PROBLEM SOLVING

Problem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping.

Considered the most complex of all intellectual 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 or an artificial intelligence system 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 over the past hundred years. There are several methods of studying problem solving, including: introspection, behaviorism, simulation, computer modeling and experiment.

Beginning with the early experimental work of the Gestaltists in Germany (e.g. Duncker, 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) 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" 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 and Herbert Simon. Simple laboratory-based tasks may be useful in explicating the steps of logic and reasoning that underlie problem solving; however, they omit the complexity and emotional valence 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 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).Characteristics of difficult problemsAs 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 (multiple goals) inexpressiveness
opposition
transience
Complexity (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. 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. Some problem-solving techniques Divide and conquer: break down a large, complex problem into smaller, solvable problems.

Hill-climbing strategy, (also called gradient descent/ascent, difference reduction, greedy algorithm) - attempting at every step to move closer to the goal situation.

The problem with this approach is that many challenges require temporarily moving farther away from the goal state. For example, traveling 1,000 miles to the west might require driving a few miles east to an airport. (see river crossing puzzle).

Means-ends analysis, more effective than hill-climbing, requires the setting of subgoals based on the process of getting from the initial state to the goal state when solving a problem.

Analogy: has a similar problem (possibly in a different field) been solved before?
Reduction (complexity): transforming the problem into another problem for which solutions exist.
Hypothesis testing: assuming a possible explanation to the problem and trying to prove the assumption.
Constraint examination: are you assuming a constraint which does not really exist?
Incubation: input the details of a problem into the mind, then stop focusing on it. The subconscious mind will continue to work on the problem, and the solution might just "pop up" while are doing something else
Build (or write) one or more abstract models of the problem
Try to prove that the problem cannot be solved. Where the proof breaks down can be the starting point for resolving it
Get help from friends or online problem solving community (e.g. 3form, InnoCentive)

delegation: delegating the problem to others.
Root Cause Analysis
Working Backwards (Halpern, 2002)
Forward-Looking Strategy (Halpern, 2002)
Simplification (Halpern, 2002)
Generalization (Halpern, 2002)
Specialization (Halpern, 2002)
Random Search (Halpern, 2002)
Split-Half Method (Halpern, 2002)

Eight Disciplines Problem Solving

Southbeach Notation

The WWXXD Method: This method requires you to ask yourself What Would Do, where is the person in question. Such variations of this method are the WWJD, What Would Jesus Do, WWUJD, What Would Uncle Jesse Do, WWCND, What would Chuck Norris Do, and WWJBD, What Would Jack Bauer Do. This method allows you to frame the question, resolve the question and act upon it in a similar way to the person in question.

See also:
Abductive reasoning
Analogy
Artificial intelligence
Brainstorming
Common sense
Common sense reasoning
Creative problem solving
Cyc
Deductive reasoning
Divergent thinking
Educational psychology
Executive function
Facilitation
Forensic engineering
General problem solver
Heuristics
Inductive reasoning
Innovation
Intelligence amplification
Inquiry
Kepner-Tregoe
Morphological Analysis
Newell, Allen
PDCA
Portal: thinking
Problem Statement
Reduction (complexity)
RPR Problem Diagnosis
Simon, Herbert
Soar (cognitive architecture)
Thought
Transdisciplinary Studies
TRIZ
Troubleshooting
Wicked problem
External links Computer Skills for Information Problem-Solving: Learning and Teaching Technology in Context
Problem solving-Elementary level
CROP (Communities Resolving Our Problems)
The Altshuller Institute for TRIZ Studies, Worcester, MA