Problem solving

Problem solving

Overview
Problem solving is a mental process and is part of the larger problem
Problem
A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal...

 process that includes problem finding
Problem finding
Problem finding means problem discovery. It is part of the larger problem process that includes problem shaping and problem solving. Problem finding requires intellectual vision and insight into what is missing. This involves the application of creativity....

 and problem shaping
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 often involves the application of critical thinking.Algorithmic approach to technical problems...

. Considered
the most complex of all intellectual
Intelligence
Intelligence has been defined in different ways, including the abilities for abstract thought, understanding, communication, reasoning, learning, planning, emotional intelligence and problem solving....

 functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills. Problem solving occurs when an organism
Organism
In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...

 or an artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...

 system
System
System is a set of interacting or interdependent components forming an integrated whole....

 needs to move from a given state to a desired goal state.

The nature of human problem solving methods has been studied by psychologist
Psychologist
Psychologist is a professional or academic title used by individuals who are either:* Clinical professionals who work with patients in a variety of therapeutic contexts .* Scientists conducting psychological research or teaching psychology in a college...

s over the past hundred years.
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Unanswered Questions
Encyclopedia
Problem solving is a mental process and is part of the larger problem
Problem
A problem is an obstacle, impediment, difficulty or challenge, or any situation that invites resolution; the resolution of which is recognized as a solution or contribution toward a known purpose or goal...

 process that includes problem finding
Problem finding
Problem finding means problem discovery. It is part of the larger problem process that includes problem shaping and problem solving. Problem finding requires intellectual vision and insight into what is missing. This involves the application of creativity....

 and problem shaping
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 often involves the application of critical thinking.Algorithmic approach to technical problems...

. Considered
the most complex of all intellectual
Intelligence
Intelligence has been defined in different ways, including the abilities for abstract thought, understanding, communication, reasoning, learning, planning, emotional intelligence and problem solving....

 functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills. Problem solving occurs when an organism
Organism
In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...

 or an artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...

 system
System
System is a set of interacting or interdependent components forming an integrated whole....

 needs to move from a given state to a desired goal state.

Overview


The nature of human problem solving methods has been studied by psychologist
Psychologist
Psychologist is a professional or academic title used by individuals who are either:* Clinical professionals who work with patients in a variety of therapeutic contexts .* Scientists conducting psychological research or teaching psychology in a college...

s over the past hundred years. There are several methods of studying problem solving, including; introspection
Introspection
Introspection is the self-observation and reporting of conscious inner thoughts, desires and sensations. It is a conscious and purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul...

, behaviorism
Behaviorism
Behaviorism , also called the learning perspective , is a philosophy of psychology based on the proposition that all things that organisms do—including acting, thinking, and feeling—can and should be regarded as behaviors, and that psychological disorders are best treated by altering behavior...

, simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....

, computer modeling and experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

.

Beginning with the early experimental work of the Gestaltist
Gestalt psychology
Gestalt psychology or gestaltism is a theory of mind and brain of the Berlin School; the operational principle of gestalt psychology is that the brain is holistic, parallel, and analog, with self-organizing tendencies...

s in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

 (e.g. Karl Duncker
Karl Duncker
Karl Duncker was a Gestalt psychologist. He attended Friedrich-Wilhelms-University from 1923 to 1923, spent 1925-1926 at Clark University in Worcester, MA as a visiting professor, where he received a masters in arts degree.Until 1935 he was a student and assistant of the founders of Gestalt...

, 1935 ), and continuing through the 1960s and early 1970s, research on problem solving typically conducted relatively simple, laboratory tasks (e.g. Duncker's "X-ray" problem; Ewert & Lambert's 1932 "disk" problem, later known as Tower of Hanoi
Tower of Hanoi
The Tower of Hanoi or Towers of Hanoi, also called the Tower of Brahma or Towers of Brahma, is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod...

) that appeared novel to participants (e.g. Mayer, 1992 ). Various reasons account for the choice of simple novel tasks: they had clearly defined optimal solutions, they were solvable within a relatively short time frame, researchers could trace participants' problem-solving steps, and so on. The researchers made the underlying assumption, of course, that simple tasks such as the Tower of Hanoi captured the main properties of "real world
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...

" problems, and that the cognitive processes underlying participants' attempts to solve simple problems were representative of the processes engaged in when solving "real world" problems. Thus researchers used simple problems for reasons of convenience, and thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research remains the work by Allen Newell
Allen Newell
Allen Newell was a researcher in computer science and cognitive psychology at the RAND corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology...

 and Herbert Simon
Herbert Simon
Herbert Alexander Simon was an American political scientist, economist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, cognitive science, computer science, public administration, economics,...

