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The Role of Science Academies in Science

Education and Teaching Science and Mathematics

in a Delightful Manner - Prof. Dr. M. Shamsher

Ali

- 1. Introduction

- Although Science and Mathematics touch our lives

in innumerable ways, the teaching of these

subjects has been far from satisfactory and has

become a global problem. There is a dearth of

qualified science and mathematics teachers. Also,

the students are no longer being attracted to

these subjects. While choosing a graduate program

of study in science and technology, the eyes of

both guardians and students are on those subjects

which are fashionable and can fetch money. The

fashionable subjects are Computer Science and

Engineering, Medicine, Biotechnology including

Genetic Engineering etc. Although these subjects

would not be what they are today without the

development of science and mathematics, the

latter seem to have fallen

- out of favor. People remember the end product,

not the hard work that went into it. The

responsibility for the loss of attraction towards

pure science and mathematics does not lie merely

with students a major part of it lies with us,

the teachers. Mathematics was once regarded as

the Queen of sciences. It is no longer so. The

beauty of that queen is hardly appreciated in

fact she is being presented as dreary and

menacing. The practitioners of mathematics are

doing little to restore the lost beauty of the

queen. Many of the high school students

(especially girls) when asked to give opinion

about mathematics reply mathematics is

difficult. They even find it dry and drab. They

study mathematics only as a requirement for study

and do not

- seem to derive any pleasure from studying the

subject. They usually cannot relate whatever

mathematics they have learnt in the classroom to

what they see in their real life and environment.

This issue of relevance to life and environment

is indeed very meaningful to anyone dealing with

pedagogy. In fact, the development of mathematics

in the ancient times started from very mundane

things like, the measurements on earth (Geometry

geo means earth and meter means measurement).

Even sophisticated branches of mathematics

including abstract mathematics can, in the final

analysis, be related to things they know already.

The challenge of mathematics pedagogy is

basically one of making mathematics

- interesting and delightful. Unfortunately, not

very many teachers address themselves to this

issue. In fact, in the meeting of Education

Ministers of Commonwealth countries it has often

been reported that the scarcity of mathematics

and science teachers is posing a great threat to

the overall development of science and technology

in the developing countries. - Obviously, no time would be more suitable than

now for addressing the issues of Science and

Mathematics Education for the 21st Century.

- 1.1 The Role of Science Academies in Science

Education and Science Promotion

- Science Academies, all over the world, are

regarded as apex scientific bodies for providing

incentives and recognition to scientists for

brilliant scientific work and for identifying

national issues on which the governments may be

advised to initiate appropriate line of research.

However, the fact remains, that except for the

Academies in Communist and Socialist countries

which own laboratories and are regarded as

government institutions (for example, the

academies of Russia and China), most of the

Academies of the world are modeled along western

lines. Although these Academies do not have

laboratories of their own, they have one great

asset, namely, a reservoir of Fellows of the

highest distinction in different

- branches of science and technology. The Fellows

are recruited absolutely on scientific merit, and

they include professors of universities, research

scientists of national laboratories and eminent

scientists who have held responsible positions,

like vice-chancellorship of universities and

chairmanship of national scientific bodies etc.

Since these Fellows have been regarded as men of

high standing, they also possess the capability

to initiate projects in different educational and

research organizations of their country. It takes

quite sometime for people to attain high

scientific standard, and hence one may not notice

very many young people in the science Academies,

which, humorously are often termed, as old boys

club.

- However, some Academies have introduced Associate

Fellowship for comparatively younger scientists

who, after some time, may qualify for election to

full Fellowships. Very recently, the IAP (Inter

Academy Panel of Science) also discussed the role

of Science Academies, and it was pointed out by

the present author, that an Academy can make a

scientific impact on the society only when it

addresses the problems faced by the government

and the people of the country. Thus, apart from

recognizing scientific talents through the

awarding of Gold Medals and through the election

of Fellowships, Academies of Sciences can make a

great social impact by undertaking serious

studies of some burning scientific issues of a

society. One such issue is Science education and

Science promotion.

- The promotion of science is an issue which is

addressed by the Academies of the developed

countries as well. For example, the Royal Society

has always been organizing, at Christmas and at

other times, public lectures on scientific issues

which are beginning to change the present world.

