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Problem solving is the way by which solutions are developed to remove an obstacle from achieving an ultimate goal. Problems in need of solutions range from basic personal issues of “how do I turn on this appliance? The former scenario falls into the category of simple problem solving SPS , whereas the latter is known as complex problem solving CPS. Simple problems have one issue, while complex problems have multiple obstacles that simultaneously need solutions.

Micro and macro problems arise constantly and therefore, problem solving is a vital part of life. Not everyone can solve a problem on their own. Lawyers, doctors, and consultants are examples of those that take on the role of being problem solvers. Many businesses have been extremely successful by recognizing a problem and creating a solution. The more people that are inconvenienced by a problem, the greater the opportunity to develop a solution. There are many problem-solving techniques and methods.

They are used daily in philosophy , medicine , societies , mathematics , engineering , business , computer science , and artificial intelligence. The mental techniques that individuals use to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Additionally, the mental obstacles preventing people from finding solutions is a widely researched topic.

Some examples of problem solving impediments include confirmation bias , mental set , and functional fixedness. The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not.

Well-defined problems allow for more initial planning than ill-defined problems. The ability to understand what the end 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. Problem solving in psychology refers to the process of finding solutions to problems encountered in life. 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 an end goal to be reached and how you get there depends upon problem orientation problem-solving coping style and skills and systematic analysis. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.

Problem solving has two major domains: mathematical problem solving and personal problem solving. Both are seen in terms of some difficulty or barrier that is encountered. One such component is the emotional valence of “real-world” problems and it can either impede or aid problem-solving performance.

Researchers have focused on the role of emotions in problem solving, [12] [13] demonstrating that poor emotional control can disrupt focus on the target task and impede problem resolution and likely lead to negative outcomes such as fatigue, depression, and inertia. Studies conclude people’s strategies cohere with their goals [15] 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.

Later this experimental work continued through the s and early s with research conducted on relatively simple but novel for participants laboratory tasks of problem solving. 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, problem solving includes techniques of algorithms , heuristics and root cause analysis.

The amount of resources e. In more general terms, problem solving is part of a larger process that encompasses problem determination, de-duplication , analysis, diagnosis, repair, and other steps.

Other problem solving tools are linear and nonlinear programming, queuing systems , and simulation. Much of computer science involves designing completely automatic systems that will later solve some specific problem—systems to accept input data and, in a reasonable amount of time, calculate the correct response or a correct-enough approximation. In addition, people in computer science spend a surprisingly large amount of human time finding and fixing problems in their programs: Debugging.

Formal logic is concerned with such issues as validity, truth, inference, argumentation and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution. The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the s.

It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine , developed by Allen Newell, Herbert A.

Simon and J. Shaw, as well as algorithmic methods, such as the resolution principle developed by John Alan Robinson. In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science.

However, already in , John McCarthy proposed the advice taker , to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in , using a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning. 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 , [22] which solves problems by problem decomposition.

He has advocated logic for both computer and human problem solving [23] and computational logic to improve human thinking [24]. Problem solving is used when products or processes fail, so corrective action can be taken to prevent further failures. It can also be applied to a product or process prior to an actual failure event—when a potential problem can be predicted and analyzed, and mitigation applied so the problem never occurs.

Techniques such as failure mode and effects analysis can be used to proactively reduce the likelihood of problems occurring. Forensic engineering is an important technique of failure analysis that involves tracing product defects and flaws.

Corrective action can then be taken to prevent further failures. Reverse engineering attempts to discover the original problem-solving logic used in developing a product by taking it apart. In military Science , problem solving is linked to the concept of “end-states”, the desired condition or situation that strategists wish to generate.

Problem-solving strategies are the steps that one would use to find the problems that are in the way to getting to one’s own goal. Some refer to this as the “problem-solving cycle”. In this cycle one will acknowledge, recognize the problem, define the problem, develop a strategy to fix the problem, organize the knowledge of the problem cycle, figure out the resources at the user’s disposal, monitor one’s progress, and evaluate the solution for accuracy. The reason it is called a cycle is that once one is completed with a problem another will usually pop up.

