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Every instance of problem solving I encounter involves conscious intentionality. As an analogy, when I get a drink from the fridge, there is a lot going on in my body to make that happen that I do not consciously control. But, overall it is taking place due to my conscious intentional control. I argue the same is going on in the mind, a lot of subconscious things going on that I do not directly control, but the overall effect is directed by my conscious control.

>>yters+(OP)
That doesn't seem like a good analogy to me, because intrinsically problem solving is about something you don't understand in the first place, whereas reaching for something you do already understand what you are doing.

If I use a mechanical grabber aid to reach something, then it isn't figuring out how to do anything. But if I ask Wolfram Alpha the answer to a math problem, it isn't me doing it.

>>perl4e+Ti
Sure, it depends on what level your intentionality is involved. But, my experience is my intentionality is quite intimately involved with my intellectual processes. I cannot just will 'answer my math problem' and my mind pops out the answer. There is a lot of intentional, mental actions that take place to arrive at an answer.