Lecture 10: Problem Solving

Question 1

What is a problem space?

Answer 1

• a place wherein a problem exists

- initial, immediate, and goal states; also the problem solver’s knowledge at each of these steps

Question 2

What are the 3 features of a problem space?

Answer 2

1 - initial state

2 - goal state

3 - operators

Question 3

What are the 7 steps to solving problems?

Answer 3

1 - Problem identification
2 - Problem definition and representation
3 - Strategy formulation
4 - Organize information
5 - Resource allocation
6 - Monitoring
7 - Evaluation

Question 4

What are well-defined problems?

Answer 4

• clearly defined initial and goal states
• can be solved using a set of procedures and/or reasoning strategies (operators)
• requires convergent thinking

Question 5

What are ill-defined problems?

Answer 5

• no clear path to the goal state
• cannot use a predetermined set of rules
• often requires insight and divergent thinking

Question 6

What is an algorithm?

Answer 6

• series of operations that can be applied repeatedly and will eventually reach the correct solution

Question 7

What is the working forward problem solving heuristic?

Answer 7

• choose alternative that appears to lead most directly to the goal

Question 8

What is the working backward problem solving heuristic?

Answer 8

• start from the goal and move backward to get to the initial state

Question 9

What is a means-end analysis?

Answer 9

• 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

Question 10

What are the 5 steps of means-end analysis?

Answer 10

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.

Question 11

What are isomorphic problems?

Answer 11

• share structural features but often have different surface features
• solved with the analogy approach

Question 12

What is Gick & Holyoak’s Radiation problem and what does it show about solving isomorphic problems?

Answer 12

• 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

Question 13

What is problem solving by analogy?

Answer 13

• 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

Question 14

What is productive thinking?

Answer 14

• unconscious problem solving

- short circuiting of regular problem solving strategies (i.e. release from mental set)

Question 15

What was Metcalf et al’s conclusion about insight?

Answer 15

• Insight problems solved suddenly (“Aha!”)

- Noninsight problems solved gradual

Question 16

What is physical evidence of productive thinking?

Answer 16

• brain activity in prefrontal cortex (and ACC) differs between solved and unsolved insight problems

Question 17

What is incubation?

Answer 17

• when the solution for a problem comes after thinking about it
• not often replicated in lab

Question 18

What was Silveira’s neclace problem study?

Answer 18

• 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

Question 19

What are factors influencing problem solving?

Answer 19

• mental set
• functional fixedness
• expertise

Question 20

What is a mental set?

Answer 20

• 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

Question 21

What is functional fixedness?

Answer 21

• occurs when we fail to realize that objects can have other uses than the assigned us

Question 22

What is negative transfer?

Answer 22

• 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

Question 23

What is positive transfer?

Answer 23

• occurs when earlier problem solving strategies help solve new problems (e.g. radiation problem)

Question 24

How does expert knowledge help problem solving?

Answer 24

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.

Question 25

What did Chase & Simon’s chess study show?

Answer 25

• experts have an improved memory for their fields of expertise
• able to chunk chess plays and replay a game to get reset a field

Question 26

What is a verbal protocol?

Answer 26

• transcription and analysis of people’s verbalizations as they solve a problem

Question 27

What is insight?

Answer 27

• deep. useful understanding of the nature of something, especially a difficult problem

Question 28

What is Kuonio et al’s theory of insight in the brain?

Answer 28

• 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

Question 29

What is incubation (in relation to problem solving)?

Answer 29

• 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

Question 30

What is multiconstraint theory?

Answer 30

• 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

Question 31

What are compound remote associates?

Answer 31

• 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

Question 32

Which areas of the brain are involved in solving problems by analogy?

Answer 32

• left frontal lobes

- left parietal lobes

Question 33

What are the characteristics of problem solving according to Anderson?

Answer 33

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

Question 34

What are operators in problem-solving?

Answer 34

• set of legal moves that can be done during problem solution