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• Outline» Problem Solving Basics

◊ 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?

04/19/23

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.

Problem Solving


◊ Subgoals

Problem Solving


◊ Subgoals– The Hobbits and Orcs problem graph

HHHOOOBoat

1 H 1 O 2 O

HHHOOBoat

O

HHH OOOBoat

HHHOBoat

OO

HO

HHOOBoat

HHOO

HHHO

OOBoat

HOBoat

1 H 1 O

2 O

1 O

2 H

1 H 1 O

HOBoat

OOBoat

HHHO

HHOO

O HHHOOBoat

OOOBoat

HHH

OO HHHOBoat

HHOOBoat

HO

1H 1O 2O

2 H

1 O

2 O

1 H 1 O

HHHOOOBoat

Problem Solving


◊ 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

Problem Solving


◊ 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

Problem Solving


◊ 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

Problem Solving


◊ 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

Problem Solving


◊ 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 2 16 (4) 4

Round 1 8 14 (2)

Ante 4 7 13

TaskIdentify chess pieceDetermine location of pieceThink about making a moveRemembering a movePlanning and executing strategies

What

Where

Premotor

HippocampusPrefrontal Cortex

Problem Solving

• Neurocognition» Problem solving involves multiple brain regions

◊ Nichelli et al. (1994)– Used PET imaging while solving various chess problems

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)

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 Objectrelations relations

Analogy

Literal

Problem Solving

• Neurocognition» Analogical reasoning

◊ Wharton et al. (2000)

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

Problem Solving

• Neurocognition» Insight (Bowden & Beeman, 1998)

◊ Results

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

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.

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.

Problem Solving

• Creativity» Neurocognition of creativity

◊ Van Gogh’s later work

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

Problem Solving


◊ 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

Problem Solving


+

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

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

Review

• Chapter 11: Decisions, Judgements, & Reasoning» Formal logic and reasoning

◊ Syllogisms

◊ Conditional reasoning

◊ Hypothesis testing

» Judgement◊ Psychophysics

◊ Symbolic distance

◊ Cognitive maps

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

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.

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.

Review• Chapter 12: Problem solving

» The Gestaltist approach◊ 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

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?

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,

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