Problem solving

Problem solving in psychology refers to the process of finding solutions to problems encountered in life.[4] Solutions to these problems are usually situation or context-specific. 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.[5] 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.[6] Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills.[7]

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.[8] Empirical research shows many different strategies and factors influence everyday problem solving.[9][10][11] Rehabilitation psychologists studying individuals with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems.[12] Interpersonal everyday problem solving is dependent upon the individual personal motivational and contextual components. 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,[13][14] 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.[15] In conceptualization, human problem solving consists of two related processes: problem orientation and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. Studies conclude people's strategies cohere with their goals[16] and stem from the natural process of comparing oneself with others.

Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, e.g., Karl Duncker in The Psychology of Productive Thinking (1935).[17] Perhaps best known is the work of Allen Newell and Herbert A. Simon.[18]

Experiments the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks.[19][20] These simple problems, such as the Tower of Hanoi, admitted optimal solutions which could be found quickly, allowing observation of the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic cognitive processes by which more complex "real world" problems are solved.

An outstanding problem solving technique found by this research is the principle of decomposition.[21]

Much of computer science and artificial intelligence involves designing automatic systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs.

Steps for designing such systems include problem determination, heuristics, root cause analysis, de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems, and simulation.[22] A large, perennial obstacle is to find and fix errors in computer 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 1950s. 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. C. 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 1958, 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 1969, 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,[23] which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving[24] and computational logic to improve human thinking[25]

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 to prevent the problem. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems.

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.[26]

In military science, problem solving is linked to the concept of "end-states", the condition or situation which is the aim of the strategy.[27]^{: xiii, E-2} Ability to solve problems is important at any military rank, but is essential at the command and control level, where it results from deep qualitative and quantitative understanding of possible scenarios. Effectiveness is evaluation of results, whether the goal was accomplished.[27]^: IV-24 Planning is the process of determining how to achieve the goal.[27]^: IV-1

Confirmation bias is an unintentional tendency to collect and use data which favors preconceived notions. Such notions may be incidental rather than motivated by important personal beliefs: the desire to be right may be sufficient motivation.[34] Research has found that scientific and technical professionals also experience confirmation bias.

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 clashing studies.[35] According to Raymond Nickerson, one can see the consequences of confirmation bias in real-life situations, which range in severity from inefficient government policies to genocide. 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 to produce favorable results.[36]

However, confirmation bias does not necessarily require motivation. In 1960, 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.[37]

Mental set is the inclination to re-use a previously successful solution, rather than search for new and better solutions. It is a reliance on habit.

It was first articulated by Abraham Luchins in the 1940s with his well-known water jug experiments.[38] Participants were asked to fill one jug with a specific amount of water using other jugs with different maximum capacities. After Luchins gave a set of jug problems that could all be solved by a single technique, he then introduced a problem that could be solved by the same technique, but also by a novel and simpler method. His participants tended to use the accustomed technique, oblivious of the simpler alternative.[39] This was again demonstrated in Norman Maier's 1931 experiment, which challenged participants to solve a problem by using a familiar tool (pliers) in an unconventional manner. Participants were often unable to view the object in a way that strayed from its typical use, a type of mental set known as functional fixedness (see the following section).

Rigidly clinging to a mental set is called fixation, which can deepen to an obsession or preoccupation with attempted strategies that are repeatedly unsuccessful.[40] In the late 1990s, researcher Jennifer Wiley found that professional expertise in a field can create a mental set, perhaps leading to fixation.[40]

Groupthink, where each individual takes on the mindset of the rest of the group, can produce and exacerbate mental set.[41] Social pressure leads to everybody thinking the same thing and reaching the same conclusions.

Functional fixedness is the tendency to view an object as having only one function, unable to conceive of any novel use, as in the Maier pliers experiment above. Functional fixedness is a specific form of mental set, and is one of the most common forms of cognitive bias in daily life.

Tim German and Clark Barrett describe this barrier: "[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."[42] Their research found that young children's limited knowledge of an object's intended function reduces this barrier[43] Research has also discovered functional fixedness in many educational instances, as an obstacle to understanding. Furio, Calatayud, Baracenas, and Padilla stated: "... functional fixedness may be found in learning concepts as well as in solving chemistry problems."[44]

As an example, imagine a man wants to kill a bug in is house, but the only thing at hand is a can of air freshener. He may start searching for something to kill the bug instead of squashing it with the can, thinking only of its main function of deodorizing.

There are several hypotheses in regards to how functional fixedness relates to problem solving.[45] It may waste time, delaying or entirely preventing the correct use of a tool.

