tag:blogger.com,1999:blog-12333518320922941492024-02-18T22:17:04.717-08:00The Road Less TraveledThis is my 'adda' -- a space for reflection and sharing for me and my friends. Eventually, I plan to post all my writings (since 1986!), on education and other things that have and continue to bother, concern and excite me...Do make use of this space and lets engage in a good conversation...do invite your friends and their friends too! That is what this 'adda' is all about...Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.comBlogger40125tag:blogger.com,1999:blog-1233351832092294149.post-11515892666066787572015-05-06T05:55:00.000-07:002015-05-06T05:55:07.586-07:00The gentleman who taught infinity<div dir="ltr" style="text-align: left;" trbidi="on">
<em>This is my first book, which is now under publication...wait for the book, whose story I have captured below</em>. <br />
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: large;">The gentle man who taught infinity</span></span></b></div>
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30 years after they have parted ways, a student suddenly remembers his math
teacher from school days. As he starts writing about him, he is surprised to
discover that he remembers a lot of the interesting stuff he was taught.
Gradually, as everything comes back, he ends up writing a full narrative. At
the heart of this narrative is Channakeshava, the gentle teacher who took his
students on a roller coaster ride of the world of mathematics. Though he worked
in a regimented school, Channa often broke the boundaries of a restrictive
school syllabus, sterile textbooks and mind numbing examinations.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman",serif; font-size: 12pt;">In <i style="mso-bidi-font-style: normal;">The gentle man who taught infinity</i>, we
journey with Channa and cross the Seven Bridges of Konigsberg, grapple with the
intriguing Barber's Paradox, understand what took mathematicians nearly 350
years to solve Fermat's Last Theorem, appreciate why mathematics is beautiful
and explore the paradoxes of infinity. Along the way, we are introduced to great
mathematicians like Euclid, Bhaskaracharya, Cantor and Euler, among others.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman",serif; font-size: 12pt;">Using
storytelling to great effect, this remarkable teacher showed that mathematics
is very much a human endeavour. It need not be the drudgery that we make of it,
in our mad pursuit of marks and grades. Instead, the learning of math can be
fun, meaningful and fulfilling for everyone. As the narrative unfolds, teacher
and taught, subject and craft all get intertwined and result in a fascinating
story.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p></o:p></span> </div>
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<span lang="EN-GB" style="font-family: "Times New Roman",serif; font-size: 12pt;"><o:p>*****************************************************************</o:p></span></div>
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Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-35884766528889535802012-06-25T03:46:00.001-07:002012-08-13T10:26:30.049-07:00The CCE Conundrum<div dir="ltr" style="text-align: left;" trbidi="on">
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The entire enterprise of organized education, with its lakhs of schools, millions of teachers and thousands of department workers who constitute its bureaucracy at the national, state, district and sub district levels, who strive to make education happen in our country, can be said to be driven at different points in time and in various ways by a few fundamental questions. These questions actually flow from one to the other, and they are all interlinked. Each question can generate many different and debatable responses, with these debates often going back hundreds of years at least. There are no clear answers even today, and that is what makes the task of educating children that much more fascinating and complex. Everybody can have an opinion here. That is the best as well as the most frustrating part.<o:p></o:p></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The questions<o:p></o:p></span></b></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The first and obvious question is: Why should children go to school? This has to do with what we usually term as educational aims or more specifically, the aims of schooling. These aims can be many and often and they can be at cross purposes, if you will. Ultimately, the aims we choose are also a reflection of the kind of world or society we want to create. There is this belief that education has a role in the creation of that society, that schools have a social role. The Naxals, for instance, will have a conception of educational aims that will be very different from the aims a capitalist or industrialist would articulate. The two worlds are quite different – the collision of these worldviews is perhaps at the heart of the Maoist problem. That is a separate debate I don’t want to get into right now.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The second question is: What should they be <i style="mso-bidi-font-style: normal;">doing</i> there (in school)? How should they pass their time there? This usually boils down to the question of <i style="mso-bidi-font-style: normal;">what</i> children should learn, since schools claim that they teach children this and that – the passing on of knowledge is seen as central to what schools do. As part of this learning, what kinds of experiences would we want children to get at school? Again, the responses are bound to be divergent, depending on who is responding and under what conditions the response is being made. If a natural disaster strikes, for example, there are often shrill cries for including disaster preparedness in the curriculum. If there is a communal conflagration, then secular elements get emphasized. And so it goes. It is a long list. And it is controversial, as we have seen in the recent instance of the <i style="mso-bidi-font-style: normal;">tamasha</i> that has been generated over the inclusion of the Ambedkar cartoon in a textbook prepared by NCERT. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I can give another example. Some years back in Jammu and Kashmir, it was decided that English would become the medium of instruction in all schools from grade 1. The story that did the rounds was that the Education Minister was very upset one year with the 10<sup>th</sup> standard exam results of the state. Someone suggested to him that this was because children were not getting an English medium education! And that is how an education policy was influenced. The point here is that what children should learn gets decided often in convoluted ways that seem to defy reason sometimes. <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Related to <i style="mso-bidi-font-style: normal;">what</i> is the question of <i style="mso-bidi-font-style: normal;">how</i> children should be taught. If getting good marks and cracking the exams is the idea, then everyone will apply their minds to beat the exam. There will be mock exams and the like, and the experts who have cracked it earlier will have tutorial sessions with the hopefuls. Bihar’s ‘Super 30’ is a classic example, where year after year children from disadvantaged backgrounds are coached to crack the entrance to the IIT. If ‘developing critical thinking’ is a key aim, then teaching methods as well as content will be different. Getting good grades in the exams may then become a peripheral concern. Of course, it can be argued that the two are not mutually exclusive. So the second question is the one that is concerned also with the methods of teaching and learning.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The third question is: How do we know if we are moving in the direction we want to go…? This is really at the heart of the assessment of the schooling experience. What should we do to find out if any child who is subjected to this system called school, is actually <i style="mso-bidi-font-style: normal;">becoming</i> what has been envisaged under question 1 above…? This is a complex one for it may be difficult to limit the response to the period of schooling. Given the vagaries of human nature, many things may happen <i style="mso-bidi-font-style: normal;">after</i> an individual has moved out of the institution of schooling. (Note here that we use the word school to indicate the various stages of formal, organized education.) <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Question 3 is inextricably linked to question 1 – if this is what we want for our children from school, we need to do something with them which will move them in this direction and, further -- we have to develop a system which will enable us to find out if we are moving in the direction sought. These aspects are all intimately linked with each other, and cannot be seen in isolation.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I would like to mention here that the preparation of teachers is at the heart of the education enterprise and we will not be able to move an inch if teachers are not prepared enough to address the above questions in their day to day practice. And since we have not yet reached a stage where machines are teaching children (if one goes by what hard core proponents of IT sometimes have to say with regard to the potential they see in digital technologies for education, it would seem as there is no other alternative but to substitute teachers with machines), we may still consider the teacher challenge as the central one in education.