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 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.
Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, and consultants are largely problem solvers for issues which require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing 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
engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
,
business,
medicine
Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...
,
mathematics,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
,
philosophy, and
social organization
In sociology, a social organization is a pattern of relationships between and among individuals and social groups.
Characteristics of social organization can include qualities such as sexual composition, spatiotemporal cohesion, leadership, s ...
. The mental techniques to identify, analyze, and solve problems are studied in
psychology
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between ...
and
cognitive sciences. Additionally, the mental obstacles preventing people from finding solutions is a widely researched topic: problem solving impediments include
confirmation bias,
mental set In psychology, rigidity or mental rigidity refers to an obstinate inability to yield or a refusal to appreciate another person's viewpoint or emotions characterized by a lack of empathy. It can also refer to the tendency to perseverate, which is the ...
, and
functional fixedness
Functional fixedness is a cognitive bias that limits a person to use an object only in the way it is traditionally used. The concept of functional fixedness originated in Gestalt psychology, a movement in psychology that emphasizes holistic proces ...
.
Definition
The term ''problem solving'' has a slightly different meaning depending on the discipline. For instance, it is a mental process in
psychology
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between ...
and a computerized process in
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
. 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.
[ Schacter, D.L. et al. (2009). Psychology, Second Edition. New York: Worth Publishers. pp. 376] Solving problems sometimes involves dealing with
pragmatics
In linguistics and related fields, pragmatics is the study of how context contributes to meaning. The field of study evaluates how human language is utilized in social interactions, as well as the relationship between the interpreter and the in ...
, the way that context contributes to meaning, and
semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...
, the interpretation of 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 the problem requires
abstract thinking
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods.
"An abstr ...
or coming up with a creative solution.
Psychology
Problem solving in psychology refers to 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
Problem shaping means revising a question so that the solution process can begin or continue.
It is part of the larger problem process that includes problem finding and problem solving. Problem shaping (or problem framing) often involves the appl ...
, 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. Mental health professionals study the human problem solving processes using methods such as
introspection
Introspection is the examination of one's own conscious thoughts and feelings. In psychology, the process of introspection relies on the observation of one's mental state, while in a spiritual context it may refer to the examination of one's sou ...
,
behaviorism,
simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the s ...
,
computer modeling
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
, and
experiment
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
. 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 the modulation and control of more routine or fundamental skills.
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.
[Bernd Zimmermann, ''On mathematical problem solving processes and history of mathematics'', University of Jena.] Empirical research shows many different strategies and factors influence everyday problem solving.
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.
Interpersonal everyday problem solving is dependent upon the individual personal motivational and contextual components. One such component is the
emotional valence
Valence, or hedonic tone, is the affective quality referring to the intrinsic attractiveness/"good"-ness (positive valence) or averseness/"bad"-ness (negative valence) of an event, object, or situation. The term also characterizes and categor ...
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,
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.
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 and stem from the natural process of comparing oneself with others.
Cognitive sciences
Among the first experimental psychologists to study problem solving were the
Gestaltists in
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
, e.g.,
Karl Duncker Karl may refer to:
People
* Karl (given name), including a list of people and characters with the name
* Karl der Große, commonly known in English as Charlemagne
* Karl Marx, German philosopher and political writer
* Karl of Austria, last Austri ...
in ''The Psychology of Productive Thinking'' (1935).
Perhaps best known is the work of
Allen Newell and
Herbert A. Simon
Herbert Alexander Simon (June 15, 1916 – February 9, 2001) was an American political scientist, with a Ph.D. in political science, whose work also influenced the fields of computer science, economics, and cognitive psychology. His primary ...
.
Experiments 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
The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle) is a mathematical game or puzzle consisting of three rods and a number of disks of v ...
, 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 process
Cognition refers to "the mental action or process of acquiring knowledge and understanding through thought, experience, and the senses". It encompasses all aspects of intellectual functions and processes such as: perception, attention, thought, ...
es by which more complex "real world" problems are solved.
An outstanding problem solving technique found by this research is the principle of
decomposition
Decomposition or rot is the process by which dead organic substances are broken down into simpler organic or inorganic matter such as carbon dioxide, water, simple sugars and mineral salts. The process is a part of the nutrient cycle and is e ...
