The Role of Science Academies The Role of Science Academies in Science Educationin Science Education

andandTeaching Science and Mathematics Teaching Science and Mathematics

in a Delightful Mannerin a Delightful Manner

- Prof. Dr. M. Shamsher Ali

1.1. Introduction:Introduction:

Although Science and Mathematics touch our lives in Although Science and Mathematics touch our lives in innumerable ways, the teaching of these subjects has innumerable ways, the teaching of these subjects has been far from satisfactory and has become a global been far from satisfactory and has become a global problem. There is a dearth of qualified science and problem. There is a dearth of qualified science and mathematics teachers. Also, the students are no mathematics teachers. Also, the students are no longer being attracted to these subjects. While longer being attracted to these subjects. While choosing a graduate program of study in science and choosing a graduate program of study in science and technology, the eyes of both guardians and students technology, the eyes of both guardians and students are on those subjects which are fashionable and can are on those subjects which are fashionable and can fetch money. The fashionable subjects are Computer fetch money. The fashionable subjects are Computer Science and Engineering, Medicine, Biotechnology Science and Engineering, Medicine, Biotechnology including Genetic Engineering etc. Although these including Genetic Engineering etc. Although these subjects would not be what they are today without the subjects would not be what they are today without the development of science and mathematics, the latter development of science and mathematics, the latter seem to have fallen seem to have fallen

out of favor. People remember the end product, not out of favor. People remember the end product, not the hard work that went into it. The responsibility for the hard work that went into it. The responsibility for the loss of attraction towards pure science and the loss of attraction towards pure science and mathematics does not lie merely with students; a mathematics does not lie merely with students; a major part of it lies with us, the teachers. Mathematics major part of it lies with us, the teachers. Mathematics was once regarded as the Queen of sciences. It is no was once regarded as the Queen of sciences. It is no longer so. The beauty of that queen is hardly longer so. The beauty of that queen is hardly appreciated – in fact she is being presented as dreary appreciated – in fact she is being presented as dreary and menacing. The practitioners of mathematics are and menacing. The practitioners of mathematics are doing little to restore the lost beauty of the queen. doing little to restore the lost beauty of the queen. Many of the high school students (especially girls) Many of the high school students (especially girls) when asked to give opinion about mathematics reply when asked to give opinion about mathematics reply ‘mathematics is difficult’. They even find it dry and ‘mathematics is difficult’. They even find it dry and drab. They study mathematics only as a requirement drab. They study mathematics only as a requirement for study and do not for study and do not

seem to derive any pleasure from studying the seem to derive any pleasure from studying the subject. They usually cannot relate whatever subject. They usually cannot relate whatever mathematics they have learnt in the classroom to mathematics they have learnt in the classroom to what they see in their real life and environment. This what they see in their real life and environment. This issue of relevance to life and environment is indeed issue of relevance to life and environment is indeed very meaningful to anyone dealing with pedagogy. In very meaningful to anyone dealing with pedagogy. In fact, the development of mathematics in the ancient fact, the development of mathematics in the ancient times started from very mundane things like, the times started from very mundane things like, the measurements on earth (Geometry; geo means earth measurements on earth (Geometry; geo means earth and meter means measurement). Even sophisticated and meter means measurement). Even sophisticated branches of mathematics including abstract branches of mathematics including abstract mathematics can, in the final analysis, be related to mathematics can, in the final analysis, be related to things they know already. The challenge of things they know already. The challenge of mathematics pedagogy is basically one of making mathematics pedagogy is basically one of making mathematics mathematics

interesting and delightful. Unfortunately, not very interesting and delightful. Unfortunately, not very many teachers address themselves to this issue. In many teachers address themselves to this issue. In fact, in the meeting of Education Ministers of fact, in the meeting of Education Ministers of Commonwealth countries it has often been reported Commonwealth countries it has often been reported that the scarcity of mathematics and science teachers that the scarcity of mathematics and science teachers is posing a great threat to the overall development of is posing a great threat to the overall development of science and technology in the developing countries.science and technology in the developing countries.

Obviously, no time would be more suitable than now Obviously, no time would be more suitable than now for addressing the issues of “Science and for addressing the issues of “Science and Mathematics Education for the 21st Century”. Mathematics Education for the 21st Century”.

1.1 1.1 The Role of Science Academies in The Role of Science Academies in Science Education and Science Science Education and Science PromotionPromotion

Science Academies, all over the world, are regarded Science Academies, all over the world, are regarded as apex scientific bodies for providing incentives and as apex scientific bodies for providing incentives and recognition to scientists for brilliant scientific work and recognition to scientists for brilliant scientific work and for identifying national issues on which the for identifying national issues on which the governments may be advised to initiate appropriate governments may be advised to initiate appropriate line of research. However, the fact remains, that line of research. However, the fact remains, that except for the Academies in Communist and Socialist except for the Academies in Communist and Socialist countries which own laboratories and are regarded as countries which own laboratories and are regarded as government institutions (for example, the academies government institutions (for example, the academies of Russia and China), most of the Academies of the of Russia and China), most of the Academies of the world are modeled along western lines. Although world are modeled along western lines. Although these Academies do not have laboratories of their these Academies do not have laboratories of their own, they have one great asset, namely, a reservoir own, they have one great asset, namely, a reservoir of Fellows of the highest distinction in different of Fellows of the highest distinction in different

branches of science and technology. The Fellows are branches of science and technology. The Fellows are recruited absolutely on scientific merit, and they recruited absolutely on scientific merit, and they include professors of universities, research scientists include professors of universities, research scientists of national laboratories and eminent scientists who of national laboratories and eminent scientists who have held responsible positions, like vice-have held responsible positions, like vice-chancellorship of universities and chairmanship of chancellorship of universities and chairmanship of national scientific bodies etc. Since these Fellows national scientific bodies etc. Since these Fellows have been regarded as men of high standing, they have been regarded as men of high standing, they also possess the capability to initiate projects in also possess the capability to initiate projects in different educational and research organizations of different educational and research organizations of their country. It takes quite sometime for people to their country. It takes quite sometime for people to attain high scientific standard, and hence one may attain high scientific standard, and hence one may not notice very many young people in the science not notice very many young people in the science Academies, which, humorously are often termed, as Academies, which, humorously are often termed, as ‘old boys’ club’. ‘old boys’ club’.

