Problem solving Flashcards
What is the simple aim of problem solving?
-there is an initial state and a goal state in a problem
*Our task is to find a path that will take us from one state to the other
*Solving a problem is influenced by how we understand the
problem (at least understanding what the goal state is)
Define ill-defined problems
-Underspecified (at the start we usually don’t know the goal state)
-Endless strategies you could adopt, how do we know which one would be most effective?
*Most everyday problems are ill-defined,psychologists focus on well-defined problems (Goel, 2010)
Define well-defined problems
All aspects of the problem are clearly specified + a well-specified goal e.g., chess (although very complex) problem
When does a problem exist?
When someone lacks the relevant
knowledge to produce an immediate solution (what constitutes a problem is thus relative to the person)
Define knowledge-rich problems
Can only be solved by those having much relevant specific knowledge (e.g., chess problems)
Define knowledge-lean problems
Don’t require such knowledge as most of the information needed to solve the problem is contained in
the initial problem statement e.g. Math problems
*Most traditional research on problem-solving involved
knowledge-lean problems since they minimise individual
differences in relevant knowledge
What type of thinking did Gestaltists distinguish?
reproductive thinking AND productive thinking
Define reproductive thinking
involves the systematic reuse of previous experiences
Define productive thinking
involves a novel restructuring of the problem and is more complex
What is often used to solve problems requiring productive thinking?
Insight
* “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 non-obvious or non-dominant interpretation” (Kounios & Beeman, 2014, p. 74)
Explain the Nine-dot problem (Öllinger et al., 2014, Springer) and how that relates to insight
Involves drawing 4 straight lines that go through all 9 dots without lifting your pencil off the page
Most people initially assume that the lines must remain within the confines of the square dots
Key insight is to realise that this constraint must be relaxed (go outside the square)
The insight needed to be followed by an efficient search process for the problem to be solved
Define the representational change theory and how it links to insight Ohlsson (1992, 2011)
We often encounter a block or impasse when solving a problem because we have represented it wrongly (which is why insight is important to rearrange this representation)
E.g., the mutilated draughtboard problem (Black, 1946)
Which 3 ways can we change the problems representation for insight to occur according to the Representational Change Theory?
1.Constraint relaxation: inhibitions on what is regarded as permitted are removed
2.Re-encoding: some aspect of the problem representation is reinterpreted
3.Elaboration: new problem information is added to the representation
How did Öllinger et al. (2014) developed Ohlsson’s Representational Change Theory?
*Prior knowledge and perceptual aspects of a problem forms the problem representation followed by a search process
-Repeatedly unsuccessful search process=an impasse or block
*A new problem representation is formed to try to overcome the impasse followed by another
search process
*A search process may be necessary even after an impasse has been overcome by insight
True or false: Hints before or after an impasse improved performance less than those given at the point of impasse (Moss et al., 2011)
True
What inconsistent findings did Fedor et al. (2015) find for the Representational Change Theory?
*Less than 50% followed the predicted sequence
*Most used complex processing sequences
No more likely to report experiencing impasse during behaviourally defined impasse than at other stages of processing
What was Knoblich et al.’s (1999) experiment testing insight?
P’s were given problems requiring Roman numeral knowledge to solve (had to move a single stick to produce a true statement to replace the initial false one) with either a Type A/B problem
What’s Knoblich et al.’s (1999) Type A problem?
Only required changing 2 values in the equation
-Easy to do as our experience of arithmetic tells us that many operations change the values (numbers) in an equation (as with Type A problems)
What’s Knoblich et al.’s (1999) Type B problem?
less obvious change in the representation of the equation
-Few operations change the operators as is required in type B problems=much harder to relax the normal constraints of arithmetic (+ show insight) for Type B problems
What did Knoblich et al. (2001) find about insight in their roman numerals experiment?
-P’s initially spent much more time fixating on the values than on the operators for both types of problem (moved values sig more)
*Thus, their initial representation was based on the assumption
that values had to be changed
Define the incubation effect
A problem is put aside for some time where the subconscious mind continues to work
What 3 findings did Sio and Ormerod (2009) report in a meta-analysis on incubation effects?
