Problem Solving Flashcards
Introduction - Problem Solving
Problems occur when there is an obstacle between a present state and a goal and it is not obvious how to get around the obstacle.
Has 3 aspects
- Goal-directed
- Involves controlled processes
- Exists when an individual lacks knowledge to solve problem and produce an immediate solution.
Two main ways to solve a problem
Algorithm - Definitely leads to a solution, methodical, logical procedure. Time consuming.
Heuristic - Simpler strategy, less time consuming. More error prone.
Insight - Sudden realisation
Different types of problems
- Well-defined problems: Problems in which the initial state, goal and methods clearly laid out.
- Ill defined problems - Imprecisely specified, goals unclear. No one correct answer, path to solution unclear.
Describe the monty hall problem
Gameshown, choice of 3 doors, behind one is a car, behind others are goats. Pick door 1, host opens another 1 and reveals a goat. Asks if you want to switch to door 2. Correct answer is to swap.
Burns & Wieth (2004) - Most people don’t switch. Don’t know there is a higher statistical probability
People don’t switch because
- Uniformity fallacy - Assume all scenarios have same probability
- Demanding task on executive functioning
- People think host not making strategic hoice
Using heuristics leads us to make mistakes
Describe the Gestalt approach to problem solving
Early approach to PS. Claim that PS is about reproductive thinking - applying previous research and productive thinking - restructuring of the problem.
Success in solving a problem is influenced by how it is represented in persons mind.
Introduced idea that restructuring is associated with insight - sudden realisation of solution.
Multilated draughtboard problem
- Can the remaining 62 squares be filled by 31 dominoes.
- If you give hint, most people get correct answer. People need a hint.
- First people try to mentally position them.
- The way a problem is stated affects its difficulity
What evidence is there to demonstrate insight?
Metcalfe and Wiebe (1987) - Insight vs non-insight problems. Insight problems lead to a sudden increase in warmth compared to non which provokes a continuous increase.
Bowden et al. (2005)
- Looked at whether insight is associated with particular pattern of brain activity
- 3 words, think of one to connect
- Right hemisphere, anterior temporal gyrus activated - role in semantic integration
- Anterior cingulate cortex - Detection of conflicts and breaking of mindset. Insight involves replacing way of thinking with new.
- Prefrontal cortex
Ellis et al. (2011)
- Anagram task
- Insight doesn’t occur unexpectedly
- Eye movements gradually decrease, unaware of accumulation of knowledge.
- People accumulate evidence below consciousness. Moment of insight is conscious realisation.
How can insight be made more likely?
Maier (1931)
- Pendulum, two-string problem, 2 strings, too far away, objects. Need to tie together.
- Ppl don’t think to use objects in room as have not encountered situation where have had to use it in that way before.
- Solution occurred once ppl restructured representation
Thomas & Lleras (2009)
- Same as above but with exercise break. Random exercises either swinging or stretching arms.
- Swinging arms - solved problem
- Hints work with or without conscious awareness
What is incubation and what have researchers discovered about it?
Incubation - Stage in PS in which come up with solution after break
Sio & Ormerod (2009) - Incubation effects in 73% of students, stronger for multiple solutions probs.
Wagner et al. (2014) - Math problems. Those who had sleep had a 59% success rate compared to 25% in awake.
Sio et al. (2013) - Sleep only good for difficult probs, not easy, Effects limited.
Describe representational change theory (Ohlsson, 1992)
Need to change problem representation for insight to happen. Happens in 3 ways
- Constraint relaxation: Things removed
- Re-encoding of task: Some aspect reinterpreted
- Elaboration: New problem info added to representation.
If search process is unsuccessful, an impasse. Have to change representation/see prob from another view.
Propose that a search process is necessary even have impasse.
Best time for a hint is after a representation of the problem has been built. Just before impasse.
What evidence has followed from representational change theory?
Knbolich et al. (1999)
- Move single stick to make statement true
Revereberi et al. (2005)
- How constraints processed in brain, processing activates lateral prefrontal cortex
- If damage to this area, no building of constraints, better performance on insight probs. 82% in matchstick problem compared to 20% in healthy.
Chi and Synder (2011)
- Stimulation of the lateral prefrontal cortex
- Reduction in the left lateral prefrontal cortex + inc in excitability of right lateral prefrontal cortex led to 60% solving hardest matchstick problem compared to 43% control.
Ollinger et al. (2014) Nine-dot Problem
- Testing theory
- Connect all 9 dots using only straight lines, no more than 4 lines without taking pencil off.
- Ppl fail bc think there is a box. Need to go beyond the constraint.
- Success likely when constraint relaxed
Evaluate representational change theory
Validation
- Rep of a problem takes time
- Past experience has impact. Hints required, many only solved with a hint.
- Additional search processes required. Before and after impasse.
Limitations
- Hard to predict when and how representation of a prob will occur
- Individual diffs not accounted for
- Theory assumes constraint relaxation enough to solve a prob, but not the case e.g. nine-dot prob
Explain the factors which hinder insight
Functional fixedness - Assumption that objects have a specific function or can only be used in certain ways
Mental set - Tendency to use a specific strategy repeatedly, despite being unsuccessful.
Provide examples of functional fixedness
Obstacle to problem solving
Candle Problem (Duncker, 1945) shows this.
- Given candle, box of matches and tacts. Task to attach candle to wall so doesn’t drip onto table below.
- Ppl fail bc fixation in tack box functioning as container rather than platform.
- Improved performance when box is empty.
Pendulum problem.
Challonder (2009) - Can be overcome by
- Noticing obscure feature
- Form a solution using obscure feature
McCaffrey (2012) - If individuals ignore what object is used for, 83% solve insight problems. Can make people focus on it by using generic parts routine - describe each object in a function free way.
Provide examples of mental set
Obstacle to problem solving
Lunchins (1942) Water Jars Problem
- Need to end up with one jar with 25 quarts of water.
- Practiced with complex situation - weren’t able to find easier strategy
- No mental set group - Short solution
- Experts not immune to this. Failed to identify shortest solution, used fast, familiar.
Describe problem solving strategies
Newell and Simon (1972) - Use heuristics when solving probs to deal with our limited processing capacity. Rely on 2 heuristics.
Means-end analysis
- Create subgoal, reduce cognitive load, smaller parts. Move solution closer to goal state.
- Can be ineffective e.g. Sweller & Levine (1982) - Invisible maze. When shown the goal, 1 out of 10 solved problem as it activated means-end, performed many moves. When not shown the goal, solved it in less moves.
Hill Climbing
- Want to reach goal quickly, find moves to allow this.
- Short-term benefits
- No understanding of problem structure
What are cognitive misliers?
People who don’t invest much time + effort into thinking tasks. Measured by cognitive reflection test.
Toplak et al. (2011) - Low scorers on test perform poorly on judgement and reasoning tasks. Performance correlates with intelligence.
