The document discusses problem solving skills and concepts. It defines problem solving as overcoming obstacles to accomplish a goal through thinking and selecting responses. It describes different types of problems like knowledge-lean, knowledge-rich, well-defined, and ill-defined problems. Problem solving approaches include trial and error, insight, heuristics like means-end analysis, and analogy. Problem spaces and operators that move between problem states are discussed. Creative and divergent thinking are important for problem solving.

1. ProblemSolvingSkills
Dr Zahiruddin Othman
GCN505 Nov2018

2. Definitions
 To accomplish a goal by overcoming the
obstacles
 Thinking directed toward the handling of a
particular situation involving both the
formation of responses and the selection
among possible responses

3. THINKING
Concepts
Problem
Solving
Decision
Making
Judgment
formation
formation of a new mental representation through the transformation of information by complex
interaction of the mental attributes

5. FEATURES
of problems
A goal, or
description of
what constitutes
a solution
A description of
objects relevant
to achieving a
solution
A set of
operations or
allowable actions
toward solution
A set of
constraints not
to be violated

6. Knowledge-Lean
Problems
Knowledge-Rich
Problems
Well-defined
Problems
Ill-defined
Problems
Types of
problems

7. All the elements are given, and the
task is to rearrange them
Arrangement
Discovery of a pattern relating
elements of a problem to each
other
Inducing Structure
Manipulation of objects or symbols
while following certain rules
Transformation

8. Problem
solving
 Mechanical solution
 A problem solution achieved by trial and error or by
fixed procedure based on learned rules
 Solution by understanding
 Understanding: a deeper comprehension of the
nature of a problem
 General solution: correctly states the requirement
for success but not enough for further action
 Functional solution: a detailed, practical, and
workable solution

9. Trial & Error
(Thorndike
1898)

11. What do
you see?

14. Problem
Solving
Insightful solution
 Insight: a sudden mental reorganization of a
problem that makes solution obvious
Heuristics
 Any strategy or technique that aids problem
solving, especially by limiting the number of
possible solution to be tried

15. Nature of
Insight
• The ability to select information relevant to
problem solving while ignoring useless or
distracting information
Selective
encoding
• The ability to connect seemingly unrelated
items of information
Selective
combination
• The ability to relate a present problem to
similar problem solved in the past or prior
experience
Selective
comparison

16. Problem solving utilizing
restructuring & insight
Productive thinking
Problem solving reusing past
experiences
Reproductive thinking

17. How would you attach
the candle to the wall?
How would you arrange
the match sticks to form
equilateral triangles?

18. A cognitive bias that limits a person to use an
object only in the way it is traditionally used
Functional fixedness
A tendency to approach a problem in a
particular way, especially if that way was
successful in the past.
Mental set

21. Problem
Space
Theory
(Newell &
Simon 1972)
The initial state
All the possible
intermediate states
The goal state
The actions that people take in order to move from one state to
another are known as operators

22. Acquiring
operators
Heuristic Analogy

23. Heuristics
• Avoid an action that would take you back to a
previous problem state
Repeat-state
avoidance
• Carry out the operation that moves you closest to
the final goal stateHill-climbing
• Similar to hill-climbing heuristic. Create sub-goal
and select operators.
Means-end
analysis
• Try solving the problem from the start to the end
Working
forward
• The problem-solver start at the end and tries to
work backward from there
Working
backward
• The problem-solver generates a list of alternative
ways of action and then notices in turn whether
each course of action will work
Generate &
test

24. Maier’s (1931) two-string problem
As hard as
Sebastian tries,
he can’t grab
the second
string. How can
he tie the two
strings
together?

25. Parking
spot
number

26. WATER LILY PROBLEM
Water lilies growing
in a pond doubles in
area every 24 hours.
On the first day of
spring, only 1 lily pad
is on the surface of
the pond. 60 days
later, the pond is
entirely covered. On
what day is the pond
half covered?

27. AMOEBA PROBLEM
There are two jars of
equal capacity. In the first
jar there is one amoeba.
In the second jar there are
two amoebas.
An amoeba can reproduce
itself in 3 minutes. It
takes the amoebas in the
second jar 3 hours to fill
the jar to capacity. How
long does it take the one
amoeba in the first jar to
fill that jar to capacity?

