S2W3Prob Flashcards
Well defined
All aspects of the problem are clearly specified
The goal is well specified
Ill-defined problems
Underspecified
Many possible strategies
Most problems we encounter are ill-defined
Psychologists have focused on well-defined problems
Knowledge-rich problems:
Only solvable by having relevant specific knowledge
Knowledge-lean problems
Most information needed to solve contained in problem statement
Do not require specific knowledge
often used in research as minimise individual differences knowledge
Insight (Gestalt)
Problems requiring productive thinking solved using insight
The flashback moment when you suddenly realised how to solve a problem
A sudden quick solving of a problem
Brain regions in insight problems
Remote Associates Test (Bowden et al., 2005)
Three words presented and participants thought of a word going with each one to form compound words (fence-post).
Participants indicated insight was involved on some trials but not others.
The right hemisphere is more associated with insight than the left .
Facilitating insight: hints
Two-string problem (Maier, 1931):
Tie two strings together when one cannot be reached while other one is held.
Function of pliers gets in the way of seeing them as a weight.
Insight when subject realizes that pliers can be attatched to one and then swung like a pendulum.
Accidentally brushing against triggers insight:
Restructure representation of:
How to achieve solution
Function of pliers
Thomas and Lleras (2009) follow up 2 string
Even subtle hints are useful.
Got participants to either swing or stretch arms.
Those who swung arms more likely to solve the problem.
Facilitating insight: incubation and sleep
Sleeping on a problem makes it easier to solve it
A problem is put aside for some time
The subconscious mind continues to work
Sio and Ormerod (2009) meta-analysis (sleep)
Incubation effects were reported in 73% of the studies
Incubation effects were stronger with creative problems having multiple solutions than with linguistic and verbal problems having a single solution
Larger effects observed when more preparation time before incubation
Other sleep insight findings
Sleep enhanced performance on difficult problems but not easy ones (Sio et al., 2013).
Forgetting misleading information is important (if you’re going down the wrong path in solving a problem you can sleep on it and forget the misleading information (Penaloza & Calvillo, 2012).
Representational change theory
Combines:
• Gestalt ideas
• Information-processing approach
Encounter impasse because we have represented problem wrongly.
Need to change the problem representation for insight to occur.
Three ways:
Constraint relaxation, reencoding, elaboration.
Elaboration (representational change)
New problem information is added to the representation
Constraint relaxation (representational change)
Inhibitions on what is regarded as permissible are removed
Re-encoding (representational change)
Some aspect of the problem representation is reinterpreted
Öllinger et al. (2014) (representational change)
Prior knowledge leads to formation of a problem representation, followed by a search process to search for solutions.
Repeatedly unsuccessful search process:
Impasse/block
New problem
New representation formed to try to overcome impasse followed by another search process.
A search process may be necessary even after an impasse has been overcome by insight
Knoblich et al. (1999) (representational change) - roman numerals
Each problem involved moving a single stick to make a correct maths sum.
Type A:
• Change two values in the equation
Type B:
• Change an operator (+/-)
Experience tells us to change numbers not operators (Type A)
Constraint relaxation harder for Type B problems.
Initial representation was based on assumption that values had to be changed so took longer.
Brain and representational change
Insight problems involve lateral prefrontal cortex – those with damage do not impose artificial constraints.
Chi and Snyder brain rep. change
Brain stimulation reduced excitability of left lateral prefrontal cortex and increased the right.
60% solved hardest matchstick problem compared to 20% controls
Nine-dot problem
Draw four straight lines that go through all nine dots without lifting pencil.
People initially assume that the lines must remain within the confines of the square formed by the dots.
Key insight is to realise that this constraint must be relaxed
Progress monitoring:
Worse performance when participants had the illusion of making progress.
Representational change: limitations
Cannot predict when/why problem’s representation will change
Individual differences not considered
Constraint relaxation often not the only thing needed to solve insight problems
functional fixedness
Failures on insight problems occur due to being misled by past experience.
Functional fixedness occurs when we mistakenly assume that any given object has only a limited number of uses.
Duncker (1945) functional fixedness
Given a candle, matches, tacks in a box and several other objects.
Task to attach the candle to a wall so it did not drip.
Most participants tried to nail the candle directly to the wall or glue it to the wall by melting it.
Participants fixated on the tack box’s function as a container rather than using it as a platform.
More correct solutions when tack box was empty because that made it appear less like a container.
mental set
Continuing to use previously successful strategy even when inappropriate.
In spite of drawbacks it allows successive problems of the same type to be solved rapidly and with few processing demands.
Experts relatively immune from mental set.
Luchins (1942) water jug
Three water jars of varying capacity
Figure out how to use the jugs to measure out the desired quantity.
Mental set:
Participants completed 8 tasks, of which two could be solved more successfully using another approach.
Participants still used the same approach as they had on other 6.
Progress monitoring:
Participants abandoned the problem in fewer moves when the problem had a smaller number of problem states.
Bilalić et al. (2008a) mental set chess
When chess experts tried to find the most rapid way to win a game, most used solution based on familiar strategy.
Vallée-Tourangeau et al. (2011) mental set modify water
Used actual jugs not paper.
Beneficial because of the dynamic nature of the perceptual input.
