Ways and means of Ways and means of increasing interest in increasing interest in

Science Education in AsiaScience Education in Asia

Prof. Dr. M. Shamsher AliProf. Dr. M. Shamsher AliPresident, Bangladesh Academy of SciencesPresident, Bangladesh Academy of Sciences

andandVice-Chancellor, Southeast University, BangladeshVice-Chancellor, Southeast University, Bangladesh

1.Introduction: 1.Introduction:

Since mathematics is the language of science, I shall in Since mathematics is the language of science, I shall in this article include mathematics education as an integral this article include mathematics education as an integral part of science education.part of science education. That interest in science education has dwindled globally. That interest in science education has dwindled globally. There are many reasons for the lack of interest in There are many reasons for the lack of interest in science education. The responsibility for this does not lie science education. The responsibility for this does not lie merely with students; a major part of it lies with us, the merely with students; a major part of it lies with us, the teachers. Thus, it is the teachers who need to address teachers. Thus, it is the teachers who need to address the issues of creating interest in science particularly in the issues of creating interest in science particularly in the countries of Asia which can not import costly the countries of Asia which can not import costly equipment from outside but still has had one of the equipment from outside but still has had one of the finest traditions of producing rare geniuses in finest traditions of producing rare geniuses in mathematics and science. The question that I would like mathematics and science. The question that I would like deal with is how to increase the interest in science deal with is how to increase the interest in science education in Asia. education in Asia.

The ways and means that I would suggest would only be The ways and means that I would suggest would only be

indicative but not at all exhaustive.indicative but not at all exhaustive.

2. Ways and means of increasing interest in Science Education2. Ways and means of increasing interest in Science Education

Some of these ways and means are:Some of these ways and means are:

a) Observance of the birthdays of the luminaries of a) Observance of the birthdays of the luminaries of science: This practice is followed by people in Arts and science: This practice is followed by people in Arts and Humanities to create great public interest in the literary Humanities to create great public interest in the literary works of the past and the present through holding birth works of the past and the present through holding birth anniversaries of people who have attained great heights anniversaries of people who have attained great heights in Art and Literature. A similar example can be followed in Art and Literature. A similar example can be followed by scientists who could, for example, observe the by scientists who could, for example, observe the birthdays of Newton, Faraday, Pasteur, Einstein, Watson birthdays of Newton, Faraday, Pasteur, Einstein, Watson & Crick and many others through holding public lectures & Crick and many others through holding public lectures in easy parlance explaining how science has changed our in easy parlance explaining how science has changed our ways at looking at our own lives and the universe around ways at looking at our own lives and the universe around us. School and College children and also the members of us. School and College children and also the members of public would greatly benefit from these lectures which public would greatly benefit from these lectures which could be telecast for the nation. This brings us to the could be telecast for the nation. This brings us to the role of the media (TV, Radio & Internet) in promoting role of the media (TV, Radio & Internet) in promoting science education.science education.

b) Role of media in promoting science education: Today a b) Role of media in promoting science education: Today a large number of lectures prepared by grand masters of large number of lectures prepared by grand masters of science can be stored in CD’s and DVD’s for distribution science can be stored in CD’s and DVD’s for distribution to a wider section of the masses who otherwise would to a wider section of the masses who otherwise would not have been exposed to such materials. Since in all not have been exposed to such materials. Since in all countries of Asia the use of the Radio and Television and countries of Asia the use of the Radio and Television and also the internet has been gradually increasing, it is only also the internet has been gradually increasing, it is only imperative that Governments in Asia have a separate imperative that Governments in Asia have a separate Knowledge Network in which the explaining of science Knowledge Network in which the explaining of science for the betterment of life and environment could be done for the betterment of life and environment could be done in a very fruitful manner. The countries of Asia could also in a very fruitful manner. The countries of Asia could also exchange materials to be shared in the Knowledge exchange materials to be shared in the Knowledge Network; these materials could then be translated or Network; these materials could then be translated or dubbed in local language. Programmes prepared in dubbed in local language. Programmes prepared in English would have a wider circulation.English would have a wider circulation.

c) Science Exhibitions and Technology Parks as c) Science Exhibitions and Technology Parks as promoters of Science Education: All countries promoters of Science Education: All countries in Asia should give considerable emphasis of in Asia should give considerable emphasis of holding of science exhibition publicly so that holding of science exhibition publicly so that children can display their query based children can display their query based innovation and make the public more innovation and make the public more interested in science. At this point I reminded interested in science. At this point I reminded of Nobel Laureate Richard Ernst, who visited of Nobel Laureate Richard Ernst, who visited this country some time ago. He informed us this country some time ago. He informed us that even in Switzerland science camps are that even in Switzerland science camps are setup at prominent places in the city so as to setup at prominent places in the city so as to attract way farers to the science camps. If attract way farers to the science camps. If Switzerland can do this why can’t countries of Switzerland can do this why can’t countries of Asia do the same? Apart from science Asia do the same? Apart from science exhibition the setting up the technology parks exhibition the setting up the technology parks can also act as promoters of science and can also act as promoters of science and technology education. technology education.

We may enumerate a number of other ways of We may enumerate a number of other ways of creating interest in science education but the creating interest in science education but the real challenge in Asia is to produce a set a real challenge in Asia is to produce a set a teachers who can enkindle the fire of teachers who can enkindle the fire of imagination and enquiry in the minds of imagination and enquiry in the minds of children. Such teachers are not always born; children. Such teachers are not always born; they have to be trained. They may be given they have to be trained. They may be given some special pedagogical guidance. In what some special pedagogical guidance. In what follows, we would outline some follows, we would outline some multidisciplinary methods of creating interest multidisciplinary methods of creating interest in science and mathematics education which in science and mathematics education which would have an element of fun and delight in it would have an element of fun and delight in it and at the same time would be easy and and at the same time would be easy and relevant to life and environment. We start with relevant to life and environment. We start with mathematics education.mathematics education.

3. Interest in Mathematics Education3. Interest in Mathematics Education One of the ways of creating interest in mathematics education One of the ways of creating interest in mathematics education is through generating interest in geometry. Incidentally, the is through generating interest in geometry. Incidentally, the secrets of all life forms are also embedded in the tiniest of secrets of all life forms are also embedded in the tiniest of spaces in the double helical geometrical structure of the spaces in the double helical geometrical structure of the hereditary blue print of life, the Master Molecule DNA. The hereditary blue print of life, the Master Molecule DNA. The interesting thing about geometry is that the teaching of interesting thing about geometry is that the teaching of geometry is not costly at all. The simple geometrical models geometry is not costly at all. The simple geometrical models that one needs can be constructed easily with the locally that one needs can be constructed easily with the locally available materials. This session is to address hands-on available materials. This session is to address hands-on projects also. What better hands-on projects in geometry projects also. What better hands-on projects in geometry could be than to ask the school children to play with either an 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 ice-cream cone or a cone made with clay and an ordinary blade and then to cut several sections of the cone. We talk of conic and then to cut several sections of the cone. We talk of conic sections: a point, a straight line, a circle, a parabola, a sections: a point, a straight line, a circle, a parabola, a hyperbola are all examples of conic sections whose hyperbola are all examples of conic sections whose mathematical equations are taught at various levels at schools mathematical equations are taught at various levels at schools and colleges. and colleges.

