1. Cognitive Psychology
Chapter 12
Problem Solving

2. Outline 4/21/2017 Problem Solving Basics Neurocognition Creativity
Problem Solving Strategies
Neurocognition
Brain systems
Analogy and Insight
The Resource Analogy
Creativity
Expertise
Improving Problem Solving
Study Questions.
• Describe any of strategies that can be applied to problem solving.
• Compare and contrast creativity and expertise. How are these qualities related to problem solving?

3. Problem Solving Problem Solving Basics Strategies for solving problems
Two boys and one man want to cross a river but the boat will only hold either the two boys or the one man. How many times must the boat cross the river to accomplish this goal? (a round trip counts as two crossings).
Subgoals
E.g., Try to get the man across with a boy there to take back the boat.

4. Problem Solving Problem Solving Basics Strategies for solving problems
Subgoals

5. Problem Solving Problem Solving Basics Strategies for solving problems
Subgoals
The Hobbits and Orcs problem graph

6. H O
Boat OO
HHH HH
OOO
1H 1O 2O
2 H
1 O
2 O
1 H
HHH
OOO
Boat
1 H 1 O
2 O HH OO
HHH O
Boat H
1 H
1 O
HHH OO
Boat O
2 O
HHH
OOO
Boat
1 O
HHH O
Boat OO
2 H H O HH OO
Boat
1 H 1 O

7. Problem Solving Problem Solving Basics Strategies for solving problems
Subgoals
The Hobbits and Orcs problem graph
Hayes (1966)
Presented a 5/5 boat transformation task
Gave subjects a subgoal
Three orcs on one side without the boat
Control group: 30 moves
Experimental group: 20 moves

8. Problem Solving Problem Solving Basics Strategies for solving problems
Brute Force
Go through all possible states until solution is found
Even in Computer science, it is a last result
Hill Climbing
Always move towards goal
We often have to move away from the goal
e.g., Hobbits and Orcs problem

9. Problem Solving Problem Solving Basics Strategies for solving problems
Means-Ends analysis
Five Steps
1. Set up a goal or subgoal
2. Look at the difference between the current state and the goal/subgoal state
3. Look for an operator that will reduce or eliminate the difference
4. Apply the operator
5. Apply steps 2 to 4 repeatedly until all goals have been achieved

10. Problem Solving Problem Solving Basics Strategies for solving problems
Analogy
The jealous husbands problem
People tended not make use of the analogy
Attack - dispersion, Radiation, & Oil fire problem
Students who read two stories and could describe the convergence schema were more likely to solve the third.
One needs to know that the analogy exists

11. Problem Solving Problem Solving Basics Strategies for solving problems
Trial and Error
Needs small problem graph/space
Type of brute force
C.f., The card game problem
Working backwards
The card game problem
A B C
Round 3 (8) 8 8
Round (4) 4
Round (2)
Ante

12. Problem Solving Neurocognition
Problem solving involves multiple brain regions
Nichelli et al. (1994)
Used PET imaging while solving various chess problems
Premotor
Task
Identify chess piece
Determine location of piece
Think about making a move
Remembering a move
Planning and executing strategies
Hippocampus
Where
Prefrontal Cortex
What

13. Problem Solving Neurocognition Role of prefrontal cortex Incubation
Allows us to return to a problem after interruption
Branching
Allows us to keep a goal in mind over time while allocating resources to other processes
I.e., multitasking
Correlate of intelligence tests
Involved in solving Raven's Advanced Progressive Matrices
• Fluid intelligence (Spearman’s inherited intelligence)

14. Problem Solving Neurocognition Analogical reasoning
Wharton et al. (2000)
Used PET imaging while solving analogy problems
Medial frontal cortex, left prefrontal/ inferior cortex
Source Correct Target Incorrect Spatial Incorrect Object
relations relations
Analogy
Literal

15. Problem Solving Neurocognition Analogical reasoning
Wharton et al. (2000)

16. Problem Solving Neurocognition Insight (Bowden & Beeman, 1998)
Solved compound remote associates
A.K.A. Trigrams
E.g,
Falling Actor Dust
Broken Clear Eye
Presented with a lateralized word to name 15s later
Either the solution or an unrelated word

17. Problem Solving
Neurocognition
Insight (Bowden & Beeman, 1998)
Results

19. Problem Solving Creativity What is creativity? How much you know
I.e., Problem solving ability and insight
Intelligence does not seem to be a factor
e.g., Fighter pilots in WWII
Convergent versus divergent thinking
Convergent: a single correct solution to a problem
• IQ tests
Divergent: Ability to find paths to unusual solutions
• Leads to multiple answers
Who you are
Personality variable (“Openness”)
Common personality traits associated with creative people

20. Problem Solving Creativity What is creativity?
Characteristics of creative people
Ideational fluency: number of ideas/sentences/associations in response to a word
Variety and flexibility: Number of different solutions in response to listing possible uses (e.g, of a newspaper)
Originality: Obtain solutions others do not get.
Problem sensitivity: ability to recognize the central challenge and difficulties in solving a task.
Redefinition: Capacity to view a known problem in a different light.

