12. Problem Solving

Question 1

what are the features of problem solving?

Answer 1

1. Goal directedness

2. Subgoal decomposition

Question 2

what is problem solving?

Answer 2

Problem solving is goal-directed behavior that often involves setting subgoals to enable the application of operators

Question 3

What did Kohler (1927) study?

Answer 3

Problem solving in other species: Kohler (1927)

Chimpanzee named Sultan was able to use tools to solve problems

Question 4

what is problem space?

Answer 4

Consists of various states of the problem

Question 5

what is problem state?

Answer 5

A representation of the problem in some degree of solution

Question 6

what is the operator in problem space and search?

Answer 6

An action that will transform the problem state into another problem state

Question 7

what are the two important questions concerning problem solving?

Answer 7

– What determines the operators available to the problem solver?
• This defines the problem space
– How does the problem solver select a particular operator?
• This determines the path the problem solver will
take

Question 8

what are the three ways to acquire new operators?

Answer 8

– Discovery
– Direct instruction
– Analogy

Question 9

what is analogy?

Answer 9

The process by which a problem solver maps the solution for one problem into a solution for another problem

Question 10

what does analogy rely on?

Answer 10

This relies upon “structural” similarities

Question 11

What was Gick and Hollyoah’s (1980) study in analogy?

Answer 11

Tumor patient problem. Most people can’t solve this.
“Dictator” Analogy.
Only a few participants spontaneously noticed the mapping.

Question 12

what are the characteristics of analogy problem solving in humans?

Answer 12

– Capability nearly unique to humans

– Seems to involve the Prefrontal cortex

Question 13

what are inhuman primates abilities in imitation?

Answer 13

• It has been considered that nonhuman primates are quite poor at imitation (e.g., Tomasello & Call, 1997)
• However, previous studies might have underestimated their imitation ability

Question 14

what did Subiaul et al (2004)’s show regarding imitation?

Answer 14

Subiaul et al. (2004) showed that rhesus monkeys can learn how to perform a certain task by looking at other monkeys

Question 15

what is the three criteria for selecting operators?

Answer 15

1. Backup avoidance
2. Difference reduction
3. Means-ends analysis

Question 16

what is backup avoidance?

Answer 16

The tendency in problem solving to avoid operators that take one back to a state already visited

Question 17

what is difference reduction?

Answer 17

The tendency in problem solving to select operators that eliminate a difference between the current state and the goal state

Question 18

what is difference reductional also known as and why?

Answer 18

“Hil-Climbing”

Difference reduction is a useful method, but not always optimal

Question 19

what does difference reduction consider?

Answer 19

Difference reduction considers only whether the next step is an improvement and not whether the larger plan will work

Many participants deviated from the correct sequence when a required move decreased the similarity to the goal state

Question 20

where do people experience difficulty in solving a problem according to difference reduction?

Answer 20

People experience difficulty in solving a problem at points where the correct solution involves increasing the differences between the current state and the goal state.

Question 21

what does means-ends analysis create?

Answer 21

Means-ends analysis creates a new subgoal to enable an operator to apply
– An operator is not abandoned even if it cannot be applied immediately

Question 22

what does means-ends analysis identify?

Answer 22

It identifies the biggest difference between the current state and the goal state and try to eliminate it first

Question 23

what is the tower of Hanoi problem?

Answer 23

Why is it called “Tower of Hanoi”?
– Based on a “legend” about a temple in Hanoi, Vietnam
– There is a large room in this temple that has three posts surrounded by 64 golden disks of varying size
– When the world was created, these disks were all in one post in the order of their size, the largest disk at the bottom and the smallest one at the top
– The priests of Hanoi have been moving these disks in accordance with the rules of the puzzle
– When the last move of the puzzle is completed, the world will end

The number of separate transfers of single disks the priests must make to transfer the tower is 2 to the 64th minus 1, or 18,446,744,073,709,551,615 moves! If the priests worked day and night, making one
move every second it would take slightly more than 580 billion years to accomplish the job!

Question 24

what disallows solving of the Hanoi problem?

Answer 24

Difference reduction doesn’t allow you to solve the Tower of Hanoi problem

People tend to adopt the difference reduction strategy first and then start using means-ends analysis when they try to solve the Tower of Hanoi problem (Kotovsky et al., 1985)

Question 25

who tends to have difficulty in backward moves in the Tower of Hanoui problem and why?

