Problem – 4 aspects:

·
__goal__:
state toward which problem solving is directed

·
__givens__:
conditions and constraints present (explicitly or implicitly) in the problem

·
__means of transforming conditions__

·
__obstacles__

Types of problems:

·
well-defined

·
four
aspects are completely specified

·
e.g.,
maze; math problems

·
ill-defined

·
aspects
are not completely specified or easy to infer

·
e.g.,
maintaining good relationship with roommates

Methods for studying problem solving:

·
reaction
time, accuracy

·
good
global measures of performance, but insensitive to

·
verbal
protocols

·
subjects
“think aloud” as they solve problems

·
infer
strategies from the protocol

·
problem:
people can’t always articulate their thoughts

·
computer
simulation

·
what
processes lead to the thoughts revealed by the protocols?

·
test
hypotheses in simulations

·
forces
people to be explicit about the processes they hypothesize

a problem space

·
Newell
& Simon

·
Problem
solvers are information processing systems

·
Constrained
by information processing limitations

·
Serial
processing

·
Limited
capacity STM

·
Essentially
unlimited LTM

·
Problem
solving requires search through a problem space

·
__Problem space__: internal representation of the problem

·
Consists
of __states__ and __operators__

·
State:
representation of the problem in some degree of solution

·
Initial
state: givens and prior knowledge

·
Goal
state: desired outcome

·
Intermediate
states: situations on the way to the goal state

·
Operators:
means of transforming on state into another state

·
permitted
moves

·
e.g.,
8-tile puzzle; Tower of Hanoi

·
serial
processing: consider current state and potential operators

Search through the problem space

·
algorithm:
systematic procedure; guaranteed to find a solution

·
e.g.,
maze strategy

·
problem:
too time-consuming to be generally useful

·
heuristic:
a useful “rule of thumb” that can be used to guide search

·
does
not guarantee a solution, but is more efficient

·
given
some set of potential next states, which one should be chosen?

·
Difference-reduction
method (simple search)

·
Choose
the state that is closest to the goal state

·
“hill
climbing”

·
problems:

·
local
maximum

·
considers
only the next step, not the larger plan

·
some
problems require move __away__ from the goal state

·
e.g.,
hobbits and orcs problem

·
Means-ends
analysis

·
Determine
difference between current state and goal state

·
Choose
operator that removes largest part of difference

·
Apply
operator; continue until goal is reached

·
If
operator cannot be applied, do not abandon it; find operator that enables it

·
i.e.,
create subgoals to enable the operator

·
e.g.,
fly from Champaign, Illinois to Providence, Rhode Island

·
the
means can become an end itself

·
General
Problem Solver: computer simulation by Newell & Simon (1972)

·
Uses
means-ends analysis

·
Powerful
problem solver

·
e.g.,
tower of Hanoi

·
successful
problem solving often depends on how the problem is represented

·
representation
of states

·
e.g.,
mutilated checkerboard; gorge/rope problem

·
it
may be useful to transform the representation of the problem

·
e.g.,
“going to the extremes” (Levine, 1988)

·
flagpole
example

·
__functional fixedness__: inability to use objects in ways other than their
typical use

·
e.g.,
Duncker’s (1945) candle problem

·
e.g.,
wrench-pendulum example

·
representation
of operators

·
e.g.,
9-dot problem

·
__set effects__: problem representation can be affected by prior experience

·
e.g.,
Luchins’s water jug problems

·
3
jugs of different capacity; need to measure out a specific quantity of water

·
e.g.,

Jug A: 5 cups B: 40 cups C: 18 cups

Need 28 cups

Solution: 2A + C

Jug A: 21 cups B: 127 cups C: 3 cups

Need 100 cups

Solution: B – A – 2C

·
Einstellung
effect (mechanization of thought)

·
group
with practice on problems of

type (B-2C-A):

·
80%
used that method when either A+C or A-C could have been used

·
64%
could not solve problem 8:

A: 28 cups B: 76
cups C: 3 cups Goal: 25

Cannot be solved by B-2C-A.

Can be solved by A-C.

·
control
group:

·
<
1% used B-2C-A when simpler solution could be used

·
5%
failed to solve problem 8

·
__set effect__: practiced subjects developed a __mental set__ -- a bias toward a
particular solution