However, some Academies have introduced However, some Academies have introduced Associate Fellowship for comparatively younger Associate Fellowship for comparatively younger scientists who, after some time, may qualify for scientists who, after some time, may qualify for election to full Fellowships. Very recently, the IAP election to full Fellowships. Very recently, the IAP (Inter Academy Panel of Science) also discussed the (Inter Academy Panel of Science) also discussed the role of Science Academies, and it was pointed out by role of Science Academies, and it was pointed out by the present author, that an Academy can make a the present author, that an Academy can make a scientific impact on the society only when it scientific impact on the society only when it addresses the problems faced by the government addresses the problems faced by the government and the people of the country. Thus, apart from and the people of the country. Thus, apart from recognizing scientific talents through the awarding of recognizing scientific talents through the awarding of Gold Medals and through the election of Fellowships, Gold Medals and through the election of Fellowships, Academies of Sciences can make a great social Academies of Sciences can make a great social impact by undertaking serious studies of some impact by undertaking serious studies of some burning scientific issues of a society. One such issue burning scientific issues of a society. One such issue is Science education and Science promotion. is Science education and Science promotion.

The promotion of science is an issue which is The promotion of science is an issue which is addressed by the Academies of the developed addressed by the Academies of the developed countries as well. For example, the Royal Society has countries as well. For example, the Royal Society has always been organizing, at Christmas and at other always been organizing, at Christmas and at other times, public lectures on scientific issues which are times, public lectures on scientific issues which are beginning to change the present world. These beginning to change the present world. These lectures are delivered in such a manner that the lectures are delivered in such a manner that the interest of the public in science is increased, and interest of the public in science is increased, and also, the science mindedness of the society at large also, the science mindedness of the society at large is enhanced. The promotion of science can be further is enhanced. The promotion of science can be further achieved by arranging regular Radio and TV shows achieved by arranging regular Radio and TV shows wherein experts can explain the importance of some wherein experts can explain the importance of some scientific ideas that have relevance to the issues of scientific ideas that have relevance to the issues of life and environment. And it has to be done in plain life and environment. And it has to be done in plain parlance and without any use parlance and without any use

of technical jargons The promotion of science can of technical jargons The promotion of science can also be done by Science Academies through the also be done by Science Academies through the holding of science exhibitions and through the holding of science exhibitions and through the promotion of ‘science clubs’ in the country. Just as promotion of ‘science clubs’ in the country. Just as literary circles observe the birth and death literary circles observe the birth and death anniversaries of poets and litterateurs, Science anniversaries of poets and litterateurs, Science Academies can do the same in respect of the birth Academies can do the same in respect of the birth and death anniversaries of great scientific figures, and death anniversaries of great scientific figures, and on these occasions, the expert Fellows may and on these occasions, the expert Fellows may describe, to the members of the public, the far describe, to the members of the public, the far reaching consequences of the scientific discoveries reaching consequences of the scientific discoveries made so far. The public interest in science can also made so far. The public interest in science can also be increased through the regular holding of be increased through the regular holding of Olympiads in subjects like Mathematics, Physics, Olympiads in subjects like Mathematics, Physics, Chemistry etc. Here, the idea would be to do some Chemistry etc. Here, the idea would be to do some brain-hunting for logical and analytical minds which brain-hunting for logical and analytical minds which could be harnessed for developing scientific talents. could be harnessed for developing scientific talents.

Science education is, however, a different matter. Science education is, however, a different matter. Science is basically doing things, not just talking, and Science is basically doing things, not just talking, and it is quite a challenge to give some hands-on it is quite a challenge to give some hands-on experiments to children through which they can find experiments to children through which they can find out the working of nature using very simple stuff that out the working of nature using very simple stuff that they may find around them. For many developing they may find around them. For many developing countries, conducting scientific experiments with countries, conducting scientific experiments with imported equipment may not be a sound economic imported equipment may not be a sound economic proposition. Also it may not be desirable to import proposition. Also it may not be desirable to import equipment on all occasions. In the early stages of equipment on all occasions. In the early stages of science education, the key point for students is to find science education, the key point for students is to find out how nature works. The emphasis, here, is not on out how nature works. The emphasis, here, is not on achieving high levels of accuracy of scientific achieving high levels of accuracy of scientific research as is the case in scientific laboratories. It research as is the case in scientific laboratories. It would be enough if only would be enough if only

the laws of science are verified through easy means the laws of science are verified through easy means at a functional level. To this end, the Bangladesh at a functional level. To this end, the Bangladesh Academy of Sciences has already formed a task-Academy of Sciences has already formed a task-force for identifying locally indigenous materials for force for identifying locally indigenous materials for performing the conventional science experiments at performing the conventional science experiments at the school level without importing scientific equipment the school level without importing scientific equipment from outside. This subject of creating interest in from outside. This subject of creating interest in science education through interesting and simple science education through interesting and simple scientific experiments is a matter that could be scientific experiments is a matter that could be tackled by almost all Science Academies of the tackled by almost all Science Academies of the developing world in Asia, particularly in those developing world in Asia, particularly in those countries where funding is a major problem.countries where funding is a major problem.

Since Mathematics is the language of nature, it is Since Mathematics is the language of nature, it is also a challenging matter to increase interest in the also a challenging matter to increase interest in the learning of Mathematics through life and learning of Mathematics through life and environment-related phenomena. Again, the Science environment-related phenomena. Again, the Science Academies can initiate innovative thinking on the part Academies can initiate innovative thinking on the part of scholars for increasing interest in Science and of scholars for increasing interest in Science and Mathematics education. In what follows in this paper, Mathematics education. In what follows in this paper, at attempt has been made to reflect some innovative at attempt has been made to reflect some innovative thinking for increasing such interest. Academies of thinking for increasing such interest. Academies of Sciences may consider the modus operandi outlined Sciences may consider the modus operandi outlined in this paper for teaching Science and Mathematics in in this paper for teaching Science and Mathematics in a delightful manner and encourage the teaching a delightful manner and encourage the teaching community to adopt these and similar techniques. community to adopt these and similar techniques.