.
Computer science
Much of computer science and
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech r ...
involves designing automatic systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly.
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s are recipes or instructions that direct such systems, written into
computer program
A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components.
A computer program ...
s.
Steps for designing such systems include problem determination,
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate ...
s,
root cause analysis
In science and engineering, root cause analysis (RCA) is a method of problem solving used for identifying the root causes of faults or problems. It is widely used in IT operations, manufacturing, telecommunications, industrial process control ...
,
de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming,
queuing systems, and simulation.
A large, perennial obstacle is to find and fix errors in computer programs:
debugging.
Logic
Formal
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...
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
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a ma ...
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
Resolution(s) may refer to:
Common meanings
* Resolution (debate), the statement which is debated in policy debate
* Resolution (law), a written motion adopted by a deliberative body
* New Year's resolution, a commitment that an individual mak ...
principle developed by
John Alan Robinson
John Alan Robinson (9 March 1930 – 5 August 2016) was a philosopher, mathematician, and computer scientist. He was a professor emeritus at Syracuse University.
Alan Robinson's major contribution is to the foundations of automated theorem pr ...
.
In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for
program verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal metho ...
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
Cordell Green (born 1941) is an American computer scientist who is the director and chief scientist of the Kestrel Institute.
Green received a B.A. and B.S. from Rice University. At Stanford University, he earned an M.S. and then a PhD in 1969.
...
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
Robert Anthony Kowalski (born 15 May 1941) is an American-British logician and computer scientist, whose research is concerned with developing both human-oriented models of computing and computational models of human thinking. He has spent mo ...
developed
logic programming
Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic pro ...
and
SLD resolution SLD resolution (''Selective Linear Definite'' clause resolution) is the basic inference rule used in logic programming. It is a refinement of resolution, which is both sound and refutation complete for Horn clauses.
The SLD inference rule
Give ...
, which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking
Engineering
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
Failure mode and effects analysis (FMEA; often written with "failure modes" in plural) is the process of reviewing as many components, assemblies, and subsystems as possible to identify potential failure modes in a system and their causes and effe ...
can proactively reduce the likelihood of problems.
Forensic engineering
Forensic engineering has been defined as ''"the investigation of failures - ranging from serviceability to catastrophic - which may lead to legal activity, including both civil and criminal".'' It includes the investigation of materials, produc ...
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.
Military science
In
military science, problem solving is linked to the concept of "end-states", the condition or situation which is the aim of the strategy.
Ability to solve problems is important at any
military rank
Military ranks are a system of hierarchical relationships, within armed forces, police, intelligence agencies or other institutions organized along military lines. The military rank system defines dominance, authority, and responsibility in a ...
, but is essential at the
command and control
Command and control (abbr. C2) is a "set of organizational and technical attributes and processes ... hatemploys human, physical, and information resources to solve problems and accomplish missions" to achieve the goals of an organization or en ...
level, where it results from deep qualitative and quantitative understanding of possible scenarios. ''Effectiveness'' is evaluation of results, whether the goal was accomplished.
''Planning'' is the process of determining how to achieve the goal.
Processes
Some models of problem solving involve identifying a
goal
A goal is an idea of the future or desired result that a person or a group of people envision, plan and commit to achieve. People endeavour to reach goals within a finite time by setting deadlines.
A goal is roughly similar to a purpose or ...
and then a sequence of subgoals towards achieving this goal. Andersson, who introduced the
ACT-R
ACT-R (pronounced /ˌækt ˈɑr/; short for "Adaptive Control of Thought—Rational") is a cognitive architecture mainly developed by John Robert Anderson and Christian Lebiere at Carnegie Mellon University. Like any cognitive architecture, ACT-R ...
model of cognition, modelled this collection of goals and subgoals as a
goal stack, where the mind contains a stack of goals and subgroals to be completed with a single task being carried out at any time.
It has been observed that knowledge of how to solve one problem can be applied to another problem, in a process known as
transfer
Transfer may refer to:
Arts and media
* ''Transfer'' (2010 film), a German science-fiction movie directed by Damir Lukacevic and starring Zana Marjanović
* ''Transfer'' (1966 film), a short film
* ''Transfer'' (journal), in management studies
...
