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 vicechancellorship 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 taskforce 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
2
2
x
y


1
2
2
a
b
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
2
x
2
a
 0and one gets
2
y
2
b
1
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 D’arcy 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. It’s
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 doesn’t close back upon itself. It’s 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 symmetry[1] 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:
2 ( r  r )  2r  25 feet
2  r  25 feet
25
r 
 4 feet (Approx.)
2
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 son’s 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 Young’s 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 biophysics 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 experiments[2] 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; don’t 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.
ELECTROMAGNE
TIC
ELECTROMA
GNETIC
CHEMICAL
Photosynthesis
(plants)
Photochemistry
(photographic film)
NUCLEAR
Gamma-neutron
reactions
CHEMICAL
NUCLEAR
THERMAL
KINETIC
(MECHANICAL)
ELECTRICAL
GRAVITATIO
NAL
Chemiluminescen
ce
(fireflies)
source)
(A-bomb)
Thermal radiation
(hot iron)
Accelerating
charge
(cyclotron)
Phosphor
Electromagnetic
radiation
(TV transmitter
Electroluminesce
nce
Unknown
Radiation catalysis
(hydrazine plant)
lonization
(cloud chamber)
Boiling
(water/steam)
Dissociation
Dissociation by
radiolysis
Electrolysis
(production of
aluminium)
Battery charging
Unknown
Unknown
Unknown
Unknown
Unknown
Friction
(brake shoes)
Resistance
heating
(electric stove)
Unknown
Motors
Electrostriction
(sonar
transmitter)
Falling objects
Unknown
Be9+y→Be8+n
THERMAL
Solar absorber
(hot sidewalk)
Combustion
(fire)
Fission (fuel
element) Fusion
KINETIC
Radiometer
Solar Cell
Muscle
Radioactivity
(alpha particles)
(A-bomb)
Thermal expansion
(turbines) Internal
combustion
(engines)
ELECTRICAL
Photoelectricity
(light meter) Radio
antenna Solar cell
Fuel cell
Batteries
Nuclear battery
Thermoelectricity
Thermionics
Thermomagetism
Ferroelectricity
†
MHD
Conventional
generator
GRAVITATIO
NAL
Unknown
Unknown
Unknown
Unknown
Rising objects
(rockets)
Unknown
Unknown
†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 doesn’t 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 that’s how it escapes the tiger’s chase, but
on certain occasions, the deer’s 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 biodiversity 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 Tahan[3]. 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 lion’s feast. But he was wrong. After two or three
weeks, the lion, angry and hungry, tired of the jackal’s 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