28. ROPE LADDER PROBLEM
A ship is at anchor. Over
its side hangs a rope
ladder with rungs a foot
apart.
The tide rises at a rate of
8 inches per hour. At the
end of 6 hours, how much
of the rope ladder will
remain above the water,
assuming that 8 feet were
above the water when the
tide began to rise?

29. Where does the man get his hair cut?
A man needing a haircut
goes into a small town
where everyone in the
town gets their haircut
by one of two barbers.
The man visits the
first—a very clean shop
where the barber has a
terrific haircut.Then he
visits the second—a
very dirty shop where
the barber has a terrible
haircut.

30. FIVE MARKS PROBLEM
Add five more
marks (lines)
and make ten.

31. THREECATS
The 1st and 2nd weigh
7kg altogether.
The 2nd and 3rd weigh
8kg altogether
The 1st and 3rd weigh
11kg altogether.
What is the weight of
each cats?

32. THE NINE DOTS PUZZLE
Link all 9 dots
using 4 straight
lines without
lifting the pen.

35. POSSIBLE OR IMPOSSIBLE?
Starting in the square
marked by the circle,
draw a line through all
the squares without
picking up your pencil,
without passing
through a square more
than once,
without diagonal lines
and without leaving the
checkerboard.

36. Initial and goal states for the Tower of Hanoi problem
Operators that govern theTower of Hanoi problem.

37. Initial steps in
solving the
Tower of Hanoi
problem,
showing how
the problem can
be broken down
into sub-goals

38. Conditions: at
least one in
the boat and
at no time can
there be more
orcs than
hobbits on a
river bank.

39. Means-end
Analysis

40. The Monk AndThe Mountain
At precisely 7:00 a.m., a monk sets out to climb a tall mountain,
so that he might visit a temple at its peak.The trail he walks is
narrow and winding, but it is the only way to reach the summit.
As he ascends the mountain, the monk walks the path at
varying speeds.Though he stops occasionally to rest and eat, he
never strays from the path, and he never walks backwards.At
exactly 7:00 p.m., the monk reaches the temple at the summit,
where he stays the night.
The following morning at 7:00 a.m. sharp, the monk departs the
temple and begins his journey back to the bottom of the
mountain. He descends by way of the same path, again walking
slowly at times and quickly at others, stopping here and there
to eat and drink and rest, but never deviating from the path and
never going backwards.Twelve hours later, at 7:00 p.m. on the
nose, the monk arrives back at the foot of the mountain.
Is there any point along the path that the monk occupied at
precisely the same time on both days?

41. 7 am

42. Problem
Solving by
Analogy
 Use of analogy, a structural similarity between
situations or events.
 An atom is a miniature solar system
 Use to explain many abstract concepts.
 Restructuring, used in the Gestalt approach, could be
aided by retrieving analogous instances

43. DUNCKER’S (1945) RADIATION PROBLEM
What procedure
might the doctor
employ to destroy
the tumor with
the rays, at the
same time
avoiding
destroying any
healthy tissue?

44. The normal cells received lower dose of radiation
than the cancer cells, where all the rays meet

45. Problem
SolvingUsing
Analogy
(Gick and
Holyoak 1980)

46. Logical thought
• Drawing conclusion on
the basis of formal
principles of reasoning
Illogical thought
• Thought that is intuitive,
haphazard, or irrational
Inductive thought
• A general rule is inferred
from a series of specific
examples
Deductive thought
• Thought that applies a
general set of rules to a
specific situation
Divergent thought
• Thinking that produce
many ideas or
alternatives
Convergent thought
• Thinking directed toward
discovery of a single
correct answer
CREATIVETHINKING
involves all these styles of thought
in varying combinations
1. Fluency: number of
solutions
2. Flexibility: number
of different type of
solutions
3. Originality: refer to
how novel the
solutions are

47. • Formulating &
beginning
Preparation
• Problem
solving at
subconscious
level
Incubation
• End of
incubation
period by rapid
insights
Illumination
• Critical
evaluation of
solution
Verification

48. Why should an
interruption
help?
Posner (1973) suggested three reasons:
 Recovery from fatigue
 Forget inappropriate approaches
 Reorganization
Problem solver
initially works
unsuccessfully
on a problem
Problem solver spend
sometime doing
something
completely different
Problem solver
has sudden
insight; solves
the problem