 .

Simple laboratory-based tasks can be useful in explicating the steps of logic and reasoning that underlie problem solving; however, they omit the complexity and emotional valence
Valence (psychology)
Valence, as used in psychology, especially in discussing emotions, means the intrinsic attractiveness or aversiveness of an event, object, or situation. However, the term is also used to characterize and categorize specific emotions. For example, the emotions popularly referred to as "negative",...

 of "real-world" problems. In clinical psychology, researchers have focused on the role of emotions in problem solving (D'Zurilla & Goldfried, 1971; D'Zurilla & Nezu, 1982), demonstrating that poor emotional control can disrupt focus on the target task and impede problem resolution (Rath, Langenbahn, Simon, Sherr, & Diller, 2004). In this conceptualization, human problem solving consists of two related processes: problem orientation, the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. Working with individuals with frontal lobe injuries, neuropsychologists
Neuropsychology
Neuropsychology studies the structure and function of the brain related to specific psychological processes and behaviors. The term neuropsychology has been applied to lesion studies in humans and animals. It has also been applied to efforts to record electrical activity from individual cells in...

 have discovered that deficits in emotional control and reasoning can be remediated, improving the capacity of injured persons to resolve everyday problems successfully (Rath, Simon, Langenbahn, Sherr, & Diller, 2003).

Europe


In Europe, two main approaches have surfaced, one initiated by Donald Broadbent
Donald Broadbent
Donald Eric Broadbent FRS was an influential English experimental psychologist. His career and his research work bridged the gap between the pre-Second World War approach of Sir Frederic Bartlett and its wartime development into applied psychology, and what from the late 1960s became known as...

 (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by Dietrich Dörner
Dietrich Dörner
Prof. Dr. Dietrich Dörner is emeritus professor for General and Theoretical Psychology at the at the Otto-Friedrich University in Bamberg, Germany....

 (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches have in common 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.

To sum up, researchers' realization that problem-solving processes differ across knowledge domains and across levels of expertise (e.g. Sternberg, 1995) and that, consequently, findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory, has during the past two decades led to an emphasis on real-world problem solving. 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 (see Funke, 1991, for an overview).

USA and Canada


In North America, initiated by the work of Herbert Simon
Herbert Simon
Herbert Alexander Simon was an American political scientist, economist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, cognitive science, computer science, public administration, economics,...

 on learning by doing in semantically rich domains (e.g. Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural knowledge domains – such as physics, writing, or chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

 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 (e.g. Anderson, Boyle & Reiser, 1985; Chase & Simon, 1973; Chi, Feltovich & Glaser, 1981).

Areas that have attracted rather intensive attention in North America include such diverse fields as:
  • Reading (Stanovich & Cunningham, 1991)
  • Writing (Bryson, Bereiter, Scardamalia & Joram, 1991)
  • Calculation (Sokol & McCloskey, 1991)
  • Political decision making (Voss, Wolfe, Lawrence & Engle, 1991)
  • Problem Solving for Business (Cornell, 2010)
  • Managerial problem solving (Wagner, 1991)
  • Lawyers' reasoning (Amsel, Langer & Loutzenhiser, 1991)
  • 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 (Polya, 1945; Schoenfeld, 1985)
  • Social problem solving (D'Zurilla & Goldfreid, 1971; D'Zurilla & Nezu, 1982)
  • Problem solving for innovations and inventions: TRIZ (Altshuller, 1973, 1984, 1994)

Characteristics of difficult problems


As elucidated by Dietrich Dörner
Dietrich Dörner
Prof. Dr. Dietrich Dörner is emeritus professor for General and Theoretical Psychology at the at the Otto-Friedrich University in Bamberg, Germany....

 and later expanded upon by Joachim Funke
Joachim Funke
Joachim Funke is professor for Experimental and Theoretical Psychology at the University of Heidelberg, Germany, and Marsilius fellow 2008/2009.His research is directed to thinking and problem solving...

, difficult problems have some typical characteristics that can be summarized as follows:
  • Intransparency (lack of clarity of the situation)
    • commencement opacity
    • continuation opacity
  • Polytely
    Polytely
    Polytely can be described as frequently, complex problem-solving situations characterized by the presence of not one, but several goals, endings.Modern societies face an increasing incidence of various complex problems...

     (multiple goals)
    • inexpressiveness
    • opposition
    • transience
  • Complexity
    Complexity
    In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

     (large numbers of items, interrelations and decisions)
    • enumerability
    • connectivity (hierarchy relation, communication relation, allocation relation)
    • heterogeneity
  • Dynamics (time considerations)
    • temporal constraints
    • temporal sensitivity
    • phase effects
    • dynamic unpredictability


The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.

