Problem solving is a mental process and is part of the larger problem A problem is an obstacle which makes it difficult to achieve a desired goal, objective or purpose. It refers to a situation, condition, or issue that is yet unresolved. In a broad sense, a problem exists when an individual becomes aware of a significant difference between what actually is and what is desired between one or more individual process that includes 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 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. Considered the most complex of all intellectual Intelligence is an umbrella term describing a property of the mind including related abilities, such as the capacities for abstract thought, understanding, communication, reasoning, learning, learning from past experiences, planning, and problem solving functions, problem solving has been defined as higher-order cognitive Cognition is the scientific term for "the process of thought." Usage of the term varies in different disciplines; for example in psychology and cognitive science, it usually refers to an information processing view of an individual's psychological functions. Other interpretations of the meaning of cognition link it to the development of process that requires the modulation and control of more routine or fundamental skills.^[1] Problem solving occurs when an 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 (single-celled) or be composed of, as in humans, many trillions of cells grouped into or an artificial intelligence Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. 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 chances of success. John McCarthy, who system System is a set of interacting or interdependent entities 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 psychologists There are many different types of psychologists, as is reflected by the 56 different divisions of the American Psychological Association . Psychologists are generally described as being either "applied" or "research-oriented". The common terms used to describe this central division in psychology are "scientists" or & over the past hundred years. There are several methods of studying problem solving, including; introspection Introspection is the self-observation and reporting of conscious inner thoughts, desires and sensations. It is a conscious mental and usually purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul. It can also be called contemplation of one's self, and is contrasted, behaviorism Behaviorism , also called the learning perspective (where any physical action is a behavior), 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. The behaviorist school of thought maintains that behaviors as such can be, simulation Simulation is used in many contexts, including the modeling of natural systems or human systems in order to gain insight into their functioning. Other contexts include simulation of technology for performance optimization, safety engineering, testing, training and education. Simulation can be used to show the eventual real effects of alternative, computer modeling A computer simulation, a computer model or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics , chemistry and biology, human systems in economics, and experiment Experiments is the step in the scientific method that arbitrates between competing models or hypotheses. Experimentation is also used to test existing theories or new hypotheses in order to support them or disprove them. An experiment or test can be carried out using the scientific method to answer a question or investigate a problem. First an.

Beginning with the early experimental work of the Gestaltists Gestalt psychology or gestaltism of the Berlin School is a theory of mind and brain positing that the operational principle of the brain is holistic, parallel, and analog, with self-organizing tendencies. The Gestalt effect refers to the form-forming capability of our senses, particularly with respect to the visual recognition of figures and whole in Germany A region named Germania, inhabited by several Germanic peoples, has been known and documented before AD 100. Beginning in the 10th century, German territories formed a central part of the Holy Roman Empire, which lasted until 1806. During the 16th century, northern Germany became the centre of the Protestant Reformation. As a modern nation-state, (e.g. Duncker, 1935 ^[2]), 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 The Tower of Hanoi or Towers of Hanoi 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. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape) that appeared novel to participants (e.g. Mayer, 1992 ^[3]). 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 is the state of things as they actually exist, rather than as they may appear or may be thought to be. In its widest definition, reality includes everything that is and has being, 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 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. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956 and Herbert Simon Herbert Alexander Simon was an American political scientist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, computer science, public administration, economics, management, philosophy of science, sociology, and political science. With ^[4].

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, as used in psychology, especially in discussing emotions, means the intrinsic attractiveness or aversiveness (negative valence) 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", such as anger and fear, 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, the actual cognitive-behavioral steps, which, if successfully implemented, lead to effective problem resolution. Working with individuals with frontal lobe injuries, neuropsychologists Neuropsychology is the basic scientific discipline that studies the structure and function of the brain related to specific psychological processes and overt 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 higher 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 Eric Broadbent was an influential English experimental psychologist. His career and his research work bridged the gap between the pre-Second World War approach of Sir Frederick Bartlett and its wartime development into applied psychology, and what from the late 1960s became known as cognitive psychology (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by Dietrich Dörner (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches 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 Alexander Simon was an American political scientist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, computer science, public administration, economics, management, philosophy of science, sociology, and political science. With on learning by doing in semantically Semantics is the study of meaning. It typically focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for rich domains (e.g. Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural knowledge domains Most generally, domain knowledge is the knowledge which is valid and directly used for a pre-selected domain of human endeavor or an autonomous computer activity – such as physics, writing, or chess Chess is a board game involving two players. It is played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. At the beginning of the game each player controls sixteen pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns. The object of the game is to checkmate the opponent's 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 An expert ( Audio (help·info)) is someone widely recognized as a reliable source of technique or skill whose faculty for judging or deciding rightly, justly, or wisely is accorded authority and status by their peers or the public in a specific well-distinguished domain. An expert, more generally, is a person with extensive knowledge or ability (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:

