A problem arises when a living creature has a goal but does not know how this goal is to be reached. \cite{Duncker1945}
Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable. Henri Poncaré \cite{Hadamard1945}
One’s knowledge concerning one’s own cognitive processes and products or anything related to them. […] Metacognition refers, among other things, to the active monitoring and consequent regulation and orchestration of these processes in relation to the cognitive objects on which they bear, usually in the service of some concrete goal or objective. \cite{Flavell1976}
Novices typically begin to solve a problem by plunging into the algebraic and numerical solution – they search for and manipulate equations until they find a combination that yields an answer. All too often they neither use their conceptual knowledge of physics to qualitatively analyze the problem situation, nor do they systematically plan a solution before they begin numerical and algebraic manipulations of equations. When they arrive at a numerical answer, they are usually satisfied – they rarely check to see if the answer makes sense. \cite{Heller1992a}