.
Problem-solving strategies
Problem-solving strategies are steps to overcoming the obstacles to achieving a goal, 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 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 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:
*
Abstraction: solving the problem in a tractable model system to gain insight into the real system
*
Analogy: adapting the solution to a previous problem which has similar features or mechanisms
*
Brainstorming
Brainstorming is a group creativity technique by which efforts are made to find a conclusion for a specific problem by gathering a list of ideas spontaneously contributed by its members.
In other words, brainstorming is a situation where a grou ...
: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum solution is found
*
Critical thinking
*
Divide and conquer: breaking down a large, complex problem into smaller, solvable problems
*
Hypothesis testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis.
Hypothesis testing allows us to make probabilistic statements about population parameters.
...
: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
*
Lateral thinking
Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. It involves ideas that may not be obtainable using only traditional step-by-step logic. The term was first u ...
: approaching solutions indirectly and creatively
*
Means-ends analysis: choosing an action at each step to move closer to the goal
*
Morphological analysis: assessing the output and interactions of an entire system
*
Proof of impossibility
In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative ...
: try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it
*
Reduction: transforming the problem into another problem for which solutions exist
*
Research
Research is " creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness ...
: employing existing ideas or adapting existing solutions to similar problems
*
Root cause analysis
In science and engineering, root cause analysis (RCA) is a method of problem solving used for identifying the root causes of faults or problems. It is widely used in IT operations, manufacturing, telecommunications, industrial process control ...
: identifying the cause of a problem
*
Trial-and-error
Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying.
According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (18 ...
: testing possible solutions until the right one is found
*
Help-seeking Help-seeking theory postulates that people follow a series of predictable steps to seek help for their inadequacies, it is a series of well-ordered and purposeful cognitive and behavioral steps, each leading to specific types of solutions.
Help-see ...
Problem-solving methods
*
Eight Disciplines Problem Solving
*
GROW model
*
How to Solve It
''How to Solve It'' (1945) is a small volume by mathematician George Pólya describing methods of problem solving.
Four principles
''How to Solve It'' suggests the following steps when solving a mathematical problem:
# First, you have to ''und ...
*
Lateral thinking
Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. It involves ideas that may not be obtainable using only traditional step-by-step logic. The term was first u ...
*
OODA loop
The OODA loop is the cycle ''observe–orient–decide–act'', developed by military strategist and United States Air Force Colonel John Boyd. Boyd applied the concept to the combat operations process, often at the operational level during m ...
(observe, orient, decide, and act)
*
PDCA
PDCA (plan–do–check–act or plan–do–check–adjust) is an iterative design and management method used in business for the control and continual improvement of processes and products. It is also known as the Shewhart cycle, or the control ...
(plan–do–check–act)
*
Root cause analysis
In science and engineering, root cause analysis (RCA) is a method of problem solving used for identifying the root causes of faults or problems. It is widely used in IT operations, manufacturing, telecommunications, industrial process control ...
*
RPR problem diagnosis (rapid problem resolution)
*
TRIZ
TRIZ (; russian: теория решения изобретательских задач, ', lit. "theory of inventive problem solving") is “the next evolutionary step in creating an organized and systematic approach to problem solving. The deve ...
(russian: теория решения изобретательских задач, translit=teoriya resheniya izobretatelskikh zadatch, translit-script=Latn, translation=theory of inventive problem solving)
*
A3 problem solving
*
System dynamics
*
Hive mind
*
Design Thinking
Design thinking refers to the set of cognitive, strategic and practical procedures used by designers in the process of designing, and to the body of knowledge that has been developed about how people reason when engaging with design problems.
Des ...
*
Help-seeking Help-seeking theory postulates that people follow a series of predictable steps to seek help for their inadequacies, it is a series of well-ordered and purposeful cognitive and behavioral steps, each leading to specific types of solutions.
Help-see ...