• Problem Solving (Kepner & Tregoe, 1958)
• Reading (Stanovich & Cunningham, 1991)
• Writing (Bryson, Bereiter, Scardamalia & Joram, 1991)
• Calculation (Sokol & McCloskey, 1991)
• Political decision making (Voss, Wolfe, Lawrence & Engle, 1991)
• Managerial problem solving (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 and later expanded upon by Joachim Funke, 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 can be described as frequently, complex problem-solving situations characterized by the presence of not one, but several goals, endings (multiple goals)
  • inexpressiveness
  • opposition
  • transience
• 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 network theory and network science. In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article. In a (large numbers of items, interrelations and decisions)
  • enumerability
  • connectivity (hierarchy relation, communication relation, allocation relation)
  • heterogeneity Heterogeneity of ion channels means diversity of different types of channels serving a specific kind of current, e.g. by channels with different constitutive subunits
• Dynamics In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion. These are in contrast to Kinematics, the branch of classical mechanics that describes the motion of objects without (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

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

In reform mathematics, greater emphasis is placed on problem solving relative to basic skills, where basic operations can be done with calculators. However some "problems" may actually have standard solutions taught in higher grades. For example, kindergarteners could be asked how many fingers are there on all the gloves of 3 children, which can be solved with multiplication.^[5]

Problem-solving techniques

• Abstraction Abstraction is a conceptual process by which higher, more abstract concepts are derived from the usage and classification of literal concepts. An "abstraction" (noun) is a concept that acts as super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category: solving the problem in a model of the system before applying it to the real system
• Analogy Analogy is a cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction,: using a solution that solved an analogous problem
• Brainstorming Brainstorming is a group creativity technique designed to generate a large number of ideas for the solution of a problem. In 1953 the method was popularized by Alex Faickney Osborn in a book called Applied Imagination. Osborn proposed that groups could double their creative output with brainstorming.t: (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: breaking down a large, complex problem into smaller, solvable problems
• Hypothesis testing A statistical hypothesis test is a method of making statistical decisions using experimental data. In statistics, a result is called statistically significant if it is unlikely to have occurred by chance. The phrase "test of significance" was coined by Ronald Fisher: "Critical tests of this kind may be called tests of significance,: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
• Lateral thinking Lateral thinking is a term coined by Edward de Bono, for the solution of problems through an indirect and creative approach. Lateral thinking is about reasoning that is not immediately obvious and about 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 is a technique used in Artificial Intelligence for controlling search in problem solving computer programs: choosing an action at each step to move closer to the goal
• Method of focal objects: synthesizing seemingly non-matching characteristics of different objects into something new
• Morphological analysis: assessing the output and interactions of an entire system
• Reduction 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 can be defined as the search for knowledge or as any systematic investigation to establish facts. The primary purpose for applied research is discovering, interpreting, and the development of methods and systems for the advancement of human knowledge on a wide variety of scientific matters of our world and the universe. Research can use: employing existing ideas or adapting existing solutions to similar problems
• Root cause analysis Root cause analysis is a class of problem solving methods aimed at identifying the root causes of problems or events. The practice of RCA is predicated on the belief that problems are best solved by attempting to correct or eliminate root causes, as opposed to merely addressing the immediately obvious symptoms. By directing corrective measures at: eliminating the cause of the problem
• Trial-and-error Trial and error, or trial by error or try an error, is a general method of problem solving, fixing things, or for obtaining knowledge. "Learning doesn't happen from failure itself but rather from analyzing the failure, making a change, and then trying again.": testing possible solutions until the right one is found

Problem-solving methodologies

• Eight Disciplines Problem Solving
• 5Φ (IAPIE)
• GROW model
• How to solve it How to Solve It is a small volume by mathematician George Pólya describing methods of problem solving
• Kepner-Tregoe Founded in 1958 by Dr. Charles Kepner and Dr. Benjamin Tregoe, Kepner-Tregoe, Inc., is a global organisation providing consulting and training services around problem solving, decision making and project execution methodologies
• Southbeach Notation
• PDCA PDCA is an iterative four-step problem-solving process typically used in business process improvement. It is also known as the Deming circle, Shewhart cycle, Deming cycle, Deming wheel, or plan-do-study-act
• RPR Problem Diagnosis RPR deals with failures, incorrect output and performance issues, and its particular strengths are in the diagnosis of ongoing & recurring grey problems. The method comprises:
• TRIZ TRIZ is a romanized acronym for Russian: Теория решения изобретательских задач (Teoriya Resheniya Izobretatelskikh Zadatch) meaning "The theory of solving inventor's problems" or "The theory of inventor's problem solving". It was developed by a Soviet engineer and researcher Genrich Altshuller (Teoriya Resheniya Izobretatelskikh Zadatch, "theory of solving inventor's problems")

Example applications

Problem solving is of crucial importance in engineering Engineering is the discipline, art and profession of acquiring and applying technical, scientific, and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or invention when products or processes fail, so corrective action can be taken to prevent further failures 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 engineering. Perhaps of more value, problem solving can be applied to a product or process prior to an actual fail event ie. a potential problem can be predicted, analyzed and mitigation applied so the problem never actually occurs. Techniques like Failure Mode Effects Analysis can be used to proactively reduce the likelihood of problems occurring. Forensic engineering is an important technique of failure analysis which involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

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