These lectures are delivered in such a manner

that the interest of the public in science is

increased, and also, the science mindedness of

the society at large is enhanced. The promotion

of science can be further achieved by arranging

regular Radio and TV shows wherein experts can

explain the importance of some scientific ideas

that have relevance to the issues of life and

environment. And it has to be done in plain

parlance and without any use

- of technical jargons The promotion of science can

also be done by Science Academies through the

holding of science exhibitions and through the

promotion of science clubs in the country. Just

as literary circles observe the birth and death

anniversaries of poets and litterateurs, Science

Academies can do the same in respect of the birth

and death anniversaries of great scientific

figures, and on these occasions, the expert

Fellows may describe, to the members of the

public, the far reaching consequences of the

scientific discoveries made so far. The public

interest in science can also be increased through

the regular holding of Olympiads in subjects like

Mathematics, Physics, Chemistry etc. Here, the

idea would be to do some brain-hunting for

logical and analytical minds which could be

harnessed for developing scientific talents.

- Science education is, however, a different

matter. Science is basically doing things, not

just talking, and it is quite a challenge to give

some hands-on experiments to children through

which they can find out the working of nature

using very simple stuff that they may find around

them. For many developing countries, conducting

scientific experiments with imported equipment

may not be a sound economic proposition. Also it

may not be desirable to import equipment on all

occasions. In the early stages of science

education, the key point for students is to find

out how nature works. The emphasis, here, is not

on achieving high levels of accuracy of

scientific research as is the case in scientific

laboratories. It would be enough if only

- the laws of science are verified through easy

means at a functional level. To this end, the

Bangladesh Academy of Sciences has already formed

a task-force for identifying locally indigenous

materials for performing the conventional science

experiments at the school level without importing

scientific equipment from outside. This subject

of creating interest in science education through

interesting and simple scientific experiments is

a matter that could be tackled by almost all

Science Academies of the developing world in

Asia, particularly in those countries where

funding is a major problem.

- Since Mathematics is the language of nature, it

is also a challenging matter to increase interest

in the learning of Mathematics through life and

environment-related phenomena. Again, the Science

Academies can initiate innovative thinking on the

part of scholars for increasing interest in

Science and Mathematics education. In what

follows in this paper, at attempt has been made

to reflect some innovative thinking for

increasing such interest. Academies of Sciences

may consider the modus operandi outlined in this

paper for teaching Science and Mathematics in a

delightful manner and encourage the teaching

community to adopt these and similar techniques.

- 2. Creating interest in Mathematics and Science

Education - 2.1 Mathematics

- One of the ways of creating interest in

mathematics education is through generating

interest in geometry. Incidentally, the secrets

of all life forms are also embedded in the

tiniest of spaces in the double helical

geometrical structure of the hereditary blue

print of life, the Master Molecule DNA. The

interesting thing about geometry is that the

teaching of geometry is not costly at all. The

simple geometrical models that one needs can be

constructed easily with the locally available

materials. This session is to address hands-on

projects also. What better hands-on projects in

geometry could be than to ask the school children

to play with either an ice-cream cone or a

cone made with clay and an ordinary blade and

then to cut several sections of the cone.

- We talk of conic sections a point, a straight

line, a circle, a parabola, a hyperbola are all

examples of conic sections whose mathematical

equations are taught at various levels at schools

and colleges. But very few teachers really bother

to ask the students to make cones of clay the

apex of the cone is ideally located at a point.

One could draw a straight line at any point of

the surface. One could cut a section parallel to

the base and get a circle. If this cut is done a

little obliquely, an ellipse will be obtained.

Similarly one can get a parabola and a hyperbola

when one makes sections, which touch the base.

This is fun and delight, which can be realized

even while one is drinking from a glass of water.

By tilting the glass one can look at the

- top of the tilted surface, which would now appear

to be elliptical. With further tilt, the ellipse

is always there but this time is slightly more

elongated. And still on further tilt, the ellipse

would grow further narrower and narrower finally

the ellipse would degenerate into a pair of

straight lines. Mathematically, this is realized

by noting that the form of the ellipse is given

by the equation

- where a and b are the lengths of the major and

minor axes. The major axis a is very large when

the ellipse is highly thin or drawn out. Then

and one gets

or y2 b2, or . Thus one notices two lines with

y b and y -b above and below the axis of the

ellipse, respectively.

- This is again fun and one can see mathematics in

action. A point that should be highlighted by

teachers is that it is not only humans that make

use of geometry the other lower forms of life

find geometry as very essential to their

existence. An example may make this point clear.

- Imagine a rectangular room in which a wasp is

sitting at the center of one wall. Exactly on the

opposite point is sitting a fly. Commonsense

dictates that if the wasp has to prey on the fly,

it has to take the shortest route which could be

down, straight and up or up, straight and down or

side ways, side ways and sideways on both sides

in an Euclidean fashion.

