The Role of Science Academies in Science Education

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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
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• 1. Introduction

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• 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

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• 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

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• 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

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• 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.

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• 1.1 The Role of Science Academies in Science
  Education and Science Promotion

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• 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

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• 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.

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• 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.

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• 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

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• 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.

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• 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

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• 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.

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• 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.

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• 2. Creating interest in Mathematics and Science
  Education
• 2.1 Mathematics

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• 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.

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• 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

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• 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

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• 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.
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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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• 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

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• 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.

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• 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.

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• 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

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• 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

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• 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.

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• 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.

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• 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

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• 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.

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• 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.

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• 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.

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• 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

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• 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

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• 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

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• 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

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• Thus five 9 inches footballs could be passed
  through the said gap! Mathematics is not always
  commonsense.

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• 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

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• 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.

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• 2.2 Science

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• 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.

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• 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.

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• 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

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• 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.

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• 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.
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• 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.

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• 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.

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• 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.

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• 3. Teaching Science and Mathematics in an
  integrated and inter-disciplinary manner.

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• 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

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• 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.

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• 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.

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• 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.

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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.

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• 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.

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• 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.

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• Magnetohydrodynamics
• Table Energy Conversion Matrix
• A lot can be achieved in science education by
  using Nature as Teacher.

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• 4. Nature as Teacher

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• 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.

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• 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

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• 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

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• 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

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• 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

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• 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.

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• 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)

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• 5. From the management of the sheep to that of
  the shepherds

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• 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

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• 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.

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• 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.

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• 6. Conclusion

75

• 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

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• 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

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• 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.

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• 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.

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• The End