Common barriers
Common barriers to problem solving are mental constructs that impede an efficient search for solutions. Five of the most common identified by researchers are:
confirmation bias,
mental set In psychology, rigidity or mental rigidity refers to an obstinate inability to yield or a refusal to appreciate another person's viewpoint or emotions characterized by a lack of empathy. It can also refer to the tendency to perseverate, which is the ...
,
functional fixedness
Functional fixedness is a cognitive bias that limits a person to use an object only in the way it is traditionally used. The concept of functional fixedness originated in Gestalt psychology, a movement in psychology that emphasizes holistic proces ...
, unnecessary constraints, and irrelevant information.
Confirmation bias
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.
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. 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
Witchcraft traditionally means the use of magic or supernatural powers to harm others. A practitioner is a witch. In medieval and early modern Europe, where the term originated, accused witches were usually women who were believed to have ...
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
Peter Cathcart Wason (22 April 1924 – 17 April 2003) was a cognitive psychologist at University College, London who pioneered the Psychology of Reasoning. He progressed explanations as to why people make certain consistent mistakes in logical r ...
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.
Mental set
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. 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. This was again demonstrated in
Norman Maier
Norman Raymond Frederick Maier (1900–1977) was an American experimental psychologist who worked primarily at the University of Michigan. He invented the two-cords problem and co-authored ''Principles of Animal Psychology.''
Biography
Although ...
'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.
In the late 1990s, researcher Jennifer Wiley found that professional expertise in a field can create a mental set, perhaps leading to fixation.
Groupthink
Groupthink is a psychological phenomenon that occurs within a group of people in which the desire for harmony or conformity in the group results in an irrational or dysfunctional decision-making outcome. Cohesiveness, or the desire for cohesiveness ...
, where each individual takes on 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
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: "subjects 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." 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 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."
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. It may waste time, delaying or entirely preventing the correct use of a tool.
Unnecessary constraints
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.
[Kellogg, R. T. (2003). Cognitive psychology (2nd ed.). California: Sage Publications, Inc.]
Visual problems can also produce mentally invented constraints. 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 allotted time.
This problem has produced the expression "think outside the box".
[Weiten, Wayne. (2011). Psychology: themes and variations (8th ed.). California: Wadsworth.] 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 the framing square requires visualizing an unconventional arrangement, a strain on working memory.
Irrelevant information
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 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.
[Walinga, Jennifer, Cunningham, J. Barton, & MacGregor, James N. (2011). Training insight problem solving through focus on barriers and assumptions. The Journal of Creative Behavior.] 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.
Avoiding barriers by changing problem representation
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 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
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
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.
Other barriers for individuals
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 load
In cognitive psychology, cognitive load refers to the amount of working memory resources used. There are three types of cognitive load: ''intrinsic'' cognitive load is the effort associated with a specific topic; ''extraneous'' cognitive load refe ...
s such as
information overload.
Dreaming: problem-solving without waking consciousness
Problem solving can also occur without waking consciousness. There are many reports of scientists and engineers who solved problems in their
dream
A dream is a succession of images, ideas, emotions, and sensations that usually occur involuntarily in the mind during certain stages of sleep. Humans spend about two hours dreaming per night, and each dream lasts around 5 to 20 minutes, althou ...
s.
Elias Howe
Elias Howe Jr. (; July 9, 1819October 3, 1867) was an American inventor best known for his creation of the modern lockstitch sewing machine.
Early life
Elias Howe Jr. was born on July 9, 1819, to Dr. Elias Howe Sr. and Polly (Bemis) Howe in ...
, inventor of the sewing machine, figured out the structure of the bobbin from a dream.
The chemist
August Kekulé
Friedrich August Kekulé, later Friedrich August Kekule von Stradonitz ( , ; 7 September 1829 – 13 July 1896), was a German organic chemist. From the 1850s until his death, Kekulé was one of the most prominent chemists in Europe, especially ...
was considering how benzene arranged its six carbon and hydrogen atoms. Thinking about the problem, he dozed off, and dreamt of dancing atoms that fell into a snakelike pattern, which led him to discover the benzene ring. As Kekulé wrote in his diary,
There also are empirical studies of how people can think consciously about a problem before going to sleep, and then solve the problem with a dream image. Dream researcher
William C. Dement told his undergraduate class of 500 students that he wanted them to think about an infinite series, whose first elements were OTTFF, to see if they could deduce the principle behind it and to say what the next elements of the series would be.
