Higher Order Thinking (HOT)
Shreepad Karmalkar
EE Department, IIT Madras
Email: karmal@ee.iitm.ac.in
1
At the end of this lecture, you should be able to recognize
• the various levels of thinking
• the difference between thinking skills required
for course based education (B.Tech, M.Tech etc.)
and research
• the difference between intelligence and creativity
• the importance of tabular and graphical
organization of data in problem solving
• the role of thinking via analogies in creative
problem solving
• the prescriptions for developing HOT in yourself
2
Levels of thinking
Low
 Memory
 Understanding
 Application
 Analysis
 Evaluation
High
HOT
 Synthesis
3
Make five squares of equal size out of a single large
square, using scissors only. Cut and paste is allowed.
1
2
3
4
5
4
Questions testing levels of thinking
Following questions assume that students are taught the
statement and proof of Pythagorus theorem.
Q. State and prove Pythagorus theorem.
- Tests memory
Q. Using Pythagorus theorem, divide a square piece of
paper into five equal squares.
- Tests application
Q. Divide a square piece of paper into five equal
squares. (No hint of Pythagorus theorem).
- Tests evaluation
Q. Formulate a question for testing the levels of thinking.
- Tests synthesis
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Difference between UG and
Research Education
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Difference between UG and Research Education
Degrees
• Bachelors: General education
• Masters:
Possession of advanced knowledge
• Doctorate: License to teach and guide others
To get the license to teach and guide others, one should
be a MANAGER OF ONE’S OWN LEARNING and an
INDEPENDENT THINKER. In bachelors and masters
education, a student’s learning is managed by her teachers.
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Difference between UG and Research Education
Manager of one’s own learning
 take initiative in choosing the research area and courses
to be undergone
Independent thinker
 not only solve a problem but also define it; this involves
asking new questions
 not only generate data but also interpret it.
8
Difference between UG and Research Education
Flawed perception about the role of a research student
and her guide – an example.
9
INTELLIGENCE versus CREATIVITY
• Marilyn vos Savant (IQ 228 – highest ever) is
merely a question and answer columnist for
Parade magazine.
• Richard Feynman (IQ 122 - less than many runof-the-mill physicists) is a Nobel prize winner
and recognized as the last American Genius.
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INTELLIGENCE versus CREATIVITY
Intelligence and creativity are not the same things.
Intelligence in a domain means the ability to
function at a high level in that domain, but
creativity involves asking new questions and
altering the domain. One can be highly intelligent
but rigid, noncreative, or lacking in the kind of
single-minded passion that drives creators.
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Examples of HOT
12
A scientist questioned the following
hypothesis regarding the cause of obesity
Overweight people overeat because their
level of hunger is higher than that of
average weight people. This higher level of
hunger is responsible for their overweight.
13
The scientist reported the following
experiment to support his doubt….
50 overweight
50 average
weight
Group A: 1 Sandwich
50 overweight
50 average
weight
Group B: 3 Sandwiches
Asking new questions is not enough;
work on a verifiable answer too !
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…. and made the following Observation
Average number of sandwiches eaten by an average weight person in both Groups A and B  2
an overweight person in Group A  1
an overweight person in Group B  3
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…. and drew the following inference
Overeating habit of overweight people is governed
by an external factor, namely – availability of food,
rather than by an internal factor, namely – hunger.
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Reduction of Systematic Error
B
D
C
A
Terminal velocity as a function of the diameter
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A
B
C
D
D
C
B
A
B
C
D
A
A
D
C
B
Reduction of Systematic Error
B
D
C
A
Measured terminal velocity
= f (diameter, viscosity, clock stability)
18
Description of attitudes with the help of “roses” and “thorns”
Optimistic
Roses
Pessimistic Thorns
Realistic
Roses and thorns
Stoic
Roses or thorns
Humane
Roses for you and Roses for me
Selfish
Roses for me and thorns for you
Sadistic
Thorns for you and your blood for me
Divine
Roses for you and your thorns for me
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Assignment
Read up the following article which highlights the
elements of productive thinking:
P. S. Blackawton et. al., “Blackawton bees”, Biology
Lett.. doi:10.1098/rsbl.2010.1056, published
online on 22nd December 2010.
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“Education is not about learning diverse subjects,
but about learning diverse ways to the same subject.”
- Aurobindo
Research involves HOT (also called productive thinking,
critical thinking) which is about generating as many
alternative approaches as possible
Creativity is the ability to look at the same thing as
everyone else, but think something different
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Example: different ways of calculating 
•  = 22
• 22 <  < 4 (square), 3 <  < 23 (hexagon)
•  / 4 = Tan-1 1 = (x – x3/3 + x5/5 – x7/7 + ….) at x = 1
• Buffon’s needle experiment
 = 2 x (total drops) / (no. of hits)
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Assignment
Find four different proofs of Pythagorus theroem, using
internet search or otherwise.
