STAGES OF PROBLEM SOLVING
• PREPARATION
– encode the “problem space” and
allowable “operators”
– retrieve relevant knowledge from LTM
• PRODUCTION
– devise strategy for searching the space
– implement the search
• EVALUATION
– has the goal been reached?
– are you rpgressing toward the goal?
UNDERSTANDING THE
PROBLEM (Greeno, 1977)
• Our internal representation (or model)
of the problem should have
– accurate CORRESPONDENCE between
relevant elements in the world and model
– good COHERENCE between elements in
the model
– appropriate links to PRIOR KNOWLEDGE
that can aid problem solving
links to prior
knowledge
coherence
correspondence
environment
model of
problem
SOLVING SCHEMATICALLY
“ODD” PROBLEMS
“odd” versions of problems are harder
to solve:
• Monsters & Globes (Simon & Hayes ‘76)
“exchange” versus “grow/shrink” rules
• “surreal” problems (Hinkley & Hayes, 1977)
• A boat takes two hours to steam 20 miles up a river
but only one and a third hours for the return trip. Find
the rate of the boat in still water. (original)
• A wine takes seven years to mature properly from
the time the grapes are harvested but only four years
for the return trip. How fast would the wine mature in
still time? (surreal)
FUNCTIONAL FIXEDNESS
Duncker’s (1940) CANDLE
problem: attach the candle to the
wall so it burns properly.
fewer than half the
subjects solve it
in 15 minutes.
Why?
s o lv in g
Adams (1952): put tacks outside of box
to reduce fixedness on “container”
function:
100
80
60
%
40
20
0
in box
out of box
Placement of Tacks
STRATEGIES FOR SEARCHING
THE PROBLEM SPACE
• RANDOM SEARCH STRATEGIES
– unsystematic search
– systematic random search
• HEURISTIC SEARCH STRATEGIES
– constraining the space
– finding analogies (transfer)
– modelling & planning
– means-end analysis
• reducing the distance between
current state and goal state
• creating subgoals
MENTAL SET (“einstellung”)
Luchins (1942)
task: given three containers of known
quantity, produce target quantity:
A
B
C
goal
2
#1:
7
17
4
5
#2:
19
30
3
4
#3:
7
17
3
prior set
use of B-A-2C on #3:
83%
control
___%
SETTING THE PROBLEM ASIDE
task: make a necklace out of the
chains for $15:
$2 to open a link
$3 to close a link
1st block
15 min
15 min
15 min
Rest 2nd block %solving
-----15 min
55%
15 min 15 min
__%
4 hr
15 min
__%
(Silviera, 1971) mental set dissipates?
incubation?
CREATIVE PROBLEM SOLVING
• the ability to (solve) (ill-defined)
problems in a novel and appropriate
way
• typically results from intensive work
and extensive knowledge
– Edison: 1% inspiration, 99%
perspiration
• individuals vary “normally” by
ability, knowledge and style
• cognitive, social, and motivational
factors influence creative potential
and achievement
MEASURING CREATIVE
PERFORMANCE
• Guilford & others develop tests for
creative aptitude stressing “divergent
production”
– Remote Associations Test
– Uses Test
– Consequences Test
• Correlations of scores with peer-rated
professional creativity are modest (+.2
to +.4)
– reliance on sheer productivity, rather than
rarity or appropriateness
– wrong mental set?
– job constraints on opportunities for
creative work
– lack of “domain-specific” aspects testing
knowledge in field