[Dement, W.C. (1972). ''Some Must Watch While Some Just Sleep''. New York: Freeman.] He asked them to think about this problem every night for 15 minutes before going to sleep and to write down any dreams that they then had. They were instructed to think about the problem again for 15 minutes when they awakened in the morning.
The sequence OTTFF is the first letters of the numbers: one, two, three, four, five. The next five elements of the series are SSENT (six, seven, eight, nine, ten). Some of the students solved the puzzle by reflecting on their dreams. One example was a student who reported the following dream:
With more than 500 undergraduate students, 87 dreams were judged to be related to the problems students were assigned (53 directly related and 34 indirectly related). Yet of the people who had dreams that apparently solved the problem, only seven were actually able to consciously know the solution. The rest (46 out of 53) thought they did not know the solution.
Mark Blechner conducted this experiment and obtained results similar to Dement's.
[Blechner, M. J. (2018) ''The Mindbrain and Dreams: An Exploration of Dreaming, Thinking, and Artistic Creation''. New York: Routledge.] He found that while trying to solve the problem, people had dreams in which the solution appeared to be obvious from the dream, but it was rare for the dreamers to realize how their dreams had solved the puzzle. Coaxing or hints did not get them to realize it, although once they heard the solution, they recognized how their dream had solved it. For example, one person in that OTTFF experiment dreamed:
In the dream, the person counted out the next elements of the series six, seven, eight, nine, ten, eleven, twelve yet he did not realize that this was the solution of the problem. His sleeping mindbrain solved the problem, but his waking mindbrain was not aware how.
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
believed that much problem solving goes on unconsciously, and the person must then figure out and formulate consciously what the mindbrain has already solved. He believed this was his process in formulating the theory of relativity: "The creator of the problem possesses the solution." Einstein said that he did his problem-solving without words, mostly in images. "The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined."
Cognitive sciences: two schools
In
cognitive sciences, researchers' realization that problem-solving processes differ across knowledge domains and across levels of expertise and that, consequently, findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory, has led to an emphasis on real-world problem solving since the 1990s. This emphasis has been expressed quite differently in North America and Europe, however. Whereas North American research has typically concentrated on studying problem solving in separate, natural knowledge domains, much of the European research has focused on novel, complex problems, and has been performed with computerized scenarios.
Europe
In Europe, two main approaches have surfaced, one initiated by
Donald Broadbent
Donald Eric (D. E.) Broadbent CBE, FRS (Birmingham, 6 May 1926 – 10 April 1993) was an influential experimental psychologist from the UK His career and research bridged the gap between the pre-World War II approach of Sir Frederic Bartlett a ...
in the United Kingdom and the other one by
Dietrich Dörner 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.
North America
In North America, initiated by the work of Herbert A. Simon on "learning by doing" in
semantically rich domains,
researchers began to investigate problem solving separately in different natural
knowledge domain
Knowledge can be defined as awareness of facts or as practical skills, and may also refer to familiarity with objects or situations. Knowledge of facts, also called propositional knowledge, is often defined as true belief that is distinc ...
ssuch as physics, writing, or
chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...
playingthus relinquishing their attempts to extract a global theory of problem solving. Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of
expertise
An expert is somebody who has a broad and deep understanding and competence in terms of knowledge, skill and experience through practice and education in a particular field. Informally, an expert is someone widely recognized as a reliable s ...
.
Areas that have attracted rather intensive attention in North America include:
* Reading
* Writing
* Calculation
* Political decision making
* Managerial problem solving
* Lawyers' reasoning
* Mechanical problem solving
* Problem solving in electronics
* Computer skills
* Game playing
* Personal problem solving
* Mathematical problem solving
* Social problem solving
* Problem solving for innovations and inventions:
TRIZ
TRIZ (; russian: теория решения изобретательских задач, ', lit. "theory of inventive problem solving") is “the next evolutionary step in creating an organized and systematic approach to problem solving. The deve ...