49. General traits
• Originality
• Verbal fluency
• Relatively high IQ
• A good imagination
Thinking
abilities
• Uses metaphors in thinking
• Flexible decision maker
• Uses broad categories
• Makes independent judgment
• Can break mental set
• Find order in chaos
Thinking styles
• Challenges assumption, ask “why?”
• Draw new ideas out of existing knowledge
Personality
Characteristics
• Persist in problem solving
• Curious and open to new experience
• Highly interested in work
• Broad range of interest
• Intuitive
• Playful with ideas

50. Perceptual
memory
Autobiographical
memory
Linguistic &
semantic
Visual
knowledge
Declarative
knowledge
Habits & motor
skills
Central
executive
Working
storage
Verbal
rehearsal
Visuospatial
sketchpad
Sensorybuffers
Actionplanning
Shared memories,
knowledge & skills
Vision
Hearing
Touch
Sensory input
Conscious
event
Top down
voluntary
attention
Bottom up
attentional
capture
Adapted from: Cognition, Brain, and Consciousness. Introduction to Cognitive Neuroscience. Baars & Gage, 2010. page 348
Response output

51. Premotor cortex:
• Response selection
• Execution of simple action
• Rule matching
Frontopolar cortex:
• Tracking of goals and sub-goals
• Relational integration
• Information-seeking behaviour
Mid-dorsolateral PFC:
• Task switching
• Categorization of sequence
• Complex stimulus-response
contingencies
Posterior lateral PFC:
• Selection of sequence of response
• Categorization of sequence
• Rule learning
Topographical
organization
in lateral
prefrontal
cortex

52. Tools for Problem
Solving

53.  Purpose
 To show sequential steps in a
process
 When to use
 To develop understanding of
how a process is done
 To study a process
improvement
 To communicate to others
how a process is done
 To document a process
 When planning a project

55.  Choose the right team and have a leader
 Ensure everyone knows the rules
 Define the problem/topic clearly
 Allow time for individual thought before generating
ideas as a group
 Ensure everyone participates
 Generate as many ideas as possible
 Ban discussion and evaluation during the idea
generation stage
 Record every idea, on a Flipchart
 Allow incubation time before evaluating the ideas
 Keep a relaxed atmosphere

56. 1.Why is there oil on the floor?
• Oil leaks from the cylinder rod when
activated.
2.Why did oil leak?
• TheO-ring was cut.
3.Why was the O-ring cut?
• The rod was flawed.
4.Why was the rod flawed?
• Dirt in the oil abrades the rod.
5.Why did dirt get in the oil?
• There are holes and gaps on the upper
plate of the tank.

57. Define the Problem
•What do you see
happening?
•What are the
specific symptoms?
Collect Data
•What proof do you
have that the
problem exists?
•How long has the
problem existed?
•What is the impact
of the problem?
Identify Possible
Causal Factors
•What sequence of
events leads to the
problem?
•What conditions
allow the problem
to occur?
Identify the Root
Cause(s)
•Why does the causal
factor exist?
•What is the real
reason the problem
occurred?
Recommend and
Implement Solutions
•What can you do to
prevent the problem
from happening
again?
•How will the
solution be
implemented?

58. Cause and
Effect
Analysis

59. Strengths and
Weaknesses
Analysis
STRENGTH
• What are the special
skills?What things go
well?What strengths do
other people perceive?
WEAKNESS
• What area needs
improvement?What is
not going so well? What
weaknesses do other
people perceive?
OPPORTUNITY
• What opportunities are
ahead?What
advantages can be
obtained from
environmental factors?
How can the
competition be
surpassed?
THREAT
• What threats are
realistic?What
environmental factors
are disadvantageous?
How can the
competition/adversary
surpass me?

60. SUMMARY
PROBLEM
SOLVING
Problem
COMPLEXITY
Knowledge-
lean/rich
Well/ill-defined
Arrangement/
inducing structure/
transformation
OBSTACLE/
BARRIER
Fixation
Solution
MECHANICAL
Trial-and-error
Algorithm
UNDERSTANDING/
INSIGHT
Heuristic
Analogy
Creativity