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The Role of Science Academies in Science Education

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Title: The Role of Science Academies in Science Education


1
The Role of Science Academies in Science
Education and Teaching Science and Mathematics
in a Delightful Manner - Prof. Dr. M. Shamsher
Ali
2
  • 1. Introduction

3
  • 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

4
  • 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

5
  • 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

6
  • 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.

7
  • 1.1 The Role of Science Academies in Science
    Education and Science Promotion

8
  • 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

9
  • 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.

10
  • 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.

11
  • 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

12
  • 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.

13
  • 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

14
  • 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.

15
  • 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.

16
  • 2. Creating interest in Mathematics and Science
    Education
  • 2.1 Mathematics

17
  • 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.

18
  • 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

19
  • 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

20
  • 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.
21
  • 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.

22
  • 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.

23
  • 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.

24
  • 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.

25
  • 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.

26
  • 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

27
  • 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.

28
  • 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.

29
  • 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

30
  • 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

31
  • 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.

32
  • 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.

33
  • 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

34
  • 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.

35
  • 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.

36
  • 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.

37
  • 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

38
  • 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

39
  • 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

40
  • 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

41
  • Thus five 9 inches footballs could be passed
    through the said gap! Mathematics is not always
    commonsense.

42
  • 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

43
  • 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.

44
  • 2.2 Science

45
  • 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.

46
  • 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.

47
  • 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

48
  • 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.

49
  • 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.
50
  • 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.

51
  • 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

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  • 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
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