Chapter 12: Problem Solving Flashcards
Problem-solving
a cognitive process that involves recognizing there is a problem, analyzing it, and solving it, then verifying the effectiveness of the solution
problem
occurs when there is an obstacle between an initial state and a goal state where you do not know the solution right away
size of problems
Problems can be small or large
what type of processing is involved in problem-solving?
involves taking bottom-up and top-down information into account
what kind of process is problem-solving?
a cyclical, recursive, and applicable process
recursive
its steps are repeated as many times as necessary
cyclical
once you arrive at a solution, you discover a new or similar problem and have to use information gained in the past to work on a solution for the next problem
problem-solving cycle
- Define the problem
- Brainstorm solutions
- Pick a solution
- Implement solution
- Review the results
initial state
the initial situation or starting point of a problem
goal state
the desired final state or ending situation
problem space theory
states that problem-solving is a search with problem space, which includes an initial state, a goal state, and intermediate states, which one moves through using operators
who developed problem space theory?
Newell & Simon, 1972
intermediate states
all the possible states in between each step in moving from an initial state to a goal state
operators
actions that transform the current problem state into another problem state
two types of problems
well-defined & ill-defined
well-defined problems
have correct answers and certain procedures that lead us to solve them
example of a well-defined problem
math problem
algorithms
a step-by-step procedure that should always produce a correct solution
what types of problems are easily solvable by algorithms?
well-defined problems
ill-defined problems
a problem that does not have clear goal states, solutions paths, or expected solutions
can ill-defined problems be solved by computers?
Computers don’t solve these problems very well because they don’t have a clear correct answer
Thorndike on problem-solving
problem-solving is a reproductive process
Thorndike was a ___
behaviourist
reproductive process
involves solving a problem by using knowledge from previous experiences and a trial-and-error strategy
trial-and-error
an approach to problem-solving that involves trying many different solutions and ruling out those that don’t work
The law of effect
states that of several responses made to the same situation, those that are accompanied or closely followed by satisfaction are more firmly connected with the situation, while those that are accompanied or closely followed by discomfort are weakened
Thorndike, 1911 trial-and-error experiment
with each trial, cats were able to escape a box faster, demonstrating their ability to learn through trial-and-error
Gestalt psychologists on behaviourism
Criticized behaviourists for their rigid approach to problem-solving that doesn’t account for phenomena like insight
insight
the phenomenon where the solution to a problem suddenly comes into consciousness
Wertheimer, 1959 on problem-solving
viewed problem-solving as a productive process
Wertheimer was a ____
gestalt psychologist
Productive process
the process of problem-solving that occurs when thinking is characterized by the restructuring of information in such a way as to provide a solution.
what type of process accounts for insight
productive process
restructuring
the process of actively manipulating information to change its representation in your mind
heuristics
Mental shortcuts for drawing inferences based on limited information without slow deliberation
The likelihood of using heuristics increases when:
- One is faced with too much information
- The time to make a decision is limited
- The decision to be made is unimportant
- There is access to very little information to use in making the decision
- An appropriate heuristic happens to come to mind at the moment
working backwards
a heuristic in which you begin the problem by focusing on the end result
means-end analysis
a heuristic in which you create sub-goals as you move closer to your final goal state. Includes forward and backward movements and constantly evaluating the difference between current and goal states
what heuristic is often involved in AI?
means-end analysis
2 barriers to solving problem
- Being unable to ignore irrelevant information
- Functional fixedness
the ability to filter out irrelevant information throughout life
Ignoring irrelevant information develops in children and declines with old age
when is filtering out irrelevant information most difficult?
when you are dealing with an ill-defined problem
functional fiixedness
the tendency to view objects for their intended purposes because of prior experience with that object
fixations
a specific characteristic of a problem
insight problem
a problem in which the solution occurs suddenly into your consciousness
non-insight problem
a problem distinguished by the process of consciously working through each step of a problem to arrive at a solution
Metcalfe and Wiebem 1987 predictions and insight vs. non-insight problems
gave participants either an insight problem or a non-insight problem. Found that while solving non-insight problems, participants were able to predict with some accuracy how close they were to solving the problem, but those solving the insight problem were very poor at estimating how close they were
the two-string problem
provided participants with useful and useless hints to solve a two-string problem. Some of the participants who correctly solved the problems mentioned the useless cues as helping them, demonstrating the lack of consciousness in the nature of insight
divergent thinking
a thought process that can generate many solutions to a problem to determine one that works well enough to solve the problem
who first defined divergent thinking
Guilford, 1967
convergent thinkings
a thought process that leads to conventional solutions
creativity
being able to produce novel ideas that are appropriate and relevant to the situation
Sternberg’s triarchic theory of human intelligence
there are three basic facets of human intelligence: analytical, practical, and creative
analytical intelligence
the basis of academic problem-solving skills
practical intelligence
the ability to understand and deal with everyday tasks
creative intelligence
the ability to use existing knowledge to deal with novelty
ideational fluency
the number of ideas a person can generate on a particular topic
relationship between problem-solving and creativity
positive directional relationship
the candle problem
participants are given a candle, a box of matches, and thumbtacks with the goal of mounting the candle on the wall so the wax won’t drip on the floor
when are participants more likely to solve the candle problem
Participants were twice as likely to solve the problem if the box of matches was presented separately from the matches
The 9 dot problem (Maier, 1930)
presented participants with a 3x3 matrix of dots and asked them to connect all of the dots using 4 straight lines drawn without lifting their pencil or retracing lines
how did the phrase “think outside of the box” originate?