But very few teachers really bother to ask the students to 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 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 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 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 circle. If this cut is done a little obliquely, an ellipse will be obtained. Similarly one can get a parabola and a hyperbola obtained. Similarly one can get a parabola and a hyperbola when one makes sections, which touch the base. This is fun when one makes sections, which touch the base. This is fun and delight, which can be realized even while one is drinking and delight, which can be realized even while one is drinking from a glass of water.from a glass of water.

By tilting the glass one can look at the top of the tilted By tilting the glass one can look at the top of the tilted surface, which would now appear to be elliptical. With further surface, which would now appear to be elliptical. With further tilt, the ellipse is always there but this time is slightly more tilt, the ellipse is always there but this time is slightly more elongated. And still on further tilt, the ellipse would grow elongated. And still on further tilt, the ellipse would grow further narrower and narrower: finally the ellipse would further narrower and narrower: finally the ellipse would degenerate into a pair of straight lines. Mathematically, this is degenerate into a pair of straight lines. Mathematically, this is realized by noting that the form of the ellipse is given by the realized by noting that the form of the ellipse is given by the equationequation

where where a a and and b b are the lengths of the major and minor axes. are the lengths of the major and minor axes. The major axis The major axis a a is very large when the ellipse is highly thin is very large when the ellipse is highly thin or or

drawn out. Then and one gets , or y2 = drawn out. Then and one gets , or y2 = b2, b2,

or y = ± b. Thus one notices two lines with y = +b and y = -b or y = ± b. Thus one notices two lines with y = +b and y = -b

above and below the axis of the ellipse, respectively.above and below the axis of the ellipse, respectively.

12

2

2

2

b

y

a

x

02

2

a

x1

2

2

b

y

This is again fun and one can see mathematics in action. A This is again fun and one can see mathematics in action. A point that should be highlighted by teachers is that it is not point that should be highlighted by teachers is that it is not only humans that make use of geometry; the other lower only humans that make use of geometry; the other lower forms of life find geometry as very essential to their existence. forms of life find geometry as very essential to their existence.

An example may make this point clear.An example may make this point clear.

Imagine a rectangular room in which a wasp is sitting at the 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. 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, Commonsense dictates that if the wasp has to prey on the fly, it has to take the shortest route which could be down, straight 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 and up or up, straight and down or side ways, side ways and

sideways on both sides in an Euclidean fashion.sideways on both sides in an Euclidean fashion.

In practice, the wasp does not follow the Euclidean Geometry: In practice, the wasp does not follow the Euclidean Geometry: it follows a path, which is curved and touches four walls it follows a path, which is curved and touches four walls including the roof. It can be verified by drawing the room on a including the roof. It can be verified by drawing the room on a reasonable scale that this curved path is actually smaller than reasonable scale that this curved path is actually smaller than the Euclidean routes described. This is the geodesic of the the Euclidean routes described. This is the geodesic of the wasp. wasp.

The idea of a wasp following geodesic may sound strange but The idea of a wasp following geodesic may sound strange but nature is stranger than fiction. An aspect of geometry, which nature is stranger than fiction. An aspect of geometry, which may fascinate young minds, is the running of parallel and anti-may fascinate young minds, is the running of parallel and anti-parallel helices in DNA, and the way in which the DNA codes parallel helices in DNA, and the way in which the DNA codes for all characteristics of life in a tiny volume showing that the for all characteristics of life in a tiny volume showing that the geometry of life is more fascinating than that one observes geometry of life is more fascinating than that one observes externally.externally.

Again, through a discourse of geometry and by having Again, through a discourse of geometry and by having reference to the shapes and sizes of biological objects (there reference to the shapes and sizes of biological objects (there are thirty million life forms in nature and we have studied only are thirty million life forms in nature and we have studied only five million so far), one comes across a stupendous variety in five million so far), one comes across a stupendous variety in the geometry of shapes of these forms and one may wonder the geometry of shapes of these forms and one may wonder whether this stupendous variety is really necessary. whether this stupendous variety is really necessary. Shakespeare in Julius Caesar (act 4, scene 3) mentioned long Shakespeare in Julius Caesar (act 4, scene 3) mentioned long ago. “…and nature must obey necessity”. ago. “…and nature must obey necessity”.

Many things can be obtained further from this statement when Many things can be obtained further from this statement when one studies the shapes of plants and animals in different areas one studies the shapes of plants and animals in different areas of the world. of the world.

The thorny spikes of plants in desert places remind one that The thorny spikes of plants in desert places remind one that the plants cannot afford to loose water; so the surface area is the plants cannot afford to loose water; so the surface area is minimized and nature must obey necessity. In this connection minimized and nature must obey necessity. In this connection students may be reminded of the “Fibonacci” Numbers 0, 1, 1, students may be reminded of the “Fibonacci” Numbers 0, 1, 1, 2, 3, 5, 8, 13….2, 3, 5, 8, 13….

If one looks at the geometrical structure of sunflowers and If one looks at the geometrical structure of sunflowers and pineapples, the proportions in which the different petals and pineapples, the proportions in which the different petals and edges are rearranged are in a Fibonacci fashion. A similar edges are rearranged are in a Fibonacci fashion. A similar structure can be observed if one studies the patterns in structure can be observed if one studies the patterns in nature, which give a wonderful illustration of bionics. nature, which give a wonderful illustration of bionics.

If one looks at the Bawa bird and looks at the way its nest is 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 prepared, one is forced to believe that it challenges the work of a modern architect. It’s complicated, light and can endure of a modern architect. It’s complicated, light and can endure severe tornadoes. The birds do it by instinct. Men devise the severe tornadoes. The birds do it by instinct. Men devise the utility of geometry through reasoning. In this connection one utility of geometry through reasoning. In this connection one

may be reminded of the discovery of Fractals.may be reminded of the discovery of Fractals.

Benoit Mandel coined the word Fractal in 1975 from Benoit Mandel coined the word Fractal in 1975 from Latin word Fractus which describes broken up and Latin word Fractus which describes broken up and irregular stone. Fractals are geometrical shapes irregular stone. Fractals are geometrical shapes that contrary to those of Euclid are not regular at that contrary to those of Euclid are not regular at all. They are irregular all over and the same degree all. They are irregular all over and the same degree of irregularity exists in all scales. A fractal object of irregularity exists in all scales. A fractal object looks the same when examined from far away and looks the same when examined from far away and nearby. The difference between classical and fractal nearby. The difference between classical and fractal geometry lies in their opposed notion of dimension. geometry lies in their opposed notion of dimension. In standard geometry, dimensions come only in In standard geometry, dimensions come only in whole numbers: a straight line has dimension 1, a whole numbers: a straight line has dimension 1, a

plane has dimension 2, a solid has dimension 3.plane has dimension 2, a solid has dimension 3.

