3. Thinking Skills for Research_Karmalkar

Thinking Skills for Research

Shreepad Karmalkar Shreepad Karmalkar

EE Department, IIT Madras

Email: [email protected]

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At the end of this session, you should be able to r ecognize

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• the difference between thinking skills required for course

based and research education


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• the various levels of thinking




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• the difference between intelligence and creativity


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• the role of the following in creative problem solvi ng

- information organization(permutations-combinations, tables, graphs)

- analogies






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• ways of developing creative thinking in yourself



- analogies

� Memory

� Application

Levels of thinking

� Application

� Critical thinking

� Creativity

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Levels of thinking

Make five squares of equal size out of a single lar ge

square, using scissors only. Cut and paste is allow ed.

Activity

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Make five squares of equal size out of a single lar ge

square, using scissors only. Cut and paste is allow ed.

Levels of thinking

Activity

1 2 3 4 510

Questions testing levels of thinking

Q. State and prove Pythagorus theorem.- Tests memory

Q. Using Pythagorus theorem, divide a square piece o f paper into five equal squares.

Following questions assume that students are taught the statement and proof of Pythagorus theorem.

paper into five equal squares.- Tests application

Q. Divide a square piece of paper into five equal s quares. (No hint of Pythagorus theorem).- Tests critical thinking

Q. Formulate a question for testing the levels of t hinking.- Tests creativity

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� Memory

� Application

Levels of thinking

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� Application


� Creativity

HOT

� Memory

� Application

Levels of thinking

Employed in research

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� Application


� Creativity

HOT

Intelligence versus Creativity

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• Marilyn vos Savant (IQ 228 – highest ever)

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• Richard Feynman (IQ 122 - less than many run-

of-the-mill physicists)

• Marilyn vos Savant (IQ 228 – highest ever) is

merely a question and answer columnist for

Parade magazine.


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of-the-mill physicists)

• Marilyn vos Savant (IQ 228 – highest ever) is

merely a question and answer columnist for

Parade magazine.


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of-the-mill physicists) is a Nobel prize winner

and recognized as the last American Genius.


• Intelligence and creativity are not the same things.

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• Intelligence in a domain means the ability to function

at a high level in that domain

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at a high level in that domain,


but

creativity involves asking new questions and altering

the domain.

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at a high level in that domain,


but

creativity involves asking new questions and altering

the domain.

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• Creativity is the ability to look at the same thing

as everyone else, but think something different

Thinking differently – Example 1

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Description of attitudes with the help of “roses” a nd “thorns”


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Optimistic Roses

Pessimistic Thorns


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Optimistic Roses

Pessimistic Thorns

Realistic Roses and thorns



Stoic Roses or thorns

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Optimistic Roses

Pessimistic Thorns



Humane Roses for you and Roses for me



Selfish Roses for me and thorns for you

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Optimistic Roses

Pessimistic Thorns







Divine Roses for you and your thorns for m e

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Optimistic Roses

Pessimistic Thorns



Metaphor






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Optimistic Roses

Pessimistic Thorns



Metaphor






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Permutation-Combination

A

C

BD

Reduction of Systematic Error


Terminal velocity as a function of the diameter34

ABCDDCBAB

A

C

BD



BCDAADCBTerminal velocity as a function of the diameter

ABCDDCBAB

A

C

BD



BCDAADCBTerminal velocity as a function of the diameter

Different ways of calculating ππππ


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• 2√√√√2 < ππππ < 4 (square), 3 < ππππ < 2√√√√3 (hexagon)



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• ππππ / 4 = Tan-1 1 = (x – x3/3 + x5/5 – x7/7 + ….) at x = 1




• ππππ / 4 = Tan 1 = (x – x /3 + x /5 – x /7 + ….) at x = 1

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• ππππ / 4 = Tan-1 1 = (x – x3/3 + x5/5 – x7/7 + ….) at x = 1




• ππππ / 4 = Tan 1 = (x – x /3 + x /5 – x /7 + ….) at x = 1

• Buffon’s needle experiment

ππππ = 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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Tabular Organization of Information

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Derive the trend in the behavior of plating adhesio n on a

silicon substrate from the measured data as a funct ion of

substrate area and doping level.

Example


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Example


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The adhesion is measured for 0.5, 1 and 2 cm 2 area, and P+,

P, N and N+ doping levels.




Example


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The adhesion is measured for 0.5, 1 and 2 cm 2 area, and P+,

P, N and N+ doping levels.

Each measurement is repeated twice.