Unnecessary constraints are arbitrary boundaries imposed unconsciously on the task at hand, which foreclose a productive avenue of solution. The solver may become fixated on only one type of solution, as if it were an inevitable requirement of the problem. Typically, this combines with mental set, clinging to a previously successful method.[46]

Visual problems can also produce mentally invented constraints.[47] A famous example is the dot problem: nine dots arranged in a three-by-three grid pattern must be connected by drawing four straight line segments, without lifting pen from paper or backtracking along a line. The subject typically assumes the pen must stay within the outer square of dots, but the solution requires lines continuing beyond this frame, and researchers have found a 0% solution rate within a brief alotted time.[48]

This problem has produced the expression "think outside the box".[49] Such problems are typically solved via a sudden insight which leaps over the mental barriers, often after long toil against them.[50] This can be difficult depending on how the subject has structured the problem in their mind, how they draw on past experiences, and how well they juggle this information in their working memory. In the example, envisioning the dots connected outside the framing square requires visualizing an unconventional arrangement, a strain on working memory.[49]

Irrelevant information is a specification or data presented in a problem that is unrelated to the solution.[46] If the solver assumes that all information presented needs to be used, this often derails the problem solving process, making relatively simple problems much harder.[51]

For example: "Fifteen percent of the people in Topeka have unlisted telephone numbers. You select 200 names at random from the Topeka phone book. How many of these people have unlisted phone numbers?"[52] The "obvious" answer is 15%, but in fact none of the unlisted people would be listed among the 200. This kind of "trick question" is often used in aptitude tests or cognitive evaluations.[53] Though not inherently difficult, they require independent thinking that is not necessarily common. Mathematical word problems often include irrelevant qualitative or numerical information as an extra challenge.

The disruption caused by the above cognitive biases can depend on how the information is represented:[53] visually, verbally, or mathematically. A classic example is the Buddhist monk problem:

A Buddhist monk begins at dawn one day walking up a mountain, reaches the top at sunset, meditates at the top for several days until one dawn when he begins to walk back to the foot of the mountain, which he reaches at sunset. Making no assumptions about his starting or stopping or about his pace during the trips, prove that there is a place on the path which he occupies at the same hour of the day on the two separate journeys.

The problem cannot be addressed in a verbal context, trying to describe the monk's progress on each day. It becomes much easier when the paragraph is represented mathematically by a function: one visualizes a graph whose horizontal axis is time of day, and whose vertical axis shows the monk's position (or altitude) on the path at each time. Superimposing the two journey curves, which traverse opposite diagonals of a rectangle, one sees they must cross each other somewhere. The visual representation by graphing has resolved the difficulty.

Similar strategies can often improve problem solving on tests.[46][54]

Individual humans engaged in problem-solving tend to overlook subtractive changes, including those that are critical elements of efficient solutions. This tendency to solve by first, only or mostly creating or adding elements, rather than by subtracting elements or processes is shown to intensify with higher cognitive loads such as information overload.[55][56]

In Europe, two main approaches have surfaced, one initiated by Donald Broadbent (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by Dietrich Dörner (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches share an emphasis on relatively complex, semantically rich, computerized laboratory tasks, constructed to resemble real-life problems. The approaches differ somewhat in their theoretical goals and methodology, however. The tradition initiated by Broadbent emphasizes the distinction between cognitive problem-solving processes that operate under awareness versus outside of awareness, and typically employs mathematically well-defined computerized systems. The tradition initiated by Dörner, on the other hand, has an interest in the interplay of the cognitive, motivational, and social components of problem solving, and utilizes very complex computerized scenarios that contain up to 2,000 highly interconnected variables (e.g., Dörner, Kreuzig, Reither & Stäudel's 1983 LOHHAUSEN project; Ringelband, Misiak & Kluwe, 1990). Buchner (1995) describes the two traditions in detail.

In North America, initiated by the work of Herbert A. Simon on "learning by doing" in semantically rich domains,[63][64] researchers began to investigate problem solving separately in different natural knowledge domains – such as physics, writing, or chess playing – thus relinquishing their attempts to extract a global theory of problem solving (e.g. Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of expertise; Chase & Simon, 1973; Chi, Feltovich & Glaser, 1981.[65]

Areas that have attracted rather intensive attention in North America include:

• Reading (Stanovich & Cunningham, 1991)
• Writing (Bryson, Bereiter, Scardamalia & Joram, 1991)
• Calculation (Sokol & McCloskey, 1991)
• Political decision making (Voss, Wolfe, Lawrence & Engle, 1991)
• Managerial problem solving ([66])
• Lawyers' reasoning[67]
• Mechanical problem solving (Hegarty, 1991)
• Problem solving in electronics (Lesgold & Lajoie, 1991)
• Computer skills (Kay, 1991)
• Game playing (Frensch & Sternberg, 1991)
• Personal problem solving (Heppner & Krauskopf, 1987)
• Mathematical problem solving (Pólya, 1945; Schoenfeld, 1985)
• Social problem solving[13][14]
• Problem solving for innovations and inventions: TRIZ[68]