Newell and Simon (1972) strategies
Limited STM capacity and complex information processing is typically serial.
A space for each problem consists of initial state, goal state, and all mental operators that can be applied to change them.
Well-defined problems rely on heuristics or rules of thumb not algorithms.
The Tower of Hanoi Problem
When all the discs are placed in the same order as they started but on the last peg, the problem has been solved.
Only one disc can be moved at a time and a larger disc cannot be placed on top of a smaller one
Many different strategies.
Means–ends analysis
Most important heuristic method:
Note the difference between the current state and the goal state
Form a subgoal to reduce the difference between the current and goal state
Select mental operator (e.g. moves) that permits attainment of subgoal
Sweller and Levine (1982) invisible maze
Participants were given the maze, most of which was not visible.
Some participants could see the goal state (goal-information group) whereas others could not (no-goal-information).
People sometimes persist with a heuristic even when it severely impairs performance.
Hill climbing
Involves changing the problem state into one closer to the goal.
Simpler than means–ends analysis
Used when no clear understanding of the problem structure.
Involves a focus on short-term goals
Does not lead to problem solution
Progress monitoring
Assessing rate of progress towards the goal.
If progress is too slow to solve the problem within the maximum number of moves allowed, people adopt a different strategy.
Planning
Prefrontal cortex associated with planning should be activated during problem solving.
Goel and Grafman (1995)
Prefrontal damage performed worse on Tower of Hanoi even though both used same strategy: patients with prefrontal damage find it harder to plan ahead.
Colvin et al. (2001):
Damage left dorsolateral prefrontal cortex performed worse than right.
Dagher et al. (1999)
Tower of London task
planning
Coloured discs must be moved one by one from an initial state to match the goal state
Participants instructed to plan the whole sequence of moves mentally first.
Complex versions associated with increased activity in several brain areas, especially dorsolateral prefrontal cortex.
Goel et al. (2013) italy planning
Participants had to organise a trip to Italy for an American couple.
Patients with right prefrontal damage had impaired planning due to premature commitments to various decisions.
Sequential processing stages
With complex tasks, only some moves are planned
Executing the initial plan is followed by a further plan and then execution.
Initial planning:
o Dorsolateral prefrontal cortex more active
Plan execution:
o Posterior temporal areas
o Inferior frontal regions
o Dorsolateral premotor cortex
Nitschke et al. (2012) tower of london Sequential processing
Tower of London require participants to engage in problem representation followed by planning.
Eye-tracking study:
High demands on forming representation = alternating gaze between start and goal.
High on planning = prolonged last fixation on start state.
Ruh (2012) brain in representation and planning
Activation in:
Left dorsolateral prefrontal cortex during problem representation
Right dorsolateral prefrontal cortex during planning
Delaney et al. (2004) how much planning
Water-jar problems:
Little evidence of planning when free to choose preferred strategy.
When instructed to generate solution before making moves they showed evidence of planning and solved problem faster.
Cognitive miserliness
someone who is typically economical with his/her time and effort on tasks requiring thinking.
Kahneman (2003) Cognitive miserliness
System 1 thinking: fast and effortless
System 2 thinking: slow and effortful
System 2 monitors answers generated by System 1
Cognitive Reflection Test
Provides evidence of the extent to which people are cognitive misers.
75% of participants failed at least one question and 20% were wrong on every one.
Low scorers perform poorly on judgement and reasoning tasks.
Low scorers are cognitive misers (correlated poorly with intelligence).
Chen (2002) similarity between problems:
Superficial similarity:
a. Solution-irrelevant details are the same
Structural similarity:
a. Some of the main components are the same
Procedural similarity:
a. Procedures for solving them are the same
Gick and Holyoak (1980) The radiation problem
10% of participants solved it when presented on its own
80% of participants solved it when informed of analogy
Only 40% did so when not informed of its relevance
Reception paradigm
in a lab people are told about analogies then presented with a problem.
Production paradigm
more realistic, participants generated their own analogies.
Blanchette and Dunbar (2000) choice of analogies
Participants given reception paradigm selected analogies based on superficial similarities.
Those given production paradigm produced analogies with structural similarities.
Analogies
The types of analogies people use depend on goal
People use analogies to solve problems when there are substantial differences between the current problem and a previous analogous problem.
Happens when people interact extensively with the first problem and are able to form a concrete mental model of it.
How can we increase people’s ability to use analogies?
Important for people to form a complete description of the structure of the current problem.
Increases the probability of retrieving a relevant analogy and increases its quality.
Four-term analogy problems
Participants decided whether two word pairs expressed the same relationship as each other.
(Flame:Candle::Steeple:Church)
The words were judged to be more closely related when they had previously been presented subliminally.
Shows that analogies can be detected unconsciously.
Sequential processing stages for four-term analogy problems:
Encoding of first pair of words based on their relationship
Mapping (connection formed between first words of each pair and an inference drawn as to the fourth word)
Response (decision on correctness of fourth word)
Processes (computational models)
Knowlton et al. (2012)
analogical problem solving has serial processing because of processing demands involved.
Stages: • Analogue retrieval • Mapping • Analogical inference • Schema induction
Schemas abstract formed by comparing analogy and problem.
