The term problem solving means slightly different things depending on the discipline.
Researchers' underlying assumption was that simple tasks such as the Tower of Hanoi correspond to the main properties of "real world" problems and thus the characteristic cognitive processes within participants' attempts to solve simple problems are the same for "real world" problems too; simple problems were used for reasons of convenience and with the expectation that thought generalizations to more complex problems would become possible.
Perhaps the best-known and most impressive example of this line of research is the work by Allen Newell and Herbert A. In computer science and in the part of artificial intelligence that deals with algorithms ("algorithmics"), problem solving includes techniques of algorithms, heuristics and root cause analysis.
The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods.
In response to criticism of his approach, emanating from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, Problem solving is used when products or processes fail, so corrective action can be taken to prevent further failures.
Mental health professionals study the human problem solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment.
Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems.Some of the problem-solving techniques developed and used in philosophy, artificial intelligence, computer science, engineering, mathematics, or medicine are related to mental problem-solving techniques studied in psychology.The process starts with problem finding and problem shaping, where the problem is discovered and simplified.The next step is to generate possible solutions and evaluate them.Finally a solution is selected to be implemented and verified.Problems have a goal to be reached and how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.The ability to understand what the goal of the problem is, and what rules could be applied, represents the key to solving the problem.Sometimes the problem requires abstract thinking or coming up with a creative solution.Studies conclude people's strategies cohere with their goals and stem from the natural process of comparing oneself with others.The early experimental work of the Gestaltists in Germany placed the beginning of problem solving study (e.g., Karl Duncker in 1935 with his book The psychology of productive thinking The use of simple, novel tasks was due to the clearly defined optimal solutions and short time for solving, which made it possible for the researchers to trace participants' steps in problem-solving process.