- In practice, the wasp does not follow the

Euclidean Geometry it follows a path, which is

curved and touches four walls including the roof.

It can be verified by drawing the room on a

reasonable scale that this curved path is

actually smaller than the Euclidean routes

described. This is the geodesic of the wasp. - The idea of a wasp following geodesic may sound

strange but nature is stranger than fiction. An

aspect of geometry, which may fascinate young

minds, is the running of parallel and

anti-parallel helices in DNA, and the way in

which the DNA codes for all characteristics of

life in a tiny volume showing that the geometry

of life is more fascinating than that one

observes externally.

- Again, through a discourse of geometry and by

having reference to the shapes and sizes of

biological objects (there are thirty million life

forms in nature and we have studied only five

million so far), one comes across a stupendous

variety in the geometry of shapes of these forms

and one may wonder whether this stupendous

variety is really necessary. Shakespeare in

Julius Caesar (act 4, scene 3) mentioned long

ago. and nature must obey necessity. - Many things can be obtained further from this

statement when one studies the shapes of plants

and animals in different areas of the world.

- The thorny spikes of plants in desert places

remind one that the plants cannot afford to loose

water so the surface area is minimized and

nature must obey necessity. In this connection

students may be reminded of the Fibonacci

Numbers 0, 1, 1, 2, 3, 5, 8, 13. - If one looks at the geometrical structure of

sunflowers and pineapples, the proportions in

which the different petals and edges are

rearranged are in a Fibonacci fashion. A similar

structure can be observed if one studies the

patterns in nature, which give a wonderful

illustration of bionics.

- One may ask if there are any mathematical

relations governing growth and form. A straight

answer may be difficult to give. As Darcy

Thompson pointed out in his book titled On Forms

and Shapes, that in case of fishes, the shape of

one can be related to that of another by

mathematical transformation. If a little oceanic

fish by the name of Argyropelecus olfersi is

placed on a Cartesian paper and if its outline is

transferred to a system of oblique coordinates

whose axes are inclined at an angle of 700, then

we get the mathematical figure of a fish which

actually represents a simple shear of the first

fish. But it is indeed fascinating to note that

such a fish by the name of sternoplys diaphana

actually exists in nature. No wonder Dirac, the

celebrated

- theoretical physicist of all times pointed out

that God is the greatest mathematician. The

humans have discovered through the discovery of

force laws and the way numbers work in nature

that without the use of mathematics, life forms

would find it difficult to survive. - If one looks at the Bawa bird and looks at the

way its nest is prepared, one is forced to

believe that it challenges the work of a modern

architect. Its complicated, light and can endure

severe tornadoes. The birds do it by instinct.

Men devise the utility of geometry through

reasoning. In this connection one may be reminded

of the discovery of Fractals.

- Benoit Mandel coined the word Fractal in 1975

from Latin word Fractus which describes broken up

and irregular stone. Fractals are geometrical

shapes that contrary to those of Euclid are not

regular at all. They are irregular all over and

the same degree of irregularity exists in all

scales. A fractal object looks the same when

examined from far away and nearby. The difference

between classical and fractal geometry lies in

their opposed notion of dimension. In standard

geometry, dimensions come only in whole numbers

a straight line has dimension 1, a plane has

dimension 2, a solid has dimension 3.

- But fractals as they have fragmented, broken

edges also have fractional dimensions. Strange

twilight zones have dimensions of 1.67, 2.60 and

log(2e) 1. One might think dimensions might

have to be whole numbers, line is a line and the

surface is a surface. But a Hilbert curve can

result by progressively dividing a square into

smaller squares and connecting the centers with a

continuous line. After a few reiterations, the

line formed by the centers approaches two

dimensional surface even though the line doesnt

close back upon itself. Its not a true bounded

plane. A fractal can be seen as a visual

representation of a simple numerical function

that has been reiterated, repeated again and

again. The Mandel Brot set as explained by

- him is a set of complex numbers, which have the

property that you make a certain operation, take

the square. You take a number Z, you take the

square of Z and add C. Then you square the result

you check to see whether you have gone outside

circle of radius 2 and you plot this on a graph.

As you keep going, the set becomes drawn with

great and greater detail. But all you are doing

is multiplying something by itself and adding

itself that is Z2 C. Everything squared C

everything squared C It may be difficult for a

teacher to teach the concept of fractional

geometry but it is quite easy to point out that

nature uses a language namely fractional

geometry to produce many of its products. The

fractals can be found everywhere in nature and

- Mandel Brot has produced an explanation which,

when graphed by the computer, mimics the fractal

structure of natural phenomena as diverse as

trees, river, human vascular systems, clouds,

coast lines, mammalian brain form etc.

