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Problem Solving
Chapter 11
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Problem SolvingWhat is a Problem?
A problem consists of several basic components:
Initial state (situation at the beginning of the problem)
Goal state (the solution to the problem)
a set of rules (or constraints) that must be followed a set of obstacles that must be overcome.
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Problem SolvingWhat is a Problem?
Problems range on a continuum from well-defined to ill-defined
Well-defined problems: Clear and structured Initial state, goal state, and constraints are all
understood; solution easy to assess.
Ill-defined problems: Fuzzy and abstract Initial state, goal state, and constraints are not
understood; solution not easy to assess.
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Problem SolvingWhat is a Problem?
Problems range on a continuum from routine to non-routine
Routine problems: can be solved by well-practiced procedures
Non-Routine problems: unique, novel, not previously encountered.
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Problem SolvingWhat is a Problem?
Problem solving processes can be difficult to assess, given their complexity and time course
Verbal protocols: reports generated by problem solvers as they “think out loud” during the solution process.
Limited by verbal ability, accessibility of processing to verbalization, and assessment
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Problem SolvingWhat is a Problem?
Types of Problems: Transformation: Move from initial state to goal state Arrangement: Arrange problem elements in desired
fashion Induction: Given specific examples, find general
principle Deduction: Given general principles, draw specific
conclusion Divergent Thinking: Generate as many solutions as
possible
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Problem SolvingApproaches to Problem Solving
Behaviorist Approach
Problem solving as associative learning
Thorndike’s studies of cats in “puzzle boxes” demonstrated gradual trial and error learning
Law of effect
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Problem SolvingApproaches to Problem Solving Gestalt Approach
Problem solving as mental restructuring and insight
Kohler’s study of apes revealed what appeared to be sudden realization of solution, rather than trial and error
Solution occurred via insight, the sudden and successful restructuring of problem elements
Insight is not a clearly defined construct
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Problem SolvingApproaches to Problem Solving
Behaviorist view is overly narrow and rigid; doesn’t account for unique and creative behavior
Gestalt view is vague and ill-specified
Information processing view explains problem solving in terms of component cognitive processes
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Problem SolvingApproaches to Problem Solving
Newell and Simon proposed the General Problem Solver, a computer model of problem solving
We attempt to minimize distance between initial state and goal state via subgoal analysis
Problem solving as a search of and progression through problem space
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Problem SolvingProblem Representation
Initial stages of problem solving involve encoding of an accurate problem representation
Rigidity in representation can be a major obstacle to problem solving Mental Set: A tendency to rely on habits and
procedures used in the past
Functional Fixedness: A tendency to view objects narrowly, in terms of the typical uses of the object
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Problem SolvingProblem Representation
Problem representation can be hindered by some seemingly unlikely variables
Stereotype threat: A member of a negatively stereotyped group feels that their behavior might fit and perpetuate the stereotype
Quinn and Spencer (2001) found that activation of a stereotype harmed women’s problem representation ability for math problems.
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Problem SolvingProblem Representation
Problem representation can be hindered by some seemingly unlikely variables
Stereotype threat: Member of a negatively stereotyped group feels that their behavior might fit and perpetuate the stereotype
Quinn and Spencer (2001) found that stereotype activation (“women are bad at math”) harmed women’s problem representation ability for math problems.
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Problem SolvingProblem Solution
Two major approaches to problem solution
Algorithms: set of rules that can be applied systematically to solve certain types of problems.