21. Problem Solving Creativity Neurocognition of creativity Synethesia
Metaphor/analogy
Fronto-temperal dementia
A symptom is increased creativity
Left Hemisphere- Convergent thinking
Right Hemisphere- Divergent thinking
Does our educational system stifle the right hemisphere?
FTD is usually associated with more left hemisphere dysfunction
The left brain keeps the right brain in check, creativity takes the entire brain.

22. Problem Solving Creativity Neurocognition of creativity
Van Gogh’s later work

23. Problem Solving Expertise Characteristics of experts
More declarative knowledge
Rich Schemas
Focus on deep vs. surface structure
More time on representation
More sophisticated representation/ use of analogy
Automated sequence of steps with solving strategies
More time efficient (can work under speed pressure)
Careful monitoring
More flexibility

24. Problem Solving Expertise Characteristics of experts
Talent or practice?
Gladwell’s “Outliers”
• To become an expert is to become an outlier in ability
• The 10,000 hr, 10 year rule -> 20 year old violinists

25. Problem Solving
Expertise
Characteristics of experts

26. Problem Solving + Neurocognition The resource analogy
Reichle, et al. (2000)
Used sentence-picture verification task
e.g., It is not true that the star is above the plus
Negative statements slower than affirmative
‘Polarity’ interacts with truth value
Unless you have high spatial abilities
Manipulated verbal and visual strategies
Increased activity in expected places
Measured verbal and spatial abilities
Negative correlations between activity level and ability for active hemispheres +

27. Problem Solving Improving your problem solving skills
Increase your domain of knowledge
Automate components
Follow a systematic plan
Draw inferences
Develop subgoals
Work Backwards
Search for contradictions
Search for relations between problems
Find a different representation
Practice

28. Review Chapter 11: Decisions, Judgements, & Reasoning
Formal logic and reasoning
Syllogisms
Conditional reasoning
Hypothesis testing
Judgement
Psychophysics
Symbolic distance
Cognitive maps

29. Review Chapter 11: Decisions, Judgements, & Reasoning Decisions
Algorithms & Heuristics
Representiveness
The law of small numbers
Ignoring Base Rates
The hot hand debate
Availability
Contributing factors
The simulation heuristic
The hindsight bias
Anchoring and adjustment
Framing Effects
Loss aversion
Sunk-cost effect
Limitations in reasoning

30. Review Chapter 11: Decisions, Judgements, & Reasoning Study questions
Describe the Wasson selection task. What common type of logical errors are made by people attempting this task?
What is the symbolic distance effect and why is it important in understanding the notion of representation?
Compare and contrast the representativeness and the availability heuristics.
What is loss aversion. Describe the effect of combining framing effects with loss aversion.

31. Review Chapter 11: Decisions, Judgements, & Reasoning Key Terms
Deductive reasoning, inductive reasoning, syllogism, validity, truth, soundness, set unions, mental model theory, mental logic theory, dual mechanism theory, conditional reasoning, modus tollens, modus ponens, affirming the consequence, denying the antecedent, Wasson selection test, bi-conditional reasoning, confirmation bias, the null hypothesis, psychophysics, just noticeable difference, Weber fraction, absolute threshold, signal detection theory, d’ (d-prime), memory operating characteristic, the distance or discriminability effect, the sybollic distance or discriminability effect, semantic congruency effect, algorithms, heuristics, the representativeness heuristic, the law of small numbers, base rate information, gambler’s fallacy, the hot hand theory, availability heuristic, simulation heuristic, counter-factual thinking, the undoing heuristic, hindsight bias, anchoring and adjustment, the framing effect, the sunk-cost effect, loss aversion, domain knowledge, conjunction fallacy.

32. Review Chapter 12: Problem solving The Gestaltist approach Analogy
Stages of thinking
Representation
Incubation
Insight
Problems in problem solving
Analogy
Multiconstraint theory
Problem Solving Basics
Characteristics of problem solving
Well-defined and ill-defined problems
Typologies
Problem Solving Strategies
Neurocognition
Brain systems
Analogy and Insight
The Resource Analogy
Creativity and Expertise
Improving Problem Solving

33. Review Chapter 12: Problem Solving Study questions
Describe Wallas’ stages of thinking during problem solving.
When do analogies work best in problem solving? Describe the multicontraint theory.
Compare and contrast creativity and expertise. How are these qualities related to problem solving?

34. Review Chapter 12: Problem Solving Key Terms
Gestalt, insight, preparation, incubation, illumination, verification, representation, verbal protocol, functional fixedness, cognitive set, elaboration, constraint relaxation, re-encoding, analogy, convergence schema, multiconstraint theory, initial state, goal state, operators, problem space, well-defined and ill-defined problems, problems of inducing structure, problems of transformation, problems of arrangement, subgoals, brute force, hill-climbing, means-ends analysis, branching, pre-frontal cortex, the resource analogy, creativity, expertise,