Fractals, Mandel Brot said are the very

substance of our flesh. - John Milner of the Institute of advance studies

printed out that, fractal may give us a more

realistic human lung system than conventional

geometry does. Think of the very fine blood

vessels and air channels inter connecting with

each other in a complicated pattern. This does

not make any sense at all from the point of view

of classical geometry, where you study smooth,

differentiable objects, but the lung structure

can be described very fruitfully as a type

fractal set.

- Cauliflower A natural fractal
- Mathematics is seen by many as a very dry subject

in the world of art and music. But little do

people realize that the question of beauty in all

artwork is intricately related to the concept of

symmetry, which results from a special branch of

mathematics dealing with Group Theory.

- Hermann Weyl in his book on symmetry1 explains

that symmetry is used in every day language in

two meanings. One, geometrical symmetry meaning

something well proportioned, well balanced and

symmetry denotes that sort of concordance of

several parts by which they integrate into a

whole. Beauty is bound up with symmetry. Without

any formal lessons about symmetry the modern

artist uses different kinds of symmetry in his

artwork. For example, bilateral symmetry is so

conspicuous in the structure of higher animals,

specially the human system. In fact, if one

thinks about a vertical plane through the middle

of the nose and if one knows the structure of the

face on one side of the plane, that on the other

can immediately

- be reconstructed. The other forms of symmetry,

which the artist exploits unknowingly, are

translation symmetry and rotational symmetry the

idea of translation symmetry is simply that if an

object has translation symmetry then by merely

shifting it laterally, one would not know at all

about the shift. This would be true of infinitely

large wallpaper with designs in it. If the

wallpaper is really long enough, by shifting the

wallpaper the design would not be altered. In the

case of a wallpaper of limited length this would

not hold because of the special marking of the

designs at the two ends of the wall.

- The spherical symmetry which has been a very

favorite concept for artists of all times simply

means that if one has a perfectly spherical ball

and it has been rotated through any diameter of

the sphere then it is virtually impossible to

know whether a sphere has at all been rotated or

not. Thus, symmetries are also inherent in the

laws of the small, which are dealt with in

Quantum Mechanics.

- There are many other kinds of symmetries that can

be visualized in the structure of different

shells, snow flakes, leaves etc group theory

which enables one to understand the symmetries of

nature on both large and small scales can be

taught in an abstract fashion alright but it can

also be taught with interesting reference to life

forms around us. Starfishes which attract

tourists on the beaches are all examples which

can be shown as realizations of certain kinds of

Group Theoretic Structures.

- So far we have referred to the application

aspects of mathematics. But the aspect of

mathematics that must not be forgotten is its

appeal to logic and analyticity. Mathematics is

not only doing sums and this is where the

students are bogged down. Mathematics enables one

to acquire an analytical frame of mind and to

argue logically. It has been found that

mathematically minded analysts should be the best

expositors of logic no matter where that logic

holds. No wonder politicians who, in general,

have no mathematical background cannot reason out

on many occasions and as a result take recourse

to emotional appeal of the sort used by Mark

Antonio in Julius Caesar. The world would be a

much better place to live in if the logic of

- mathematics found its expression in public

dealings also. Many often view mathematics as

brainteasers but one does not realize that the

logic inherent in the brainteasers is actually

the logic that drives the electronic circuits and

computer network. The logic is simply of FALSE

and TRUTH. Here one may be reminded of one simple

brain teaser a man proceeds to a city A and

while driving to that city he comes to a

roundabout in which he has either to take a right

or left turn to that city. Unfortunately the road

sign has been blown off by the wind. He could ask

the petrol station on the left or on the right

and find out whether he has to turn to left or

right. He has been advised that the people on one

side always speak the truth and

- those on the other side tell lie. Now, how does

he find out about the right direction by posing

one question to people there on either side of

the road? We all know the right question should

be which way the people on the other side of the

road would point me to the city A? Obviously, he

has to take the opposite of the answer. Now, in

this very example, one is dealing with logic and

it is logic that is at the heart of operation of

modern electronic circuitry. Many tend to think

that people having good commonsense should not

have problems in comprehending how mathematics

works. Although there is quite some truth in

this, the fact remains that mathematics often

defeats common sense. An example could make this

point clear. Consider the

- circumference of the earth, which is

approximately twenty five thousand miles. Now, a

student may be asked the following question if

you take a string which is larger than the

circumference of the earth only by 25 feet and

make a concentric circle around the circumference

of the earth, there will be a gap between the two

concentric circles. Now, could an orange pass

through this gap? Common sense says that it would

be almost impossible to do so. The common

thinking is that the extra 25 feet length of the

second circle concentric to the earth circle will

be so distributed that there would hardly be any

gap for a pea to pass through. Mathematics says

otherwise. Let ?r be the gap between the two

concentric circles. And if r and r ?r be the

two radii of the two concentric circles, then

- Thus five 9 inches footballs could be passed

through the said gap! Mathematics is not always

commonsense.