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The question of assessment<o:p></o:p></span></b></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I will primarily address question 3 and the difficulties that come with it. Not because questions 1 and 2 are not important. They are, but at the moment, we are a bit obsessed with question 3, thanks to the emphasis on ‘Continuous and Comprehensive Evaluation’ (CCE) in the Right to Education Act. Perhaps very few of the many Education Acts enacted by countries across the world mention exactly how children should be taught, and how what they have learnt should be assessed. Ours does. I will come to this a little later.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Perhaps the easiest way of developing a system of finding out if children have moved in the directions we want them to go, (or, in more direct terms, to find out if they ‘have made the cut’) is to have exams. This is what we have been doing for a long, long time, with great effect. It feeds our collective anxiety and it has spawned a huge industry. Many years ago, when I was in school and later in the pre-university course (11<sup>th</sup> and 12<sup>th</sup> std.) we often heard that so and so college or school in Bangalore was the ‘best’, or provided ‘good education’. Then we would hear some name or the other of faculty members who were ‘fantastic’ and whose tuition classes if you attended would guarantee you good marks in the public exams and a passport to a better life. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">It dawned on me much later that this entire discussion of best schools and colleges was more or less centred round how many ranks they obtained in public exams, and what percentage their ‘best students’ got in those exams. ‘Good education’ therefore got focused on questions two and three – for instance, what were the best methods of teaching which would lead to great marks? What kind of exams would ensure that children would make the cut? Now, exam performance is not the same as academic excellence, which is a much broader idea. Further, it certainly cannot be equated to ‘good education’, which can and does mean many more things. But a certain dominant interpretation of ‘good education’ can make it look as if exam performance is the main thing involved. Ultimately, every other consideration falls by the wayside. So it may not be uncommon to hear parents and teachers compare two schools and say one is better than the other since it churns out good results every year. It does not matter <i style="mso-bidi-font-style: normal;">how </i>those results are churned out and if children have understood (for instance) what they have studied -- or if they have inculcated along the way, a love for learning. They are treated much like the race horses which get whipped every now and then to run faster and faster and cross the finishing line.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I must delve a little more on exams -- the system of exams with their marks can result in certain amusing and painful results and realities. When I was in 12<sup>th</sup> standard with a science combination, we had two clear options – engineering or medicine. The IT industry had still not entered the scene in Bangalore in a big way in 1987 when I cleared my 12<sup>th</sup> std. exams. The Call Centres and various other options that this thing called IT has spawned were still far away. So our teachers kept egging us on to do either engineering or medicine. It was made to look as if life would not be worth living if we didn’t become engineers or doctors. Since Karnataka those days (more so now) had a greater number of engineering colleges than colleges that made you doctors, the cut off percentage for engineering was lower than that of medicine. Those aspiring to become doctors had to study that wee bit harder and they had to get well above 95% or 97% if they had to secure a merit seat in a reasonably good medical college. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">So, we had a system which decided who would build bridges and design machines and who would look after people’s lives, based just on a mischievous combination of their exam marks! No other attributes necessary to these professions were considered. And that is how I became an engineer, only to leave the profession some years later. The system has not changed a bit since those days.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The second thing about exams, which some argue is very practical, is that they play the role of the perfect filter for the educational system. Not everyone who starts out in school stays long enough ends up doing the same things. Imagine if they did! There is the rural-urban divide, there is the boy-girl divide and then there is a divide depending on which community you come from and where you are located. The system then resembles a pyramid, and children keep routinely falling off it as they try and negotiate its steep and treacherous climb. Only a few get to the pinnacle. This, the exams achieve perfectly. Don’t just ask what happens to the ones who fall off the pyramid. They do not get the goodies that the others get. They get this message that they are second rate performers, relegated to some menial jobs. Knowing fully well that we have a system that produces inequality, we still go on saying that education is the fundamental right of every child -- as if by just saying it things will fall in place!<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">CCE as Saviour<o:p></o:p></span></b></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">This limited approach has been the cause of some concern for many years – that we have the grandest of educational aims, enshrined in the various documents that we have routinely produced for more than a hundred years, but had the narrowest and harmful ways of ascertaining if we were moving in the directions we wanted to go. Of course, there are problems with the kinds of textbooks that the state produces, as well as the ways in which teachers are prepared. Along with this, no one had cracked the puzzle of assessment – how can we put in place a system which reflects the educational aims that we set out to achieve? <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">In the nineties, much before the struggles for instituting a law that recognizes education as a fundamental right in our country occurred, we started hearing about ‘Continuous and Comprehensive Evaluation’ (CCE). The usual lament was: ‘How can we just go on with a system that pronounces judgment on that one day and within those few hours…? We need to have a system that is fairer and which just doesn’t rely on marks at the end of the day…’ To add to this was the other refrain that the current system was not looking at the child as a ‘whole’ – exams, at best, tested short term memories whereas the child was much, much more than a person who was expected to give standard answers and repeat what was taught. So the terms ‘continuous and comprehensive’ came into being. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The idea behind the term continuous was that a child’s learning must be assessed continuously instead of only relying on term end tests and exams. This cumulative assessment would then provide a truer picture of the child’s abilities, difficulties etc. and would also provide the teacher useful reference points to intervene in case there were difficulties that needed to be addressed. The idea behind the term comprehensive was that we were assessing children only on the subject matter areas – math, language, science and so on. Would this provide a complete picture of the child’s abilities? Was education all about learning only these subjects? Obviously not! So went the arguments for an alternative or more comprehensive way of finding out where children were going. ‘Comprehensive’ was then understood in terms of expanding our understanding of what children could actually do, other than engaging with and learning the ‘core’ subject matter, other than just reading, writing and arithmetic – things we made them do. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I remember the jokes that usually did the rounds. ‘What’s the fuss anyway?’ Someone asked. ‘All this is important if teaching takes place in the first place!!’ Indeed, that was one concern which many were just not prepared to look at in the eye. Where was teaching happening? Survey after survey showed how little children learned, even on the most basic aspects of reading, writing and arithmetic (the three R’s, as we called it) even after 5-8 years of schooling. We talked about teacher absenteeism, non-teaching duties of the teacher and the poor quality of teacher preparation. What was the point of erecting a grand plan for evaluation with ill equipped teachers who could not even manage the basics? We seemed to have assumed that the basics were all in place, and that schools were now prepared to do this CCE. But there was also this argument that this examination paranoia was mostly applicable to urban areas fuelled by unhealthy competition.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Anyway, in workshops, meetings and many formal and informal interactions, we kept hearing this clarion call for CCE. It was seen as a part of what was broadly termed as ‘education reform’ – the set of policies and actions that were needed at all levels to improve the education that children got which we were all unhappy about. Many years passed, but CCE didn’t find the light of day. There may have been smaller experiments and pilots but these did not end up influencing day to day practice on a larger scale. