Problem-solving can be defined as a mental process comprising the discovery, analysis and resolution of problems. This process is primarily aimed at tackling obstacles and discovering a resolution that best solves the issue. According to J.R. Anderson, any goal-directed sequence of cognitive operations can be defined as problem-solving.
Problems can be placed in categories depending on several factors. These include the prior knowledge required for their solution; the nature of the goal involved; their complexity; whether the problem suggests its own solution, or a solution should be discovered; whether the problem-solver has already solved such problem and whether the problem requires a long process to be resolved or it can be solved in just one step, if recognized.
The initial stage of problem-solving is always a situation or a statement of a problem. The process moves toward the goal stage as a solution is found. In between these stages there are several steps individuals should go through in order to solve the problem. These actions are commonly known as the problem-solving cycle.
First, a problem should be identified and defined. It is vital to identify what causes the problem, otherwise all efforts may be fruitless. There are many questions to ask such as what makes one think there is a problem? Where is it happening? How is it happening? When is it happening? With whom is it happening? Why is it happening? After answering all of these questions, an individual should be able to define the problem or the problems and set the priorities for their solution.
The next step of the problem-solving cycle is to form a strategy to solve the problem. The chosen strategy will depend on the nature of the problem, the situation and the individual characteristics of the problem-solver. It is always suitable to look for alternative ways for a solution. The problem-solver may prefer to keep other people involved in the process. For example, techniques such as brainstorming are useful for generating various ideas and selecting the most appropriate approach to solving the problem.
When choosing the best strategy, problem-solvers may need to consider a number of factors. Which strategy is most likely to resolve the issue in the long term? Which strategy is most realistic to be accomplished and are the necessary resources for its implementation available? What risk is involved in each strategy?
On the way to reaching the goal, problem-solvers should gather and organize as much information about the issue as possible, taking into account both what they know and do not know. Establishing the problem's priority will help decide what and how much resources should be used to solve it. Not all problems require an individual's entire energy and time, or financial resources. Problem-solvers should monitor the progress of their efforts. If the problem-solving process does not work efficiently, the problem-solver may need to redefine the problem itself or to draw up a different strategy.
At the final stage of the problem-solving cycle when a solution is reached, problem-solvers should assess what has been accomplished and decide whether they have come to the best possible solution to a given problem. Sometimes the evaluation takes just a minute, for example when solving a mathematical problem one only needs to check whether the answer is correct. However, it may take much more time with other problems to verify the effectiveness of the solution.
Problem-solving has long been an object of research in cognitive psychology. Researchers in the field of problem-solving have shown that there are three general approaches to investigating problem-solving. The first method involves laboratory experiments with controlled variables. In this case the nature of the problem is controlled by the researcher. The second approach comprises analyses of verbal protocols, where problem-solvers talk aloud during the process. The third method uses artificial intelligence models to insert human problem-solving theories into computer programmes.
Under the so-called "move problems" method of problem-solving, a group of tasks or objects needs to be manipulated by problem-solvers and arranged so that a goal configuration is accomplished. Problem-solvers try various move sequences while attempting to reach a solution. In the famous Tower of London task, problem-solvers have to figure out how to move a set of coloured same-sized disks piled over three pegs by moving only one disk at a time, aiming a specific target configuration.