- The language of nature is basically mathematical

and logic is the kingpin of mathematics. The

logic of mathematics can be entertaining also. An

interesting example can be the following. A

person A meets his old college friend B at a

market place after a long time. A asks B, I

gather that you have married do you have

children? B replied Yes, I have 3 children.

What are their ages, A asked. B said, We were

both students of mathematics so, you have to

figure out the ages, yourself I shall of course,

give you some tips. The first tip B gives to A

is the product of the three ages is thirty six.

That is not enough and you know it also, said A.

B now gives a second tip, the sum of their ages

is the roll number you had in

- your college. A now ponders for a moment and

says that something else is required. Then B

gives the last tip, today is my eldest sons

birthday, I am going to by him some musical

equipment. A now immediately figures out the

ages of the three children without any further

delay. But how? The reader would do well to

determine the ages and find out that the logic is

very entertaining indeed! - The greatest challenge of mathematics teachers is

to unfold to the students the language and the

logic of mathematics through fun and delight and

in ways directly comprehensible to the students.

In this age of computer technology, we are

talking of various types of software but there is

nothing like the pleasure of understanding

mathematics as the logical software behind the

working of nature.

- 2.2 Science

- During the last few decades, the development of

science and technology has been so rapid, that it

is becoming gradually difficult for a teacher to

cope with such developments. Should the teacher

be conversant with all the scientific development

and teach all of those? This may sound to be a

difficult question. But the answer is simple. The

teacher may want to know many thing but (s)he

should not attempt to teach the students

everything under the sun. (S)he should teach them

the very basics on which the whole edifice of

science hinges, e.g. the conservation laws of

nature, the least principles of nature namely the

principle of least path, the principle of least

energy, principle of least action, the symmetry

principles in science, the multi-disciplinary

nature of science etc.

- A science teacher should consider himself or

herself successful if (s)he has been able to make

his/her students ask the right question at the

right time. The principal goal of the science

teacher would be to generate a spirit of enquiry

in the minds of the students. Not all enquires

can be satisfied with words. Action is needed.

Science is not merely talking. Science is doing

things. But doing things for what? The answer is

for verifying how Nature works. And who should

do these things. Again, the answer is Yes for

students and No for teachers. In doing

scientific experiments, it must be ensured that

students are the key players and teachers are

passive watchers. Even for doing very simple

things, students need some equipment.

- And it is in respect of equipment that a sorry

state of affairs exists in the schools and

colleges of developing countries. True, equipment

costs money. The effort then should be to do the

same set of science experiments as is performed

in developed countries, but using local materials

in the students own environment. Experiments

thus designed, have to be innovative in nature

and must have the potential for attracting

students through elements of fun and delight. For

example, for the purposes of creation and of

sound in a media, tuning forks imported from

abroad may not be necessary in a rural setting a

mango seed with a little opening in it can act as

an excellent material for the vibration of air

and creation of sound two

- children can dive into a pond and while under

water at a distance from one another, one can

make a sound by clapping his hands and the other

can hear it these kinds of things are fun and

delight and make science easy and attractive.

Similarly, the demonstration of the working

principles of the flight of an aero plane or the

flight of a bird (which led to the idea of the

flight of an aero plane) can be made by holding a

sheet of paper before a running table fan. On the

curved sheet of paper (resembling the wings of

the plane), there is a net upward thrust which

keeps it upward thus the basic scientific

principle in the flight of the plane is simple

the rest is the matter of involved technologies.

- That water finds its own level is another

experiment that can be performed using local

pottery rather than imported glassware and the

students can have fun when they pour water into

the following pitchers having openings at

different heights.

Figure Two pitchers having openings at different

heights.

- The abovementioned simple principle namely water

finds its own level has profound applications in

the dredging of rivers. Dredging a river is of no

use unless a slope exists in the river bed --- a

point often missed out by administrators and

politicians. - Similarly the law of cooling can be verified by a

student who could put some boiling water in two

buckets, and in one of the buckets some water at

room temperature could be added to one of the

buckets. The student could then verify by

measuring the temperature of water in both

buckets and find out that the one that has high

temperature water is cooling faster. This is one

of the simplest hands-on projects that one can

think of.