2. 2. Creating interest in Mathematics Creating interest in Mathematics and Science Educationand Science Education

2.1 2.1 MathematicsMathematics

One of the ways of creating interest in mathematics One of the ways of creating interest in mathematics education is through generating interest in geometry. education is through generating interest in geometry. Incidentally, the secrets of all life forms are also Incidentally, the secrets of all life forms are also embedded in the tiniest of spaces in the double embedded in the tiniest of spaces in the double helical geometrical structure of the hereditary blue helical geometrical structure of the hereditary blue print of life, the Master Molecule DNA. The interesting print of life, the Master Molecule DNA. The interesting thing about geometry is that the teaching of geometry thing about geometry is that the teaching of geometry is not costly at all. The simple geometrical models is not costly at all. The simple geometrical models that one needs can be constructed easily with the that one needs can be constructed easily with the locally available materials. This session is to address locally available materials. This session is to address hands-on projects also. What better hands-on hands-on projects also. What better hands-on projects in geometry could be than to ask the school projects in geometry could be than to ask the school children to play with either an ice-cream cone or a children to play with either an ice-cream cone or a cone made with clay and an ordinary blade and then cone made with clay and an ordinary blade and then to cut several sections of the cone. to cut several sections of the cone.

We talk of conic sections: a point, a straight line, a We talk of conic sections: a point, a straight line, a circle, a parabola, a hyperbola are all examples of circle, a parabola, a hyperbola are all examples of conic sections whose mathematical equations are conic sections whose mathematical equations are taught at various levels at schools and colleges. But taught at various levels at schools and colleges. But very few teachers really bother to ask the students to very few teachers really bother to ask the students to make cones of clay; the apex of the cone is ideally make cones of clay; the apex of the cone is ideally located at a point. One could draw a straight line at located at a point. One could draw a straight line at any point of the surface. One could cut a section any point of the surface. One could cut a section parallel to the base and get a circle. If this cut is done parallel to the base and get a circle. If this cut is done a little obliquely, an ellipse will be obtained. Similarly a little obliquely, an ellipse will be obtained. Similarly one can get a parabola and a hyperbola when one one can get a parabola and a hyperbola when one makes sections, which touch the base. This is fun makes sections, which touch the base. This is fun and delight, which can be realized even while one is and delight, which can be realized even while one is drinking from a glass of water. By tilting the glass one drinking from a glass of water. By tilting the glass one can look at the can look at the

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

12

2

2

2

b

y

a

x

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

02

2

a

xand one gets 1

2

2

b

y

or y2 = b2, or . Thus one notices two lines with y = or y2 = b2, or . Thus one notices two lines with y = +b and y = -b above and below the axis of the ellipse, +b and y = -b above and below the axis of the ellipse, respectively. respectively.

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

Imagine a rectangular room in which a wasp is sitting Imagine a rectangular room in which a wasp is sitting at the center of one wall. Exactly on the opposite at the center of one wall. Exactly on the opposite point is sitting a fly. Commonsense dictates that if the point is sitting a fly. Commonsense dictates that if the wasp has to prey on the fly, it has to take the shortest wasp has to prey on the fly, it has to take the shortest route which could be down, straight and up or up, route which could be down, straight and up or up, straight and down or side ways, side ways and 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 In practice, the wasp does not follow the Euclidean Geometry: it follows a path, which is curved and Geometry: it follows a path, which is curved and touches four walls including the roof. It can be verified touches four walls including the roof. It can be verified by drawing the room on a reasonable scale that this by drawing the room on a reasonable scale that this curved path is actually smaller than the Euclidean curved path is actually smaller than the Euclidean routes described. This is the geodesic of the wasp. routes described. This is the geodesic of the wasp.

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

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

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

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

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

One may ask if there are any mathematical relations One may ask if there are any mathematical relations governing growth and form. A straight answer may be governing growth and form. A straight answer may be difficult to give. As D’arcy Thompson pointed out in difficult to give. As D’arcy Thompson pointed out in his book titled “On Forms and Shapes”, that in case his book titled “On Forms and Shapes”, that in case of fishes, the shape of one can be related to that of of fishes, the shape of one can be related to that of another by mathematical transformation. If a little another by mathematical transformation. If a little oceanic fish by the name of Argyropelecus olfersi is oceanic fish by the name of Argyropelecus olfersi is placed on a Cartesian paper and if its outline is placed on a Cartesian paper and if its outline is transferred to a system of oblique coordinates whose transferred to a system of oblique coordinates whose axes are inclined at an angle of 700, then we get the axes are inclined at an angle of 700, then we get the mathematical figure of a fish which actually mathematical figure of a fish which actually represents a simple shear of the first fish. But it is represents a simple shear of the first fish. But it is indeed fascinating to note that such a fish by the indeed fascinating to note that such a fish by the name of sternoplys diaphana actually exists in nature. name of sternoplys diaphana actually exists in nature. No wonder Dirac, the celebrated No wonder Dirac, the celebrated

theoretical physicist of all times pointed out that God theoretical physicist of all times pointed out that God is the greatest mathematician. The humans have is the greatest mathematician. The humans have discovered through the discovery of force laws and discovered through the discovery of force laws and the way numbers work in nature that without the use the way numbers work in nature that without the use of mathematics, life forms would find it difficult to of mathematics, life forms would find it difficult to survive.survive.

If one looks at the Bawa bird and looks at the way its If one looks at the Bawa bird and looks at the way its nest is prepared, one is forced to believe that it nest is prepared, one is forced to believe that it challenges the work of a modern architect. It’s challenges the work of a modern architect. It’s complicated, light and can endure severe tornadoes. complicated, light and can endure severe tornadoes. The birds do it by instinct. Men devise the utility of The birds do it by instinct. Men devise the utility of geometry through reasoning. In this connection one 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 that irregular stone. Fractals are geometrical shapes that contrary to those of Euclid are not regular at all. They contrary to those of Euclid are not regular at all. They are irregular all over and the same degree of are irregular all over and the same degree of irregularity exists in all scales. A fractal object looks irregularity exists in all scales. A fractal object looks the same when examined from far away and nearby. the same when examined from far away and nearby. The difference between classical and fractal The difference between classical and fractal geometry lies in their opposed notion of dimension. In geometry lies in their opposed notion of dimension. In standard geometry, dimensions come only in whole standard geometry, dimensions come only in whole numbers: a straight line has dimension 1, a plane has numbers: a straight line has dimension 1, a plane has dimension 2, a solid has dimension 3. dimension 2, a solid has dimension 3.

