Problem Solving

Chapter 11

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.

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.

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.

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

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

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

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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?

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

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

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.

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

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

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

Problem SolvingCreativity

Dietrich (2004) proposes two dimensions along which creative products can be assessed

Processing Mode (Spontaneous – Deliberate) Knowledge Domain (Cognitive – Emotional)

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

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

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