- Another interesting hands-on science experiment

could be the measurement of Youngs Modulus, not

of a steel wire (which is one of the conventional

experiments in laboratories and does not greatly

ignite the imagination of students) but of the

biological material collagen tendon. This

experiment could demonstrate one of the

interesting examples of bio-physics and could

explain the mystery of lifting heavy weights with

the help of our muscles. The key point to note

here is that science is all around us in the form

of a wonderful interplay between living and inert

matter.

- UNESCO, quite sometime ago, listed some 700

science experiments2 which everyone can do in a

book titled 700 Science Experiments. Many of

these are very interesting no doubt. But the

performing of some of these experiments involves

a cultural shock. For example, in a certain

experiment, a student has been asked to use a

beer can. The fact is that not only many people

in developing countries do not drink beer, they

simply do not know what a beer can looks like.

The materials chosen in scientific experiments,

especially in the case of improvised ones, must

be familiar and available to the students.

- 3. Teaching Science and Mathematics in an

integrated and inter-disciplinary manner.

- During the last few decades, in all major

scientific developments, especially in the areas

of ICT (Information and Communication Technology)

and bio-technology including genetic engineering,

the interdisciplinary nature of science has been

brought out in a prominent way. The role of

physicists in unraveling the structures and

secrets of the DNA molecule, the role of

material scientists and of metallurgists in

devising special materials are becoming well

known. As explained earlier, even the symmetry

concepts of group theory including translational

invariance, reflection in variance, rotational

invariance and time reversal invariance are not

topics of interest to physicists and chemists but

also

- to artists who use some of these symmetries

(knowingly or unknowingly) in their art work, and

in their concepts of beauty. Thus, the

physicist teaching symmetry properties in the

laws of nature should draw the attention of

students to numerous fascinating examples of

these principles around their own life and

environment difficult things would look easy and

familiar. - Now that all eyes are on Biology and many

people very rightly say that the twenty first

century might very well belong to molecular

biology and all its ramifications, let me cite an

example involving physics, biology and

environment.

- In a Unesco sponsored workshop at Puna in 1986, I

made a documentary film titled The hand that

rocks the cradle rules the world in which I

tried to show that if a house has a mother having

a science background, then she could explain some

difficult concepts of physics, chemistry and

mathematics to her children in the cozy

environment of the garden, kitchen, drawing room

etc. In a scene in the film, a mother was calling

her son to breakfast as he had an examination to

take in the morning. The son came downstairs

running and as he touched some worm potatoes on

his plate on the dining table, he said Ma it

is very warm. The mother cut the potato with a

knife into four pieces and was fanning those.

- When the son returned home, the mother eagerly

asked him how was your exam? the son replied,

It was all right Ma, but there was an odd

question which I could not reply in the question

it was asked why is it that in winter, we curl

up our bodies while sleeping in bed, while in

summer, we stretch our hands and feet while

resting. The mother said you could not answer

only one question dont be upset about this.

Then I appeared in the film and explained that

the mother could have taught her son the answer

to this question at the breakfast table.

Figure A Sliced Potato

- As the mother sliced the potato into four pieces,

she was unknowingly but with a cultural practice,

generating more and more surfaces for the potato

to give out heat and cool down fast it is known

that the amount of heat an object exchanges with

its surroundings depends on the surface area of

the object. In winter, we curl up our bodies in

order to reduce the surface areas of body so that

we can remain warm. In summer, we maximize the

area, by stretching our arms and legs, so that we

lose more heat and keep cool.

- This simple principle of heat exchange is also

operative at the very root of different shapes

and sizes of biological objects. Polar bears

are large as they have smaller surface areas

compared to their volume whereas desert bears are

small having large surface areas compared to

their volumes. Their shapes and sizes are

commensurate with the environment they are in.

These matters of biology and biodiversity and of

thermodynamic principles in physics are

interconnected with each other these things

should be taught by the science teacher in an

interesting manner.

- An interesting example of the (interdisciplinary)

nature of science and mathematics can be cited

while teaching matrices. Most of the students

know a matrix as being an array of numbers and

also are familiar with the addition and

multiplication of matrices etc. But when asked to

cite some (from life or nature) applications of

matrices, many seem to be groping for examples.

That the bus conductor follows a matrix while

collecting bus fares is not known to many .Also,

the following energy conversion matrix could

prove to be of immense interest to

mathematicians, physicists as well as energy

planners. One matrix could speak a million words.