Characteristics of complex problems
Complex problem solving (CPS) is distinguishable from simple problem solving (SPS). When dealing with SPS there is a singular and simple obstacle in the way. But CPS comprises one or more obstacles at a time. In a real-life example, a surgeon at work has far more complex problems than an individual deciding what shoes to wear. As elucidated by Dietrich Dörner, and later expanded upon by Joachim Funke, complex problems have some typical characteristics as follows:
*
Complexity (large numbers of items, interrelations and decisions)
*
enumerability
*
heterogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
*
connectivity
Connectivity may refer to:
Computing and technology
* Connectivity (media), the ability of the social media to accumulate economic capital from the users connections and activities
* Internet connectivity, the means by which individual terminal ...
(hierarchy relation, communication relation, allocation relation)
*
Dynamics (time considerations)
** temporal constraints
** temporal sensitivity
** phase effects
** dynamic
unpredictability
Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively.
Predictability and causality
Causal determinism has a strong relationship with predictability. Perfe ...
* Intransparency (lack of clarity of the situation)
** commencement opacity
** continuation opacity
*
Polytely __NOTOC__
Polytely (from Greek roots ''poly-'' and ''-tel-'' meaning "many goals") comprises complex problem-solving situations characterized by the presence of multiple simultaneous goals.Funke 2001, p.72. These goals may be contradictory or othe ...
(multiple goals)
** inexpressivenes
** opposition
** transience
Collective problem solving
Problem solving is applied on many different levels − from the individual to the civilizational. Collective problem solving refers to problem solving performed collectively.
Social issues and global issues can typically only be solved collectively.
It has been noted that the complexity of contemporary problems has exceeded the cognitive capacity of any individual and requires different but complementary expertise and collective problem solving ability.
Collective intelligence is shared or group intelligence that emerges from the
collaboration, collective efforts, and competition of many individuals.
Collaborative problem solving is about people
working together face-to-face or in
online workspaces with a focus on solving real world problems. These groups are made up of members that share a common concern, a similar passion, and/or a commitment to their work. Members are willing to ask questions, wonder, and try to understand common issues. They share expertise, experiences, tools, and methods. These groups can be assigned by instructors, or may be student regulated based on the individual student needs. The groups, or group members, may be fluid based on need, or may only occur temporarily to finish an assigned task. They may also be more permanent in nature depending on the needs of the learners. All members of the group must have some input into the decision-making process and have a role in the learning process. Group members are responsible for the thinking, teaching, and monitoring of all members in the group. Group work must be coordinated among its members so that each member makes an equal contribution to the whole work. Group members must identify and build on their individual strengths so that everyone can make a significant contribution to the task. Collaborative groups require joint intellectual efforts between the members and involve
social interactions to solve problems together. The
knowledge shared during these interactions is acquired during communication, negotiation, and production of materials. Members actively seek information from others by asking questions. The capacity to use questions to acquire new information increases understanding and the ability to solve problems. Collaborative group work has the ability to promote critical thinking skills, problem solving skills,
social skills, and
self-esteem. By using collaboration and communication, members often learn from one another and construct meaningful knowledge that often leads to better learning outcomes than individual work.
In a 1962 research report,
Douglas Engelbart linked collective intelligence to organizational effectiveness, and predicted that pro-actively 'augmenting human intellect' would yield a multiplier effect in group problem solving: "Three people working together in this augmented mode
ould Ould is an English surname and an Arabic name ( ar, ولد). In some Arabic dialects, particularly Hassaniya Arabic, ولد (the patronymic, meaning "son of") is transliterated as Ould. Most Mauritanians have patronymic surnames.
Notable p ...
seem to be more than three times as effective in solving a complex problem as is one augmented person working alone".
Henry Jenkins, a key theorist of new media and media convergence draws on the theory that collective intelligence can be attributed to media convergence and
participatory culture
Participatory culture, an opposing concept to consumer culture, is a culture in which private individuals (the public) do not act as consumers only, but also as contributors or producers ( prosumers). The term is most often applied to the produc ...
. He criticizes contemporary education for failing to incorporate online trends of collective problem solving into the classroom, stating "whereas a collective intelligence community encourages ownership of work as a group, schools grade individuals". Jenkins argues that interaction within a knowledge community builds vital skills for young people, and teamwork through collective intelligence communities contributes to the development of such skills.
