I. Problem Solving

 A. defined

1. "thinking that is directed toward the solving of a specific problem that involves both the formulation of responses and the selection among those possible responses"

 B. as studied by cognitive psychologists

  1. introspection: think aloud protocols

 C. well-defined to ill-defined problem continuum

1. well-defined: clear goal, small set of info to begin with, often guidelines for working towards a solution (of which there is one)

 a. e.g., figuring tax on a purchase

2. ill-defined: no clear goal, no starting info, no guidelines

   a. e.g., composing a "Dear John/Jane" letter

 D. the problem space

1. the set of all states that can be reached in solving a problem

2. leads from the initial to the goal state

3. good problem solving is the creation of efficient paths through the problem space

 a. often involves a mental search

 b. expertise allows better hunches about where to search

II. Methods

A. algorithms (trace through the entire problem space)

B. heuristics (more efficient strategies that may lead to errors)

  1. generate and test

a. trial-and-error

b. works best with a small number of possible solutions that can be kept track of

  2. working forward (hill-climbing)

a. moving forward to a solution without needing/using subgoals

  3. means-ends analysis

a. subgoals & transformations

b. basis for Newell & Simon's GPS

c. allows analysis of the problem so one is less likely to "work blindly"

  4. working backward

a. move backward from the goal state

b. Towers of Hanoi problem

c. works best when the backward path is unique

 C. insight

   a. potentially important in some types of problems

b. can be unreliable

III. Aids & Blocks to Problem Solving

 A. the problem solving cycle

  1. problem identification

  2. problem definition & representation

a. one of the most important steps

b. examples

    1. the mutilated checkerboard

  3. planning the solution

a. strategy formation

    1. analysis and synthesis

  2. divergent and convergent thinking

b. organization of information

  4. executing the plan

a. resource allocation

b. monitoring

  5. evaluation

a. evaluating the plan

b. evaluating the solution

 B. reasoning by analogy

  1. analogical transfer (Gick & Holyoak, 1980, 1983)

a. lack of spontaneous, uninstructed use

b. construction of a schema

1. likely to occur with hints, or more than one analogous problem which were compared

  2. increasing analogical reasoning

a. instruction

b. attention to the deep structure

c. present more than one analogy

d. comparison/understanding

    1. memory oriented 69% vs. problem-oriented 90%

 C. mental set

1. mental set -  the tendency to adopt a certain framework

 a. strategy use

1. Luchins water jar problem

2. 64% fail to break set

 b. problem definition

1. the nine dot problem, the match stick problem

2. functional fixedness

a. rigid mental set about an object and its use

b.  fewer than 40% solved without the hint

3. stereotypes

 D. using incomplete or incorrect representations

1. the mutilated checkerboard problem

2. influences success in problem solving

 E. lack of problem specific knowledge or expertise

IV. Expertise

 A. examples

  1. Chase & Simon (1973, after de Groot, 1965)

a. chess players vs. chess novices

  2. Gobet & Simon (1996)

a. studied Kasparov in tournament and simultaneous games

1. pattern recognition

  3. Lesgold et al. (1988)

a. expert radiologists noted more specific properties, hypothesized more causes and effects, and clustered more symptoms together

 B. characteristics (Glaser & Chi, 1988)

1. excel in their own domains

2. perceive large meaningful patterns

3. fast

4. use STM & LTM more effectively

5. represent problems at a deeper level

6. time is spent qualitatively analyzing a problem

7. self-monitoring skills

 C. nature of expertise

1. 10 years or 10,000 hours of practice

2. greater, more connected, better organized knowledge base

3. use of working forward strategies

 D. drawbacks

1. no advantage if problem is not recognized

2. domain specific

3. memory for gist only

 A. computer games

  1. Deep Blue vs. Kasparov

 B. Newell & Simon’s GPS

C. expert systems

  1. model the judgments of human experts

a. based on interviews, think-aloud protocols, & observations

2. include a knowledge base, inference rules, search engine, & interface

3. an example: MUckraker

   a. used to advise about the best way to approach a source

A. defined

1. "a cognitive activity that results in a new or novel way of viewing a problem or situation"

2. often used with ill-defined problems

3. incubation & insight

a. a period of time away from the problem during which unconscious processing occurs leads to illumination about how to approach the problem

 B. incubation

  1. support

a. introspective rather than empirical

  2. Smith & Blankenship (1989)

a. presented rebuses with misleading cues to solve

b. conditions: continue working, 5-15 min filled or empty break; presented the rebus w/o the cue

c. those with longer, filled intervals were more successful

d. but failure to replicate; most report revisiting the problem

3. possible explanations for incubation other than a "nonconscious processing" explanation

a. with time, meaningful aspects remain

b. mental set may weaken

c. new stimuli activate new perspectives

d. a stimulus helps analogical transfer

e. lower cortical arousal inc. attention

 C. Psychometric approaches

1. creativity as a special process

2. Guilford - convergent vs. divergent thinking

a. fluency, originality, & flexibility

b. curvilinear relationship with IQ

 D. Cognitive approaches

1. creativity as relying on everyday mechanisms

2. Perkins (1981)

a. directed remembering: searching memory for specific, relevant information

b. noticing: attending to the essentials of a problem

    1. may play a role in the "Eureka" experience

c. contrary recognition: seeing things in new ways

    1. strong evidence for this relationship

3. spreading activation & analogical reasoning

 E. teaching creativity

1. develop a knowledge base

2. create the right atmosphere

3. search for analogies

VII. Critical Thinking

A. defined: evaluation of ideas; reflective thinking

B. Wertheimer (1945)

1. working in the Gestalt tradition

2. emphasized the grasping of the essential structure

 a. formula for parallelograms: A=2(B*H)

b. rote solution was less effective than essential structure

 C. Perkins et al. (1983)

1. reasoning on controversial issues

2. critical thinking measured as the ability to challenge one’s own thinking

a. need for a large knowledge base

b. objection raising

3. encouraged looking for other possibilities and interpretations