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Meanwhile, document after document lamented our insensitive system of assessment which stifled all creativity and created distress instead. Much was written about it in 2005, the year that saw yet another National Curriculum Framework document being prepared. There were these ‘position’ papers – 21 in all, that elaborated the main document. One of them was entirely about examination reforms – how to make exams more appropriate for the ‘knowledge society’ of the 21<sup>st</sup> century, and so on. The position paper on ‘Curriculum, Syllabus and Textbooks’ carried, in the end a very angry and powerful quote from the Scottish pilot turned educator, David Horsburgh thanks to whose efforts in a small school in Andhra Pradesh many states are now attempting to follow ‘Activity Based Learning’ based on his ideas (that is a different story altogether!): <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Book Antiqua','serif'; font-size: 10pt; mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: Batang;">‘…evaluation has been one of the most important forces in the gradual degeneration of all school education…the whole antiquated evaluation process, should as speedily as possible be hurled lock, stock and barrel out of the windows of our educational system in just the same way as the chamber pots were emptied in eighteenth century London…’ <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">CCE travelled some distance before it we saw it appear as part of law – the Right to Education (RTE) Act, in 2009. The Act stated in no uncertain terms that in order to find out what a child was learning, one had to do it continuously and in non-threatening ways and not just use term end tests and exams. You could talk to the child and get her involved in assessing what she had learnt, observe from a distance the various things that the child did and note them, provide descriptive feedback, give exercises of different kinds (useful things that we do very little about), or you could resort to some paper-pencil activity that was really engaging (again, something teachers don’t do much of). <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">All these methods could be employed together or separately – but they had to be done again and again, and not just once or twice in a year to brand the child in any which way. One had to build up some sort of a history to construct a more complete picture. And then, the whole process had to be ‘comprehensive’ – one had to look at the ‘whole’ child, something that we are woefully lacking in at the moment. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>It is interesting to see the initial scramble that results when anything becomes a law. Suddenly, something changes in the air. The RTE Act, which came into being after a tortuous journey, became the reference point of sorts after August 2009. In workshop after workshop, we started hearing statements like this one, which we started using in our various interactions as well: “This is not a scheme…it is a law. And do you know what will happen if this law is violated…? You can be punished -- <i style="mso-bidi-font-style: normal;">Ye Dandaneeya hai</i>!!” Further, we understood that the compulsion and responsibility of providing education is on the Government, and that Government alone is answerable -- as if it was not all these years! <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">It will be interesting to see how the government gets ‘punished’ as we go along. In any case, we have a poor track record of punishing or taking the government to task on the several promises it has made over all these decades to its people. <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">While the Act has several provisions along with clear timelines and targets, parameters related to quality come into effect immediately. So we can start taking the government to task right away, and fill the court rooms with all sorts of pedagogical cases! There will be interesting court cases, I’m sure, if one takes the judicial route as the last resort to change the educational system. I’m not sure if this will alone work. And judges will then need to be educated about child centred education and the like. We can prepare primers for this. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The aspect of Continuous and Comprehensive Evaluation sits squarely within the notion of quality of education because this is what helps us find out, using various ways, the inherent abilities and potential of the child, and also if what we are doing in school is having the desired results in the directions we have set out. As I write this, state after state has, among other things, attempted to do something about CCE which was on the backburner for all these years. Workshops and trainings have been held galore and many states have developed manuals for teachers. The CCE lexicon sounds like this – formative and summative evaluation, scholastic and co-scholastic areas…rubrics and tools for this…phew! All of these are supposed to take care of CCE. It is now becoming a nice business and many organizations are beginning to become ‘experts’ who will deliver ‘CCE Products’ for our thankful consumption, both online and through workshops. <o:p></o:p></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Assessment as a tool for reform…?<o:p></o:p></span></b></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">A question that has consistently bothered me is – how fundamentally different are these developments from what we have been up to so far? It is one thing to define or lay out the aspects that we would want to assess in a child. This wish list can be really long, and we can include all our fantasies of ‘good education’ in it. The issue, however, is whether the teacher is prepared to do it. From all accounts, the answer to this is in the negative. I do not wish to take stock of the results of efforts over the last twenty years to improve what happens inside the classrooms, but I do believe that the outlook is still gloomy. For one, if we map what children learn on even the most basic aspects – such as 3R’s – reading, writing and arithmetic, we find worrisome gaps. We know that children at the end of five years barely end up learning stuff that is equal to grade 1 or 2. Further, there are many studies that show just how un-child friendly, monotonous and inequitable our classrooms are, barring some exceptions. In such a scenario, one wonders if reform which uses assessment as a basis is going to make any difference. In fact, it may only end up causing more confusion. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">So far, CCE looks like old wine in a new bottle, which is what happens when we do tinkering. The earlier tests and term exams seem to have now morphed into this formative and summative evaluation business, which is now called the ‘CCE method’ of teaching! The spirit, therefore, has not changed. To add to this, teachers seem to be making effective use of the ‘no detention’ policy – that a child should never be detained in a classroom, at least till he reaches the eighth grade. The spirit behind this no detention policy was that the child should not be penalized for under achievement or no achievement. The argument was – why wouldn’t any child want to learn, provided we made learning interesting, engaging, meaningful, and provided all obstacles in the family, school and community, were removed? The problem was thus located outside the child. Fair enough. But teachers seem to have interpreted it quite differently, and this has resulted in ‘automatic’ promotion from one grade to the other – never mind if the child has learnt anything or not! In many ways, this is an excuse for not teaching which teachers can exploit. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">So, CCE has become continuous promotion with little or no learning.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Teachers have so far been adept at giving paper-pencil tests and scoring answer sheets using red ink. It gives them a sense of pleasure, of power, to be able to point out mistakes and slot the child. Even here, we can ask if understanding is assessed on these paper-pencil tests and exams. Currently, it is assessed in limited ways, since that is not the emphasis in teaching. Now we are saying that the teacher should move away and not be limited by this. We are saying that the nature of paper-pencil exercises and tests should change and assess whether the child has understood something or not. Secondly, we are saying that there is something beyond the so-called scholastic/subject matter areas – any child comes to school with a range of abilities – children can express and imagine in a variety of ways, and they may be good in certain kinds of physical activities and so on. These must be recognized (we use the term ‘co-scholastic’ to underline this) and must contribute to the overall assessment of the child. So, if a child draws a three headed elephant using his imagination, or if a child draws a parrot with red feathers and a green beak (which I have actually seen in a school in Chhattisgarh), what do we expect the teacher to do…? How does one evaluate this in CCE? What is the reference point? First of all, how does one evaluate expression, say, a drawing? I have a problem with this. We might at best say that the child can do such and such a thing, and make a record of his abilities, and celebrate these. It would be such a pity if a teacher sees these drawings and says, “But this is wrong! Such animals don’t exist! What have you done?” <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Teachers, who have a very clear conception of ‘right’ and ‘wrong’ (and most teachers belong to this group), and who are schooled to believe that there is only one right answer, will take such children to task. They have not been prepared for this. Similarly, if children start asking questions which the teacher may not be able to answer, what is the teacher supposed to do under CCE? So far, we have shut them up. But are we prepared to let them ask? <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The more I think about CCE, the more I am inclined to believe that it is much more than evaluation. It is first of all about understanding the child <span style="mso-spacerun: yes;"> </span>– where she comes from – her background, her family, her identity, her various abilities and the challenges that she faces as she negotiates school and its requirements. So let me add CCU – Continuous and Comprehensive Understanding, as a pre-requisite to CCE. Without this, can we say that our evaluations are going to be sound and helpful to the child? Secondly, is everything about evaluation? I suppose, no. Like I mentioned above, not everything that the child does needs to be judged on some grading scale. We may describe and narrate what the child does. This becomes a cumulative record of that child’s experiences and abilities as she passes through school. A well-kept record will read like a story of that child. It tells us a lot, actually.