Problem-solving techniques

  • Abstraction
    Abstraction
    Abstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....

    : solving the problem in a model of the system before applying it to the real system
  • Analogy
    Analogy
    Analogy is a cognitive process of transferring information or meaning from a particular subject to another particular subject , and a linguistic expression corresponding to such a process...

    : using a solution that solved an analogous problem
  • Brainstorming
    Brainstorming
    Brainstorming is a group creativity technique by which a group tries to find a solution for a specific problem by gathering a list of ideas spontaneously contributed by its members...

    : (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum is found
  • Divide and conquer
    Analysis
    Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle , though analysis as a formal concept is a relatively recent development.The word is...

    : breaking down a large, complex problem into smaller, solvable problems
  • Hypothesis testing: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
  • Lateral thinking
    Lateral thinking
    Lateral thinking is solving problems through an indirect and creative approach, using reasoning that is not immediately obvious and involving ideas that may not be obtainable by using only traditional step-by-step logic...

    : approaching solutions indirectly and creatively
  • Means-ends analysis
    Means-ends analysis
    Means-Ends Analysis is a technique used in Artificial Intelligence for controlling search in problem solving computer programs.It is also a technique used at least since the 1950s as a creativity tool, most frequently mentioned in engineering books on design methods...

    : choosing an action at each step to move closer to the goal
  • Method of focal objects
    Method of focal objects
    The technique of focal object for problem solving involves synthesizing the seemingly non-matching characteristics of different objects into something new....

    : synthesizing seemingly non-matching characteristics of different objects into something new
  • Morphological analysis: assessing the output and interactions of an entire system
  • Reduction
    Reduction (complexity)
    In computability theory and computational complexity theory, a reduction is a transformation of one problem into another problem. Depending on the transformation used this can be used to define complexity classes on a set of problems....

    : transforming the problem into another problem for which solutions exist
  • Research
    Research
    Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...

    : employing existing ideas or adapting existing solutions to similar problems
  • Root cause analysis
    Root cause analysis
    Root cause analysis is a class of problem solving methods aimed at identifying the root causes of problems or events.Root Cause Analysis is any structured approach to identifying the factors that resulted in the nature, the magnitude, the location, and the timing of the harmful outcomes of one...

    : eliminating the cause of the problem
  • Trial-and-error: testing possible solutions until the right one is found
  • Proof: try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it


"A solution, to be a solution, must share some of the problems characteristics." Richard L Kempe

Problem-solving methodologies

  • Eight Disciplines Problem Solving
    Eight Disciplines Problem Solving
    Eight Disciplines Problem Solving is a method used to approach and to resolve problems, typically employed by quality engineers or other professionals.D0: The Planning Phase: Plan for solving the problem and determine the prerequisites....

  • GROW model
    GROW model
    The GROW model is a technique for problem solving or goal setting. It was developed in the United Kingdom and was used extensively in the corporate coaching market in the late 1980s and 1990s....

  • How to solve it
    How to Solve It
    How to Solve It 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:...

  • Kepner-Tregoe
    Kepner-Tregoe
    Kepner-Tregoe, Inc. is a multinational management consulting and training services company. It provides consultation and training to companies in industries such as manufacturing, electronics, chemical, pharmaceuticals, and financial services....

  • PDCA
    PDCA
    PDCA is an iterative four-step management method used in business for the control and continuous improvement of processes and products...

  • Productive Thinking Model
    Productive Thinking Model
    The Productive Thinking Model was developed by Tim Hurson, a Canadian author, speaker, and creativity theorist. It is a structured approach to solving problems or generating creative ideas that is based in part on the Creative Problem Solving Process and NASA's IDEF...

  • RPR Problem Diagnosis
    RPR Problem Diagnosis
    RPR is a problem diagnosis method specifically designed to determine the root cause of IT problems.- Overview :RPR deals with failures, incorrect output and performance issues, and its particular strengths are in the diagnosis of ongoing & recurring grey problems...

  • TRIZ
    TRIZ
    TRIZ is "a problem-solving, analysis and forecasting tool derived from the study of patterns of invention in the global patent literature". It was developed by the Soviet inventor and science fiction author Genrich Altshuller and his colleagues, beginning in 1946...