Answer 25

Patients with prefrontal damage often have difficulty in making backward moves in the Tower of Hanoi problem (Goel & Grafman, 1995)
– They cannot maintain the goal in working memory very well

Question 26

what is involved in problem representation?

Answer 26

– Functional fixedness
– Set effects
– Incubation effects and insights

Question 27

what does successful problemsolving depend on?

Answer 27

Successful problem solving depends on representing problems in such a way that appropriate operators can apply

Question 28

what does the Mutilated-checkerboard problem task require?

Answer 28

– Cover the 62 remaining squares using 31 dominos. Each domino covers two adjacent squares
– Or prove logically why such a covering is impossible

• Each domino covers two adjacent squares
–> one white square and one black square will be covered
• If you use 31 dominos, 31 white squares and 31 black squares will be covered
• However, in this mutilated checkerboard there are 30 30 white squares an 32 black squares

Question 29

what do inappropriate problem representations cause?

Answer 29

Inappropriate problem representation prevents us from using a proper analogy
– Choice of examples tends to be guided by superficial similarities

Question 30

what is functional fixedness?

Answer 30

The tendency to represent objects as serving conventional problem-solving functions and thus failing to see that they can serve novel functions
• A problem becomes difficult when it requires representing an object’s novel function

Question 31

what did Maier’s two string problem show?

Answer 31

The increased difficulty of problems due to
functional fixedness demonstrates that
how to represent a problem has a significant influence on operator selection

Question 32

what are set effects?

Answer 32

The biasing of a solution to a problem as a result of past experiences in solving that kind of problem
• Often observed when the knowledge relevant to a particular type of problem solution is strengthened

Question 33

what was Luchin (1942) study on set effects?

Answer 33

– For problems 1-5, the formula B - 2C - A provides
the simplest solution
– Problems 6-10 are either solvable by a simpler
formula (e.g., A - C for problems 6 and 9) or
unsolvable by B - 2C - A (problem 8)
– When participants were given the whole set
of 10 problems, they tended to keep using
B - 2C - A for all problems
– As a result, 64% of them failed to solve
problem 8
– On the other hand, when another group of
participants were given only problems 6-10,
they didn’t show any bias toward B - 2C - A
and had little difficulty with problem 8

Question 34

what did Lychin’s (1942) study show us?

Answer 34

Sometimes set effects can be dissipated
easily
• In Luchins’s (1942) study, just telling
participants “Don’t be blind” after
problem 5 allowed more than 50% of
them to overcome the bias

Question 35

what is the incubation effect?

Answer 35

– The phenomenon that sometimes solutions to
a particular problem come easier after a
period of time in which one has ignored trying
to solve the problem

Question 36

when does the incubation effect occur?

Answer 36

– Occur when inappropriate strategies are forgotten

Question 37

what was Silveira (1971) study on the incubation effect?

Answer 37

– You are given chains A-D
– Opening a link: 2¢; closing it: 3¢
– Join all chains into a circle at a cost of 15¢ or less

• Three groups of participants (they all worked on
the problem for 30 min)
– Control: continuous 30 min 55%
– Group 1: interrupted by 30-min of other activities 64%
– Group 2: interrupted by a 4-hour break 85%
• After the break, participants initially tried to solve
the problem in the same manner as before the
break
– Unlike a common brief that we are subconsciously
solving a problem while we are away from it

Question 38

what was Smith and Blakenship (1989, 1991)’s study on the incubation effect and insight?

Answer 38

– Fixation group: given an inappropriate way of
thinking about the problem
– Control group: no particular instruction
– Findings:
• The fixation group showed larger incubation effects
• Participants who had a break more frequently forgot the inappropriate instruction

Question 39

why do incubation effects occur?

Answer 39

Incubation effects occur because people forget inappropriate ways of solving problems

Question 40

what are insight problems?

Answer 40

– Problems in which people are not aware that
they are close to a solution (Metcalfe & Wiebe,
1987)
– Contrary to a common brief, the solution does
not come in a single “aha!” moment
– People often do not recognize what is critical
for solving the (insight) problems until they
see the final solution