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

him is a set of complex numbers, which have the him is a set of complex numbers, which have the property that you make a certain operation, take 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 . Then you square the result you check to see whether you have gone outside circle of radius 2 see whether you have gone outside circle of radius 2 and you plot this on a graph. As you keep going, the and you plot this on a graph. As you keep going, the set becomes drawn with great and greater detail. But set becomes drawn with great and greater detail. But all you are doing is multiplying something by itself and all you are doing is multiplying something by itself and adding itself that is Z2 + C. Everything squared +C; adding itself that is Z2 + C. Everything squared +C; everything squared +C; It may be difficult for a everything squared +C; It may be difficult for a teacher to teach the concept of fractional geometry teacher to teach the concept of fractional geometry but it is quite easy to point out that nature uses a but it is quite easy to point out that nature uses a language namely “fractional geometry” to produce language namely “fractional geometry” to produce many of its products. The fractals can be found many of its products. The fractals can be found everywhere in nature and everywhere in nature and

Mandel Brot has produced an explanation which, Mandel Brot has produced an explanation which, when graphed by the computer, mimics the fractal when graphed by the computer, mimics the fractal structure of natural phenomena as diverse as trees, structure of natural phenomena as diverse as trees, river, human vascular systems, clouds, coast lines, river, human vascular systems, clouds, coast lines, mammalian brain form etc. “Fractals”, Mandel Brot mammalian brain form etc. “Fractals”, Mandel Brot said “are the very substance of our flesh.”said “are the very substance of our flesh.”

John Milner of the Institute of advance studies printed John Milner of the Institute of advance studies printed out that, “fractal may give us a more realistic human out that, “fractal may give us a more realistic human lung system than conventional geometry does. Think lung system than conventional geometry does. Think of the very fine blood vessels and air channels inter of the very fine blood vessels and air channels inter connecting with each other in a complicated pattern. connecting with each other in a complicated pattern. This does not make any sense at all from the point of This does not make any sense at all from the point of view of classical geometry, where you study smooth, view of classical geometry, where you study smooth, differentiable objects, but the lung structure can be 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 fractal Cauliflower – 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[1] explains Hermann Weyl in his book on symmetry[1] explains that symmetry is used in every day language in two that symmetry is used in every day language in two meanings. One, geometrical symmetry meaning meanings. One, geometrical symmetry meaning something well proportioned, well balanced and something well proportioned, well balanced and symmetry denotes that sort of concordance of several symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is parts by which they integrate into a whole. Beauty is bound up with symmetry. Without any formal lessons bound up with symmetry. Without any formal lessons about symmetry the modern artist uses different kinds about symmetry the modern artist uses different kinds of symmetry in his artwork. For example, bilateral of symmetry in his artwork. For example, bilateral symmetry is so conspicuous in the structure of higher symmetry is so conspicuous in the structure of higher animals, specially the human system. In fact, if one animals, specially the human system. In fact, if one thinks about a vertical plane through the middle of the thinks about a vertical plane through the middle of the nose and if one knows the structure of the face on nose and if one knows the structure of the face on one side of the plane, that on the other can one side of the plane, that on the other can immediately immediately

be reconstructed. The other forms of symmetry, which be reconstructed. The other forms of symmetry, which the artist exploits unknowingly, are translation the artist exploits unknowingly, are translation symmetry and rotational symmetry: the idea of symmetry and rotational symmetry: the idea of translation symmetry is simply that if an object has translation symmetry is simply that if an object has translation symmetry then by merely shifting it translation symmetry then by merely shifting it laterally, one would not know at all about the shift. laterally, one would not know at all about the shift. This would be true of infinitely large wallpaper with This would be true of infinitely large wallpaper with designs in it. If the wallpaper is really long enough, by designs in it. If the wallpaper is really long enough, by shifting the wallpaper the design would not be altered. shifting the wallpaper the design would not be altered. In the case of a wallpaper of limited length this would In the case of a wallpaper of limited length this would not hold because of the special marking of the not hold because of the special marking of the designs at the two ends of the wall. designs at the two ends of the wall.

The spherical symmetry which has been a very The spherical symmetry which has been a very favorite concept for artists of all times simply means favorite concept for artists of all times simply means that if one has a perfectly spherical ball and it has that if one has a perfectly spherical ball and it has been rotated through any diameter of the sphere then been rotated through any diameter of the sphere then it is virtually impossible to know whether a sphere has it is virtually impossible to know whether a sphere has at all been rotated or not. Thus, symmetries are also at all been rotated or not. Thus, symmetries are also inherent in the laws of the small, which are dealt with inherent in the laws of the small, which are dealt with in Quantum Mechanics. in Quantum Mechanics.

There are many other kinds of symmetries that can There are many other kinds of symmetries that can be visualized in the structure of different shells, snow be 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 understand the symmetries of nature on both large and small scales can be taught in an abstract fashion and small scales can be taught in an abstract fashion alright but it can also be taught with interesting alright but it can also be taught with interesting reference to life forms around us. Starfishes which reference to life forms around us. Starfishes which attract tourists on the beaches are all examples which attract tourists on the beaches are all examples which can be shown as realizations of certain kinds of can be shown as realizations of certain kinds of Group Theoretic Structures.Group Theoretic 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 mathematics. But the aspect of mathematics that must not be forgotten is its appeal to logic and must not be forgotten is its appeal to logic and analyticity. Mathematics is not only doing sums and analyticity. Mathematics is not only doing sums and this is where the students are bogged down. this is where the students are bogged down. Mathematics enables one to acquire an analytical Mathematics enables one to acquire an analytical frame of mind and to argue logically. It has been frame of mind and to argue logically. It has been found that mathematically minded analysts should be found that mathematically minded analysts should be the best expositors of logic no matter where that logic the best expositors of logic no matter where that logic holds. No wonder politicians who, in general, have no holds. No wonder politicians who, in general, have no mathematical background cannot reason out on many mathematical background cannot reason out on many occasions and as a result take recourse to emotional occasions and as a result take recourse to emotional appeal of the sort used by Mark Antonio in “Julius appeal of the sort used by Mark Antonio in “Julius Caesar”. The world would be a much better place to Caesar”. The world would be a much better place to live in if the logic of live in if the logic of

mathematics found its expression in public dealings mathematics found its expression in public dealings also. Many often view mathematics as brainteasers also. Many often view mathematics as brainteasers but one does not realize that the logic inherent in the but one does not realize that the logic inherent in the brainteasers is actually the logic that drives the brainteasers is actually the logic that drives the electronic circuits and computer network. The logic is electronic circuits and computer network. The logic is simply of FALSE and TRUTH. Here one may be simply of FALSE and TRUTH. Here one may be reminded of one simple brain teaser – a man reminded of one simple brain teaser – a man proceeds to a city A and while driving to that city he proceeds to a city A and while driving to that city he comes to a roundabout in which he has either to take comes to a roundabout in which he has either to take a right or left turn to that city. Unfortunately the road a right or left turn to that city. Unfortunately the road sign has been blown off by the wind. He could ask the sign has been blown off by the wind. He could ask the petrol station on the left or on the right and find out petrol station on the left or on the right and find out whether he has to turn to left or right. He has been whether he has to turn to left or right. He has been advised that the people on one side always speak the advised that the people on one side always speak the truth and truth and

