ECON 1 Lecture Notes - Lecture 9: Monty Hall Problem, Talc, Problem Solving
Task 3 – Problem solving
Chapter 12 (Eyseneck)
• Problem solving requires the following:
1) there are two states of affairs;
2) the agent is in one talc and wants to be in the other state;
3) it is not apparent to the agent how the gap between the two states is to be bridged
4) bridging the gap is a con consciously guided multi-step process.
• Well-defined problems – all aspects of the problem are clearly specified (= initial state, goal, methods available) (e.g. maze or chess)
→ Used in research as there is an optimal strategy and errors/deficiencies can easily be identified
→ The goal is well specified lied because it is clear when it has been reached
→ planning is much less necessary with well-defined problems
• Ill-defined problems – definition of problem is underspecified, initial state, goal state & methods unclear (e.g. keys locked in car)
→ Most everyday problems
• Knowledge-rich problems – can only be solved with considerable amounts of prior knowledge
• Knowledge-lean problems – can be solved without prior knowledge as necessary info is provided by problem statement
→ Most traditional research on problem solving involved knowledge-lean problems because such problems minimise individual
differences in relevant knowledge
Major Aspects of Problem Solving
1. It is purposeful (goal-directed)
2. Involves controlled rather than automatic processes
3. A problem only exists if someone lacks the relevant knowledge to produce an immediate solution
In the real world: Monty Hall Problem
• People perform poorly on it
→ Adopt too complex strategies
• typically use a heuristic or rule of thumb known as the uniformity fallacy
→ This fallacy involves assuming all available options are equally likely whether
they are or not
• Problem places substantial demands on the central executive
• Most people mistakenly believe the host’s actions are random
• Shows our fallibility as problem solvers
→ Produce wring answers because we use heuristics or rules of thumb because
our processing capacity is limited
Theories
Gestalt Approach
• Early research on problem solving was dominated by the Gestaltists
• Trial-and-error learning – a solution is reached by producing fairly random responses
rather than by a process of thought
• Reproductive thinking – re-use of previous experiences/ knowledge to solve a current problem (Thorndike’s cat experiment)
• Productive thinking – solving a problem by developing an understanding of the problem’s underlying structure (Gestalt approach)
→ Object the fact that there’s a purely arbitrary relationship between the cats’ behaviour and the desired consequence
Insight
= the experience of suddenly realizing how to solve a problem
• involves a sudden restructuring of a problem
• Sometimes accompanied by the “aha-experience”
• insight is any sudden comprehension, realisation, or problem solution that involves a reorganisation
of the elements of a person's mental representation of a stimulus, situation or event to yield a
nonobvious or nondominant interpretation
• controversy as to whether insight is a special process or whether it involves the same processes as
other thinking tasks
• Involves replacing one way of thinking about a problem with a new & more efficient way cognitive
conflict
Findings
• Non-insight problems: “warmth” (closeness to solution) gradually rises
• Insight problems: warmth stays rather low until it suddenly rises before solution
→ However, as tasks can be solved in various ways you cannot say that there are specific tasks (not) involving insight (e.g. remote
associate problems)
Three words were presented (e.g fence, card, master) and participants thought of a word (e.g., post) going with each
one to form compound words. The participant indicated insight was involved on some trials but not others
Brain
• Right hemisphere plays an important role
→ Support: When solution word to remote associate problem was shown to both
hemispheres separately, the right responded much faster
• Anterior superior temporal gyrus in the right hemisphere only activated when solutions
involved insight
→ brain area associated with processing distant semantic relations between word as well
as reinterpretation and semantic integration
• Integration of weakly active & distant associations occurs mostly in the right hemisphere
(strong activation of closely connected associations mostly in left hemisphere) relevant for
insight
• Anterior cingulate cortex activated during cognitive conflict and breaking of mindsets
→ important given that insight involve replacing one way of thinking about a problem with a new and more efficient way
→ Associated with insight
• There’s a preparation for conflict resolution as those 2 areas are activated even before the problems were presented
• insight was associated with activation of the prefrontal cortex
• eye-movement findings indicated participants were gradually accumulating knowledge relevant to anagram solution even though they
were unaware that was happening
→ insight depends on processes operating below the level of conscious awareness
Facilitating insights: hints
• hints increase the number of solutions produced on insight problems
• even subtle hints are useful
• research with strings that had to be brought together, however, they were too far away to reach them at the same time
→ exercise breaks in between helped them to tie the pliers to one string and swing it like a pendulum → participants could hold one
string and catch the other on its upswing
→ unaware of the relationship between their arm movements during the break and the task
→ hints can be effective without conscious awareness of their task relevance
Facilitating insight: incubation and sleep
• incubation – a stage of problem solving in which the problem is put to one side for some time; it is claimed to facilitate problem solving
• subconscious mind continues to work towards a solution during incubation and so incubation facilitates it
• research on it involved comparing an experimental group having an incubation period away from an unsolved problem with a control group
working continuously
→ incubation effects reported in 73% of the studies
→ incubation effects stronger with creative problems having multiple solutions than linguistic and verbal problems having a single
solution → incubation often widens the search for knowledge, which may be more useful with multiple-solution problems
→ the effects were larger when there was a fairly long preparation time prior to incubation → may have occurred because an
impasse or bloc in thinking is more likely to develop when preparation time is long
• sleep enhanced performance on difficult problems but not on easy ones
• control information relating to the strategies tried by the problem solver is forgotten during incubation
→ this forgetting makes it easier for problem solvers to adopt a new approach after the incubation period
• forgetting misleading information is important
Representational Change Theory – Ohlsson
• we often encounter a block or impasse when solving a problem because we have represented it wrongly
• Largely based on gestalt approach combined with information-processing approach, emphasising insight
→ Main difference to gestalt: more detailed explanation of how one gets to insight
→ emphasising that efficient search processes arc often needed after as well as before an impasse leading to insight
• Prior knowledge and perceptual aspects of a problem lead to the formation of a problem representation
→ This is followed by a search process
→ If this search process is repeatedly unsuccessful, there is an impasse or block
→ A new problem representation is formed to try to overcome the impasse and this is followed by a new search process
• Assumption that a search process ay be necessary even after an impasse has been overcome by insight
• The way in which a problem is currently represented/ structured in the solver’s mind serves as a memory probe to retrieve related
knowledge from LTM (= operators/ possible actions) The retrieval process is based on spreading activation among concepts/ items of
knowledge in LTM Impasse/ block occurs when the way a problem is
represented does not permit retrieval of the necessary operators/ possible actions
Impasse is broken when the problem representation is changed (= INSIGHT!)