1.Incubation effects were reported in 73% of the studies
2.Incubation effects were stronger with creative problems having
multiple solutions>linguistic and verbal problems having a single solution
3.Sleep enhanced performance on difficult problems but not on easy ones
*Forgetting misleading info is important (Penaloza & Calvillo, 2012)
*The strategies tried by the problem solver are forgotten during incubation (Simon, 1966)
*This forgetting makes it easier to adopt a new approach after the incubation period
Define mental set (past experience)
continuing to use a previously
successful problem-solving strategy even when it is
inappropriate or suboptimal
Why are mental sets useful despite their drawbacks?
It allows successive problems of the same type to be solved
rapidly and with fewer processing demands
What did Luchins (1942) find in relation to mental sets?
1.Used problems involving 3 water jars of varying capacity
2.If experts were given a problem in their area of expertise they’d be relatively immune from the damaging effects of mental set
What did Vallée-Tourangeau et al. (2011) find replicating Luchin’s water jar experiment on paper but using actual water jars instead?
*Luchin’s water-jar problems on paper (as in the original research) or using actual water jars at a sink
*It was beneficial and had more of an effect using actual water jars because of the rich and dynamic nature of the perceptual input
What did Bilalić et al. (2008a) find in relation to insight/mental sets?
When chess experts tried to find the most rapid way to win a chess game, most failed to identify the shortest solution instead using a longer solution based on a familiar strategy
*Their direction of attention remained partly under the control of processes producing the initial familiar solution (i.e. damaging effects of mental sets)
Define functional fixedness
Occurs when we mistakenly assume that any given object has only a limited number of uses
Why do we have numerous failures on insight problems according to Gestaltists?
*Past experience typically increases our ability to solve problems
*However the Gestaltists argued that numerous failures on insight problems occur due to being misled by past experience
What’s the Tower of Hanoi experiment?
-3 poles with 3 circular hoops varying in size on one
-the aim is to transfer them all to the other side without the smaller one being underneath the bottom one
Explain what hill climbing is as a problem-solving strategy
*Involves changing the present state within the problem into one closer to the goal (simpler than means-ends analysis)
*Used when the problem solver has no clear understanding of the problem structure (focuses on short-term goals)
*Often doesn’t lead to problem solution
*Like a climber who tries to reach the highest mountain peak in the area by using the strategy of always moving upwards it may work, but it is likely that the climber will find himself/herself trapped on a hill separated by several valleys from the highest peak
Explain what means-end analysis is as a problem-solving strategy
*The most important heuristic method (Newell & Simon, 1972)
1.Notes the difference between the current problem state and the goal state
2.Then forms a subgoal to reduce this difference between the current and goal states
3.Selects a mental operator (e.g., move or moves) to permit the attainment of the subgoal
*It’s beneficial and assists problem solution BUT it was reported that people sometimes persist with that heuristic even when it severely impairs performance (Sweller & Levine, 1982)
Meta-reasoning: What’s Progress monitoring according to Ackerman & Thompson, 2017?
It’s assessing their rate of progress towards the goal (Individuals engaged in problem-solving use this heuristic)
-If progress too slow to solve the problem within the maximum number of moves allowed, people adopt a different strategy
How does the nine-dot problem (MacGregor et al., 2001) contradict the benefits of progress monitoring and meta-reasoning?
Worse performance when participants had the illusion of
making progress (and so were slow to switch strategies)
than where it was more obvious that little progress was being made.
How much planning do good problem-solvers usually do?
*Most problem solvers engage in only a modest amount of
planning because of limited STM capacity (Newell & Simon, 1972)
*Most problem solvers engage in little planning (Patsenko & Altmann, 2010)
*Individual differences in planning when students performed the
Tower of London task (Koppenol-Gonzalez et al. 2010)
How much planning was seen in the water-jar problem? (Delaney et al., 2004)
-Little evidence of planning when free to choose a preferred strategy
-When participants were instructed to generate the complete solution before making moves they showed clear evidence of being able to plan and solved the problem much faster than controls
