Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence , versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices.
46-465: A problem is a difficulty which may be resolved by problem solving . Problem ( s ) or The Problem may also refer to: Problem solving Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing
92-661: A facial expression is represented in the right posterior superior temporal sulcus and medial prefrontal cortex . "Negative" emotions like anger and fear have a negative valence . But positive emotions like joy have a positive valence . Positively valenced emotions are evoked by positively valenced events, objects, or situations. The term is also used to describe the hedonic tone of feelings , certain behaviors (for example, approach and avoidance), goal attainment or non-attainment, and conformity with or violation of norms . Ambivalence can be viewed as conflict between positive and negative valence-carriers. Theorists taking
138-440: A hypothesis in the form of 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. Mental set is the inclination to re-use a previously successful solution, rather than search for new and better solutions. It
184-496: A hypothesis with empirical data (asking "how much?"). The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert. In the Peircean logical system, the logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details (empirical substantiation) to our conceptual knowledge. Forensic engineering
230-502: A problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution. There are many specialized problem-solving techniques and methods in fields such as science , engineering , business , medicine , mathematics , computer science , philosophy , and social organization . The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences . Also widely researched are
276-413: A process known as transfer . Problem-solving strategies are steps to overcoming the obstacles to achieving a goal. The iteration of such strategies over the course of solving a problem is the "problem-solving cycle". Common steps in this cycle include recognizing the problem, defining it, developing a strategy to fix it, organizing knowledge and resources available, monitoring progress, and evaluating
322-594: A product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems. In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypotheses (asking "how?"); deduction evaluates and refines hypotheses based on other plausible premises (asking "why?"); and induction justifies
368-442: 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. In the late 1990s, researcher Jennifer Wiley found that professional expertise in a field can create a mental set, perhaps leading to fixation. Groupthink , in which each individual takes on
414-399: Is a characteristic of emotions that determines their emotional affect (intrinsic appeal or repulsion). Positive valence corresponds to the "goodness" or attractiveness of an object, event, or situation, making it appealing or desirable. Conversely, negative valence relates to "badness" or averseness, rendering something unappealing or undesirable. This concept is not only used to describe
460-400: Is a reliance on habit. It was first articulated by Abraham S. Luchins in the 1940s with his well-known water jug experiments. Participants were asked to fill one jug with a specific amount of water by 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
506-412: 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 disassembling the product and developing a plausible pathway to creating and assembling its parts. In military science , problem solving
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#1732765411874552-403: Is an issue for psychological researchers who reject the existence of neutral emotions (e.g. surprise , sublimation). However, other psychological researchers assume that neutral emotions exist. Two contrasting views in the phenomenology of valence are that of a constrained valence psychology, where the most intense experiences are generally no more than 10 times more intense than the mildest, and
598-573: 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. Scientific and technical professionals also experience confirmation bias. One online experiment, for example, 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. According to Raymond Nickerson, one can see
644-554: Is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization, human problem solving consists of two related processes: problem orientation, and
690-433: Is linked to the concept of "end-states", the conditions or situations which are the aims of the strategy. Ability to solve problems is important at any military rank , but is essential at the command and control level. It results from deep qualitative and quantitative understanding of possible scenarios. Effectiveness in this context is an evaluation of results: to what extent the end states were accomplished. Planning
736-460: 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: 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
782-407: Is one of the most common forms of cognitive bias in daily life. As an example, imagine a man wants to kill a bug in his 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. Tim German and Clark Barrett describe this barrier: "subjects become 'fixed' on
828-438: 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 allotted time. This problem has produced
874-563: Is the process of determining how to effect those end states. Some models of problem solving involve identifying a goal and then a sequence of subgoals towards achieving this goal. Andersson, who introduced the ACT-R model of cognition, modelled this collection of goals and subgoals as a goal stack in which the mind contains a stack of goals and subgoals to be completed, and a single task being carried out at any time. Knowledge of how to solve one problem can be applied to another problem, in
920-489: Is the work of Allen Newell and Herbert A. Simon . Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi , admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit
966-470: Is to find and fix errors in computer programs: debugging . Formal logic concerns issues like 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
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#17327654118741012-949: 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, who used 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 that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution , which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking. When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures . Such techniques can also be applied to