- Magnetohydrodynamics
- Table Energy Conversion Matrix
- A lot can be achieved in science education by

using Nature as Teacher.

- 4. Nature as Teacher

- It will take quite sometime before school

laboratories in developing countries are

thoroughly equipped for providing science

education to children. Should a science teacher

really wait for that time to come, or do his/her

utmost in teaching science with whatever little

resources (s)he has around himself/herself ?

Doing more with less needs an innovative mind

which could discover resources where there is

none. Nature is one such. Many of us observe

nature only casually, but fail to understand its

silent working and the language in which it

speaks. The purpose of the present proposal is to

stimulate science education by looking at several

examples in Nature.

- Coming to the theme of nature as a teacher, let

us take the example of ponds which abound in

almost all countries. A pond can be a very good

example of studying numerous flora and fauna. A

science teacher can take children to a pond and

ask them to study different phenomena that have

been occurring in the pond all through the day. A

child would simply be delighted to notice the

diving of the beautifully colored kingfisher into

the water off and on in order to catch some small

fishes. He would notice, that the diving of the

kingfisher is perfect, no doubt, but it doesnt

come out with the fish in its beak in every

attempt. If the kingfisher were really successful

in every attempt, all the fished of the pond

- would have disappeared. Thus, there is a check

and balance in nature which the student can learn

from experience. The same sort of experience can

also be obtained when one notices how the deer

and the tiger, both dwelling in the forest, can

live in a sort of ecological balance. The deer

jumps more than the tiger, and thats how it

escapes the tigers chase, but on certain

occasions, the deers head may get stuck in a

bush, to the advantage of the tiger. Coming back

to the pond, it would be quite thrilling for

children to watch how insects walk on the water

surface of the pond, using the property of

surface tension of water, a fact with which the

children would be familiar much later in their

educational

- endeavor. The months of June and July are the

months where monsoon comes with its welcome

showers. The dry hollows in the fields and the

countryside are filled-up, and still waters of

ponds and pools mirror hurrying clouds above and

pleasant grassy banks beside. Although the pond

may look ordinary, a child can discover a world

of wonders hidden in and around it. One could

notice frogs spawn in masses of grey jelly

floating on the warm water. Peer down into the

water one can see young tadpoles wriggling among

the weeds or clinging to leaves of plants with

their suckers. Water snails are also a pleasant

sight on the edge of the pond or on stems of

water plants. Unlike the land snail, a water

snail has a single pair of feelers with eyes

raised on swellings at the bottom of each

- feeler. The little round opening in the side is

the breathing hole. They come to the surface of

the water for a fresh supply of air. Young

snails, complete with tiny shells, hatch and

search for food among stones and plants of the

water world. They are useful in keeping the water

of the pond clean, for they devour all kinds of

rotting matter. One of the most interesting

objects to see in the pond, is the water-crabs.

The slightest movement sends them scurrying off

sideways to a hideout. One occasionally may

encounter a water snake swimming gracefully. It

lifts its head out of the water to look at people

as it swims past. One also can witness

pond-beetles, which are fierce and attacks

smaller creatures very savagely. It snaps up

tadpoles and other pond creatures in its

pincer-like jaws and sucks the juices from their

soft bodies. One of the curious creatures of the

- pond is the Pond Skate. This long-legged insect

glides on the water almost as if it were ice. It

is one of the many water-bugs that has a

beak-like mouth for sucking juices from the pond

insects on which it thrives. Then there are water

scorpions and the brilliant dragon-flies. The

pond also presents a lively picture of the best

known of all plants, namely, the water-lily. The

sacred lotus belongs to the same family of water

lily. A pond contains duckweed which grow rapidly

and covers the surface. During summer, it offers

a pleasant shape for water creatures exposed to

the glare of the strong sunlight. Ducks eat it

with relish, and that is how the weed gets its

name. A student can learn something even from the

water hyacinth in the pond. Now we know, that

water hyacinths can be a boon in disguise, rather

than a nuisance. If one third of every pond is

filled with water hyacinth, it keeps the water

soft and becomes beneficial for the fishes.

- All in all, the pond could serve as a good

example for the interactions of many living

organisms. All the organisms that dwell in the

pond may serve to give an illustration of

bio-diversity existing even in a limited area of

nature. Thus, before a student could learn about

bio-diversity by studying the various life forms

in Asia, Africa and Latin-America, a rural child

can have a very early scientific exposure to the

concept of bio-diversity, merely from a study of

the life forms that the village pond contains.

