problem solving Flashcards
why is thinking so hard
- higher-order cognition is built on other aspects of cognition
- does something with the product of perception, memory, and language
– key aspect is creating new knowledge, rather than extracting knowledge
– especially involves frontal lobes of the brain
higher order cognition “thinking”
problem solving: generating a way to a goal
creativity: generating new ideas
decision making: evaluating alternative outcomes or making choices
reasoning: drawing further inferences from current knowledge and beliefs
problems - Karl Dunker
a problem eists if a living organism has a goal but does not know how the goal is to be reached
problem solving
problem solving is achievement of goal not currently in grasp
- getting a good grade
- cooking peruvian
- making space travel safer
- design a house
- write a story
Well-defined problems
- clear goal
- cear starting point
- clear rules or guidelines
math, physics, chess
ill-defined problems
- no clear goal
- no starting point
- no clear rules or guidelines
choosing a career
problems & Problem solving
problem solving is selecting a sequence of operators that will transform the current state into the goal state
Tower of Hanoi problem
states: the set of disk configurations
operators: the movement of disks from one peg to another
types of problems
incremental problem
* problem that can be solved by following a particular set of rules that lead to the answer
insight problem
* no discernable path the solving the problem
* in this problem type, you think about it for a while and then you have a sudden insight (ah ha) experience which gives you a critical pieve of the puzzle that allows you to solve it
Insight problems
the subjective “feeling of warmth” increased more gradually and predictably for non-insight problems, but showed a sudden, unexpected rise for insight problems, reflecting the distinct phenomenology of insight problem solving
- ranked problems for probability of success
- insight problems opaque to prediction of performance
Gestalt approach
- how people represent a problem matters a lot
- solving a problem involves a reorganization or restructuring of problem representation
Insight problems:
– solutions for insight problems often require gestalt process (re-organizing representation)
information processing approach
- problem space
- problem solving search through problem space of possibilities (Maze)
- start with situation want to transform into something new
- apply different options
Information-processing theories of problem solving focus on constructing a problem space and finding a path through the problem space
* A problem space consists of a representation of the initial state, goal state, and all intervening states.
searches – methods of solution
- problem solving can be seen as a search through the problem space
Methods:
1. algorithm – generate and test
2. heuristics – difference reduction, means end analysis, analogy
algorithm – generate test
randomly generate solution, then test it
* Brute-force approach
* no knowledge taken into account (eg: trying to break into a safe
advantage: requires no knowledge
disadvantage: problem space may be very large
heuristics – difference reduction
try to reduce difference between current state and goal state using knowledge
advantage: get to solution in small steps
disadvantage: it may not be possible to get closer on each step
Hobbits and Orcs
backup avoidance: people do not generally want to undo what we have already done
illustrates conflict between difference reduction and backup avoidance
* want to reduce differences
* don’t want to go against this tendency and back up
means-ends analysis
reducing distance between you and your ultimate goals by setting up subgoals
set up several subgoals that don’t always have to move you closer
means-ends analysis steps
- compare current state to goal and identify the difference
- select an operator to reduce the largest difference
- if operator cannot be applied, set subgoal of creating preconditions for its application
- return to (1) until goal is reached
Example
– i want to be in Tahoe
– I am not in Tahoe
– Flying seems best
– I don’t have a ticket
– subgoal: get ticket
– on-line seems best
means-ends analysis conclusions
- evidence comes from verbal protocols
- Egan & Greeno (1974) found a problem with more subgoals are more difficult
6-disk version of Tower of Hanoi
* probability of error increased with the number of sub-goals that had been set up between the current and preceeding move
working backwards
- similar to means-ends, but reverse initial and goal states
- some problems may be easier to solve in one direction than the other
– some particularly when there are many possible options in the initial state
transfer
application of previous experience to problem
positive transfer – using prior knowledge to help solve a problem (analogy)
negative transfer – prior knwoledge hurts problem solving
(mental set, fixation, and functional fixedness)
analogy
analogies are relationships between 2 similar situations, problems, or concepts
on standardized test
* Merchant: Sell
* Customer: ______ (buy?)
analogy example
suppose a patient has an inoperabe stomach tumor, there are certain rays that can destroy this tumor if their intensity is great enough. At this intensity however, the rays will destroy the healthy tissue that surrounds the tumor. how can the tumor be destroyed without damaging the healthy tissue through which the rays must travel on their way?
analogy positive transfer
story about fortress
problem: many roads lead to a fortress
* mines that detonated with large force
* general with large army
analogy
- X-ray problem
- results: without the analogy, 10% found the solution
—- with the fortress story, 75% solved it
this was only when they were told to look for an analogy. only 30% saw the analogy without prompting
obstacles to problem solving negative transfer
occurs when the process of solving an earlier problem makes later problems harder to solve
example: water jugs
negative transfer
participatns learn a complex rule for solving the water jug problem
later, this method prevents participants from seeing an obvious and simpler method
mental set: a tendency to only see solutions that have worked in the past
obstacles to problem solving
fixation: inability to see problem from new perspective
dots problem: only thinking about staying within dots
matches problem: only thinking about matches in 2D
functional fixedness
dunkers (1945) – Candle Problem
- using the materials shown (matches in a match box, some tacks) find a way to mount a candle on the corkboard on the wall so it will burn without dripping
functional fixedness: the failure to see another use for an object
method to overcome problem solving obstacles
incubation
incubation
setting a problem aside for a while sometimes helps and can lead to insights
- step away and do something else
- come back to problem
why might this work?
– let unimportant stuff go
– mental set may weaken
– new stimuli may change view
– can find new analogy
– relax and see new cues
expertise and problem solving
expert: someone with at least 10 years of experience
physics experts and novices
* experts grouped problems based on structural similarities, novices on surface similarities.
experts see problems differently
* they see patterns in information and are able to identify solutions
* experts develop extensive knowledge that impacts the way they identity problems, organize and interpret data and formulate solutions
– so moving from novice to expert involves much more than simply developing a set of generic skills and strategies