1058-732: The Heavy-Tailed Valence hypothesis, which states that the range of possible degrees of valence is far more extreme. Valence could be assigned a number and treated as if it were measured, but the validity of a measurement based on a subjective report is questionable. Measurement based on observations of facial expressions, using the Facial Action Coding System and microexpressions (see Paul Ekman ) or muscle activity detected through facial electromyography , or on modern functional brain imaging may overcome this objection. The perceived emotional valence of
1104-501: The ability of a verb to require a number of additional terms (e.g. subject and object) to form a complete sentence. The term chemical valence has been used in physics and chemistry to describe the mechanism by which atoms bind to one another since the nineteenth century. Valence is an inferred criterion from instinctively generated emotions; it is the property specifying whether feelings/affects are positive, negative or neutral. The existence of at least temporarily unspecified valence
1150-800: 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 . Much of computer science and artificial intelligence involves designing automated 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. A large, perennial obstacle
1196-626: 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. 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
1242-457: 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. Visual problems can also produce mentally invented constraints. A famous example
1288-622: The design function of the objects, and problem solving suffers relative to control conditions in which the object's function is not demonstrated." Their research found that young children's limited knowledge of an object's intended function reduces this barrier Research has also discovered functional fixedness in educational contexts, as an obstacle to understanding: "functional fixedness may be found in learning concepts as well as in solving chemistry problems." There are several hypotheses in regards to how functional fixedness relates to problem solving. It may waste time, delaying or entirely preventing
1334-512: The difficulty. Similar strategies can often improve problem solving on tests. People who are engaged in problem solving tend to overlook subtractive changes, even 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 . Valence (psychology) Valence , also known as hedonic tone ,
1380-423: The effectiveness of the solution. Once a solution is achieved, another problem usually arises, and the cycle starts again. Insight is the sudden a ha! solution to a problem, the birth of a new idea to simplify a complex situation. Solutions found through insight are often more incisive than those from step-by-step analysis. A quick solution process requires insight to select productive moves at different stages of
1426-424: The expression " think outside the box ". Such problems are typically solved via a sudden insight which leaps over the mental barriers, often after long toil against them. 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
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1472-604: 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. In 1958, John McCarthy proposed
1518-421: The framing square requires visualizing an unconventional arrangement, which is a strain on working memory. Irrelevant information is a specification or data presented in a problem that is unrelated to the solution. 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. For example: "Fifteen percent of
1564-405: 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 has been defined as a higher-order cognitive process and intellectual function that requires
1610-451: The intrinsic qualities of objects and events but also categorizes emotions based on their inherent attractiveness or averseness . The use of the term in psychology entered English with the translation from German ("Valenz") in 1935 of works of Kurt Lewin . The original German word suggests "binding", and is commonly used in a grammatical context to describe the ability of one word to semantically and syntactically link another, especially
1656-812: The mental obstacles that prevent people from finding solutions; 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. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of
1702-466: The mindset of the rest of the group, can produce and exacerbate mental set. 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, and to be unable to conceive of any novel use, as in the Maier pliers experiment described above. Functional fixedness is a specific form of mental set, and
1748-471: The modulation and control of more routine or fundamental skills. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people 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. Interpersonal everyday problem solving
1794-458: 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
1840-584: The motivational/attitudinal/affective approach to problematic situations and problem-solving skills. People's strategies cohere with their goals and stem from the process of comparing oneself with others. Among the first experimental psychologists to study problem solving were the Gestaltists in Germany , such as Karl Duncker in The Psychology of Productive Thinking (1935). Perhaps best known
1886-485: 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?" 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. Though not inherently difficult, they require independent thinking that
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1932-447: The problem). 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 a problem requires abstract thinking or coming up with a creative solution. Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered. Problem solving in psychology refers to
1978-491: The problem-solving cycle. Unlike Newell and Simon's formal definition of a move problem , there is no consensus definition of an insight problem . Some problem-solving strategies include: Common barriers to problem solving include mental constructs that impede an efficient search for solutions. Five of the most common identified by researchers are: confirmation bias , mental set , functional fixedness , unnecessary constraints, and irrelevant information. Confirmation bias
2024-582: The process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping , in which 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; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis. Mental health professionals study
2070-486: The same technique, but also by a novel and simpler method. His participants tended to use the accustomed technique, oblivious of the simpler alternative. 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,
2116-434: 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
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