What is a problem?
When there is an obstacle between our present state and our goal state, and it isn’t obvious how to get around the obstacle.
Different types of problems
- well defined/ill defined
- knowledge rich/knowledge lean
Well defined problems
- Have a correct answer
- set rules
- require certain procedures to be applied to arrive at the goal state.
Ill-defined problems
-don’t necessarily have a single correct answer
-generally multiple pathways to reaching the solution
Eg breaking up with your bf/gf is an ill-defined problem
Knowledge lean problems
-don’t require any specialised knowledge on the part of the problem solver.
Knowledge rich problems
-require specialised knowledge on the part of the solver (eg medical diagnoses)
What type of research has the majority of research on problem solving focused on?
Well defined, knowledge lean problems
These are generally easier to replicate in the lab.
Gestalt view on problem solving
-problem solving depends upon how a problem is REPRESENTED mentally, and how the problem could be RE-STRUCTURED to reach a solution.
Eg: the triangle inside the circle example, what is the circles radius?
Gestalt view - an obstacle to problem solving
-fixation: the problem solver focuses on an aspect of the problem that prevents them from moving towards the solution,
An example of fixation as an obstacle to problem solving
Functional fixedness - where the problem solver unwittingly restricts the use of an object to its more familiar/usual use.
Eg the candle problem
Present state: box of thumb tacks, matches, a candle.
Goal state: fix the candle to the wall so that it doesnt drip was when lit.
-In order to solve the problem, you need to see the box as a potential shelf for the candle, not as a container. (You have to RESTRUCTURE the problem space).
What is insight?
A rapid realisation of a problem’s solution… An “a-ha!!” Moment.
- Gestalt psychologists took this as evidence of rapid restructuring.
- However later research has questioned whether this is a real phenomena or not.
The results of studies looking at the insight effect
- results (Metcalfe & Wiebe) indicated that participants experienced insight v non sight problems in different ways.
- used warmth ratings to see how close the participant felt they were to completing the problem.
- in non-insight problems (algebra), participants indicated a steady increase in their warmth ratings.
- in insight problems, participants did indeed experience an “A-Ha!” moment leading to a rapid representation change and the solution.
Basic theory of computational models
If a computational model behaves in a similar way to empirical human performance, then it can be considered to be a useful model of the processes underlying human behaviour on that task.
General Problem Solver - Early computational approach
- was shown to be able to provide solutions to a number of well defined,multi step problems (eg towers of Hanoi)
- at the heart of this approach is the idea of specifying the “Problem Space” for the task.
- problem space contains all of the potential problem States or legitimate steps that can be taken in order to move from the initial state to the goal state.
The Travelling Salesperson Problem (TSP) - problem space
- enormous problem space (a 20 point problem has around 6x10^16 solutions)
- no known algorithm that can solve TSP’s in a linear time frame.
- however, human solves are able to produce solutions that are close to optimal in a linear time frame.
Why are humans so good at solving TSP’s so quickly?
- we solve in a different manner to computer algorithms.
- Computer algorithms tend to operate in a ‘brute force’ manner, considering potential solutions that humans would never consider as viable.
- humans appear to search a much smaller problem space.
- we apply certain heuristics that allow us to limit our search of ‘plausible’ potential solutions.
field of dots
- can join them up in which ever way they choose.
- Participants tend to produce minimal structures.
Dry et al. - testing Kohler’s assumption
(Presented participants with star constellations - participants weren’t aware of this, mirror-transformed them. Asked them to join up the dots)
-results indicated that there was an enormous degree of agreement across the participants in regards to what the salient structure was.
The ability of computational models to mimic human performance
- varies across different models and tasks.
- this is because solving a given problem requires multiple cognitive processes: attention, working memory, semantic info, visual heuristics etc.