Table(List)

Doping Area (cm 2)

Expt 1 Expt 2

P+0.5 10 10.2

1 7 7.2

2 5 6

P0.5 8 9

1 4.3 4.7

AdhesionStrength(106 N / m2)

2 3 3.1

N0.5 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 46

AreaDoping

0.5 cm 2 1 cm 2 2 cm 2

P+ 10 10.2 7 7.2 5 6

P 8 9 4.3 4.7 3 3.1

Table (Matrix)

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 (10 6 N / m2)

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Graphical Organization of Information

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0.5 cm 2

1 cm 2

Adh

esio

n st

reng

thN

/ m

2 )10

8

6


Example 1: Adhesion measurements

2 cm 2

Adh

esio

n st

reng

th(1

06N

/ m

N+ N P P+

6

4

2

0

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Example 2: Solution of two linear equations

A1x + B1y = C1


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A1x + B1y = C1

A2x + B2y = C2

Example 2: Solution of two linear equations

A1x + B1y = C1

y


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A1x + B1y = C1

A2x + B2y = C2

x

Example 3: Teaching-learning Process


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5353

Time



Teacher talk

Using chalkboard

5454

Time

Teacher question



Teacher response

Teacher talk

Using chalkboard

5555

Time

Student question

Student response

Teacher question



Teacher response

Teacher talk

Using chalkboardTime

5656

Student action

Student question

Student response

Teacher question



Teacher response

Teacher talk

Using chalkboardTime

5757

Student action

Student question

Student response

Teacher question



Teacher response

Teacher talk

Using chalkboard

Using charts

Using projections

Using multimedia

Time

5858

Student action

Student question

Student response

Teacher question



Teacher response

Teacher talk

Using chalkboard

Using charts

Using projections

Using multimedia

Time

5959

Assignment

Solve this problem graphically

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Assignment


Tirupati temple problem…..

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Exactly at sunrise one morning, you set out to climb the

Thirupati temple.

Assignment



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Thirupati temple.

The path wound round the mountain .

Assignment




You climbed the path at varying rates of speed.

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Thirupati temple.


Assignment





You stopped many times along the way to rest and to eat

the fruit you carried with you.

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Thirupati temple.


Assignment





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 …..65

After fasting and meditating for several days, you began

your journey down along the same winding path, starting at


Assignment


sunrise and walking, as before, at variable speeds.

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Assignment



Your average speed down the hill was more than your

average climbing speed.

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Assignment



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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Example: Discoveries through analogy

• Solar system ⇔⇔⇔⇔ Atomic structure

Analogy / Metaphor

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• Solar system ⇔⇔⇔⇔ Atomic structure

• Electromagnetic wave ⇔⇔⇔⇔ Matter wave

Analogy / Metaphor

Example: Discoveries through analogy

• Electromagnetic wave ⇔⇔⇔⇔ Matter wave

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• An analogy enables a look at a situation as an

inter-related whole.

Analogy / Metaphor

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• Analytical approach on the other hand dismembers

a whole into parts, and may destroy the attributes

Analogy / Metaphor


which may pertain to the phenomenon as a whole.

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• Analytical approach on the other hand dismembers


Analogy / Metaphor


which may pertain to the phenomenon as a whole.

• Problems are solved and creative works are generate d

by transfer of existing ideas to new surroundings

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1) Describe at least two analogies you have come acr oss

in your area of interest.

Assignment

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Assignment

1) Describe at least two analogies you have come acr oss

in your area of interest.

2) Pick up a book in the library that deals with a subject

outside your area of expertise. Carefully go throug h all

the figures and tables in the book to see if you fi nd

some new ways of organizing information.

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• Good thinking is a skill which can be developed by

practice .

Conscious application is needed, not the vagaries o f

“inspiration”, in order to achieve a creative outpu t.

Prescriptions for developing thinking skills


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• Good thinking is a skill which can be developed by

practice .

Conscious application is needed, not the vagaries o f




• Good thinking is a matter of organizing one’s basic

skills, not regretting that one was not born with a

“quick” or “logical” mind.

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Creativity can be nurtured by

• Learning about different ways to a problem and

• Visualization of situations in terms of graphs and


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• Visualization of situations in terms of graphs and

analogies

Noting ideas as they occur


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- helps you to remember them


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- speeds up your thinking


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- focuses attention on your subject

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- stimulates cross-fertilization of ideas

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If you do not record your ideas you will spend all

your mental energy trying to resurrect old ones.85


- stimulates cross-fertilization of ideas

Have an open mind


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An open mind -

- is receptive to alternate points of view, regardles s

of the present level of commitment to a belief

Have an open mind

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of the present level of commitment to a belief

An open mind -

- is receptive to alternate points of view, regardles s

of the present level of commitment to a belief.


Have an open mind

of the present level of commitment to a belief.

- acknowledges areas of common ground with those

who hold alternate beliefs, and allows dialogue wit h

someone with opposing views without attacking the

proponent of those views.

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• Arrange and rearrange what you read or hear, from

different points of view.


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• Allow opportunities for cross-fertilization of idea s

so as to generate new problems.


- interact: discuss, answer doubts, teach, explain.

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- set aside time to read in other disciplines, keepi ng

track of what others are doing that seems original.

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- set aside time to read in other disciplines, keepi ng

track of what others are doing that seems original.

- if possible, work in areas outside of areas we are

currently learning about

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“Education is not about learning diverse subjects,

but about learning diverse ways to the same subject .” but about learning diverse ways to the same subject .”

- Aurobindo

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• ways of developing creative thinking in yourself



- analogies

Documents

3. Thinking Skills for Research_Karmalkar