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Ways of representing information
in tabular and graphical form
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Graphical Representation
Derive the trend in the behavior of plating adhesion
on a silicon substrate from the measured data as a
function of substrate area and doping level. The
adhesion is measured for 0.5, 1 and 2 cm2 area, and
P+, P, N and N+ doping levels. Each measurement
is repeated twice.
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Table
(List)
Doping
Expt 1 Expt 2
0.5
1
10
7
10.2
7.2
2
0.5
1
2
5
8
4.3
3
6
9
4.7
3.1
N
0.5
1
2
4.1
4.1
3.9
4.8
5
5.8
N+
0.5
1
2
3
2.9
3.2
6.1
P+
Adhesion
Strength
(106 N / m2)
Area
(cm2)
P
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Table (Matrix)
Area
Doping
P+
P
N
N+
0.5 cm2
10
8
4.1
-
10.2
9
4.8
-
1 cm2
7
4.3
4.1
3
7.2
4.7
5
3.2
2 cm2
5
3
3.9
2.9
6
3.1
5.8
6.1
Adhesion strength ( 106 N / m2)
27
Graph
Adhesion strength
(106 N / m2)
10
1 cm2
8
0.5 cm2
6
4
2 cm2
2
0
N+
N
P
P+
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Graphical Representation
Student action
Student question
Student response
Teacher question
Teacher response
Teacher talk
Using chalkboard
Time
Using charts
Using projections
Using multimedia
Teaching-learning Process 29
Assignment
Solve this problem graphically
Tirupati temple problem…..
Exactly at sunrise one morning, you set out to climb the
Thirupati temple. The path wound round the mountain.
You climbed the path at varying rates of speed. You
stopped many times along the way to rest and to eat the
fruit you carried with you. You reached the temple just
before sunset.
Continued …..
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Assignment
Solve this problem graphically
Tirupati temple problem…..
After fasting and meditating for several days, you began
your journey down along the same winding path, starting at
sunrise and walking, as before, at variable speeds. Your
average speed down the hill was more than your average
climbing speed.
Prove that there must be a spot along the path that you will
pass on both trips at exactly the same time of the day.
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Assignment
Find out different ways of graphical representation of data.
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Analogy
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• An analogy enables a look at a situation as an
inter-related whole.
• Analytical approach on the other hand dismembers
a whole into parts, and may destroy the attributes
which may pertain to the phenomenon as a whole.
• Problems are solved and creative works are generated
by transfer of existing ideas to new surroundings
34
Examples of great discoveries
through analogy
• Electromagnetic wave  Matter wave
• Solar system  Atomic structure
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Assignment
Describe at least two analogies you have come across
in your area of interest.
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Prescriptions for developing HOT
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Practice, Organization and Motivation
• HOT is a skill which can be developed by PRACTICE.
Conscious application is needed, not the vagaries of
“inspiration”, in order to achieve a creative output.
• HOT is a matter of ORGANIZING one’s basic skills,
not regretting that one was not born with a “quick” or
“logical” mind.
38
Practice, Organization and Motivation
MOTIVATION is recognized as a crucial factor in the
development of HOT.
Following is the conclusion based on a study of 301
geniuses.
“High but not the highest intelligence, combined with
the greatest degrees of persistence, will achieve
greater eminence than the highest degree of
intelligence with somewhat less persistence”.
[Cox, 1926]
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Have an open mind
An open mind - is receptive to alternate points of view, regardless
of the present level of commitment to a belief.
- acknowledges areas of common ground with those
who hold alternate beliefs, and allows dialogue with
someone with opposing views without attacking the
proponent of those views.
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Keep Notes
Noting ideas as they occur
- helps you to remember them
- speeds up your thinking
- focuses attention on your subject
- stimulates cross-fertilization of ideas
If you do not record your ideas you will spend all
your mental energy trying to resurrect old ones.
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More prescriptions ……..
• Arrange and rearrange what you read or hear, from
different points of view.
• Allow opportunities for cross-fertilization of ideas
so as to generate new problems.
- interact: discuss, answer doubts, teach, explain.
- set aside time to read in other disciplines, keeping
track of what others are doing that seems original.
- if possible, work in areas outside of areas we are
currently learning about
42
More prescriptions ……..
Learning about different ways to a problem and
visualization of the world in terms of analogies,
are two ways of nurturing HOT.
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At the end of this lecture, you should be able to recognize
• the various levels of thinking
• the difference between thinking skills required
for course based education (B.Tech, M.Tech etc.)
and research
• the difference between intelligence and creativity
• the importance of tabular and graphical
organization of data in problem solving
• the role of thinking via analogies in creative
problem solving
• the prescriptions for developing HOT in yourself
44