Collective impact is the commitment of a group of actors from different sectors to a common agenda for solving a specific social problem, using a structured form of collaboration.
After
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...
the
UN, the
Bretton Woods organization and the
WTO
The World Trade Organization (WTO) is an intergovernmental organization that regulates and facilitates international trade. With effective cooperation
in the United Nations System, governments use the organization to establish, revise, and e ...
were created; collective problem solving on the international level crystallized around these three types of organizations from the 1980s onward. As these global institutions remain state-like or state-centric it has been called unsurprising that these continue state-like or state-centric approaches to collective problem-solving rather than alternative ones.
Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern
information technologies
Information technology (IT) is the use of computers to create, process, store, retrieve, and exchange all kinds of data . and information. IT forms part of information and communications technology (ICT). An information technology system (I ...
allow for massive number of subjects to be involved as well as systems of managing these suggestions that provide good results. With the
Internet
The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, pub ...
a new capacity for collective, including planetary-scale, problem solving was created.
See also
*
Actuarial science
*
Analytical skill
Analytical skill is the ability to deconstruct information into smaller categories in order to draw conclusions. Analytical skill consists of categories that include logical reasoning, critical thinking, communication, research, data analysis an ...
*
Creative problem-solving
Creative problem-solving (CPS) is the mental process of searching for an original and previously unknown solution to a problem. To qualify, the solution must be novel and reached independently. The creative problem-solving process was originally d ...
*
Collective intelligence
*
Community of practice
*
Coworking
Coworking is an arrangement in which workers for different companies share an office space. It allows cost savings and convenience through the use of common infrastructures, such as equipment, utilities and receptionist and custodial services, a ...
*
Crowdsolving
*
Divergent thinking
Divergent thinking is a thought process or method used to generate creative ideas by exploring many possible solutions. It typically occurs in a spontaneous, free-flowing, "non-linear" manner, such that many ideas are generated in an emergent co ...
*
Grey problem In IT, a grey problem (or, gray problem) is a problem where the causing technology is unknown or unconfirmed. Common grey problems are:
* Intermittent errors;
* Intermittent incorrect output, or;
* Transient performance problems.
Because the cau ...
*
Innovation
Innovation is the practical implementation of ideas that result in the introduction of new goods or services or improvement in offering goods or services. ISO TC 279 in the standard ISO 56000:2020 defines innovation as "a new or changed entit ...
*
Instrumentalism
In philosophy of science and in epistemology, instrumentalism is a methodological view that ideas are useful instruments, and that the worth of an idea is based on how effective it is in explaining and predicting phenomena.
According to instrumenta ...
*
Problem statement
A problem statement is a concise description of an issue to be addressed or a condition to be improved upon. It identifies the gap between the current (problem) state and desired (goal) state of a process or product. Focusing on the facts, the prob ...
*
Problem structuring methods
Problem structuring methods (PSMs) are a group of techniques used to model or to map the nature or structure of a situation or state of affairs that some people want to change. PSMs are usually used by a group of people in collaboration (rather t ...
*
Psychedelics in problem-solving experiment
Psychedelics are a subclass of hallucinogenic drugs whose primary effect is to trigger non-ordinary states of consciousness (known as psychedelic experiences or "trips").Pollan, Michael (2018). ''How to Change Your Mind: What the New Science of ...
*
Structural fix
*
Subgoal labeling
*
Troubleshooting
Troubleshooting is a form of problem solving, often applied to repair failed products or processes on a machine or a system. It is a logical, systematic search for the source of a problem in order to solve it, and make the product or process op ...
*
Wicked problem
In planning and policy, a wicked problem is a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize. It refers to an idea or problem that cannot be fi ...
Notes
Further reading
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* Tonelli M. (2011)
Unstructured Processes of Strategic Decision-Making Saarbrücken, Germany: Lambert Academic Publishing.
*
*
External links
*
{{Authority control
Reasoning
Artificial intelligence
Educational psychology
Neuropsychological assessment
Psychology articles needing expert attention