the 9 dot problem
Water-jug problem (Luchins, 1942)
participants are given a few jugs, each with a different capacity to hold water and asked to measure out a very specific amount of water to end up with
mental set
the tendency to use solutions that have worked in the past, or the tendency to respond to something in a given, or set, way
experts
know a great deal about a particular topic or skill
novices
know little and have little, if any, experience about a particular topic or skill
Sheridan & Reingold, 2014 eye fixations and chess study
tracked the eye movements of expert and novice chess players and found that while both groups spent more time fixating on relevant areas of the board, the experts were faster at detecting which areas were relevant in the first place
chunks
any combination of letters, numbers, or sounds that constitute a meaningful whole. It is the proposed unit for measuring capacity in STM
Chase & Simon, 1973 chess study
expert chess players are far superior to novice players in their memory for chess arrangements but were no better than novices when the pieces were arranged randomly
who spends more time thinking about what steps to take?
novices
who spends more time analyzing problems?
experts
speed of experts vs. novices in problem-solving
Experts take more time to analyze and organize a solution before they being working to solve it, but they quickly catch up and outperform novices who take more time in the trial-and-error stage
thinking of novices vs. experts
Novices benefit from creative thinking, while experts are stuck in conventional ways of thinking
information processing approach to problem-solving
- Describes what happens between a stimulus and a response
- Sees people as processors of information
- We draw related information in LTM to WM to help us arrive at a solution
heuristics vs. algorithms
- Computers use algorithms while humans use heuristics
- Heuristics are less predictable than algorithms
Tower of Hanoi
consists of three pegs with three or more discs stacked on the first peg with the largest peg on the bottom and the smallest on the top. The challenge is to move the discs to another peg and restack them with the largest on the bottom and the smallest on the top, while only moving one disc at a time and not placing a larger disc on top of a smaller disc
what problems are computers better at solving?
Computers can calculate all possible moves at once, making them faster at solving well-defined problems like the Tower of Hanoi and chess
applicable
apply successful cycles (solutions) to new problems
social problem-solving is an example of ___
an ill-defined problem
brain activity during ill-defined problems
Greater activity in the right lateral prefrontal cortex for ill-defined anagrams
cognitive load
the amount of information held in mind at one time
what kind of problems carry a greater cognitive load?
ill-defined problems
Moravec’s Paradox
Artificial intelligence (AI) can solve well-defined problems well, but not ill-defined problems and simple skills. AI is often defined by the use of algorithms, deep neural networks, that work well with certainty but not with uncertainty
brute force approach to problem-solving
A systematic algorithm that represents all the possible steps from the problem to the goal state
pro of the brute force approach to problem-solving
guaranteed to find a solution
con of the brute force approach to problem-solving
inefficient
combinatorial explosion
computing too many alternatives
examples of heuristics
- Hill climbing strategy
- Means end analysis
- Working backwards
hill climbing strategy
Select the operation that brings you closer to the goal without examining the whole problem space
downsides to the hill climbing strategy
This strategy can lead to a false outcome, a local maximum (subgoal) is mistaken as the final goal
why doesn’t the hill climbing strategy always work?
because some problems require you to move away from the goal to solve it
the hobbits and orcs problem
- There are 3 hobbits and 3 orcs who need to cross a river
- The boat can only hold 2 creatures
- The number of orcs can never exceed the number of hobbits
- At least one creature must bring the boat back each time
what does the hobbits and orcs problem demonstrate?
that the hill-climbing approach doesn’t always work
the benefit of the means-end heuristic
More flexible approach than hill-climbing
expert radiologists vs. novices
Expert radiologists use global visual processes when viewing scans
the tumour problem demonstrates
the benefits of analogical problem-solving
the tumour problem
- Only about 8% of people can solve the tumour problem
- But, the story about the invading army gives you some hints for solving the tumour problem, making it easier to solve
- With the invading army story, 76% of participants can solve the tumour problem
analogical problem-solving
Making comparisons between two situations; applying the solution from one of these situations to the other situation
target problem
the situation the person is currently in
source problem
the situation that shares similarities with the target
are people good at analogical problem-solving?
People aren’t very good at using analogies unless they are reminded
The Einstellung Effect
The bias to use familiar methods to solve problems
downsides of the Einstellung Effect
- This can result in an inability to seek and use a better method to solve a given problem
- This leads to rigid thinking and blocks in problem-solving
children and the candle problem
Children of different ages solved the candle problem because they have less fixedness without pre-utilization
pre-utilization
experience with the objects
mental fixedness
Responding with previously learned rule sequences even when they are inappropriate or less productive
order of problems in the water jug problem
- People will implement the less effective solution if they are given a set of problems in order (harder ones at the start)
- Those who are only given the easier task will use the easier solution
gestalt switches
the experience of having a sudden switch in how you see something
the four features of insight
- suddenness
- ease
- positive
- confidence
suddenness
the solution pops into mind with a surprise
ease
the solution comes quickly and fluently
positive
a pleasant experience, even before assessing if the solution is effective
confidence
the solution is believed to be the right one
the triangle problem
Participants must move three circles to get the triangle to point to the bottom of the page
the necklace problem
- Participants are given four separate chains that are each three links in length
- It costs 2 cents to open a link and 3 to close one
- All links are closed at the start
- Join all links of a chain into a single circle at a cost of no more than 15 cents
is the necklace problem an insight problem?
The solution involves restructuring the problem, a key characteristic of insight
mental impasse
being stuck in a solution path
does insight problem-solving come with awareness?
no, people can’t accurately predict performance
does non-insight problem-solving come with awareness
yes, step-by-step algorithms help predict performance
warmth ratings
a person’s feeling that they are approaching a solution
do feelings of knowing predict problem-solving abilities?
The feeling of knowing ratings predicted algebra performance but not insight problem-solving ability
metacognitive assessment
what you know about what you know
is metacognitive assessment accurate for problem-solving?
it’s accurate for non-insight problems, but not for insight problems