But fractals as they have fragmented, broken edges also have But fractals as they have fragmented, broken edges also have fractional dimensions. Strange twilight zones have dimensions fractional dimensions. Strange twilight zones have dimensions of 1.67, 2.60 and log(2e) + 1. One might think 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 might have to be whole numbers, line is a line and the surface is a surface. But a Hilbert curve can result by progressively is a surface. But a Hilbert curve can result by progressively dividing a square into smaller squares and connecting the dividing a square into smaller squares and connecting the centers with a continuous line. After a few reiterations, the centers with a continuous line. After a few reiterations, the line formed by the centers approaches two dimensional line formed by the centers approaches two dimensional surface even though the line doesn’t close back upon itself. surface even though the line doesn’t close back upon itself. It’s not a true bounded plane. A fractal can be seen as a visual It’s not a true bounded plane. A fractal can be seen as a visual representation of a simple numerical function that has been representation of a simple numerical function that has been

reiterated, repeated again and again.reiterated, repeated again and again. “The Mandel Brot set” “The Mandel Brot set”

as explained by him is a set of complex numbers, which have as explained by him is a set of complex numbers, which have the property that you make a certain operation, take the the property that you make a certain operation, take the square. You take a number square. You take a number ZZ, you take the square of , you take the square of Z Z and add and add CC. .

Then you square the result you check to see whether you Then you square the result you check to see whether you have gone outside circle of radius 2 and you plot this on have gone outside circle of radius 2 and you plot this on a graph. As you keep going, the set becomes drawn with a graph. As you keep going, the set becomes drawn with great and greater detail. But all you are doing is great and greater detail. But all you are doing is multiplying something by itself and adding itself that is multiplying something by itself and adding itself that is Z2 + C. Everything squared +C; everything squared +C; It Z2 + C. Everything squared +C; everything squared +C; It may be difficult for a teacher to teach the concept of may be difficult for a teacher to teach the concept of fractional geometry but it is quite easy to point out that fractional geometry but it is quite easy to point out that nature uses a language namely “fractional geometry” to nature uses a language namely “fractional geometry” to produce many of its products. The fractals can be found produce many of its products. The fractals can be found everywhere in nature and Mandel Brot has produced an everywhere in nature and Mandel Brot has produced an explanation which, when graphed by the computer, explanation which, when graphed by the computer, mimics the fractal structure of natural phenomena as mimics the fractal structure of natural phenomena as diverse as trees, river, human vascular systems, clouds, diverse as trees, river, human vascular systems, clouds, coast lines, mammalian brain form etc. “Fractals”, coast lines, mammalian brain form etc. “Fractals”, Mandel Brot said “are the very substance of our flesh.”Mandel Brot said “are the very substance of our flesh.”

John Milner of the Institute of advance studies printed out John Milner of the Institute of advance studies printed out that, “fractal may give us a more realistic human lung system that, “fractal may give us a more realistic human lung system than conventional geometry does. Think of the very fine blood than conventional geometry does. Think of the very fine blood vessels and air channels inter connecting with each other in a vessels and air channels inter connecting with each other in a complicated pattern. This does not make any sense at all from complicated pattern. This does not make any sense at all from the point of view of classical geometry, where you study the point of view of classical geometry, where you study smooth, differentiable objects, but the lung structure can be smooth, differentiable objects, but the lung structure can be described very fruitfully as a type fractal set.”described very fruitfully as a type fractal set.”

Cauliflower – A natural fractalCauliflower – A natural fractal

Mathematics is seen by many as a very dry subject in the Mathematics is seen by many as a very dry subject in the world of art and music. But little do people realize that the world of art and music. But little do people realize that the question of beauty in all artwork is intricately related to the question of beauty in all artwork is intricately related to the concept of symmetry, which results from a special branch of concept of symmetry, which results from a special branch of

mathematics dealing with Group Theory.mathematics dealing with Group Theory.

Hermann Weyl in his book on symmetry explains that Hermann Weyl in his book on symmetry explains that symmetry is used in every day language in two meanings. One, symmetry is used in every day language in two meanings. One, geometrical symmetry meaning something well proportioned, geometrical symmetry meaning something well proportioned, well balanced and symmetry denotes that sort of concordance well balanced and symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty of several parts by which they integrate into a whole. Beauty is bound up with symmetry. Without any formal lessons about is bound up with symmetry. Without any formal lessons about symmetry the modern artist uses different kinds of symmetry symmetry the modern artist uses different kinds of symmetry in his artwork. For example, bilateral symmetry is so in his artwork. For example, bilateral symmetry is so conspicuous in the structure of higher animals, specially the conspicuous in the structure of higher animals, specially the

human system.human system.

In fact, if one thinks about a vertical plane through the middle 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 of the nose and if one knows the structure of the face on one side of the plane, that on the other can immediately be side of the plane, that on the other can immediately be reconstructed. The other forms of symmetry, which the artist reconstructed. The other forms of symmetry, which the artist exploits unknowingly, are translation symmetry and rotational exploits unknowingly, are translation symmetry and rotational symmetry: the idea of translation symmetry is simply that if symmetry: the idea of translation symmetry is simply that if an object has translation symmetry then by merely shifting it an object has translation symmetry then by merely shifting it laterally, one would not know at all about the shift. This would laterally, one would not know at all about the shift. This would be true of infinitely large wallpaper with designs in it. If the be true of infinitely large wallpaper with designs in it. If the wallpaper is really long enough, by shifting the wallpaper the wallpaper is really long enough, by shifting the wallpaper the design would not be altered. In the case of a wallpaper of design would not be altered. In the case of a wallpaper of limited length this would not hold because of the special limited length this would not hold because of the special

marking of the designs at the two ends of the wall.marking of the designs at the two ends of the wall.

The spherical symmetry which has been a very favorite The spherical symmetry which has been a very favorite concept for artists of all times simply means that if one concept for artists of all times simply means that if one has a perfectly spherical ball and it has been rotated has a perfectly spherical ball and it has been rotated through any diameter of the sphere then it is virtually through any diameter of the sphere then it is virtually impossible to know whether a sphere has at all been impossible to know whether a sphere has at all been rotated or not. Thus, symmetries are also inherent in the rotated or not. Thus, symmetries are also inherent in the laws of the small, which are dealt with in Quantum laws of the small, which are dealt with in Quantum Mechanics.Mechanics. There are many other kinds of symmetries that can be There are many other kinds of symmetries that can be visualized in the structure of different shells, snow visualized in the structure of different shells, snow flakes, leaves etc; group theory which enables one to flakes, leaves etc; group theory which enables one to understand the symmetries of nature on both large and understand the symmetries of nature on both large and small scales can be taught in an abstract fashion alright small scales can be taught in an abstract fashion alright but it can also be taught with interesting reference to but it can also be taught with interesting reference to life forms around us. Starfishes which attract tourists on life forms around us. Starfishes which attract tourists on the beaches are all examples which can be shown as the beaches are all examples which can be shown as realizations of certain kinds of Group Theoretic realizations of certain kinds of Group Theoretic Structures.Structures.