Correctly applied, will always lead to correct solution
Unfeasible approach for human problem solvers, and most problems, because formulas don’t exist
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Problem SolvingProblem Solution
Heuristics: general strategies, or rules of thumb, that can be applied to various problems
No guarantee of correct solution
Quicker, more efficient than algorithms
Specific heuristics can be developed for any problem
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Problem SolvingProblem Solution
General purpose heuristics
Means-End Analysis: breaking a problem into sub-goals; accomplishing
each sub-goal gets the solver closer to the solution
Analogy using already-solved problems as aids for
representing and solving the current problem
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Problem SolvingProblem Solution
Analogies are a powerful problem-solving aid, but use tends to be limited; three things must occur:
Noticing: Solver realizes an analogous problem exists
Mapping: Solver maps elements of previous problem to elements of current one
Schema Development: General schema underlying the problems must be developed
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Problem SolvingProblem Solution
Problems with use of analogy usually arise because the solver fails to notice analogous relationships
Noticing depends on similarity between problems
Surface Similarity: The specific elements of a problem
Structural Similarity: The underlying relationships
among the elements of a problem
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Problem SolvingExperts
Expertise exceptional knowledge and/or performance in
some specific problem domain.
Skilled Memory Theory proposes a number of expert advantages:
Richly elaborated knowledge networks More efficient access to long-term memory More efficient encoding processes
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Problem SolvingExperts
Lemaire & Siegler (1995) conceptualize expert-novice differences in terms of strategy use.
Experts show advantages over novices in: Strategy existence Strategy base rate Strategy choice Strategy execution
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Problem SolvingExperts
Experts do show a number of expertise-related disadvantages
Intermediate effect: Those at an intermediate level of knowledge actually remember more information than do experts
Wiley (1998) found that expertise can serve as mental set, interfering with divergent thinking
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Problem SolvingInsight
Insight refers to the sudden realization of a problem’s solution
Related issues
Does insight exist? Is problem-solving sudden or incremental? Is there a difference between insight and non-insight
problems?
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Problem SolvingInsight
Insight problems are those in which the solution seems to occur suddenly
Non-insight problems are those in which the processes of solution are incremental and conscious
Two assumptions about insight It involves removal of a mistaken assumption The solution is arrived at suddenly
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Problem SolvingInsight
Does removal of a mistaken assumption lead to sudden solution?
This is (at best) oversimplified; most problems are over-determined, with many sources of difficulty.
Providing a single “hint” rarely leads to a sudden solution
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Problem SolvingInsight
Does incubation lead to insight?
Incubation: the idea that taking a break leads to quicker problem solution than does continuing effort
Although intuitive, not much empirical evidence
Smith (1995) offers a contextual view of incubation Incubation will aid problem-solving to the degree that
it’s associated with a change in context.
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Problem SolvingCreativity
Creativity involves arriving at appropriate and novel solutions to problems
Creativity is associated with a number of variables related to person, process, press, and product. Person Factors
Personality characteristics Intrinsic motivation for area of expertise Flexibility, reactivity Challenging life experience
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Problem SolvingCreativity
Process Factors Does creativity require special processes, or is it the
result of “garden-variety” cognition?
Creative cognition approach: Creative thinking can result from either or both types of processes
Specific processes: Attentional deployment, memory
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Problem SolvingCreativity
Press Factors Creativity is subject to external pressures and
contextual factors Interpersonal factors can affect problem solving
Product Factors Creativity as reflected by the endpoint of the creative
process One measure of creativity: productivity
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Problem SolvingCreativity
Dietrich (2004) proposes two dimensions along which creative products can be assessed
Processing Mode (Spontaneous – Deliberate) Knowledge Domain (Cognitive – Emotional)
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Problem SolvingCreativity
Creativity and the Brain Some research implicates right-hemisphere
processing as especially important in creativity
Bowden & Beeman (1998) used the Remote Associates Test to assess processes involved in creativity
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Problem SolvingCreativity
Subjects were presented triads of words, all of which related to a non-obvious target word
After a delay, target was presented to either left or right hemisphere.
Right hemisphere presentation led to enhanced priming in pronunciation, relative to a baseline
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Problem SolvingCreativity
In a second study, subjects were presented with a word after a triad had been presented
Y/N judgment: (“Is this the solution word?”)
Right hemisphere presentation led to faster verification RT, indicating RH role