Lecture 10: Problem Solving Flashcards
What is a problem space?
- a place wherein a problem exists
- initial, immediate, and goal states; also the problem solver’s knowledge at each of these steps
What are the 3 features of a problem space?
1 - initial state
2 - goal state
3 - operators
What are the 7 steps to solving problems?
1 - Problem identification 2 - Problem definition and representation 3 - Strategy formulation 4 - Organize information 5 - Resource allocation 6 - Monitoring 7 - Evaluation
What are well-defined problems?
- clearly defined initial and goal states
- can be solved using a set of procedures and/or reasoning strategies (operators)
- requires convergent thinking
What are ill-defined problems?
- no clear path to the goal state
- cannot use a predetermined set of rules
- often requires insight and divergent thinking
What is an algorithm?
- series of operations that can be applied repeatedly and will eventually reach the correct solution
What is the working forward problem solving heuristic?
- choose alternative that appears to lead most directly to the goal
What is the working backward problem solving heuristic?
- start from the goal and move backward to get to the initial state
What is a means-end analysis?
- break the problem into subproblems and minimize the distance between the initial state and the goal state
→ i.e. Tower of Hanoi, early AI programs
What are the 5 steps of means-end analysis?
1 - Set up goal/subgoal
2 - Look for difference between current state and goal/subgoal.
3 - Look for operator that will reduce/eliminate this difference.
4 - Apply operator.
5 - Apply steps 2-4 repeatedly until all subgoals and final goal are achieved.
What are isomorphic problems?
- share structural features but often have different surface features
- solved with the analogy approach
What is Gick & Holyoak’s Radiation problem and what does it show about solving isomorphic problems?
- presented with Duncker’s radiation problem, where a malignant tumor can be destroyed through radiation but radiation would also kill healthy tissue
→ also presented with story about a general and his army attacking a palace with mines - results:
→ w/o convergence problem: 8%
→ w/ convergence problem: 20%
→ w/ convergence problem, self-generated solution: 41%
→ w/ convergence problem, solution, hint: 76% - difficult to solve isomorphic problems without convergence
What is problem solving by analogy?
- use information from one domain (the source or analogy) to help solve a problem in another domain (the target)
- biggest difficulty is mapping elements between multiple problems
What is productive thinking?
- unconscious problem solving
- short circuiting of regular problem solving strategies (i.e. release from mental set)
What was Metcalf et al’s conclusion about insight?
- Insight problems solved suddenly (“Aha!”)
- Noninsight problems solved gradual
What is physical evidence of productive thinking?
- brain activity in prefrontal cortex (and ACC) differs between solved and unsolved insight problems
What is incubation?
- when the solution for a problem comes after thinking about it
- not often replicated in lab
What was Silveira’s neclace problem study?
- costs $2 to open link, $3 to close link
→ join all 12 links to single circle for >$15 - most people got it after taking longer and longer breaks
What are factors influencing problem solving?
- mental set
- functional fixedness
- expertise
What is a mental set?
- existing belief about how to represent or solve a problem that prevents us from solving a problem
- occurs with too much reliance on top-down processing
→ demonstrated in Duncker’s candle problem
What is functional fixedness?
- occurs when we fail to realize that objects can have other uses than the assigned us
What is negative transfer?
- occurs when earlier problem solving strategies interferes with new problems (e.g. candle problem)
- also called negative set effects
- bias or tendency to solve problems in a particular way. using a single specific approach, even when a different approach might be more productive
- think of Luchins’s water jugs
What is positive transfer?
- occurs when earlier problem solving strategies help solve new problems (e.g. radiation problem)
How does expert knowledge help problem solving?
1 - More time spent at beginning of problem solving cycle (systematic plan).
2 - Identify structural features of the problems.
3 - Have better domain memory.
4 - Use more efficient problem solving strategies (develop subgoals).
5 - Use more automatic processing.
6 - Think ahead/Draw inferences.
What did Chase & Simon’s chess study show?
- experts have an improved memory for their fields of expertise
- able to chunk chess plays and replay a game to get reset a field
What is a verbal protocol?
- transcription and analysis of people’s verbalizations as they solve a problem
What is insight?
- deep. useful understanding of the nature of something, especially a difficult problem
What is Kuonio et al’s theory of insight in the brain?
- frontal lobe suppresses irrelevant information that dominates thinking up until that point of insight
- allows more weakly activated ideas, such as those drawn in the right hemisphere, to come to the fore, possibly offering a solution
What is incubation (in relation to problem solving)?
- process by which someone may stop working on a difficult problem only to go back later and come up with the solution
- theorized that while on break the faulty/misleading ideas they had lose strength, allowing more successful alternatives to present themselves
What is multiconstraint theory?
- proposed by Holyoak & Thagard; predicts how people use analogies to solve problems
- analogies require degree of similarity from source domain to target domain
- must have parallel problem structure to map elements from source to elements from target
- purpose of both analogies should match i.e. the goal/solution to both analogies are the same
What are compound remote associates?
- task where a word/phrase can combine with three other words
- i.e. what one word can form a compound word/phrase with each of the following? pie luck belly
Which areas of the brain are involved in solving problems by analogy?
- left frontal lobes
- left parietal lobes
What are the characteristics of problem solving according to Anderson?
1 - goal directedness - must achieve some sort of purpose
2 - sequence of operations - must be steps to problem-solving that are done in a certain way
3 - cognitive operations - involves application of various operators
4 - subgoal decomposition - each step is a goal in itself
What are operators in problem-solving?
- set of legal moves that can be done during problem solution