So far we have referred to the application aspects of So far we have referred to the application aspects of mathematics. But the aspect of mathematics that must not be mathematics. But the aspect of mathematics that must not be forgotten is its appeal to logic and analyticity. Mathematics is forgotten is its appeal to logic and analyticity. Mathematics is not only doing sums and this is where the students are bogged not only doing sums and this is where the students are bogged down. Mathematics enables one to acquire an analytical frame down. Mathematics enables one to acquire an analytical frame of mind and to argue logically. It has been found that of mind and to argue logically. It has been found that mathematically minded analysts should be the best expositors mathematically minded analysts should be the best expositors of logic no matter where that logic holds. No wonder of logic no matter where that logic holds. No wonder politicians who, in general, have no mathematical background politicians who, in general, have no mathematical background cannot reason out on many occasions and as a result take cannot reason out on many occasions and as a result take recourse to emotional appeal of the sort used by Mark Antonio recourse to emotional appeal of the sort used by Mark Antonio in “Julius Caesar”. The world would be a much better place to in “Julius Caesar”. The world would be a much better place to live in if the logic of mathematics found its expression in live in if the logic of mathematics found its expression in public dealings also. Many often view mathematics as public dealings also. Many often view mathematics as brainteasers but one does not realize that the logic inherent in brainteasers but one does not realize that the logic inherent in the brainteasers is actually the logic that drives the electronic the brainteasers is actually the logic that drives the electronic circuits and computer network. The logic is simply of FALSE circuits and computer network. The logic is simply of FALSE and TRUTH. Here one may be reminded of one simple brain and TRUTH. Here one may be reminded of one simple brain teaser – a man proceeds to a city A and while driving to that 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 city he comes to a roundabout in which he has either to take a right or left turn to that city. right or left turn to that city.

Unfortunately the road sign has been blown off by the wind. 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 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 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 advised that the people on one side always speak the truth and those on the other side tell lie. Now, how does he find out and those on the other side tell lie. Now, how does he find out about the right direction by posing one question to people about the right direction by posing one question to people there on either side of the road? We all know the right there on either side of the road? We all know the right question should be “which way the people on the other side of 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 the road would point me to the city A”? Obviously, he has to take the opposite of the answer. Now, in this very example, 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 one is dealing with logic and it is logic that is at the heart of operation of modern electronic circuitry. Many tend to think operation of modern electronic circuitry. Many tend to think that people having good commonsense should not have that people having good commonsense should not have problems in comprehending how mathematics works. Although problems in comprehending how mathematics works. Although there is quite some truth in this, the fact remains that there is quite some truth in this, the fact remains that mathematics often defeats common sense. An example could mathematics often defeats common sense. An example could make this point clear. Consider the circumference of the earth, make this point clear. Consider the circumference of the earth, which is approximately twenty five thousand miles. which is approximately twenty five thousand miles.

Now, a student may be asked the following question: if you Now, a student may be asked the following question: if you take a string which is larger than the circumference of the take a string which is larger than the circumference of the earth only by 25 feet and make a concentric circle around the earth only by 25 feet and make a concentric circle around the circumference of the earth, there will be a gap between the circumference of the earth, there will be a gap between the two concentric circles. Now, could an orange pass through this two concentric circles. Now, could an orange pass through this gap? Common sense says that it would be almost impossible to gap? Common sense says that it would be almost impossible to do so. The common thinking is that the extra 25 feet length of do so. The common thinking is that the extra 25 feet length of the second circle concentric to the earth circle will be so the second circle concentric to the earth circle will be so distributed that there would hardly be any gap for a ‘pea’ to distributed that there would hardly be any gap for a ‘pea’ to pass through. Mathematics says otherwise. Let ∆pass through. Mathematics says otherwise. Let ∆r r be the gap be the gap between the two concentric circles. And if between the two concentric circles. And if r r and and r r + ∆+ ∆r r be the be the

two radii of the two concentric circles,two radii of the two concentric circles,

r

Then,Then,

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

The language of nature is basically mathematical and logic is The language of nature is basically mathematical and logic is the kingpin of mathematics. The logic of mathematics can be the kingpin of mathematics. The logic of mathematics can be entertaining also. An interesting example can be the following. entertaining also. An interesting example can be the following. A person A person A A meets his old college friend meets his old college friend B B at a market place at a market place after a long time. after a long time. AA asks asks B, B, “I gather that you have married; “I gather that you have married; do you have children?” do you have children?” B B replied: “Yes, I have 3 children.” replied: “Yes, I have 3 children.” “What are their ages”, “What are their ages”, A A asked. asked. B B said, “We were both said, “We were both students of mathematics; so, you have to figure out the ages, students of mathematics; so, you have to figure out the ages, yourself; I shall of course, give you some tips.”yourself; I shall of course, give you some tips.”

(Approx.) 42

25

25 2

252)( 2

feetr

feetr

feetrrr

The first tip The first tip B B gives to gives to A A is “the product of the three ages is is “the product of the three ages is thirty six”. That is not enough and you know it also, said thirty six”. That is not enough and you know it also, said AA. . BB now gives a second tip, “the sum of their ages is the roll now gives a second tip, “the sum of their ages is the roll number you had in your college”. number you had in your college”. AA now ponders for a moment now ponders for a moment and says that something else is required. Then and says that something else is required. Then B B gives the last gives the last tip, “today is my eldest son’s birthday, I am going to by him tip, “today is my eldest son’s birthday, I am going to by him some musical equipment.” some musical equipment.” A A now immediately figures out the now immediately figures out the ages of the three children without any further delay. But how? ages of the three children without any further delay. But how? The reader would do well to determine the ages and find out The reader would do well to determine the ages and find out that the logic is very entertaining indeed!that the logic is very entertaining indeed!

The greatest challenge of mathematics teachers is to unfold to The greatest challenge of mathematics teachers is to unfold to the students the language and the logic of mathematics the students the language and the logic of mathematics through fun and delight and in ways directly comprehensible through fun and delight and in ways directly comprehensible to the students. In this age of computer technology, we are to the students. In this age of computer technology, we are talking of various types of software but there is nothing like talking of various types of software but there is nothing like the pleasure of understanding mathematics as the logical the pleasure of understanding mathematics as the logical software behind the working of nature. Fishes provide an software behind the working of nature. Fishes provide an interesting example of the geometrical programming of interesting example of the geometrical programming of nature.nature.

