Cognitive Psychology

1
Cognitive Psychology Chapter 12 Part I Problem
Solving
2
6/1/2014

• Outline
• Problem solving
• The Gestaltist approach
• Stages of thinking
• Analogy
• Multiconstraint theory
• Problem Solving Basics
• Characteristics of problem solving
• Well-defined and ill-defined problems
• Problem typologies

Study Question. Describe Wallas stages of
thinking during problem solving When do
analogies work best in problem solving? Describe
the multicontraint theory.
3
Problem Solving

• Two flagpoles are standing, each 20 meters tall.
  A 30 meter rope is strung from the top of one of
  the flagpoles to the top of the other and hangs
  freely between them. The lowest point of the rope
  is 5 meters above the ground. How far apart are
  the two flagpoles?

4
Problem Solving

• The Gestaltist tradition
• The goal of problem solving is the achievement of
  a Gestalt.
• A form, configuration or whole pattern.
• Parallels between perception and problem solving

5
Problem Solving

• The Gestaltist tradition
• Wolfgang Kohler (Circa WW I)

6
Problem Solving

• The Gestaltist tradition
• Wolfgang Kohler (Circa WW I)
• Studied visual discrimination in animals
• Applied gestalt principles to animal perception
• Coined the term insight to describe the sudden
  perception of proper relations.
• Observed insightful behaviour in chimps
  solving problems

7
Problem Solving

• The Gestaltist tradition
• Wallas (1926) stages of thinking
• Preparation
• Recognize a problem exists
• Find a representation for the problem
• Preliminary attempts at solution
• Incubation
• After failing to solve the problem it is set
  aside
• No longer work on the problem at a conscious
  level
• Work proceeds at an unconscious level

8
Problem Solving

• The Gestaltist tradition
• Wallas (1926) stages of thinking
• Illumination
• Flash of insight
• Answer suddenly appears in consciousness
• Verification
• Confirm the insight
• Usually involves simple checking.

9
Problem Solving

• The Gestaltist tradition
• Preparation The role of representation
• A game of 15s.

10
Problem Solving

• The Gestaltist tradition
• Preparation The role of representation
• The Buddhist monk problem

11
Problem Solving

• The Gestaltist tradition
• Incubation
• Fulgosi Guilford (1968)
• Imagine that all power stations shut down, then
  list all possible consequences.
• Waiting 20 min before listing improved retrieval
  of obvious (but not remote) consequences
• No effect for 10 min waiting interval

12
Problem Solving

• The Gestaltist tradition
• Incubation

13
Problem Solving

• The Gestaltist tradition
• Incubation
• Silveira (1971)
• The chain necklace problem
• Control Group Works on problem for 30 min
• Four Experimental Groups
• Brief or long preparation
• 30 min or 4 hr interuption
• Everyone works on the problem for a total of 30
  min

14
Problem Solving

• The Gestaltist tradition
• Incubation
• Silveira (1971)

15
Problem Solving

• The Gestaltist tradition
• Incubation
• Is it unconscious problem solving?
• Silverias verbal protocol
• Subjects tended to pick up the problem where they
  left off
• Another explanation
• Incubation allows us to change inappropriate sets
• Improves performance
• Incubation can impair performance as well
• If the initial set had been appropriate

16
Problem Solving

• The Gestaltist tradition
• Illumination and insight
• T T F F S S E N
• Archimedes
• Insight problems
• The fourth tree
• Metcalfe Wiebe (1987)
• Had subjects complete either algebra or insight
  problems
• Recorded warmth ratings

17
Problem Solving

• The Gestaltist tradition
• Metcalfe Wiebe (1987)
• Results

18
Problem Solving

• The Gestaltist tradition
• Difficulties in problem solving
• Functional Fixedness
• Dunckers candle problem

19
Problem Solving

• The Gestaltist tradition
• Difficulties in problem solving
• Negative set (Einstellung)
• Luchins water jugs problem
• Prepare subjects with a set
• B-2C-A
• Then switch to a simpler A - C
• (1 vs. 80)

20
Problem Solving

• The Gestaltist tradition
• Representational change theory
• Insight involves first establishing the correct
  representation
• The checkerboard - domino problem

21
Problem Solving

• The Gestaltist tradition
• The checkboard-domino problem
• Two ways to solve the problem
• Brute force
• Try each of the 758,148 ways the first 30 dominos
  can be placed.
• In each case, note that the 31st domino cannot be
  placed anywhere.
• Insight answer
• Note that each domino must cover one red one
  black square
• There are 30 red squares and 32 black squares
  left

22
Problem Solving

• The Gestaltist tradition
• Three ways the representation can be changed
• Elaboration - Add new information
• E.g.s, Letters can be used to symbolically
  represent something else
• There are 30 red and 32 black squares
• Constraint relaxation - removing assumed
  constraints
• The Nine dots problem
• The landscaping problem
• E.g., Lines drawn outside of the box, trees not
  planted on a flat surface
• Re-encoding
• E.g., A box can be used as candle holder, pliers
  can be a pendulum
• Dominoes cover one red one black square

23
The biggest problem in the world Could have been
solved when it was small - Lao Tsu
24
Problem Solving

• Analogy
• Gick and Holyoaks convergence schema
• The parade problem
• A small country was controlled by a dictator.
  The dictator ruled the country from a strong
  fortress. The fortress was situated in the middle
  of the country, surrounded by farms and villages.
  Many roads radiated outward from the fortress,
  like spokes on a wheel. To celebrate the
  anniversary of his rise to power, the dictator
  ordered his general to conduct a full-scale
  military parade. On the morning of the
  anniversary, the general?s troops were gathered
  at the head of one of the roads leading to the
  fortress, ready to march. However, a lieutenant
  brought the general a disturbing report. The
  dictator was demanding that his parade had to be
  more impressive than any previous parade. He
  wanted his army to be seen and heard at the same
  time in every region of the country.
  Furthermore, the dictator was threatening that if
  the parade was not sufficiently impressive he was
  going to strip the general of his medals and
  reduce him to the rank of private. But it seemed
  impossible to have a parade that could be seen
  throughout the country.

