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Productive Thinking
Shreepad KarmalkarProfessor, Electrical Engineering Department
Core Team Member, Teaching Learning Center
Indian Institute of Technology Madras
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How can I develop my thinking to generate
ideas ?
In how many different ways (tabular, graphical
or other) can I present the data ?
We discuss answers the following questions
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Thinking is said to be
- reproductive when it isbasedon similar problems
encountered in the past, or taught to solve
- productive when it generates as many alternative
approaches as possible
Research is all about productive thinking which is
also called higher order thinking consisting of
critical thinking and creativity
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Marilyn vos Savant (IQ 228 highest ever) is
merely a question and answer columnist for
Parademagazine.
Richard Feynman (IQ 122 - less than many run-
of-the-mill physicists) is a Nobel prize winner
and recognized as the last American Genius.
INTELLIGENCE versus CREATIVITY
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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 creativityinvolves 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.
INTELLIGENCE versus CREATIVITY
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Example what kind of questions alterthe domain
6
Overweight people overeat because their level of
hunger is higher than that of average weightpeople. This higher level of hunger is responsible
for their overweight.
A scientist questioned the following hypothesis
regarding the cause of obesity
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50 overweight
50 averageweight
50 overweight
50 averageweight
Group A: 1 Sandwich Group B: 3 Sandwiches
The scientist reported the followingexperiment to support his doubt.
Asking new questions is not enough;
work on a verifiable answer too !
Example what kind of questions alterthe domain
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8
. 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
Example what kind of questions alterthe domain
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Overeating habit of overweight people is governed by
an external factor, namely availability of food,
rather than by an internal factor, namely hunger.
. and drew the following inference
Example what kind of questions alterthe domain
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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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Creativity 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.
That creativity is beyond analysis is a romantic
illusion we must now outgrow Peter Medawar.
Creativity is a matter of organizing ones basic skills,
not regretting that one was not born with a quick
or logical mind.
GIFT OR SKILL ?
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Motivation is recognized as a crucial factor in the
development of talent and the application ofcreativity. The importance ofIntrinsic Motivation in
driving an individual to practice and work hard to
master a specific domain, is undisputed. Cox
(1926), in his study of 301 geniuses, wrote: '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'.
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Education is not about learningdiverse subjects,
but about learningdiverse ways to the same subject.
- Aurobindo
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Low
High
Knowing or memory
Application or Problem solving
Evaluation or Critical thinking
Creativity
ACTIVITY
Aim: To gain an appreciation of the levels of thinking
Make five squares of equal size out of a single large
square. You are allowed to cut and paste.
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1 2 3 4 5
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Questions testing levels of thinking
Q. State and prove Pythagorus theorem.
- Tests memory
Q. Using Pythagorus theorem, divide a square piece ofpaper into five equal squares.
- Tests application or problem solving ability
Q. Divide a square piece of paper into five equal
squares. (No hint of Pythagorus theorem).- Tests critical thinking
Q. Formulate a question for testing the levels of thinking.
- Tests creativity
Following questions assume that students are taught the
statement and proof of Pythagorus theorem.
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Assignment
Understand critical thinking in detail using an internet search.
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18/42Imagination is more important than
Reason can answer questions, but
imagination has
to ask them
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What is Creativity
Ability to look at the same thing as everyone
else and think something different.
Ability to take a fresh look at familiar objects and
situations, enriched by past experience, but not
constrained by it.
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Description of attitudes with the help of roses and thorns
Humane Roses for you and Roses for me
Optimistic RosesPessimistic Thorns
Realistic Roses and thorns
Stoic Roses or thorns
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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STRATEGIES OF PROBLEM SOLVING
Representation
Logical thinking
Division into sub-problems
Stretch to the extreme
Verbalization
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Well begun is
half-done
REPRESENTATION
Because of the uncertainties involved in ill-
defined problems, the problem solver must
often devote a great deal of time to both the
step of forming an initial representation of the
problem and the step ofreformulating it.
A picture is worth a
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TECHNIQUES OF REPRESENTATION
Symbolic representation
Reformulation
Table: list, matrix
Graph
Venn diagram
Drawing diagram to scale
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The first term is the product of the given sine and radius of the desired
arc divided by the cosine of the arc. The succeeding terms are obtained
by a process of iteration when the first term is repeatedly multiplied by
the square of the sine and divided by the square of the cosine. All the
terms are then divided by the odd numbers 1, 3, 5, .... The arc is
obtained by adding and subtracting respectively the terms of odd rank
and those of even rank. It is laid down that the sine of the arc or that of
its complement whichever is the smaller should be taken here as the
Problem:Represent the following symbolically
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How can you become more productive ?
Problem:
Solution by reformulation:
How can you make your job easier ?
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Powerful Reformulation orTransformation Techniques
Binary number system
Logarithm
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Problem: The Tirupati Temple Problem
Exactly at sunrise one morning, you set out to climb theThirupati 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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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.
Tirupati temple problem..
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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.
PROBLEM
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TABLE(LIST)
Doping Area(cm2)
Expt 1 Expt 2
P+
0.5 10 10.2
1 7 7.2
2 5 6
P
0.5 8 9
1 4.3 4.72 3 3.1
N
0.5 4.1 4.8
1 4.1 5
2 3.9 5.8
N+
0.5 - -
1 3 3.2
2 2.9 6.1
Adhesion
Strength
(106 N / m2)
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Area
Doping
0.5 cm2 1 cm2 2 cm2
P+ 10 10.2 7 7.2 5 6
P 8 9 4.3 4.7 3 3.1
N 4.1 4.8 4.1 5 3.9 5.8
N+ - - 3 3.2 2.9 6.1
Adhesion strength ( 106 N / m2)
TABLE (MATRIX)
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GRAPH
0.5 cm2
1 cm2
2 cm2
Adhesionst
rength
(106N
/m
2)
N+ N P P+
10
8
6
4
2
0
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Solve the equation: X = e-X
PROBLEM
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X LHS RHS
0 0 1
0.4 0.4 0.67
0.5 0.5 0.61
0.6 0.6 0.55
0.55 0.55 0.577
0.57 0.57 0.566
TABLE (LIST)
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y = e-x
y = x
x
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TABULAR SOLUTION
y = e-x
y = x
x
LHS
RHSLHS
RHS
0 0.4 0.5 0.6
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ITERATIVE SOLUTION
y = e-x
y = x
x
x0
x1
x2
x3
x4
x5
Xn+1 = e-Xn
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How good is a particular classroom teaching
learning process ?
PROBLEM
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Graphical Representation
Student action
Student question
Student response
Teacher questionTeacher response
Teacher talk
Using chalkboard
Using charts
Using projections
Using multimedia
Time
Teaching-learning Process
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Venn Diagram
SI
SS
E
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Drawing diagrams to Scale
8
11
8
0.11
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Assignment
Find out different ways of graphical representation of data.