FishesFishes

One may ask if there are any mathematical One may ask if there are any mathematical relations governing growth and form. A relations governing growth and form. A straight answer may be difficult to give. As straight answer may be difficult to give. As D’arcy Thompson pointed out in his book titled D’arcy Thompson pointed out in his book titled “On Forms and Shapes”, that in case of fishes, “On Forms and Shapes”, that in case of fishes, the shape of one can be related to that of the shape of one can be related to that of another by mathematical transformation. If a another by mathematical transformation. If a little oceanic fish by the name of Argyropelecus little oceanic fish by the name of Argyropelecus olfersi is placed on a Cartesian paper and if its olfersi is placed on a Cartesian paper and if its outline is transferred to a system of oblique outline is transferred to a system of oblique coordinates whose axes are inclined at an coordinates whose axes are inclined at an angle of 700, then we get the mathematical angle of 700, then we get the mathematical figure of a fish which actually represents a figure of a fish which actually represents a simple shear of the first fish.simple shear of the first fish.

But it is indeed fascinating to note that such a fish by the But it is indeed fascinating to note that such a fish by the name of sternoplys diaphana actually exists in nature. No name of sternoplys diaphana actually exists in nature. No wonder Dirac, the celebrated theoretical physicist of all wonder Dirac, the celebrated theoretical physicist of all times pointed out that God is the greatest mathematician. times pointed out that God is the greatest mathematician. The humans have discovered through the discovery of The humans have discovered through the discovery of force laws and the way numbers work in nature that force laws and the way numbers work in nature that without the use of mathematics, life forms would find it without the use of mathematics, life forms would find it difficult to survive.difficult to survive.

So far we have considered the ways and means of So far we have considered the ways and means of teaching mathematics, the language of science in an teaching mathematics, the language of science in an interesting manner. Let us now turn to interest in science interesting manner. Let us now turn to interest in science education.education.

4. Interest in Science Education4. Interest in Science Education

During the last few decades, the development of science During the last few decades, the development of science and technology has been so rapid, that it is becoming and technology has been so rapid, that it is becoming gradually difficult for a teacher to cope with such gradually difficult for a teacher to cope with such developments. Should the teacher be conversant with all developments. Should the teacher be conversant with all the scientific development and teach all of those? This the scientific development and teach all of those? This may sound to be a difficult question. But the answer is may sound to be a difficult question. But the answer is simple. The teacher may want to know many thing but simple. The teacher may want to know many thing but (s)he should not attempt to teach the students everything (s)he should not attempt to teach the students everything under the sun. (S)he should teach them the very basics under the sun. (S)he should teach them the very basics on which the whole edifice of science hinges, e.g. the on which the whole edifice of science hinges, e.g. the conservation laws of nature, the least principles of nature conservation laws of nature, the least principles of nature namely the principle of least path, the principle of least namely the principle of least path, the principle of least energy, principle of least action, the symmetry principles energy, principle of least action, the symmetry principles

in science, the multi-disciplinary nature of science etc.in science, the multi-disciplinary nature of science etc.

A science teacher should consider himself or herself A science teacher should consider himself or herself successful if (s)he has been able to make his/her students successful if (s)he has been able to make his/her students ask the right question at the right time. The principal goal ask the right question at the right time. The principal goal of the science teacher would be to generate a spirit of of the science teacher would be to generate a spirit of enquiry in the minds of the students. Not all enquires can enquiry in the minds of the students. Not all enquires can be satisfied with words. Action is needed. Science is not be satisfied with words. Action is needed. Science is not merely talking. Science is “doing” things. But doing merely talking. Science is “doing” things. But doing things for what? The answer is: for verifying how Nature things for what? The answer is: for verifying how Nature works. And who should “do” these things. Again, the works. And who should “do” these things. Again, the answer is “Yes” for students and “No” for teachers. In answer is “Yes” for students and “No” for teachers. In doing scientific experiments, it must be ensured that doing scientific experiments, it must be ensured that students are the key players and teachers are passive students are the key players and teachers are passive watchers. Even for doing very simple things, students watchers. Even for doing very simple things, students need some equipment. And it is in respect of equipment need some equipment. And it is in respect of equipment that a “sorry state” of affairs exists in the schools and that a “sorry state” of affairs exists in the schools and colleges of developing countries. True, equipment costs colleges of developing countries. True, equipment costs money. money.

The effort then should be to do the same set of science The effort then should be to do the same set of science experiments as is performed in developed countries, but experiments as is performed in developed countries, but using local materials in the students’ own environment. using local materials in the students’ own environment. Experiments thus designed, have to be innovative in nature Experiments thus designed, have to be innovative in nature and must have the potential for attracting students through and must have the potential for attracting students through elements of fun and delight. For example, for the purposes of elements of fun and delight. For example, for the purposes of creation and of sound in a media, tuning forks imported from creation and of sound in a media, tuning forks imported from abroad may not be necessary in a rural setting; a mango seed 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 with a little opening in it can act as an excellent material for the vibration of air and creation of sound; two children can the vibration of air and creation of sound; two children can dive into a pond and while under water at a distance from one 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 another, one can make a sound by clapping his hands and the other can hear it; these kinds of things are fun and delight other can hear it; these kinds of things are fun and delight and make science easy and attractive. Similarly, the and make science easy and attractive. Similarly, the demonstration of the working principles of the flight of an 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 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 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 before a running table fan. On the curved sheet of paper (resembling the wings of the plane), there is a net paper (resembling the wings of the plane), there is a net upward thrust which keeps it upward; thus the basic scientific upward thrust which keeps it upward; thus the basic scientific principle in the flight of the plane is simple; the rest is the principle in the flight of the plane is simple; the rest is the matter of involved technologies.matter of involved technologies.

That water finds its own level is another That water finds its own level is another experiment that can be performed using local experiment that can be performed using local pottery rather than imported glassware and the pottery rather than imported glassware and the students can have fun when they pour water students can have fun when they pour water into the following pitchers having openings at into the following pitchers having openings at

different heights.different heights.

Figure: Two pitchers having openings at different heights.Figure: Two pitchers having openings at different heights.

The abovementioned simple principle namely ‘water finds The abovementioned simple principle namely ‘water finds its own level’ has profound applications in the dredging of its own level’ has profound applications in the dredging of rivers. Dredging a river is of no use unless a slope exists rivers. Dredging a river is of no use unless a slope exists in the river bed --- a point often missed out by in the river bed --- a point often missed out by administrators and politicians.administrators and politicians.

Similarly the law of cooling can be verified by a student Similarly the law of cooling can be verified by a student who could put some boiling water in two buckets, and in who could put some boiling water in two buckets, and in one of the buckets some water at room temperature could one of the buckets some water at room temperature could be added to one of the buckets. The student could then be added to one of the buckets. The student could then verify by measuring the temperature of water in both verify by measuring the temperature of water in both buckets and find out that the one that has high buckets and find out that the one that has high temperature water is cooling faster. This is one of the temperature water is cooling faster. This is one of the

simplest hands-on projects that one can think of.simplest hands-on projects that one can think of.