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">What is currently happening in the name of CCE is sad. We have centrally developed manuals and formats which the teachers have to fill out routinely. There is very little of remedial teaching or support to address problems. Ideally, if we use this approach, we should be able to map out each child’s abilities, challenges and prepare plans to help the child overcome these challenges. We must also be in a position to truly appreciate each child as a person. But ‘filling the format’ has become the end rather than the means. <o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">In order to look at the child differently, and in a more wholesome manner, the teacher’s conception of education, its purposes, its processes and its possible outcomes, has to undergo radical changes. This, I believe, has not taken place. All these years, we have focused more on techniques of teaching. There has been very little discussion on the ‘why’ and ‘what’ of education and how the teacher sees these things. Further, we have also not looked at the teacher as we would want the teacher to look at the child. Teachers, like children, need to be nurtured. Instead, we treat them with distrust at best.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">To sum up, it seems pertinent to ask – how will you measure or evaluate something when in the first place you are not doing most of what is required to make that thing happen? We are trying to evaluate the outcomes of a teaching-learning process which is meant to be child centred but which is actually anything but that, which still requires children to learn by rote. Then we add a few things we need to measure under the so-called ‘co-scholastic’ domain without seriously asking whether we are doing them (sports, music, art and craft and the like) in the first place in our schools. These aspects, which should actually be central to the educational experience of every child, are relegated to mere formalities. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">You cannot just do something all of a sudden because some law or Act requires you to it. Presently, everyone is running around preparing CCE manuals and the like, hoping that these missing elements in a child’s education will somehow appear in the classroom once training on CCE is done. We need to dig deeper and ask why, in the first place we were not doing these things earlier.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I believe that the route to reforming, changing, improving or transforming (call it what you want) classrooms cannot come alone from assessment. Something else needs to happen first in the way children are taught. This contains the seed for measuring what they have learnt. Assessment cannot be seen isolation, as we are seeing it now.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Which is why, I say that CCE as it exists now will remain at best another scratching on the surface. We have put the cart before the horse. Then we have missed the wood for the trees. They exist together and cannot be seen in separation. <o:p></o:p></span></div>
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Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com3tag:blogger.com,1999:blog-1233351832092294149.post-11135819597794257242012-05-27T04:46:00.001-07:002012-06-01T06:23:55.015-07:00Enjoycation<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman"; font-size: 16pt;">T</span></b><span lang="EN-GB" style="font-family: "Times New Roman"; font-size: 12pt;">he word ‘education’ can have a variety of meanings depending on how you look at it and what you want from it. Thus, we hear the clichéd ‘Education is a contested terrain…’ statement often in discourses. The multiple meanings that we derive from education may or may not have anything to do with the etymology of the word -- which, from various accounts, comes from the 16<sup>th</sup> century usage of the term ‘Educere’ in Latin, essentially meaning “</span><span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">bring out” or “lead forth.” Another Latin word, ‘Educatio’ means ‘breeding, bringing up, or rearing.’ What we do in the name of education is thus related to the etymology of the term, at least where it concerns the usage of the word in English.</span><br />
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Interestingly, the word ‘Siksha’ which we use to denote education (for instance, as in Sarva Siksha Abhiyan) has its origins in Sanskrit. Its meaning doesn’t quite come anywhere close to the meanings we ascribe to the educating of children and actually means the study of pronunciation of words and syllables through correct intonation. This is not central to the process of education now though it may have had critical importance during Vedic or pre-Vedic times especially when transmission of knowledge occurred orally. But I have seen discussions and debates about how important it is for children to correctly pronounce words. ‘<i style="mso-bidi-font-style: normal;">Uccharan theek nahi karte ye bacche</i>’ (note the emphasis on <i style="mso-bidi-font-style: normal;">these children</i>) is a constant refrain we hear from teachers. ‘Uccharan’ (pronunciation) is thus a frustrating area for some teachers, while others do not seem to be bothered too much about it. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Anyway, I think this is like missing the forest for the trees. Thankfully, in this huge Government of India flagship program called the Sarva Shiksha Abhiyan, we are not talking about universalization of correct pronunciation. Imagine if we did! We would have then spent much on establishing studio facilities everywhere and would have supplied headphones to every teacher and child to pronounce their way to success. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Further, I must add that this business of pronunciation (not ‘pronounciation’, remember!) is related to the dimension of Class, and how we use Class as a category for choosing who we relate to, and to what extent we relate to that person or persons. But this is a topic that needs separate discussion.</span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">This is what fascinates me about education. It is a bit like searching for the Holy Grail, and it refuses to get tied down. There is no one formula that defines it, though there may be some underlying principles. Even here, there can be disagreement. Everyone -- educated or not, can have their opinion about it.<span style="mso-spacerun: yes;"> </span>For some, education is like a passport to success – you get good grades in all your exams, land up a good job and fall into a certain slot in which you keep going all your life. This is the ‘reward’ that society gives you for studying hard. For others, like that great Brazilian educator Paulo Friere, education can lead to ‘critical consciousness’ in society – an interesting state in society in which a huge mass of (mostly poor) people start asking why they are that way, and why the rich stay rich. This realization, flash point or critical consciousness can then spur them into action like it did for instance in Naxalbari in West Bengal in May 1967, when poor peasants chose not to keep quiet about their exploitation at the hands of the landlords. Forty five years later, the ‘Naxals’ have been described as the biggest internal security threat by our Prime Minister. That’s another story which is unfolding. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Of course, one can ask – did the peasants develop that critical consciousness as a result of schooling? Very unlikely. But I am prepared to argue that they underwent a process that must have included, at various points in time, thinking about their condition and questioning it. We cannot also say if everyone thought in the same way. There must have been local leadership that goaded people to do something. Anger must have played its role. The point is not whether the poor peasants went to school. Friere believed that schools or organized learning in particular and education in general, whether it is inside or outside the boundary wall of the school, could result in critical enquiry leading to emancipation of oppressed people. He was able to demonstrate this through his work.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Apart from yielding diverse meanings, what is equally interesting is the way the word education gets morphed to yield newer words with different meanings. In a sense, you can say that the word constantly gets bastardized. This is what I keep pointing out in conversations with friends. For instance, my daughter attended a preschool called ‘Jumbo Kids’ which stated in no uncertain terms that it provided ‘Kiducation’. This is what happens when kids get education. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">There is a school called ‘Brighton Academy’ in Raipur which is on the way to the N. H Goel ‘World School’ which my daughter goes to. Interesting are the ways in which schools get named. Interesting too are their claims. The names of many schools contain the word ‘International’ nowadays. In my daughter’s case, her school’s claim is that it is ‘Global’. Do we mean international or global citizens as an outcome for children attending these schools? I’m not sure. Or, are they using international or global methods in teaching? Any school that has a swimming pool, air conditioned classrooms, dining spaces where five star caterers serve food, horse riding and golf, and exposure visits to other countries considers itself as a prime candidate for using ‘international’ or ‘global’ as part of its name. Even schools that do not have these facilities use these words in their names. Of course, to be fair, some schools try and use some innovative or progressive approaches to teaching children. So I will not entirely deny their claims.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">What is the message these schools want to send out to parents? Since I have not yet figured this out, I’ll just say that it’s a marketing gimmick. Just naming something does not change its nature. The very same schools will provide the most conventional education, as we have seen, far from what Friere wanted. Just as names do not change the nature of things fundamentally, appearances too do not contribute significantly to the educational experiences of children. You can have wi-fi enabled classrooms and web enabled systems where your child’s progress may be recorded, or horse rides for that matter but the teaching-learning can still be rote and stifle the child’s potential and creative impulse. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">The Brighton Academy which actually looks like a corporate office from the front will supposedly produce ‘bright’ children, whatever that means. What takes the cake, however, is that this academy claims that they provide ‘Enjoycation’. This, I believe, is their version of a particular form or kind of education. Or education itself, in a new form -- you can take your pick. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">I can hazard a guess and can imagine what the principal of the Brighton Academy would have to say: ‘Education should be enjoyable, you see. We should not burden children. That is why we use a new term: Enjoycation!’ How noble! This sounds a little like the term ‘Joyful learning’ which was bandied around mostly in the nineties. Also, in the nineties, we were also subjected to other terms, such as ‘child centered’ and ‘activity based’ education. On the whole, the idea was that education should become less burdensome on the child and actually should be more play and fun. Several slogans like ‘<i style="mso-bidi-font-style: normal;">Khel Khel mein Siksha</i>’ were coined. Then, there was that famous committee called the Yashpal Committee, which talked about the burden of non-comprehension and the weight of the school bag on the child’s delicate shoulders.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">I can understand the reaction to educational processes that are boring, do not allow the child to express, get involved, ask, do, understand, and all that. I can also understand the need to change the environment in schools which induces fear in the name of discipline. Yet, I feel that we did not work hard enough to understand the implications of these terms in practice. We are very good at writing documents, including that great sounding National Curriculum Framework of 2005 but pretty poor when it comes to these ideas in the reality of the Indian classroom. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">In our half-hearted efforts, these terms often assume quite different meanings from their original intent. Thus, it was a common sight to see thousands of teachers across the country do a physical activity (like some action song, for instance) before the ‘actual teaching’ began – this was how activity based learning was interpreted. ‘Actual teaching’ which followed the activity, was business as usual. And then, in the thousands of workshops all over the country, we did discuss these terms but I suspect we did not really grapple with them deeply enough. For instance, take child centered – should we provide education based on the interests, needs, moods etc., of the child? Should we make it easy so that children do not have to struggle…? These and other questions require deeper engagement. Child centred does not just mean doing what the child likes to do.</span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">My contention is that the whole business of enjoyment and fun and less boredom in education has the effect of diluting the educational process. What is the process of education without a struggle? The human mind has to struggle and apply all its powers to understand patterns in nature and in society. There is real enjoyment and fun in doing this. The ‘Aha!’ moment that a child experiences and the ‘Ahaa!’ that the teacher experiences on seeing the child thus, come as a result of great struggle which we are all capable of. This is a different view of Enjoycation. In any case, as we get along in life, there will be several instances where we will be forced to give up cherished notions, forced to move out of our neat little grooves, our comfort zones, reconsider our understanding of ourselves, people, relationships, society and the kinds of lives we would want to lead. Sometimes, it can be all very painful. All of these, which I believe are experiences of learning, leading to one’s education, do not come easily – one can actually run away from them if one wishes to, if one does not want to confront them head on. The enjoyment, however, consists in the savoring of the moment of discovery, insight and the individual liberation that these experiences bring. </span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">I’m not sure what drives the thinking behind the Enjoycation that the Brighton Academy would like to give. I would beg to differ with them if they have coined the term merely as a marketing strategy. I suspect they have.</span></div>
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<span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Raipur</span><span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;"></span></div>
<i style="mso-bidi-font-style: normal;"><span lang="EN" style="color: black; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">May 2012</span></i></div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-22773109654660960822012-05-09T04:29:00.001-07:002012-05-09T04:29:09.424-07:00Channakeshava<div dir="ltr" style="text-align: left;" trbidi="on">
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<place w:st="on"><b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Baldwins</span></b></place><b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"></span></b></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 18pt;">M</span></b><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">y father would not have settled for anything other than a church managed school for my education. This school was for him an epitome of educational quality. The emphasis on instruction in English, seen by many as a passport to success in today’s world, and the ‘discipline’ that he thought was part of the ethos of every Christian educational institution, would help me go forward in life. I’m not sure what my mother or granny thought of this argument, or even if they did, if it made any difference to my father’s outlook. I remember heated discussions at home about the ‘excessive fees’ of Rs. 56/- per month in <place w:st="on">Baldwins</place> in 1978, but my father was adamant in his belief. He was prepared to scrounge around from his meagre salary to give me what he thought was a good education. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The first school that I attended was St. Anne’s Convent on <street w:st="on"><address w:st="on">
Cunningham Road</address>
</street>, a couple of kilometres away from our cantonment residence in a much quieter and more beautiful <place w:st="on"><city w:st="on">Bangalore</city></place> those days. An ageing rickshaw puller took a bunch of four or five of us every morning to this school, which was co-educational up to the fourth grade. I had some interesting experiences in this school about which I will write separately. When I reached grade 3, my father must have worried about my next school. Since he had set his sights on the well-known Baldwin Boys’ High School located near Johnson Market on <street w:st="on"><address w:st="on">
Hosur Road</address>