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

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

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

(Approx.) 42

25

25 2

252)( 2

feetr

feetr

feetrrr

The language of nature is basically mathematical and The language of nature is basically mathematical and logic is the kingpin of mathematics. The logic of logic is the kingpin of mathematics. The logic of mathematics can be entertaining also. An interesting mathematics can be entertaining also. An interesting example can be the following. A person example can be the following. A person A A meets his meets his old college friend old college friend B B at a market place after a long at a market place after a long time. time. AA asks asks B, B, “I gather that you have married; do “I gather that you have married; do you have children?” you have children?” B B replied: “Yes, I have 3 replied: “Yes, I have 3 children.” “What are their ages”, children.” “What are their ages”, A A asked. asked. B B said, “We said, “We were both students of mathematics; so, you have to were both students of mathematics; so, you have to figure out the ages, yourself; I shall of course, give figure out the ages, yourself; I shall of course, give you some tips.” The first tip you some tips.” The first tip B B gives to gives to A A is “the is “the product of the three ages is thirty six”. That is not product of the three ages is thirty six”. That is not enough and you know it also, said enough and you know it also, said AA. . BB now gives a now gives a second tip, “the sum of their ages is the roll number second tip, “the sum of their ages is the roll number you had in you had in

your college”. your college”. AA now ponders for a moment and says now ponders for a moment and says that something else is required. Then 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 tip, “today is my eldest son’s birthday, I am going to by him some musical equipment.” by him some musical equipment.” A A now immediately now immediately figures out the ages of the three children without any figures out the ages of the three children without any further delay. But how? The reader would do well to further delay. But how? The reader would do well to determine the ages and find out that the logic is very determine the ages and find out that the logic is very entertaining indeed!entertaining indeed!

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

2.2 2.2 ScienceScience

During the last few decades, the development of During the last few decades, the development of science and technology has been so rapid, that it is science and technology has been so rapid, that it is becoming gradually difficult for a teacher to cope with becoming gradually difficult for a teacher to cope with such developments. Should the teacher be such developments. Should the teacher be conversant with all the scientific development and conversant with all the scientific development and teach all of those? This may sound to be a difficult teach all of those? This may sound to be a difficult question. But the answer is simple. The teacher may question. But the answer is simple. The teacher may want to know many thing but (s)he should not attempt want to know many thing but (s)he should not attempt to teach the students everything under the sun. (S)he to teach the students everything under the sun. (S)he should teach them the very basics on which the should teach them the very basics on which the whole edifice of science hinges, e.g. the conservation whole edifice of science hinges, e.g. the conservation laws of nature, the least principles of nature namely laws of nature, the least principles of nature namely the principle of least path, the principle of least the principle of least path, the principle of least energy, principle of least action, the symmetry energy, principle of least action, the symmetry principles in science, the multi-disciplinary nature of principles in science, the multi-disciplinary nature of science etc. 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 successful if (s)he has been able to make his/her students ask the right question at the right time. The students ask the right question at the right time. The principal goal of the science teacher would be to principal goal of the science teacher would be to generate a spirit of enquiry in the minds of the generate a spirit of enquiry in the minds of the students. Not all enquires can be satisfied with words. students. Not all enquires can be satisfied with words. Action is needed. Science is not merely talking. Action is needed. Science is not merely talking. Science is “doing” things. But doing things for what? Science is “doing” things. But doing things for what? The answer is: for verifying how Nature works. And The answer is: for verifying how Nature works. And who should “do” these things. Again, the answer is who should “do” these things. Again, the answer is “Yes” for students and “No” for teachers. In doing “Yes” for students and “No” for teachers. In doing scientific experiments, it must be ensured that scientific experiments, it must be ensured that students are the key players and teachers are students are the key players and teachers are passive watchers. Even for doing very simple things, passive watchers. Even for doing very simple things, students need some equipment. students need some equipment.

And it is in respect of equipment that a “sorry state” of And it is in respect of equipment that a “sorry state” of affairs exists in the schools and colleges of affairs exists in the schools and colleges of developing countries. True, equipment costs money. developing countries. True, equipment costs money. The effort then should be to do the same set of The effort then should be to do the same set of science experiments as is performed in developed science experiments as is performed in developed countries, but using local materials in the students’ countries, but using local materials in the students’ own environment. Experiments thus designed, have own environment. Experiments thus designed, have to be innovative in nature and must have the potential to be innovative in nature and must have the potential for attracting students through elements of fun and for attracting students through elements of fun and delight. For example, for the purposes of creation and delight. For example, for the purposes of creation and of sound in a media, tuning forks imported from of sound in a media, tuning forks imported from abroad may not be necessary in a rural setting; a abroad may not be necessary in a rural setting; a mango seed with a little opening in it can act as an mango seed with a little opening in it can act as an excellent material for the vibration of air and creation excellent material for the vibration of air and creation of sound; two of sound; two

children can dive into a pond and while under water children can dive into a pond and while under water at a distance from one another, one can make a at a distance from one another, one can make a sound by clapping his hands and the other can hear sound by clapping his hands and the other can hear it; these kinds of things are fun and delight and make it; these kinds of things are fun and delight and make science easy and attractive. Similarly, the science easy and attractive. Similarly, the demonstration of the working principles of the flight of demonstration of the working principles of the flight of an aero plane or the flight of a bird (which led to the 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 idea of the flight of an aero plane) can be made by holding a sheet of paper before a running table fan. holding a sheet of paper before a running table fan. On the curved sheet of paper (resembling the wings On the curved sheet of paper (resembling the wings of the plane), there is a net upward thrust which of the plane), there is a net upward thrust which keeps it upward; thus the basic scientific principle in keeps it upward; thus the basic scientific principle in the flight of the plane is simple; the rest is the matter the flight of the plane is simple; the rest is the matter of involved technologies.of involved technologies.

