Psychology 3130A/B Lecture Notes - Lecture 10: Visual Cortex, Graham Wallas, Functional Fixedness
22 Jun 2018
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Week 13/Chapter 10: Problem Solving, Heuristics, and Insight
What is a problem?
- A gap or barrier between current state and goal state
A General Description
-Parts of a Problem
oProblem – a gap or barrier between the current state and some goal state
oGivens – an aspect, condition and or constraint that the problem solver must deal with when
solving the problem
Can be explicit or implicit
Not necessarily stated explicitly in original problem but is an implicit aspect of the
situation
oObstacles – things that interfere with a direct path between the current state and the goal state
May be reduced or eliminated when the problem solver is very familiar with the problem
context (ex. An expert who can recall a solution immediately from memory)
oMeans – the operations that are used to change the original state and move closer to the goal state
Can be cognitive operations such as mental imagery, verbalization or memory retrieval
Imagining the problem from a different perspective, imagining the solution, representing
the problem in a different way
Can be physical operations
- Well-Defined and Ill-Defined Problems
oWell-defined problem – problem with completely specified initial states and goals, well-
articulated gives and obstacles and a specified means of attaining that goal or goals
oIll-defined problem – if one or more aspects of the problem is missing or not defined
- Problem Representation
oA mental representation constructed by the problem-solver to assist in solving the problem
-Stages of Problem-Solving
oPreparation Stage – Understands that the problem exists & examines conditions/constraints
o Production – the problem solver begins to generate or produce potential solutions
Could be the result of general-purpose problem-solving heuristics (hill climbing, means
end, working backwards)
If prior knowledge is brought to bear or if previous examples need to be recalled it takes
place in this stage
oJudgement/Evaluation Stage – tentative solution paths may be explored further, evaluated for the
likelihood of success
If no correct solution is applicable, problem solver may either stop working on problem
or persist
oIncubation stage – Spreading activation in semantic memory may continue
May occur even if the problem-solver gives up or moves on to another task
Problem Space
- Newel and Simon (1972) – Human problem solving – defined problem solving as a search through
problem space
oA step by step process, a search for the correct solution
- General Problem-Solving Heuristics
Algorithmic VS. Heuristic problem-solving
- Algorithm – a strategy that is guaranteed to find a solution (Math formula/Recipe)
- Heuristic – takes advantage of general knowledge to find a solution more quickly (Short-cut)
oMay be faster than an algorithm but are not always guaranteed to find a solution
find more resources at oneclass.com
find more resources at oneclass.com
General Problem-Solving Heuristics and Strategies
- Exhaustive Search
oExhaustive search – problem solver searchers all the possible routes to the problem space and
chooses the one that is more efficient (Algorithmic)
oGood sometimes if there is a small problem space (Like looking for a lost toy in a room)
oNot good at other times when there are lots of options available (Like playing chess)
- Hill Climbing
oAssumes the problem solver only searches for steps that move the current state closer to the goal
state (a search Heuristic)
oComparing the current state to the goal state and making some form of similarity calculation (in
hope of moving towards the goal state)
oConsiders only steps that reduce the distance or increase the similarity between the current and
goal state
oLimitation – in cases where the solution requires first working towards a goal and then working
away from the goal, the heuristic will fail (subject to local maxima)
- Means End Analysis
oProblem solver breaks an ill-defined problem into several smaller well-defined problems
(reduction of problem space)
oSolution can be attained by attending to and solving these smaller more tractable problems
Cooking/meal preparation
- Working Backwards
oStarting at the goal state and working backwards
oInsight problems – often accompanied by a sudden flash of insight or illumination
- Transforming or re-representing
The Importance of Problem Representation
- Choosing an Appropriate Representation (what best represent the initial state)
oThere are multiple ways to approach most problems, some will have solutions some will not
oIt is important to pick the right approach in order to solve the problem
oSpatial, Abstract, Quantitative
- Functional Fixedness
oDunker’s candle problem – participants given a candle, a box of tacks and a box of matches.
Asked to use these objects to provide a way to mount the candle so that it would illuminate the
room
One condition: tacks and matches removed from the boxes and placed in piles on the
table so that the participants saw empty boxes and the objects (100% solved)
Second condition: functional fixedness condition. Matches were in their box and the
tacks were in their box. (43% solved)
The correct solution is to tack one of the boxes to the wall and tack the candle to the box
Why?
When participant’s see the box of tacks there were less likely to perceive the box
as a potential shelf. Function was fixes as being a container for the tacks
Certain problems can only be solved with the correct representation (Monk
Problem)
Tumor Problem
- Gick & Holyoak (1980)
- Before each person read the story of the General, some were told the story of the General had a hint
relevant to the tumour problem and others were not
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Week 13/chapter 10: problem solving, heuristics, and insight. A gap or barrier between current state and goal state. Parts of a problem: problem a gap or barrier between the current state and some goal state, givens an aspect, condition and or constraint that the problem solver must deal with when solving the problem. Not necessarily stated explicitly in original problem but is an implicit aspect of the situation: obstacles things that interfere with a direct path between the current state and the goal state. May be reduced or eliminated when the problem solver is very familiar with the problem context (ex. An expert who can recall a solution immediately from memory: means the operations that are used to change the original state and move closer to the goal state. Can be cognitive operations such as mental imagery, verbalization or memory retrieval. Imagining the problem from a different perspective, imagining the solution, representing the problem in a different way.
