Chủ Nhật, 1 tháng 5, 2011

Problem solving

In North America, initiated by the work of Herbert Simon 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 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:

[edit] 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 (multiple goals)
    • inexpressiveness
    • opposition
    • transience
  • Complexity (large numbers of items, interrelations and decisions)
  • 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.[5]

Problem-solving techniques
  • Abstraction: solving the problem in a model of the system before applying it to the real system
  • Analogy: using a solution that solved an analogous problem
  • Brainstorming: (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: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
  • Lateral thinking: approaching solutions indirectly and creatively
  • Means-ends analysis: 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: transforming the problem into another problem for which solutions exist
  • Research: employing existing ideas or adapting existing solutions to similar problems
  • Root cause analysis: eliminating the cause of the problem
  • Trial-and-error: testing possible solutions until the right one is found
"A solution, to be a solution, must share some of the problems characteristics." Richard L Kempe

Problem-solving methodologies
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