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

Figure: Two pitchers having openings at different heights.

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

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

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

UNESCO, quite sometime ago, listed some 700 UNESCO, quite sometime ago, listed some 700 science experiments[2] which everyone can do in a science experiments[2] which everyone can do in a book titled ‘700 Science Experiments’. Many of these book titled ‘700 Science Experiments’. Many of these are very interesting no doubt. But the performing of are very interesting no doubt. But the performing of some of these experiments involves a cultural shock. some of these experiments involves a cultural shock. For example, in a certain experiment, a student has For example, in a certain experiment, a student has been asked to use a “beer can”. The fact is that not been asked to use a “beer can”. The fact is that not only many people in developing countries do not drink only many people in developing countries do not drink beer, they simply do not know what a beer can looks beer, they simply do not know what a beer can looks like. The materials chosen in scientific experiments, like. The materials chosen in scientific experiments, especially in the case of improvised ones, must be especially in the case of improvised ones, must be familiar and available to the students.familiar and available to the students.

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

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 developments, especially in the areas of ICT (Information and Communication Technology) and (Information and Communication Technology) and bio-technology including genetic engineering, the bio-technology including genetic engineering, the interdisciplinary nature of science has been brought interdisciplinary nature of science has been brought out in a prominent way. The role of physicists in out in a prominent way. The role of physicists in unraveling the structures and secrets of the DNA unraveling the structures and secrets of the DNA molecule, the role of “material scientists” and of molecule, the role of “material scientists” and of “metallurgists” in devising special materials are “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, translational invariance, reflection in variance, rotational invariance and time reversal invariance are rotational invariance and time reversal invariance are not topics of interest to physicists and chemists but not topics of interest to physicists and chemists but also also

to artists who use some of these symmetries to artists who use some of these symmetries (knowingly or unknowingly) in their art work, and in (knowingly or unknowingly) in their art work, and in their concepts of “beauty”. Thus, the physicist their concepts of “beauty”. Thus, the physicist teaching symmetry properties in the laws of nature teaching symmetry properties in the laws of nature should draw the attention of students to numerous should draw the attention of students to numerous fascinating examples of these principles around their fascinating examples of these principles around their own life and environment; difficult things would look own life and environment; difficult things would look easy and familiar.easy and familiar.

Now that all eyes are on “Biology” and many people Now that all eyes are on “Biology” and many people very rightly say that the twenty first century might very very rightly say that the twenty first century might very well belong to molecular biology and all its well belong to molecular biology and all its ramifications, let me cite an example involving ramifications, let me cite an example involving physics, biology and environment. physics, biology and environment.

In a Unesco sponsored workshop at Puna in 1986, I In a Unesco sponsored workshop at Puna in 1986, I made a documentary film titled ‘The hand that rocks made a documentary film titled ‘The hand that rocks the cradle rules the world” in which I tried to show that the cradle rules the world” in which I tried to show that if a house has a mother having a science if a house has a mother having a science background, then she could explain some difficult background, then she could explain some difficult concepts of physics, chemistry and mathematics to concepts of physics, chemistry and mathematics to her children in the cozy environment of the garden, her children in the cozy environment of the garden, kitchen, drawing room etc. In a scene in the film, a 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 examination to take in the morning. The son came downstairs running and as he touched some worm downstairs running and as he touched some worm potatoes on his plate on the dining table, he said “Ma potatoes on his plate on the dining table, he said “Ma – it is very warm”. The mother cut the potato with a – it is very warm”. The mother cut the potato with a knife into four pieces and was fanning those. knife into four pieces and was fanning those.

When the son returned home, the mother eagerly When the son returned home, the mother eagerly asked him “how was your exam?”; the son replied, “It asked him “how was your exam?”; the son replied, “It was all right Ma, but there was an odd question which was all right Ma, but there was an odd question which I could not reply; in the question it was asked: why is I could not reply; in the question it was asked: why is it that in winter, we curl up our bodies while sleeping it that in winter, we curl up our bodies while sleeping in bed, while in summer, we stretch our hands and in bed, while in summer, we stretch our hands and feet while resting. The mother said “you could not feet while resting. The mother said “you could not answer only one question; don’t be upset about this”. answer only one question; don’t be upset about this”. Then I appeared in the film and explained that the Then I appeared in the film and explained that the mother could have taught her son the answer to this mother could have taught her son the answer to this question at the breakfast table. question at the breakfast table.

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

Figure: A Sliced Potato

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

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

ELECTROMAGNETIC

CHEMICAL NUCLEAR THERMAL KINETIC(MECHANICAL)

ELECTRICAL GRAVITATIONAL

ELECTROMAGNETIC

Chemiluminescence

(fireflies)

source)(A-bomb)

Thermal radiation(hot iron)

Accelerating charge

(cyclotron)Phosphor

Electromagnetic radiation

(TV transmitter Electroluminesce

nce

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-neutron

reactions

Be9+y→Be8+n 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

KINETIC RadiometerSolar Cell

Muscle Radioactivity(alpha particles)

(A-bomb)

Thermal expansion(turbines) Internal

combustion(engines)

MotorsElectrostriction

(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

††MagnetohydrodynamicsMagnetohydrodynamicsTable: Energy Conversion MatrixTable: Energy Conversion Matrix

A lot can be achieved in science education by using Nature as Teacher.A lot can be achieved in science education by using Nature as Teacher.

4. 4. Nature as TeacherNature as Teacher

It will take quite sometime before school laboratories It will take quite sometime before school laboratories in developing countries are thoroughly equipped for in developing countries are thoroughly equipped for providing science education to children. Should a providing science education to children. Should a science teacher really wait for that time to come, or science teacher really wait for that time to come, or do his/her utmost in teaching science with whatever do his/her utmost in teaching science with whatever little resources (s)he has around himself/herself ? little resources (s)he has around himself/herself ? Doing more with less needs an innovative mind which Doing more with less needs an innovative mind which could discover resources where there is none. Nature could discover resources where there is none. Nature is one such. Many of us observe nature only casually, is one such. Many of us observe nature only casually, but fail to understand its silent working and the but fail to understand its silent working and the language in which it speaks. The purpose of the language in which it speaks. The purpose of the present proposal is to stimulate science education by present proposal is to stimulate science education by looking at several examples in Nature. looking at several examples in Nature.

