Problem Solving Flashcards
How do we solve problems?
Define, shape, simplify the problem
Generate possible solutions, evaluate them
Implement best solution… verify it!
Ways to solve problems?
Guesswork (luck!)
•Intuition, hunches
•Elimination
•Pragmatics (logical reasoning)
•Semantics (interpreting underlying meaning)
•Abstract thinking
•Mental flexibility
•Creativity & insight
Problem solving characteristics?
Problems must have a goal (goal directed behaviour)
- Daydreaming about achieving “the good life” is not problem solving
Sequential steps
- Must involve multiple operations
Simple recall is not problem solving
If I lock my keys in my car, or lose them, that’s a problem
- Goal = retrieve my keys
- Breaking-in causes (counter-intuitive) damage, searching requires multiple (time-consuming) steps (or “operations”)
What is a goal?
The ultimate destination, solution, or state of a problem
May need problem “decomposition” (breaking down into necessary steps)
Whats an ill-defined goal?
No explicit goal
E.g., “I need to buy my boss an impressive gift”
Several different results could satisfy the goal of “impressive gift”
What are operators?
Discrete moves, functions or steps towards goal
E.g., recall, logical reasoning, mathematics, motor movements
What are legal and illegal operators?
Permissible given the problem constraints (rules)
Not permissible given problem constraints
What are heuristic approaches?
Mental short cuts to help us reach a solution with less time and cognitive effort – this is their weakness
Trial and error, educated guesses, intuition
No guarantee these quick solutions are the best solutions – often they’re not
We use heuristics all the time
- e.g., deciding on the best deals, choosing your next book, considering the least congested route through town, etc.
What are working backwards heuristics?
A heuristic in which you solve by working backwards from the goal state
E.g., Dan gave Isobel 4 sweets, Jane 3 sweets and Steve 6 sweets. Dan now only has 4 sweets left.
•How many sweets did Dan start with?
Handy for mazes, and maths formulae:
•e.g., SE of mean = SD/SQRT of sample size
•So, if you need the SD but only have SE, reverse the formula:
•SD = SE x SQRT of the sample size
What are trial and error heuristics?
Successively trying various different responses, seemingly at random, until one is successful
Maze learning, with its eventual elimination of blind-alley entrances, is an example of trial-and-error learning
Derived from Thorndike’s stimulus–response theory of instrumental learning (“trial-and-accidental success”)
- In animals, the reward reinforces the successful response, allowing the problem to be solved faster and faster
What are hill climbing heuristics?
Find some measure of the distance between the present- and goal-state
Take a step in the direction that most reduces that distance
Can be problematic – solution may involve moving away from the goal state before returning to it later
Prone to errors and suboptimal solutions (e.g., hill climbing robot)
What is mean ends analysis?
Somewhat like a “divide-and-conquer” approach
Identify obstacles between the current and goal state
Eliminate each obstacle in turn (each obstacle is a simpler sub-goal)
Once each sub-goal is achieved, you’ve reached your goal
E.g., GOAL=paint the house:
•Get paint and brush! (SUBGOAL 1)
•Go to hardware store (SUBGOAL 2)
•Buy paint and brush (SUBGOAL 3)
•Return home (SUBGOAL 4)
•Paint the house (GOAL)
What did Schacter do?
The Tower of Hanoi is a well-defined problem:
- Fully specified initial conditions
- Explicit goal state
- Clearly defined operators for transforming conditions
- Small solution space
Ill-defined problems
- No clear goals, or solution paths
- Unpredictable solutions
- Big solution space
Whats the Gestalt approach?
We perceive scenes and objects as familiar organised patterns or wholes (Gestalt grouping)
The key to problem solving is to deconstruct familiar “Gestalt” perceptions into their component parts
The problem can then be restructured in novel and more helpful ways
Revealing new (less obvious) relationships between items leads to insight
Whats the Gestalt Approach: The Einstellung Effect?
Mental set (persistence of set, negative set, entrenchment)
Old strategies continue to be used, when obviously ineffective
Incorrect problem representations
Relates to functional fixedness
- Tendency to use objects in conventional ways
Whats representational change theory?
Relax constraints on the problem to overcome mental set (Knoblich et al., 2001)
Have you decomposed all the problem features?
Try incubation: problems solved more easily if time set aside
Ormerod et al. (2009) meta-analysis (117 studies)
•Small but significant effect of incubation
•Larger effects for creative problems with multiple possible solutions
•Larger effects when more time had been spent on the task
Sleep on it (Beijamini et al., 2021)
Whats the algorithmic approach?
A systematic sequence of steps that always provides the correct answer to a particular problem
E.g. finding your way out of a maze could be done simply be walking in the direction of the goal/target point
Generally, although it would guarantee a solution, it would be time-consuming
What are brute force algorithms?
Go through all possible states until a solution is found
Guaranteed to work (eventually)
Impractical with large problem spaces
Problem: Unscramble the 10 letters to make a word
Almost a million alternative combinations!
Whats analogical problem solving?
Analogies: relationship between two similar situations, problems, concepts
Difficulty lies in recognising structural commonalities between problems
Many problems are superficially dissimilar, yet strikingly similar at their core