25
Problem Solving

• Analogy
• Gick and Holyoaks convergence schema
• Attack-Despersion problem
• A small country was controlled by a dictator.
  The dictator ruled the country from a strong
  fortress. The fortress was situated in the
  middle of the country, surrounded by farms and
  villages. Many roads radiated outward from the
  fortress like spokes on a wheel. A general arose
  who raised a large army and vowed to capture the
  fortress and free the country of the dictator.
  The general knew that if his entire army could
  attack the fortress at once it could be captured.
  The general?s troops were gathered at the head
  of one of the roads leading to the fortress,
  ready to attack. However, a spy brought the
  general a disturbing report. The ruthless
  dictator had planted mines on each of the roads.
  The mines were set so that small bodies of men
  could pass over them safelybecause the dictator
  needed to be able to move troops and workers to
  andfrom the fortress. However, any large force
  would detonate the mines. Not only would this
  blow up the road and render it impassible, but
  the dictator would then destroy many villages in
  retaliation. It therefore seemed impossible to
  mount a full-scale direct attack on the fortress.

26
Problem Solving

• Analogy
• Gick and Holyoaks convergence schema
• The parade problem
• Attack-dispersion problem
• The radiation problem
• Three manipulations
• X-ray problem alone or with an analogous problem
• Similar or dissimilar story
• Given hints or not given hints

27
Problem Solving

• Analogy
• Gick and Holyoaks (1980) results
• Group Order Use of analogy
• 1 (hint) Parade, radiation 49
• 2 (hint) Attack dis., radiation 76
• 3 (no hint) no story, radiation 8
• Effect of providing a hint
• 1 (hint) Attack dis., radiation 92
• 2 (no hint) Attack dis., radiation 20

28
Problem Solving

• Analogy
• Keane (1987)
• presented with either
• very similar analogy (another story about a
  surgeon using X-rays)
• moderately similar analogy (the story about the
  generals attack).
• Given the x-ray problem a week later.
• Results
• 88 vs. 12
• people tend to use relevant analogies only if
  they strongly resemble the problem (or are told
  the analogy exists).

29
Problem Solving

• Analogy
• Multiconstraint Theory (Holyoak Thagard, 1997)
• Three factors constraining the use of analogy
• Similarity
• Between the source and the target domain
• Similarity can be used as a red herring
• Structure
• Establish parallel structures between the source
  and target problems
• Mapping
• e.g, Attack -------gt Radiation
• Fortress -----gt Tumor
• Etc.

30
Problem Solving

• Analogy
• Multiconstraint Theory (Holyoak Thagard, 1997)
• Three factors constraining the use of analogy
• Purpose of the analogy
• Problem solvers goals vs. goal of the problem
• e.g., Parading out vs. marching in

31
Problem Solving

• Problem Solving Basics
• Characteristics of problem solving
• Three parts to a problem (Newell Simon)
• Initial state
• Goal state
• Operations to move through intermediate states
• Rules to get you from the initial state to the
  goal state
• E.g., The Tower of Hanoi

32
Problem Solving

• Problem Solving Basics
• E.g., The Tower of Hanoi

33
Problem Solving

• Problem Solving Basics
• E.g., The Tower of Hanoi

34
Problem Solving

• Problem Solving Basics
• E.g., The Tower of Hanoi
• Operations through intermediate states
• Disks may be moved one at a time to any post
• A larger disk may NOT rest on top of a smaller
  disk
• The problem space
• The initial state, the goal state, and the
  intermediate steps to reach the goal. Also
  includes the problem-solvers knowledge at each
  step
• E.g., Problem graphs

35
(No Transcript)
36
Problem Solving

• Problem Solving Basics
• Well-defined and ill-defined problems
• Well defined problems
• Clearly defined start state and goal state
• Operations for moving from one state to the next
  are clearly defined
• E.g.s.
• The Tower of Hanoi
• Hobbits and Orcs
• Most of the problems we look at in this chapter

37
Problem Solving

• Problem Solving Basics
• Well-defined and ill-defined problems
• Ill-defined problems
• One or more of the above three are not clearly
  defined
• E.g.s.
• Making a purse from a sows ear
• Many of the day to day problems that we attempt
  to solve

38
Problem Solving

• Problem Solving Basics
• Typologies of problems (Greeno, 1978)
• Transformation
• Find the sequence of operations necessary to
  transform an initial state into a goal state.
• E.g.s
• The Tower of Hanoi
• Hobbits and Orcs

39
Problem Solving

• Problem Solving Basics
• Typologies of problems (Greeno, 1978)
• Inducing Structure
• Determine the relationship among several given
  elements
• E.g., Analogies
• If all the gems in the world were made of foam
  rubber
• Wood Hard Diamond ?
• A. Valuable, B. Soft, C. Brittle, D. Hardest

40
Problem Solving

• Problem Solving Basics
• Typologies of problems (Greeno, 1978)
• Inducing Structure
• Factors affecting completion time (Mulholland et
  al.)

41
Problem Solving

• Problem Solving Basics
• Typologies of problems (Greeno, 1978)
• Arrangement
• Some element must be rearranged according to some
  criteria
• E.g., Anagrams
• YBO, AIFMA, PSAKKASCN
• Global - local distinction
• Difficulty is affected by the number of ways the
  component letters can be (legitimately) combined