Coming to the theme of nature as a teacher, let us Coming to the theme of nature as a teacher, let us take the example of ponds which abound in almost all take the example of ponds which abound in almost all countries. A pond can be a very good example of countries. A pond can be a very good example of studying numerous flora and fauna. A science teacher studying numerous flora and fauna. A science teacher can take children to a pond and ask them to study can take children to a pond and ask them to study different phenomena that have been occurring in the different phenomena that have been occurring in the pond all through the day. A child would simply be pond all through the day. A child would simply be delighted to notice the diving of the beautifully colored delighted to notice the diving of the beautifully colored kingfisher into the water off and on in order to catch kingfisher into the water off and on in order to catch some small fishes. He would notice, that the diving of some small fishes. He would notice, that the diving of the kingfisher is perfect, no doubt, but it doesn’t come the kingfisher is perfect, no doubt, but it doesn’t come out with the fish in its beak in every attempt. If the out with the fish in its beak in every attempt. If the kingfisher were really successful in every attempt, all kingfisher were really successful in every attempt, all the fished of the pond the fished of the pond

would have disappeared. Thus, there is a check and would have disappeared. Thus, there is a check and balance in nature which the student can learn from balance in nature which the student can learn from experience. The same sort of experience can also be experience. The same sort of experience can also be obtained when one notices how the deer and the obtained when one notices how the deer and the tiger, both dwelling in the forest, can live in a sort of tiger, both dwelling in the forest, can live in a sort of ecological balance. The deer jumps more than the ecological balance. The deer jumps more than the tiger, and that’s how it escapes the tiger’s chase, but tiger, and that’s how it escapes the tiger’s chase, but on certain occasions, the deer’s head may get stuck on certain occasions, the deer’s head may get stuck in a bush, to the advantage of the tiger. Coming back in a bush, to the advantage of the tiger. Coming back to the pond, it would be quite thrilling for children to to the pond, it would be quite thrilling for children to watch how insects walk on the water surface of the watch how insects walk on the water surface of the pond, using the property of surface tension of water, a pond, using the property of surface tension of water, a fact with which the children would be familiar much fact with which the children would be familiar much later in their educational later in their educational

endeavor. The months of June and July are the endeavor. The months of June and July are the months where monsoon comes with its welcome months where monsoon comes with its welcome showers. The dry hollows in the fields and the showers. The dry hollows in the fields and the countryside are filled-up, and still waters of ponds and countryside are filled-up, and still waters of ponds and pools mirror hurrying clouds above and pleasant pools mirror hurrying clouds above and pleasant grassy banks beside. Although the pond may look grassy banks beside. Although the pond may look ordinary, a child can discover a world of wonders ordinary, a child can discover a world of wonders hidden in and around it. One could notice frogs hidden in and around it. One could notice frogs spawn in masses of grey jelly floating on the warm spawn in masses of grey jelly floating on the warm water. Peer down into the water one can see young water. Peer down into the water one can see young tadpoles wriggling among the weeds or clinging to tadpoles wriggling among the weeds or clinging to leaves of plants with their suckers. Water snails are leaves of plants with their suckers. Water snails are also a pleasant sight on the edge of the pond or on also a pleasant sight on the edge of the pond or on stems of water plants. Unlike the land snail, a water stems of water plants. Unlike the land snail, a water snail has a single pair of feelers with eyes raised on snail has a single pair of feelers with eyes raised on swellings at the bottom of each swellings at the bottom of each

feeler. The little round opening in the side is the feeler. The little round opening in the side is the breathing hole. They come to the surface of the water breathing hole. They come to the surface of the water for a fresh supply of air. Young snails, complete with for a fresh supply of air. Young snails, complete with tiny shells, hatch and search for food among stones tiny shells, hatch and search for food among stones and plants of the water world. They are useful in and plants of the water world. They are useful in keeping the water of the pond clean, for they devour keeping the water of the pond clean, for they devour all kinds of rotting matter. One of the most interesting all kinds of rotting matter. One of the most interesting objects to see in the pond, is the water-crabs. The objects to see in the pond, is the water-crabs. The slightest movement sends them scurrying off slightest movement sends them scurrying off sideways to a hideout. One occasionally may sideways to a hideout. One occasionally may encounter a water snake swimming gracefully. It lifts encounter a water snake swimming gracefully. It lifts its head out of the water to look at people as it swims its head out of the water to look at people as it swims past. One also can witness pond-beetles, which are past. One also can witness pond-beetles, which are fierce and attacks smaller creatures very savagely. It fierce and attacks smaller creatures very savagely. It snaps up tadpoles and other pond creatures in its snaps up tadpoles and other pond creatures in its pincer-like jaws and sucks the juices from their soft pincer-like jaws and sucks the juices from their soft bodies. One of the curious creatures of the bodies. One of the curious creatures of the

pond is the Pond Skate. This long-legged insect glides on the pond is the Pond Skate. This long-legged insect glides on the water almost as if it were ice. It is one of the many water-bugs 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 that has a beak-like mouth for sucking juices from the pond insects on which it thrives. Then there are water scorpions and insects on which it thrives. Then there are water scorpions and the brilliant dragon-flies. The pond also presents a lively the brilliant dragon-flies. The pond also presents a lively picture of the best known of all plants, namely, the water-lily. picture of the best known of all plants, namely, the water-lily. The sacred lotus belongs to the same family of water lily. A The sacred lotus belongs to the same family of water lily. A pond contains duckweed which grow rapidly and covers the pond contains duckweed which grow rapidly and covers the surface. During summer, it offers a pleasant shape for water surface. During summer, it offers a pleasant shape for water creatures exposed to the glare of the strong sunlight. Ducks creatures exposed to the glare of the strong sunlight. Ducks eat it with relish, and that is how the weed gets its name. A eat it with relish, and that is how the weed gets its name. A student can learn something even from the water hyacinth in student can learn something even from the water hyacinth in the pond. Now we know, that water hyacinths can be a boon 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 disguise, rather than a nuisance. If one third of every pond is filled with water hyacinth, it keeps the water soft and becomes filled with water hyacinth, it keeps the water soft and becomes beneficial for the fishes. beneficial for the fishes.