     (Teoriya Resheniya Izobretatelskikh Zadatch, "theory of solving inventor's problems")

Example applications


Problem solving is of crucial importance in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

 when products or processes fail, so corrective action can be taken to prevent further failure
Failure
Failure refers to the state or condition of not meeting a desirable or intended objective, and may be viewed as the opposite of success. Product failure ranges from failure to sell the product to fracture of the product, in the worst cases leading to personal injury, the province of forensic...

s. Perhaps of more value, problem solving can be applied to a product or process prior to an actual fail event i.e. a potential problem can be predicted, analyzed and mitigation applied so the problem never actually occurs. Techniques like Failure Mode Effects Analysis
Failure mode and effects analysis
A failure modes and effects analysis is a procedure in product development and operations management for analysis of potential failure modes within a system for classification by the severity and likelihood of the failures...

 can be used to proactively reduce the likelihood of problems occurring. Forensic engineering
Forensic engineering
Forensic engineering is the investigation of materials, products, structures or components that fail or do not operate or function as intended, causing personal injury or damage to property. The consequences of failure are dealt with by the law of product liability. The field also deals with...

 is an important technique of failure analysis
Failure analysis
Failure analysis is the process of collecting and analyzing data to determine the cause of a failure. It is an important discipline in many branches of manufacturing industry, such as the electronics industry, where it is a vital tool used in the development of new products and for the improvement...

 which involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

See also



  • Artificial intelligence
    Artificial intelligence
    Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...

  • C-K theory
    C-K Theory
    thumb|A graphical representation of a Design Process using C-K Design Theory.C-K design theory or concept-knowledge theory is both a design theory and a theory of reasoning in design. It defines design reasoning as a logic of expansion processes, i.e. a logic that organizes the generation of...

  • Creative problem solving
    Creative problem solving
    Creative problem solving is the mental process of creating a solution to a problem. It is a special form of problem solving in which the solution is independently created rather than learned with assistance.Creative problem solving always involves creativity....

  • Divergent thinking
    Divergent thinking
    Divergent thinking is a thought process or method used to generate creative ideas by exploring many possible solutions. It is often used in conjunction with convergent thinking, which follows a particular set of logical steps to arrive at one solution, which in some cases is a "correct" solution...

  • Educational psychology
    Educational psychology
    Educational psychology is the study of how humans learn in educational settings, the effectiveness of educational interventions, the psychology of teaching, and the social psychology of schools as organizations. Educational psychology is concerned with how students learn and develop, often focusing...

  • Executive function
  • Forensic engineering
    Forensic engineering
    Forensic engineering is the investigation of materials, products, structures or components that fail or do not operate or function as intended, causing personal injury or damage to property. The consequences of failure are dealt with by the law of product liability. The field also deals with...

  • Grey problem
    Grey problem
    Grey problem is a term for an IT problem where the causing technology is unknown or unconfirmed. Common grey problems are:* Intermittent errors;* Intermittent incorrect output, or;* Transient performance problems....

  • Heuristics
  • Innovation
    Innovation
    Innovation is the creation of better or more effective products, processes, technologies, or ideas that are accepted by markets, governments, and society...

  • Intelligence amplification
    Intelligence amplification
    Intelligence amplification refers to the effective use of information technology in augmenting human intelligence...

  • Inquiry
    Inquiry
    An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...

  • Logical reasoning
    Logical reasoning
    In logic, three kinds of logical reasoning can be distinguished: deduction, induction and abduction. Given a precondition, a conclusion, and a rule that the precondition implies the conclusion, they can be explained in the following way:...

  • Problem statement
    Problem statement
    A problem statement is a concise description of the issues that need to be addressed by a problem solving team and should be presented to them before they try to solve the problem. When bringing together a team to achieve a particular purpose provide them with a problem statement...

  • Herbert Simon
    Herbert Simon
    Herbert Alexander Simon was an American political scientist, economist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, cognitive science, computer science, public administration, economics,...

  • Thought
    Thought
    "Thought" generally refers to any mental or intellectual activity involving an individual's subjective consciousness. It can refer either to the act of thinking or the resulting ideas or arrangements of ideas. Similar concepts include cognition, sentience, consciousness, and imagination...

  • Transdisciplinary studies
    Transdisciplinary studies
    Transdisciplinary Studies are an area of research and education that addresses contemporary issues that cannot be solved by one or even a few points-of-view...

  • Troubleshooting
    Troubleshooting
    Troubleshooting is a form of problem solving, often applied to repair failed products or processes. It is a logical, systematic search for the source of a problem so that it can be solved, and so the product or process can be made operational again. Troubleshooting is needed to develop and...

  • Wicked problem
    Wicked problem
    "Wicked problem" is a phrase originally used in social planning to describe a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize. Moreover, because of complex interdependencies, the effort to solve...



External links