</street>, I was coached to clear the entrance test. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">I joined the 98 year old <place w:st="on">Baldwins</place> in 1978. But I would meet Channakeshava (Channa, as he was affectionately called), the mathematics teacher only in 1983 in the eighth grade. For reasons I could not understand, I had to repeat grade 3 despite passing the entrance test -- may be the chaps who gave me admission thought that my grade 3 pass certificate from St. Anne’s was not good enough. They made me lose a year, though.</span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Beginning</span></b></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">There is nothing unique about my mathematical experiences up to the seventh grade. We had sincere teachers, all ladies who went through their motions of teaching to the syllabus and preparing us for the exams. I don’t recall being excited about math. Mrs. Thomas, our class teacher in sixth who also taught us math, was perhaps the best of the lot – she was always pleasant, never lost her patience, and once told me that she could solve all the problems from the fat and complicated looking 10<sup>th</sup> std. ICSE textbook written by someone called O. P Sinhal. My respect for her increased several notches after that even if I did not have the chance to verify what she claimed! That complex looking book which my seniors brought to school every day gave rise to both fascination and fear, and if someone told me she could solve everything in it, I could not help but only admire her for that. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">I have memories of two ‘mathematical events’, both rooted in incomprehension, in class 6 and 7. The first was to do with the idea of inequalities. Since my father was confident of teaching me till things got mathematically tough around grade 7, he took it upon himself to teach me those vexed inequalities using signs like >, <, ≤, ≥ which appeared in between two or three numbers. Some thing was greater than or equal to something, while it was lesser than or equal to something else – and so it went! One evening, when much of it went overhead, my father asked me to do what he called <i style="mso-bidi-font-style: normal;">Guddi-patam</i> – ‘Mug it up!’ He said when he saw me struggling with some problems. In fact, that was his constant message throughout my school and college days, even when I was doing my engineering. If you couldn’t understand it, it had to be ‘mugged’ up only to be vomited in the exams. I couldn’t figure out the concept of inequalities despite his best efforts that evening. My reward for incomprehension was a hard slap! That was the only time he slapped me, for I could see that he was ashamed, apologetic and emotional about what he had done. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The second event was to happen in grade 7. I found the idea of Integers, those negative numbers that extended the other way from zero on the number line, difficult to understand. Till then, everything seemed fine in mathematics. One had to ‘solve’ problems and get the right answers. Or so I thought. Little did I realize then that the world of mathematics was full of strange numbers (rational, irrational, surreal, transcendental and the imaginary and complex, among many other such creatures) which were related to each other through even stranger relationships. Beautiful relationships, many mathematicians would say, as we will see a little later. </span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Beauty</span></b></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">I reached the eighth grade in 1983, finally. It was Channakeshava’s first class with us in June that year and it had very little to do with our syllabus and textbooks. He could have so easily started off with the first chapter, and we would have plodded through, as usual. Instead, he wanted to begin by showing us ‘beauty’ in mathematics (This, I say in hindsight. It wasn’t so obvious then). So he posed the following question on the blackboard:</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X1?</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">This was easy. Next, he asked:</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">While we all got busy with the multiplication, he quickly wrote the answer – 285714. Then, he asked again:</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">428571 is the answer, which he had written down as if he knew it all along while we were busy multiplying! Then he went on to show what happens when 142857 is multiplied by 4, 5 and 6. Interesting stuff was emerging:</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X1 = 142857 </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X 2 = 2857<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><u>14</u></i></b></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X 3 = 4285<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><u>71</u></i></b></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X4 = <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><u>57</u></i></b>1428</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X 5 = <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><u>7</u></i></b>14285</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">142857 X 6 = <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><u>857</u></i></b>142</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">What we saw was a ‘cyclic permutation’ of the number’s original digits even as we multiplied it by 2, till 6. It was difficult to discern <i style="mso-bidi-font-style: normal;">a</i> pattern in the manner the digits got shifted -- sometimes one digit got shifted, sometimes two, and sometimes three but in all cases the ones getting shifted were consecutive digits. But what was startling was that it was the same number whose digits got shuffled around. Such numbers are called ‘cyclic numbers’, CK told us. And mathematics is full of such curiosities, he added, which can be studied by just about anyone. In conclusion, he asked: what happens when we multiply 142857 by 7? We wondered if the original number would get recycled again. But no! What we got instead was 999999! This was puzzling, indeed! While we were soaking in all in, CK just smiled.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">That is how we were introduced to the beauty of mathematics in grade 8. I use the word beauty because it hits you, as a beautiful sunrise would – everything appears to be in place and it cannot get better than that moment. In mathematics, beauty lies in the patterns that unfold, like in the above example. At the risk of deviating from Channakeshava’s story, let me illustrate mathematical beauty through another example.<i style="mso-bidi-font-style: normal;"></i></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">It is acknowledged that among the most beautiful relationships or patterns in mathematics is perhaps the Euler equation (after the great Swiss mathematician, Leonhard Euler) or identity e</span><b style="mso-bidi-font-weight: normal;"><sup><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 14pt;">i</span></sup></b><b style="mso-bidi-font-weight: normal;"><sup><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 10pt;">∏</span></sup></b><sub><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 10pt;"> </span></sub><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">= --1. To put it another way: e<b style="mso-bidi-font-weight: normal;"><sup>i</sup></b></span><b style="mso-bidi-font-weight: normal;"><sup><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 10pt;">∏ </span></sup></b><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">+ 1 = 0. Now each of these numbers – e, i, Pi and 0, are unique numbers which keep recurring in mathematics. Without getting into the details, for one can write pages and pages about each of these numbers, let’s just note that ‘e’ is what is called as an irrational number (simply put, a number that has a decimal/fractional portion that never ends and which can never be computed!) whose value is 2.7182818284…this ‘e’ is also the base for the natural logarithms.. There are different ways of arriving at <i style="mso-bidi-font-style: normal;">e, </i>and I don’t want to get into this discussion here. But I will just say that if you start operating the expression (1+1/n)<sup>n</sup> as ‘n’ gets bigger and bigger, you will approach ‘e’.<sup> </sup><span style="mso-spacerun: yes;"> </span>Try it out and see!<sup><span style="mso-spacerun: yes;"> </span></sup></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">But ‘i’ is another equally crazy number (called the imaginary number) which is the square root of minus 1 – written as √-1. This is like asking ‘What number when squared (multiplied by itself) gives – 1?’ This ‘i’ is neither 1 nor minus 1 and is therefore called imaginary! </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Well, well, well! Why on earth does one need such numbers? You may very well ask. These numbers were invented to derive solutions to certain types of equations is all that I can say here. And then, you have the mysterious Pi, which has had a long and chequered history and can claim to really be the king of all numbers, sitting proud on a pedestal in the number world, and daring anyone to claim him! One would think that the <i style="mso-bidi-font-style: normal;">ratio</i> of the circumference of the circle and its diameter (that is, the number Pi as it is defined) would yield a decent number – after all, we can easily construct circles of definite sizes in terms of their diameters and radii. When people attempted to find this ratio centuries ago and in different cultures across the world, they found that it was a little more than 3 and so they approximated the ratio to 3. But that little portion beyond 3 kept nagging everyone and as the years progressed, it was discovered that that little portion is a never ending stream of decimal digits! And so, Pi (the symbol is ‘<b style="mso-bidi-font-weight: normal;"><sup>∏</sup></b></span><b style="mso-bidi-font-weight: normal;"><sup><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 10pt;">’</span></sup></b><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">), as this ratio was called, looked something like 3.14159265…ad infinitum! You can draw the circle and its diameter but can never measure the ratio of its circumference to its diameter accurately! This was what stumped Pythagoras and quite shattered him – that there could be numbers whose actual values we might never know. Let me give another example – we can draw a right angled triangle whose sides are one unit each – we know from the Pythagorean Theorem that the length of the hypotenuse (the side opposite the angle that measures 90</span><span lang="EN-GB" style="font-size: 12pt;"><span style="font-family: Calibri;">⁰)</span></span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"> is<i style="mso-bidi-font-style: normal;"> </i>√2, which is an irrational number. So there you are – you can draw this triangle but can never measure the length of its hypotenuse! It cannot get crazier than this!