new mental representation acts as new memory probe
• Decreased excitability of the left lateral prefrontal cortex probably reduced
inhibitions about constraint relaxation
→ Increased excitability on the right side may have enhanced insight processes
• Solution hints are most useful when individuals have just reached a block or
impasse
→ At that point, they have formed a problem representation, however, they
have not become fixated on it
• Can be tested with the nine-dot problem
→ Insight is useful but still leaves an incredibly large number of possible options
• Ways of changing a problem representation
→ Elaboration/ additional info
→ Constraint relaxation inhibitions on what is regarded as permissible are removed
→ Re-encoding some aspect of the problem is reinterpreted
• Limitations
→ Often not possible to predict when/how the representation of a problem will change
→ Single-factor theory – constraint relaxation as single solution to insight problems (actually only has modestly beneficial effect)
→ De-emphasised individual differences
→ Theory mistakenly implies that constraint relaxation is typically sufficient to solve insight problems
Past experience: functional fixedness
• Past experience increases our ability to solve problems
→ The Gestaltists argued that this is not always the case
→ Numerous failures on insight problems occur because we are misled by our past experience
• Functional fixedness – the inflexible focus on the usual function(s) of an object in problem solving
→ Mistakenly assume that any given object has only a limited number of uses
Duncker’s candle task
• To overcome it:
→ Notice an infrequently noticed or new feature
→ Form a solution based on that obscure feature
• Crucial obscure features a ignored because people focus on the typical functions of object based on their shape, size, material of which
they made and so on
• Functional fixedness can be reduced by the generic-parts technique:
→ Function-free descriptions of each part of an object are produced
→ People decide whether each description implies a use
• High levels of cognitive control can produce functional fixedness
Past experience: mental set
• Another way past experience can impair problem solving: mental set
→ Mental set – the tendency to use a familiar problem-solving strategy that has proved successful in the past even when it is not
appropriate
→ Often useful in spite of its drawbacks, it allows successive problems of the same type to be solved rapidly and with few processing
demands
Problem-solving strategies
Problem Space Hypothesis – Newell & Simon
• Central insight is that the strategies we use when tackling complex problems take account of our limited ability to process and store
information
→ Assume that we have very limited short-term memory capacity and that complex information processing is typically serial (one
process at a time)
• Problem space – an abstract description of all the possible states that can occur in a problem situation
→ Consists of the initial state of the problem, the goal state, all possible mental operators that can be applied to any state to change it
into a different state, and all the intermediate problem states
• Said it’s possible to produce a computer simulation of human problem solving (= general problem solver) actually wasn’t
• Rely heavily on heuristics (= rules of thumb) that produce approx. accurate answers (unlike algorithms that guarantee solution)
→ Algorithms – a computational procedure providing a specified set of steps to problem solution
Means-ends analysis
• Means-ends analysis – heuristic method based on creating a sub-goal to reduce the difference between the current & goal state
→ Support: few fast moves break few fast moves …
• Not the difference between the current problem state and the goal state
→ Form a subgoal to reduce the difference between the current and goal states
→ Select a mental operator that permits attainment of the subgoals
• Generally, very useful and assists problem solution
• Dramatic evidence that people sometimes persist with that heuristic even when it severely impairs performance
• Use of means-ends analysis requires knowledge of goal location
Hill climbing
• Hill climbing – change the present state of a problem into one apparently closer to the goal (e.g. maze) simpler than means-ends
• Most used when the problem solver has no clear understanding for the problem structure
• Focus on short-term goals and so often does not lead to problem solution
Progress monitoring
• Progress monitoring – A simple heuristic used by problem solvers in which they focus on making moves that will apparently put them closer
to the goal
• Involves assessing their 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
• Support: 9-dot-problem less likely to experience criterion failure = less likely to shift strategies
Planning
• Most people presented with complex problems will engage in some preliminary planning