Another interesting hands-on science Another interesting hands-on science experiment could be the measurement of experiment could be the measurement of Young’s Modulus, not of a steel wire (which is Young’s Modulus, not of a steel wire (which is one of the conventional experiments in one of the conventional experiments in laboratories and does not greatly ignite the laboratories and does not greatly ignite the imagination of students) but of the biological imagination of students) but of the biological material collagen tendon. This experiment could material collagen tendon. This experiment could demonstrate one of the interesting examples of demonstrate one of the interesting examples of bio-physics and could explain the mystery of bio-physics and could explain the mystery of lifting heavy weights with the help of our lifting heavy weights with the help of our muscles. The key point to note here is that muscles. The key point to note here is that science is all around us in the form of a science is all around us in the form of a wonderful interplay between living and inert wonderful interplay between living and inert

matter.matter.

UNESCO, quite sometime ago, listed some 700 UNESCO, quite sometime ago, listed some 700 science experiments which everyone can do in a science experiments which everyone can do in a book titled ‘700 Science Experiments’. Many of book titled ‘700 Science Experiments’. Many of these are very interesting no doubt. But the these are very interesting no doubt. But the performing of some of these experiments performing of some of these experiments involves a cultural shock. For example, in a involves a cultural shock. For example, in a certain experiment, a student has been asked to certain experiment, a student has been asked to use a “beer can”. The fact is that not only many use a “beer can”. The fact is that not only many people in developing countries do not drink people in developing countries do not drink beer, they simply do not know what a beer can beer, they simply do not know what a beer can looks like. The materials chosen in scientific looks like. The materials chosen in scientific experiments, especially in the case of experiments, especially in the case of improvised ones, must be familiar and available improvised ones, must be familiar and available to the students.to the students.

5. Teaching Science and Mathematics in an integrated and 5. Teaching Science and Mathematics in an integrated and inter-disciplinary manner.inter-disciplinary manner.

During the last few decades, in all major scientific During the last few decades, in all major scientific developments, especially in the areas of ICT (Information developments, especially in the areas of ICT (Information and Communication Technology) and bio-technology and Communication Technology) and bio-technology including genetic engineering, the interdisciplinary nature including genetic engineering, the interdisciplinary nature of science has been brought out in a prominent way. The of science has been brought out in a prominent way. The role of physicists in unraveling the structures and secrets role of physicists in unraveling the structures and secrets of the DNA molecule, the role of “material scientists” and of the DNA molecule, the role of “material scientists” and of “metallurgists” in devising special materials are of “metallurgists” in devising special materials are becoming well known. As explained earlier, even the becoming well known. As explained earlier, even the symmetry concepts of group theory including symmetry concepts of group theory including translational invariance, reflection in variance, rotational translational invariance, reflection in variance, rotational invariance and time reversal invariance are not topics of invariance and time reversal invariance are not topics of interest to physicists and chemists but also to artists who interest to physicists and chemists but also to artists who use some of these symmetries (knowingly or use some of these symmetries (knowingly or unknowingly) in their art work, and in their concepts of unknowingly) in their art work, and in their concepts of “beauty”. “beauty”.

Thus, the physicist teaching symmetry properties in the laws Thus, the physicist teaching symmetry properties in the laws of nature should draw the attention of students to numerous of nature should draw the attention of students to numerous fascinating examples of these principles around their own life fascinating examples of these principles around their own life and environment; difficult things would look easy and and environment; difficult things would look easy and familiar.familiar.

Now that all eyes are on “Biology” and many people very Now that all eyes are on “Biology” and many people very rightly say that the twenty first century might very well rightly say that the twenty first century might very well belong to molecular biology and all its ramifications, let me belong to molecular biology and all its ramifications, let me cite an example involving physics, biology and environment. cite an example involving physics, biology and environment. In a Unesco sponsored workshop at Puna in 1986, I made a In a Unesco sponsored workshop at Puna in 1986, I made a documentary film titled ‘The hand that rocks the cradle rules documentary film titled ‘The hand that rocks the cradle rules the world” in which I tried to show that if a house has a the world” in which I tried to show that if a house has a mother having a science background, then she could explain mother having a science background, then she could explain some difficult concepts of physics, chemistry and some difficult concepts of physics, chemistry and mathematics to her children in the cozy environment of the mathematics to her children in the cozy environment of the garden, kitchen, drawing room etc. In a scene in the film, a garden, kitchen, drawing room etc. In a scene in the film, a mother was calling her son to breakfast as he had an mother was calling her son to breakfast as he had an examination to take in the morning. The son came downstairs examination to take in the morning. The son came downstairs running and as he touched some worm potatoes on his plate running and as he touched some worm potatoes on his plate on the dining table, he said “Ma – it is very warm”. The on the dining table, he said “Ma – it is very warm”. The mother cut the potato with a knife into four pieces and was mother cut the potato with a knife into four pieces and was

fanning those.fanning those.

When the son returned home, the mother eagerly asked When the son returned home, the mother eagerly asked him “how was your exam?”; the son replied, “It was all him “how was your exam?”; the son replied, “It was all right Ma, but there was an odd question which I could not right Ma, but there was an odd question which I could not reply; in the question it was asked: why is it that in reply; in the question it was asked: why is it that in winter, we curl up our bodies while sleeping in bed, while winter, we curl up our bodies while sleeping in bed, while in summer, we stretch our hands and feet while resting.in summer, we stretch our hands and feet while resting.

The mother said “you could not answer only one The mother said “you could not answer only one question; don’t be upset about this”. Then I appeared in question; don’t be upset about this”. Then I appeared in the film and explained that the mother could have taught the film and explained that the mother could have taught her son the answer to this question at the breakfast her son the answer to this question at the breakfast table.table.

Figure: A Sliced PotatoFigure: A Sliced Potato

As the mother sliced the potato into four pieces, she was As the mother sliced the potato into four pieces, she was unknowingly but with a cultural practice, generating more and unknowingly but with a cultural practice, generating more and more surfaces for the potato to give out heat and cool down fast; 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 it is known that the amount of heat an object exchanges with its surroundings depends on the surface area of the object. In surroundings depends on the surface area of the object. In winter, we curl up our bodies in order to reduce the surface areas 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 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 the area, by stretching our arms and legs, so that we lose more heat and keep cool. heat and keep cool.

This simple principle of heat exchange is also operative at the This simple principle of heat exchange is also operative at the very root of different shapes and sizes of biological objects. Polar very root of different shapes and sizes of biological objects. Polar bears are large as they have smaller surface areas compared to bears are large as they have smaller surface areas compared to their volume whereas desert bears are small having large surface their volume whereas desert bears are small having large surface areas compared to their volumes. Their shapes and sizes are areas compared to their volumes. Their shapes and sizes are commensurate with the environment they are in. These matters commensurate with the environment they are in. These matters of biology and biodiversity and of thermodynamic principles in of biology and biodiversity and of thermodynamic principles in physics are interconnected with each other; these things should physics are interconnected with each other; these things should

be taught by the science teacher in an interesting manner.be taught by the science teacher in an interesting manner.