This study needs only a little bit of imagination

of a teacher, and learning science can then

become fun and pleasure for the young learners. - So far we have discussed the instructional

management of the sheep (the students) it would

be in order to say a few words about the

management of the shepherds (teachers)

- 5. From the management of the sheep to that of

the shepherds

- Tending sheep has been regarded as a holy job and

most of the Prophets who were given Divine

Messages were regarded basically as teachers

(Ustads) and were shepherds. The teachers of all

subjects in general, and of science and

mathematics in particular, must be accorded the

honor for meeting the challenges of the times.

They must also be given incentives. In this

connection, I am reminded of a book titled The

Man Who Counted authored by Malba Tahan3. In

this book which is a collection of mathematical

adventures, is given the legend of Beremiz Samir

who, coming from the village of Khoi in Persia,

was a shepherd and used to tend vast flocks of

sheep. For fear of losing lambs and therefore

being punished, he counted them several times a

day. He became

- so good in counting, that he could count all the

bees in a swarm and all the leaves in a tree.

Satisfied with his mathematical agility his

master granted him four months leave. During

this leave he showed wonderful feats to many, and

finally was offered the post of Vizier by Caliph

al-Mutasim of Baghdad. But Samir did not accept

the post. Science and Mathematics teachers do not

want to be Viziers but they at least want to be

paid reasonable salaries so that for purposes of

meeting the costs of living, they do not take up

many jobs and can remain faithful to one

profession only, namely teaching. In some of the

countries of Asia and presumably of other

continents, teachers salaries are very low, and

as a result they often do other jobs to the

detriment of their own profession. This practice

must be stopped.

- A recommendation that could be made in respect of

salaries of science and mathematics teachers is

that once a teacher is evaluated for his

qualification, experiences and teaching

potential, his salary could remain the same

whether he works in a school, college or

university. In other words, a teacher should be

judged by his intrinsic merit and not by the

place he is working in. Universities cannot

flourish if schools are neglected. We must

remember the saying The battle of Waterloo was

won in the playground of Eton.

- 6. Conclusion

- Science and mathematics are the essential tools

for the study of nature. While utmost care should

be taken to attract students to these basic

subjects through teaching in a delightful manner,

the teachers to be appointed must be selected

very judiciously. And once selected, his salary

structure must be logical. It would be a great

irony if teachers responsible for upholding the

logic of science and mathematics are themselves

not dealt with in a logical way. - Talking of logic which connects science with

mathematics, one might come forward and say

rather pessimistically what is the use of

teaching logic in the present day world where

force is prevailing over logic? In this

connection, I would like to narrate a story told

in the book of Malba Tahan

- A lion, a tiger and a jackal hunted a sheep, a

pig and a rabbit. The tiger was given the

responsibility by the lion of dividing the prey

amongst themselves. The tiger gave the tastiest

of the prey, the sheep, to the lion, kept the

dirty pig for himself and gave the miserable

rabbit to the jackal. The lion was very angry at

this division and said who has ever seen three

divided by three giving a result like that?

Raising his paw, the lion swiped the head of the

unsuspecting tiger so fiercely that he fell dead

a few feet away. The lion then gave the charge of

the division to the jackal who, having already

witnessed the tragedy of the tiger said to the

lion, the sheep is a feed worthy of a king, the

appetizing pig should be destined for your royal

plate. And the skittish rabbit with its large

ears is a savory bite for a king like you. The

lion praised the jackal and asked him how

- he learnt this kind of division of three by two

so perfectly! The jackal replied I learnt from

the tiger. In the mathematics of the strong, the

quotient is always clear while to the weak must

fall only the remainder. The ambitious jackal

felt that he could live in tranquility only as a

parasite, receiving only the leftovers from the

lions feast. But he was wrong. After two or

three weeks, the lion, angry and hungry, tired of

the jackals servility ended up killing him, just

as he had the tiger. Thus, the division of three

by two realized with no remainder could not save

the jackal. This story contains a moral lesson

adulators and politicians who move obediently in

the corridors of the powerful may gain something

in the beginning but in the end, they are always

punished. Therefore, there is no use in going

away from logic which is so inherent in science

and mathematics. The greater the number of people

who follow logic, the safer will be our earth to

live in.

- References
- 1 Symmetry by Herman Weyl, Princeton

University Press, Princeton, New Jersey, 1952 - 2 700 Science Experiments for everyone,

compiled by UNESCO, Doubleday and Company, Inc,

Garden City, New York, 1958. - 3 The Man who Counted by Malba Tahan, W.W.

Norton Company, USA, 1994.

- The End