Insight is the sudden solution to a long-vexing problem, a sudden recognition of a new idea, or a sudden understanding of a complex situation, an Aha! Solutions found through insight are often more accurate than those found through step-by-step analysis. To solve more problems at a faster rate, insight is necessary for selecting productive moves at different stages of the problem-solving cycle. This problem-solving strategy pertains specifically to problems referred to as insight problem.

Unlike Newell and Simon’s formal definition of move problems, there has not been a generally agreed upon definition of an insight problem Ash, Jee, and Wiley, ; [28] Chronicle, MacGregor, and Ormerod, ; [29] Chu and MacGregor, Blanchard-Fields [31] looks at problem solving from one of two facets.

The first looking at those problems that only have one solution like mathematical problems, or fact-based questions which are grounded in psychometric intelligence. The other is socioemotional in nature and have answers that change constantly like what’s your favorite color or what you should get someone for Christmas.

The following techniques are usually called problem-solving strategies [32]. Common barriers to problem solving are mental constructs that impede our ability to correctly solve problems.

These barriers prevent people from solving problems in the most efficient manner possible. Five of the most common processes and factors that researchers have identified as barriers to problem solving are confirmation bias , mental set , functional fixedness , unnecessary constraints, and irrelevant information.

Confirmation bias is an unintentional bias caused by the collection and use of data in a way that favors a preconceived notion. The beliefs affected by confirmation bias do not need to have motivation , the desire to defend or find substantiation for beliefs that are important to that person.

Andreas Hergovich, Reinhard Schott, and Christoph Burger’s experiment conducted online, for instance, suggested that professionals within the field of psychological research are likely to view scientific studies that agree with their preconceived notions more favorably than studies that clash with their established beliefs.

Nickerson argued that those who killed people accused of witchcraft demonstrated confirmation bias with motivation. Researcher Michael Allen found evidence for confirmation bias with motivation in school children who worked to manipulate their science experiments in such a way that would produce favorable results.

In , Peter Cathcart Wason conducted an experiment in which participants first viewed three numbers and then created a hypothesis that proposed a rule that could have been used to create that triplet of numbers. When testing their hypotheses, participants tended to only create additional triplets of numbers that would confirm their hypotheses, and tended not to create triplets that would negate or disprove their hypotheses.

Thus research also shows that people can and do work to confirm theories or ideas that do not support or engage personally significant beliefs. Mental set was first articulated by Abraham Luchins in the s and demonstrated in his well-known water jug experiments.

After Luchins gave his participants a set of water jug problems that could all be solved by employing a single technique, he would then give them a problem that could either be solved using that same technique or a novel and simpler method. Luchins discovered that his participants tended to use the same technique that they had become accustomed to despite the possibility of using a simpler alternative. However, as Luchins’ work revealed, such methods for finding a solution that have worked in the past may not be adequate or optimal for certain new but similar problems.

Therefore, it is often necessary for people to move beyond their mental sets in order to find solutions. This was again demonstrated in Norman Maier ‘s experiment, which challenged participants to solve a problem by using a household object pliers in an unconventional manner.

Maier observed that participants were often unable to view the object in a way that strayed from its typical use, a phenomenon regarded as a particular form of mental set more specifically known as functional fixedness, which is the topic of the following section. When people cling rigidly to their mental sets, they are said to be experiencing fixation , a seeming obsession or preoccupation with attempted strategies that are repeatedly unsuccessful.

Functional fixedness is a specific form of mental set and fixation, which was alluded to earlier in the Maier experiment, and furthermore it is another way in which cognitive bias can be seen throughout daily life.

Tim German and Clark Barrett describe this barrier as the fixed design of an object hindering the individual’s ability to see it serving other functions. In more technical terms, these researchers explained that “[s]ubjects become ‘fixed’ on the design function of the objects, and problem solving suffers relative to control conditions in which the object’s function is not demonstrated. In research that highlighted the primary reasons that young children are immune to functional fixedness, it was stated that “functional fixedness For instance, imagine the following situation: a man sees a bug on the floor that he wants to kill, but the only thing in his hand at the moment is a can of air freshener.

If the man starts looking around for something in the house to kill the bug with instead of realizing that the can of air freshener could in fact be used not only as having its main function as to freshen the air, he is said to be experiencing functional fixedness.

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