<i style="mso-bidi-font-style: normal;"><span style="mso-spacerun: yes;"> </span></i></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">In the case of Pi, You can use mnemonics to remember the decimal places if you want (this is a little bit of consolation, anyway). Once, when I was invited as a math teacher to a creative writing class in English (talk of integrating the disciplines!), I wrote out the first 100 decimal places for Pi and asked the children to write a paragraph in such a manner that each word that was used would have as many letters as the value of that digit, in that sequence – for example, if you say, ‘May(3) I(1) have(4) a(1) large(5) container(9) of(2) coffee(6)?’ you can write out the first seven digits of Pi: 3.1415926. And when they followed this rule, the children wrote out some hilarious stuff which made us all roll with laughter for the next few days. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The other thing we did in the same school where I taught many years ago was that we (the children and I) prepared a ‘Pi tail’ using old newspapers – we made these newspaper strips, and used marker pens to write out the first 2500 decimal places of Pi – this resulted in a Pi tail some 850 feet long! On Science Day in 1994 in that school, we took out this paper tail and wound it round the school, starting from the library. Throughout the day, I saw children running around, following the tail – along the walls, inside the rooms, inside one of the toilets and then out all the way into the jungle gym, where the tail finally climbed a tree and went all the way up, and we left it dangling there. Finally, when a group of children who I was teaching about Pi, came to me and said they understood then why Pi was called irrational, I knew I had managed to convey a fundamental mathematical truth. I’m not sure if any of them thought about it beyond the science day.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Now, let us visualise the Euler identity: </span><span lang="EN-GB" style="font-family: "Batang", "serif"; font-size: 10pt;">(2.7182818284…)<sup>(</sup></span><sup><span lang="EN-GB" style="font-family: "Batang", "serif";">3.14159265…) X (√-1</span></sup><sup><span lang="EN-GB" style="font-family: "Batang", "serif"; font-size: 10pt;">)</span></sup><span lang="EN-GB" style="font-family: "Batang", "serif"; font-size: 10pt;"> + 1= 0</span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Note that ‘raising one number to a certain power’ (which is what we do in the above expression) simply means this – if you raise a number ‘a’ to the power ‘n’, it means you multiply ‘a’ by itself ‘n’ times. So if we say a<sup>3</sup>, it would look like this: a x a x a. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">There is something very intricate and crazy happening with the Euler identity which we lay persons can only intuitively grasp. You have this irrational <i style="mso-bidi-font-style: normal;">e</i> which when raised to the product of another irrational (Pi) and the imaginary <i style="mso-bidi-font-style: normal;">i, </i>gives –1. Then you bring this –1 on the left side and that leaves us with zero on the right hand side. What beats me is how this happens. First of all, you have this <i style="mso-bidi-font-style: normal;">e </i>and </span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 10pt;">∏</span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"> whose decimal portions are never ending or recurring as even the most powerful supercomputers of our age have found. If one can find a way of adding them, it might result in another irrational number. Ditto, if one is subtracted from the other. If they are multiplied by each other, we might end up with yet another irrational number. But if <i style="mso-bidi-font-style: normal;">e </i>is raised to the power of the product of <i style="mso-bidi-font-style: normal;">i </i>and </span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 10pt;">∏, </span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">then the strangest of things occurs – the infinite strings of digits <i style="mso-bidi-font-style: normal;">just disappears</i>, leaving us with –1! And when this is added to +1 as we see in the Euler identity, we are left with <i style="mso-bidi-font-style: normal;">nothing</i>! </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">How can this be...? What is happening…and what is the role that ‘<i style="mso-bidi-font-style: normal;">i’ </i>plays in this? Euler, the great genius he was, discovered this profound relationship more than 300 years ago. How did he come to it understand it, and what would he have said about it to a layman he would have met on the street? The Euler identity tells us something fundamental about how the world of numbers is structured and ordered.<i style="mso-bidi-font-style: normal;"> </i>You can visualise this in terms of a number line and try and locate all these numbers there.<span style="mso-spacerun: yes;"> </span><i style="mso-bidi-font-style: normal;"></i></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">It struck me that the Euler identity in many ways is like the alchemy (or so I thought) I once saw in the chemistry lab of our school. Our chemistry teacher was demonstrating how different acids react with each other. So there was this colourful liquid which was mixed with another colourful liquid and Voila! The mixture became colourless! There was a collective gasp in the room, and since fairly large glass containers were used to pour out these liquids, the entire exercise looked spectacular. While we were all aware of the chemicals involved and the chemical reaction itself, there was no discussion on what made the coloured liquids transparent when they came into contact with each other. Obviously, it had to do something with the change in the structure at the molecular level, and the way the new molecules interacted with light. But these aspects were probably complex to be discussed at that stage in that chemistry class. We did not know enough of quantum physics or chemistry to answer that question.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The Euler identity is similar in terms of mathematical alchemy and results in zero, the midpoint on the number line, the mathematical nothingness. I was explaining this to a friend recently and he said his hair stood on end when he thought long and hard about what was happening. I’m sure that any mathematician worth his or her salt might be able to explain away or prove this phenomenon (I use the word phenomenon quite deliberately here) theoretically. There is fun, however, in keeping it a bit mysterious and struggling with the infinity of digits that appear and disappear in the problem, much like the colours we saw disappearing in the lab. I’m tempted to quote Benjamin Pierce the American mathematician below:</span></div>
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<span lang="EN-GB" style="font-family: "Batang", "serif"; font-size: 10pt;">“Gentlemen, that <i style="mso-bidi-font-style: normal;">(e<b style="mso-bidi-font-weight: normal;"><sup>i∏ </sup></b>+ 1 = 0)</i> is surely true, but it is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore, we know it must be the truth.”<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">You could spend your entire life unravelling these relationships, like mathematicians did. What was even more fascinating, as I realized much later in my explorations of physics, were the intimate connections these abstract relationships had with the ordering of the natural world. Surely, there is something fascinating here and I’m not sure if even the best mathematicians have understood why this is so.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">But human relationships are far more complicated, I think!</span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Channakeshava</span></b></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">CK had cast a spell with his cyclic number example. And there was more to come that year as well as in grades 9 and 10! There wasn’t much exploration of numbers after that session on cyclic numbers -- it had to be business as usual in a school that prided itself on exam results. But there was a definite difference in the way we were taught mathematics. First, CK came across as very calm and self-assured both as a human being and teacher. We couldn’t get close to him, and there was no question of getting friendly with him – he ensured that there was always some distance between us and him – fair enough, I think, given that he may have been in his late forties or early fifties then. But when it came to learning math with him, it was sheer fun. With his partly bald head and bespectacled face and his immaculate suit, he looked quite the archetypal mathematician himself! </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">When I look back on those three years that he taught us, I realized how grounded he was in the knowledge of the subject itself. Years later, I realized that he was indeed an avid explorer of the mathematical world. This, I now believe, is a pre-requisite for every teacher of the subject – a teacher of mathematics cannot limit his or her teaching to some sharing of procedures to solve problems but share the real excitement that comes from exploring patterns and relationships in the mathematical world. And he must do this in a manner that children can understand. While access to good reference materials would certainly help, the fundamental requirement is curiosity, and that is sadly in short supply among most teachers – how can one convey excitement to the child when one is not generally curious…?<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">There was this unmistakable gleam in CK’s eyes whenever he conveyed something fundamental or profound. When he emphasized some deeper aspect of the topic at hand, his mouth would open a bit wider than usual and he would pull his lips backward to make a point -- like I remember when we first heard the Latin phrase ‘<i style="mso-bidi-font-style: normal;">Quod Erat Demonstrandum</i>’ when we were grappling with proof in geometry. Q.E.D, literally meaning ‘What was required to be proved’ is what one says when one has demonstrated a proof. A proof is a kind of achievement in the mathematical world through which one demonstrates underlying patterns and relationships between numbers, spaces and the like.