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.
