Problem Solving
What is a problem?
Types of problem
Theories
Transfer
What is it?: when prior knowledge of a problem/ schemas of problem solving influence cognition in solving of a new problem
Helping
Duncker "when a living organism has a goal, but does not know how this goal is to be reached"
Takes several steps, involved conscious cognition, requires planning, has a well-defined goal
problem solving could involve: perceptions, learning, decision-making, communication etc
Eysenck & Keane: problem solving is: purposeful, cognitive, occurs when someone doesn't possess the relevant knowledge to produce an immediate solution (i.e. new knowledge is needed & in future this wont be a problem as you will already have obtained knowledge from the first instance)
Insight
Non-insight
require one specific piece of knowledge
eg. Two string room Maier: insight that can tie object to one string and swing it towards the other
require incremental & sequential problem solving: gradually work out what you need to do as you go
eg. mathematics (algebra) or the Tower of Hanoi
Jung-Beeman Right anterior superior temporal gyrus (RASTGyrus) activated only during these type of problems
Representational change theory Ohlsson
Insight: use current representation of problem to search memory for solution/relevant info... get stuck ("block") when mental representation does not match the true nature of the problem
e.g. candle on wall problem: need to recognise that tack box can be used as something other than a tack box (to hold candle!)
"blocks" can be overcome
elaboration (hint)
relaxation of constraints (think outside the box)
re-encoding (tack box)
Examples
Mutilated chess board: opposite corners taken off- is it possible to cover with dominos which cover 2 squares each? Kaplan
Matchstick problem Ohlsson& Raney: (IV = III - I) "move one stick to produce a true statement"
only solution is (IV - III = I) which is difficult as schemas of maths make us expect that numbers will change rather than operators (=)... ppts did spend longer looking at figures over operations
logical solution: two of the same colour are removed (elaboration) and dominos must cover one of each colour therefore impossible
ppts attempts: thinking aloud, visualisation
re-encoding
requires constraint relaxation to see that the = can be altered
9 dot problem: have to make a triangle but assume lines cant go outside the 'box' so struggle to find solution... constraint relaxation aided with cues: 30-53% get it with cues
MacGregor, Ormerod & Chronicle
Newell & Simon: General Problem Solver
there are lots of different 'knowledge states' between initial and end goal - problems are represented in 'problem space'
in a complex problems we use 'rules of thumb' to achieve sub-goals and progress toward end goal
theory generated by observations of people 'thinking out loud' while problem solving
Thomas (1974): river, sheep & wolves problem
lots of little decisions to edge closer to end goal: BUT must go against end goal (bring them back across river) in order to follow rules and meet goal
restricted problems with conditions and regulations
tend to be descriptive and not predicative & may not apply to real-life decision making
Hindering
Duncker candle
the "functional fixedness" = idea that the box is used to hold tacks and not candles
if box empty at beginning of task then success increases as it can be seen as a container for any possible object
If we are well practiced in a certain strategy we may try to use it when it is inappropriate, hence hindering success
Habituation effects: we become blind to the actual problem at hand and are led by a mechanical application of tried & tested methods
beginners luck? perhaps it is not luck at all - perhaps more experienced people make more mistakes due to this?
Analogical problem solving
James "men reason by analogy"
Spearman "all intellectual acts involve analogical reasoning"
Tumour and army example (we did this in the lecture!)
previous knowledge of the army analogy: entering fortress via 4 different methods, can aid problem solving later in tumour problem! (need to attack tumour without damaging surrounding tissue)
different types of solution (show whether schema of army was used for tumour)
Convergence, Open passage or Surgery
Gick
0-50% when not hinted to use 1st for 2nd
70%+ when hinted to use 1st analogy to aid 2nd
Holyoak
1 week later: 80%+ correct solutions in analogy condition
if problems look alike they probably are alike: superficial features indicate deeper structural similarities Medin
Keane: surface similarity of problems increased spontaneous transfer of methods:
lab studies encourage surface similarity? When ptts created their own analogies they were more structurally similar than on the surface