An interesting example of the (interdisciplinary) nature of An interesting example of the (interdisciplinary) nature of science and mathematics can be cited while teaching science and mathematics can be cited while teaching matrices. Most of the students know a matrix as being an matrices. Most of the students know a matrix as being an array of numbers and also are familiar with the addition array of numbers and also are familiar with the addition and multiplication of matrices etc. But when asked to cite and multiplication of matrices etc. But when asked to cite some (from life or nature) applications of matrices, many some (from life or nature) applications of matrices, many seem to be groping for examples. That the bus conductor seem to be groping for examples. That the bus conductor follows a matrix while collecting bus fares is not known to follows a matrix while collecting bus fares is not known to many .Also, the following energy conversion matrix could many .Also, the following energy conversion matrix could prove to be of immense interest to mathematicians, prove to be of immense interest to mathematicians, physicists as well as energy planners. One matrix could physicists as well as energy planners. One matrix could speak a million words.speak a million words.

TO FROM

ELECTROMAGNETIC

CHEMICAL

NUCLEAR THERMAL

KINETIC(MECHANI

CAL)

ELECTRICAL GRAVITATION

AL

ELECTROMAGNETIC

Chemiluminescence(fireflies)

Gamma reactions

(Co60 source)(A-bomb)

Thermal radiation(hot iron)

Accelerating charge

(cyclotron)Phosphor

Electromagnetic radiation

(TV transmitter Electroluminesc

ence

Unknown

CHEMICAL Photosynthesis(plants)

Photochemistry(photographic

film)

Radiation catalysis

(hydrazine plant)

lonization(cloud

chamber)

Boiling(water/steam)

Dissociation

Dissociation by

radiolysis

Electrolysis(production of

aluminium)Battery

charging

Unknown

NUCLEAR Gamma-neutronreactions Be9 + y Be8 +n

Unknown Unknown Unknown Unknown Unknown

THERMAL Solar absorber(hot sidewalk)

Combustion

(fire)

Fission (fuel element) Fusion

Friction(brake shoes)

Resistance heating

(electric stove)

Unknown

MatricesMatrices

KINETIC RadiometerSolar Cell

Muscle Radioactivity

(alpha particles)(A-bomb)

Thermal expansion

(turbines) Internal combustion(engines)

MotorsElectrostrict

ion(sonar

transmitter)

Falling objects

ELECTRICAL Photoelectricity(light meter)

Radioantenna Solar

cell

Fuel cellBatteries

Nuclear battery

Thermoelectricity Thermionics

Thermomagetism Ferroelectricity

†MHD

Conventional

generator

Unknown

GRAVITATIONAL

Unknown Unknown Unknown Unknown Rising objects

(rockets)

Unknown

†Magnetohydrodynamics

Table: Energy Conversion MatrixTable: Energy Conversion Matrix

Examples of matrix elements: a fire fly Examples of matrix elements: a fire fly

Chemiluminescence Chemiluminescence

Solar cellSolar cell (Matrix element: Electromagnetic to electrical) (Matrix element: Electromagnetic to electrical)

Hydro electrical PlantHydro electrical Plant::

Matrix element: Kinetic to electricalMatrix element: Kinetic to electrical

There can be nothing more innovative than making the children There can be nothing more innovative than making the children understand the fact that nature works according to laws of science, understand the fact that nature works according to laws of science, and that the very observant of the working of nature can identify and that the very observant of the working of nature can identify nature in the role of a teacher. In fact, a good student of science, even nature in the role of a teacher. In fact, a good student of science, even at very advanced stages, learns only a limited amount of science from at very advanced stages, learns only a limited amount of science from teachers and text-books, but can learn a lot by simply looking at teachers and text-books, but can learn a lot by simply looking at nature. The teachers of science would do well to make the students nature. The teachers of science would do well to make the students treat nature as teacher.treat nature as teacher.

6. NATURE AS TEACHER6. NATURE AS TEACHER::

Consider for example a pond which is found in almost all Consider for example a pond which is found in almost all countries. A pond can be a very good example of studying countries. A pond can be a very good example of studying numerous flora and fauna.numerous flora and fauna.

King fisherKing fisher

Insects walking on the water surface of the pond using the Insects walking on the water surface of the pond using the property of surface tension of water.property of surface tension of water.

Frogs spawning in massesFrogs spawning in masses of grey jelly floating on the of grey jelly floating on the warm water.warm water.

Tadpoles Tadpoles wriggling among the weeds.wriggling among the weeds.

Water snailsWater snails on the edge of the pond or on the stems of on the edge of the pond or on the stems of water plants, devouring all kinds of rotting matter and water plants, devouring all kinds of rotting matter and keeping the water of the pond clean.keeping the water of the pond clean.

Water snakeWater snake swimming gracefully. swimming gracefully.

Pond-beatlesPond-beatles attacking smaller creatures savagely. attacking smaller creatures savagely.

Pond Skate gliding on the water.Pond Skate gliding on the water.

Water scorpionsWater scorpions

Water spiderWater spider

Brilliant Brilliant dragon-fliesdragon-flies

Water lillyWater lilly

DuckweedDuckweed

Water hyacinthsWater hyacinths

All the organisms that dwell in the pond may serve All the organisms that dwell in the pond may serve to give an illustration of bio-diversity existing even to give an illustration of bio-diversity existing even in a limited area of nature.in a limited area of nature.

So far we have discussed the instructional management of the So far we have discussed the instructional management of the sheep (the students); it would be in order to say a few words sheep (the students); it would be in order to say a few words

about the management of the shepherds (teachers)about the management of the shepherds (teachers)

7. From the management of the sheep to that of the 7. From the management of the sheep to that of the shepherds shepherds

Tending sheep has been regarded as a holy job and Tending sheep has been regarded as a holy job and most of the Prophets who were given Divine most of the Prophets who were given Divine Messages were regarded basically as teachers Messages were regarded basically as teachers (Ustads) and were shepherds. The teachers of all (Ustads) and were shepherds. The teachers of all subjects in general, and of science and mathematics subjects in general, and of science and mathematics in particular, must be accorded the honor for in particular, must be accorded the honor for meeting the challenges of the times. They must also meeting the challenges of the times. They must also be given incentives. In this connection, I am be given incentives. In this connection, I am reminded of a book titled “The Man Who Counted” reminded of a book titled “The Man Who Counted” authored by Malba Tahan[3]. In this book which is a authored by Malba Tahan[3]. In this book which is a collection of mathematical adventures, is given the collection of mathematical adventures, is given the legend of Beremiz Samir who, coming from the legend of Beremiz Samir who, coming from the village of Khoi in Persia, was a shepherd and used village of Khoi in Persia, was a shepherd and used

to tend vast flocks of sheep.to tend vast flocks of sheep.