All in all, the pond could serve as a good example for the All in all, the pond could serve as a good example for the interactions of many living organisms. All the organisms that interactions of many living organisms. All the organisms that dwell in the pond may serve to give an illustration of bio-dwell in the pond may serve to give an illustration of bio-diversity existing even in a limited area of nature. Thus, before diversity existing even in a limited area of nature. Thus, before a student could learn about bio-diversity by studying the a student could learn about bio-diversity by studying the various life forms in Asia, Africa and Latin-America, a rural various life forms in Asia, Africa and Latin-America, a rural child can have a very early scientific exposure to the concept child can have a very early scientific exposure to the concept of bio-diversity, merely from a study of the life forms that the of bio-diversity, merely from a study of the life forms that the village pond contains. This study needs only a little bit of village pond contains. This study needs only a little bit of imagination of a teacher, and learning science can then imagination of a teacher, and learning science can then become fun and pleasure for the young learners. become fun and pleasure for the young learners.

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)

5.5. From the management of the From the management of the sheep to that of the shepherdssheep to that of the 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 meeting in particular, must be accorded the honor for meeting the challenges of the times. They must also be given the challenges of the times. They must also be given incentives. In this connection, I am reminded of a incentives. In this connection, I am reminded of a book titled “The Man Who Counted” authored by book titled “The Man Who Counted” authored by Malba Tahan[3]. In this book which is a collection of Malba Tahan[3]. In this book which is a collection of mathematical adventures, is given the legend of mathematical adventures, is given the legend of Beremiz Samir who, coming from the village of Khoi Beremiz Samir who, coming from the village of Khoi in Persia, was a shepherd and used to tend vast in Persia, was a shepherd and used to tend vast flocks of sheep. For fear of losing lambs and flocks of sheep. For fear of losing lambs and therefore being punished, he counted them several therefore being punished, he counted them several times a day. He became times a day. He became

so good in counting, that he could count all the bees so good in counting, that he could count all the bees in a swarm and all the leaves in a tree. Satisfied with in a swarm and all the leaves in a tree. Satisfied with his mathematical agility his master granted him four his mathematical agility his master granted him four months’ leave. During this leave he showed wonderful months’ leave. During this leave he showed wonderful feats to many, and finally was offered the post of feats to many, and finally was offered the post of Vizier by Caliph al-Mutasim of Baghdad. But Samir Vizier by Caliph al-Mutasim of Baghdad. But Samir did not accept the post. Science and Mathematics did not accept the post. Science and Mathematics teachers do not want to be Viziers but they at least teachers do not want to be Viziers but they at least want to be paid reasonable salaries so that for want to be paid reasonable salaries so that for purposes of meeting the costs of living, they do not purposes of meeting the costs of living, they do not take up many jobs and can remain faithful to one take up many jobs and can remain faithful to one profession only, namely teaching. In some of the profession only, namely teaching. In some of the countries of Asia and presumably of other continents, countries of Asia and presumably of other continents, teachers’ salaries are very low, and as a result they teachers’ salaries are very low, and as a result they often do other jobs to the detriment of their own often do other jobs to the detriment of their own profession. This practice must be stopped.profession. This practice 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 should college or university. In other words, a teacher should be judged by his intrinsic merit and not by the place be judged by his intrinsic merit and not by the place he is working in. Universities cannot flourish if schools he is working in. Universities cannot flourish if schools are neglected. We must remember the saying “The are neglected. We must remember the saying “The battle of Waterloo was won in the playground of battle of Waterloo was won in the playground of Eton”.Eton”.

6. 6. Conclusion:Conclusion:

Science and mathematics are the essential tools for Science and mathematics are the essential tools for the study of nature. While utmost care should be the study of nature. While utmost care should be taken to attract students to these basic subjects taken to attract students to these basic subjects through teaching in a delightful manner, the teachers through teaching in a delightful manner, the teachers to be appointed must be selected very judiciously. to be appointed must be selected very judiciously. And once selected, his salary structure must be And once selected, his salary structure must be logical. It would be a great irony if teachers logical. It would be a great irony if teachers responsible for upholding the logic of science and responsible for upholding the logic of science and mathematics are themselves not dealt with in a mathematics are themselves not dealt with in a logical way. logical way.

Talking of logic which connects science with Talking of logic which connects science with mathematics, one might come forward and say rather mathematics, one might come forward and say rather pessimistically “what is the use of teaching logic in pessimistically “what is the use of teaching logic in the present day world where force is prevailing over the present day world where force is prevailing over logic?” In this connection, I would like to narrate a logic?” In this connection, I would like to narrate a story told in the book of Malba Tahan:story told in the book of Malba 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 the 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 lion, kept the dirty pig for himself and gave the miserable rabbit to the jackal. The lion was very angry miserable rabbit to the jackal. The lion was very angry at this division and said “who has ever seen three at this division and said “who has ever seen three divided by three giving a result like that?” Raising his divided by three giving a result like that?” Raising his paw, the lion swiped the head of the unsuspecting paw, the lion swiped the head of the unsuspecting tiger so fiercely that he fell dead a few feet away. The tiger so fiercely that he fell dead a few feet away. The lion then gave the charge of the division to the jackal lion then gave the charge of the division to the jackal who, having already witnessed the tragedy of the who, having already witnessed the tragedy of the tiger said to the lion, “the sheep is a feed worthy of a tiger said to the lion, “the sheep is a feed worthy of a king, the appetizing pig should be destined for your king, the appetizing pig should be destined for your royal plate. And the skittish rabbit with its large ears is royal plate. And the skittish rabbit with its large ears is a savory bite for a king like you”. The lion praised the a savory bite for a king like you”. The lion praised the jackal and asked him how jackal and asked him how

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

References: References:

[1] [1] “Symmetry” by Herman Weyl, Princeton “Symmetry” by Herman Weyl, Princeton University Press, Princeton, New Jersey, 1952University Press, Princeton, New Jersey, 1952

[2] [2] “700 Science Experiments for everyone”, “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] [3] “The Man who Counted” by Malba Tahan, W.W. “The Man who Counted” by Malba Tahan, W.W. Norton & Company, USA, 1994. Norton & Company, USA, 1994.

The EndThe End