productive thinking 1

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Productive Thinking

Shreepad KarmalkarProfessor, Electrical Engineering Department

Core Team Member, Teaching Learning Center

Indian Institute of Technology Madras

[email protected]


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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

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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 !



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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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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



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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.


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.

productive thinking 1

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