For fear of losing lambs and therefore being For fear of losing lambs and therefore being punished, he counted them several times a day. He punished, he counted them several times a day. He became so good in counting, that he could count all became so good in counting, that he could count all the bees in a swarm and all the leaves in a tree. the bees in a swarm and all the leaves in a tree. Satisfied with his mathematical agility his master Satisfied with his mathematical agility his master granted him four months’ leave. During this leave granted him four months’ leave. During this leave he showed wonderful feats to many, and finally was he showed wonderful feats to many, and finally was offered the post of Vizier by Caliph al-Mutasim of offered the post of Vizier by Caliph al-Mutasim of Baghdad. But Samir did not accept the post. Science Baghdad. But Samir did not accept the post. Science and Mathematics teachers do not want to be Viziers and Mathematics teachers do not want to be Viziers but they at least want to be paid reasonable but they at least want to be paid reasonable salaries so that for purposes of meeting the costs of salaries so that for purposes of meeting the costs of living, they do not take up many jobs and can living, they do not take up many jobs and can remain faithful to one profession only, namely remain faithful to one profession only, namely

teaching.teaching.

In some of the countries of Asia and presumably of In some of the countries of Asia and presumably of other continents, teachers’ salaries are very low, other continents, teachers’ salaries are very low, and as a result they often do other jobs to the and as a result they often do other jobs to the detriment of their own profession. This practice detriment of their own profession. This practice must be stopped.must be stopped.

A recommendation that could be made in respect of A recommendation that could be made in respect of salaries of science and mathematics teachers is that salaries of science and mathematics teachers is that once a teacher is evaluated for his qualification, once a teacher is evaluated for his qualification, experiences and teaching potential, his salary could experiences and teaching potential, his salary could remain the same whether he works in a school, remain the same whether he works in a school, college or university. In other words, a teacher college or university. In other words, a teacher should be judged by his intrinsic merit and not by should be judged by his intrinsic merit and not by the place he is working in. Universities cannot the place he is working in. Universities cannot flourish if schools are neglected. We must flourish if schools are neglected. We must remember the saying “The battle of Waterloo was remember the saying “The battle of Waterloo was won in the playground of Eton”.won in the playground of Eton”.

8. Conclusion:8. Conclusion:

Science and mathematics are the essential Science and mathematics are the essential tools for the study of nature. While utmost tools for the study of nature. While utmost care should be taken to attract students to care should be taken to attract students to these basic subjects through teaching in a these basic subjects through teaching in a delightful manner, the teachers to be delightful manner, the teachers to be appointed must be selected very judiciously. appointed must be selected very judiciously. And once selected, his salary structure must And once selected, his salary structure must be logical. It would be a great irony if be logical. It would be a great irony if teachers responsible for upholding the logic teachers responsible for upholding the logic of science and mathematics are themselves of science and mathematics are themselves

not dealt with in a logical way.not dealt with in a logical way.

Talking of logic which connects science with Talking of logic which connects science with mathematics, one might come forward and say mathematics, one might come forward and say rather pessimistically “what is the use of teaching rather pessimistically “what is the use of teaching logic in the present day world where force is logic in the present day world where force is prevailing over logic?” In this connection, I would prevailing over logic?” In this connection, I would like to narrate a story told in the book of Malba like to narrate a story told in the book of Malba Tahan:Tahan:

A lion, a tiger and a jackal hunted a sheep, a pig and A lion, a tiger and a jackal hunted a sheep, a pig and a rabbit. The tiger was given the responsibility by a rabbit. The tiger was given the responsibility by the lion of dividing the prey amongst themselves. the lion of dividing the prey amongst themselves. The tiger gave the tastiest of the prey, the sheep, to The tiger gave the tastiest of the prey, the sheep, to the lion, kept the dirty pig for himself and gave the the lion, kept the dirty pig for himself and gave the miserable rabbit to the jackal. The lion was very miserable rabbit to the jackal. The lion was very angry at this division and said “who has ever seen angry at this division and said “who has ever seen

three divided by three giving a result like that?”three divided by three giving a result like that?”

Raising his paw, the lion swiped the head of the Raising his paw, the lion swiped the head of the unsuspecting tiger so fiercely that he fell dead a unsuspecting tiger so fiercely that he fell dead a few feet away. The lion then gave the charge of the few feet away. The lion then gave the charge of the division to the jackal who, having already witnessed division to the jackal who, having already witnessed the tragedy of the tiger said to the lion, “the sheep the tragedy of the tiger said to the lion, “the sheep is a feed worthy of a king, the appetizing pig should is a feed worthy of a king, the appetizing pig should be destined for your royal plate. And the skittish be destined for your royal plate. And the skittish rabbit with its large ears is a savory bite for a king rabbit with its large ears is a savory bite for a king like you”. The lion praised the jackal and asked him like you”. The lion praised the jackal and asked him how he learnt this kind of division of three by two how he learnt this kind of division of three by two so perfectly!” The jackal replied “I learnt from the so perfectly!” The jackal replied “I learnt from the tiger. In the mathematics of the strong, the quotient tiger. In the mathematics of the strong, the quotient is always clear while to the weak must fall only the is always clear while to the weak must fall only the

remainder”.remainder”.

The ambitious jackal felt that he could live in The ambitious jackal felt that he could live in tranquility only as a parasite, receiving only the tranquility only as a parasite, receiving only the leftovers from the lion’s feast. But he was wrong. leftovers from the lion’s feast. But he was wrong. After two or three weeks, the lion, angry and After two or three weeks, the lion, angry and hungry, tired of the jackal’s servility ended up hungry, tired of the jackal’s servility ended up killing him, just as he had the tiger. Thus, the killing him, just as he had the tiger. Thus, the division of three by two realized with no remainder division of three by two realized with no remainder could not save the jackal. This story contains a could not save the jackal. This story contains a moral lesson: adulators and politicians who move moral lesson: adulators and politicians who move obediently in the corridors of the powerful may gain obediently in the corridors of the powerful may gain something in the beginning but in the end, they are something in the beginning but in the end, they are always punished. Therefore, there is no use in going always punished. Therefore, there is no use in going away from logic which is so inherent in science and away from logic which is so inherent in science and mathematics. The greater the number of people mathematics. The greater the number of people who follow logic, the safer will be our earth to live who follow logic, the safer will be our earth to live

in.in.

(The author is President, Bangladesh Academy of (The author is President, Bangladesh Academy of Sciences and Vice Chancellor, Southeast University, Sciences and Vice Chancellor, Southeast University, Dhaka)Dhaka)

References: References: [1] “Symmetry” by Herman Weyl, Princeton [1] “Symmetry” by Herman Weyl, Princeton University Press, Princeton, New Jersey, University Press, Princeton, New Jersey, 19521952

[2] “700 Science Experiments for everyone”, [2] “700 Science Experiments for everyone”, compiled by UNESCO, Doubleday and compiled by UNESCO, Doubleday and Company, Inc, Garden City, New York, 1958.Company, Inc, Garden City, New York, 1958.

[3] “The Man who Counted” by Malba Tahan, [3] “The Man who Counted” by Malba Tahan,

W.W. Norton & Company, USA, 1994.W.W. Norton & Company, USA, 1994.