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Everyone was attentive in Channakeshava’s class, from the first to the last bench because we knew that we would end up learning <i style="mso-bidi-font-style: normal;">something.</i></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The other unique element of his teaching was his impeccable running handwriting and use of blackboard space. I have not come across another teacher who used the blackboard as effectively and as beautifully as he did. His handwriting was a visual treat, not flamboyant but clear and pleasing to the eye. The sense of proportion he had when using the blackboard was just amazing. He would clearly demarcate areas on the blackboard – for instance, for drawing diagrams, for arguing, and writing down the steps of the analysis, and for rough work or calculations.</span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Proof</span></b></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">That year, we encountered the idea of the theorem for the first time in geometry. We had earlier learnt that most common property of triangles – that the sum of the three angles of a triangle always adds up to 180</span><span lang="EN-GB" style="font-size: 12pt;"><span style="font-family: Calibri;">⁰</span></span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"> (Well, I later realized that it doesn’t, always, and depends very much on what kind of surface you draw the triangle on – this kind of thinking has led to the development of different kinds of geometries, such as Riemannian and Lobachevskian geometry, for instance.). The geometry we have studied in school is called Euclidean, after <city w:st="on"><place w:st="on">Euclid</place></city>, the great Greek geometer who lived more than 2000 years ago. His brand of geometry – Euclidean geometry is what you do on flat surfaces. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">‘How do you know this is true?’ CK asked as a matter of fact. ‘Measure and see and you will get 180</span><span lang="EN-GB" style="font-size: 12pt;"><span style="font-family: Calibri;">⁰</span></span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">!’ we said. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">‘How many triangles should I draw and measure?’ This question stumped us a bit and I remember that we didn’t agree on any one number. In fact, any number would have been arbitrary – 10, 50, 100, 1000…? ‘In any case’, CK said, what if the 1001<sup>st</sup> triangle’s angles <i style="mso-bidi-font-style: normal;">do not</i> add up to <a href="" name="OLE_LINK2"></a><a href="" name="OLE_LINK1"><span style="mso-bookmark: OLE_LINK2;">180</span></a></span><span style="font-family: Calibri;"><span style="mso-bookmark: OLE_LINK1;"><span style="mso-bookmark: OLE_LINK2;"><span lang="EN-GB" style="font-size: 12pt;">⁰</span></span></span><span style="mso-bookmark: OLE_LINK2;"></span><span style="mso-bookmark: OLE_LINK1;"></span></span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">?’ There was no response from the class.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">‘For this reason, we have to <i style="mso-bidi-font-style: normal;">prove </i>that <i style="mso-bidi-font-style: normal;">no matter what</i>, the angles of a triangle add up to 180</span><span lang="EN-GB" style="font-size: 12pt;"><span style="font-family: Calibri;">⁰</span></span><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">.’ And so we went about proving this elementary theorem and learnt along the way that the word ‘theorem’ is nothing but a statement claiming such and such a thing, which has a proof that is generated using deductive reasoning – this is something like saying ‘If A, then B’. Now, all these theorems in geometry that one encounters in school (and usually breaks one’s head against) rest on certain foundational statements called <i style="mso-bidi-font-style: normal;">axioms. </i>In his <i style="mso-bidi-font-style: normal;">Elements, </i><city w:st="on"><place w:st="on">Euclid</place></city> had proposed five axioms on which the whole of his Euclidean geometry rests! I had difficulty in accepting these axioms as ‘self-evident truths’ which did not need proving but from which all of Euclidean geometry flowed. Later, one realised that there had to be certain starting points anyway without which, one couldn’t even move forward.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">I’m recounting all of this because CK shared this fascinating history with us. Imagine -- we were learning something that was thought of two millennia ago and put down in a book! In the coming months and years, we would prove many theorems, in geometry and algebra and trigonometry, and in algebraic geometry. I enjoyed the study of theorems and their proofs only intermittently and kept wishing that CK would tell us more and more stories instead. There were days when the proof of a theorem would just appear effortlessly and then there were days when one would struggle. Channa would go on, as enthusiastically as ever, adorning blackboard space with these eternal theorems and their mind bending logical proofs!</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Years later, when I read that great book <i style="mso-bidi-font-style: normal;">Men of Mathematics </i>by E. T Bell (a feminist would have questioned the title itself!), it struck me when he said that the Euclidean method that insisted on proof may have actually hampered the development of mathematics by at least two thousand years. On the other hand, if mathematicians had followed the unfettered thinking of Archimedes, one of the three greatest mathematicians ever (along with <city w:st="on">Newton</city> and Gauss, and, I would add, our own Ramanujan) that <city w:st="on"><place w:st="on">Bell</place></city> identifies, the age of modern mathematics (and with it, science) could have occurred two millennia earlier. Anyway, that’s a discussion for another day.<i style="mso-bidi-font-style: normal;"> </i>I wonder what position Channa would have taken. Would he have taken <city w:st="on"><place w:st="on">Euclid</place></city>’s side or would he have plumped for Archimedes…?</span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Famous problems we discussed</span></b></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">As we journeyed with Channa, we were always treated to snippets from the fascinating history of mathematics. Some years later, when I took to teaching mathematics at The Valley School in <city w:st="on"><place w:st="on">Bangalore</place></city>, I realized how well he had employed the history of mathematics as an effective tool to make the subject absorbing. In fact, I realized later that this was the cornerstone of his teaching and was perhaps one of the most effective ways in which one could fire the imagination of the learner. That there were hundreds of stories of mathematical discovery, many of them rooted in daily life problems and that mathematicians were as human as anyone else, hadn’t occurred to most of us who by then had reconciled to our highly developed math phobias. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The Seven Bridges of Konigsberg, the Barber’s Paradox, Fermat’s problem and the Four Colour Problem are among<b style="mso-bidi-font-weight: normal;"> </b>the most interesting and intricate problems of mathematics which have defied the best minds for generations. Attempts at their resolutions have given rise to entire branches of mathematics. CK told us those fascinating stories. I remember them to this day. I passed them on to my students in the best manner I could. <b style="mso-bidi-font-weight: normal;"><span style="mso-spacerun: yes;"> </span></b></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">First, the ‘Seven Bridges of Konigsberg’ -- I must share this. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">I’m not sure which grade it was, may be 9<sup>th</sup> or 10<sup>th</sup>, around the time when we were supposed to learn the idea of matrices. Any lesser teacher would have plunged headlong into the subject and would have introduced matrices as ‘an array of numbers…arranged horizontally and vertically…and these are the rules for their addition and multiplication…’ This would have been followed by boring problem solving from the exercises in the textbook. With CK, that was not to be. He simply had to get to the root of the idea, to the bottom of the matter, and share the excitement of his explorations with his students. And that is how we were treated to the 300 year old ‘Seven Bridges of Konigsberg’ problem. I do not remember the connections that were made (or mentioned) between the Konigsberg problem and the idea of matrices in mathematics, but I do remember we spent a couple of periods discussing this puzzle that originated in daily life and informed the development of new areas of mathematics such as graph theory, which finds wide applications.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Briefly, the Seven Bridges problem originated in the town of Konigsberg (founded in 1254 A.D) in Prussia (Kaliningrad in modern day Russia). The town itself was made of four land masses that were connected to each other and the mainland by a network of seven bridges built on the <placename w:st="on">Pregel</placename> <placetype w:st="on">River</placetype> which ran through <place w:st="on">Konigsberg</place>. The seven bridges (not all of them exist now) were named ‘Blacksmith, Connecting, Green, Merchant, Wooden, High’ and ‘Honey’, and the problem, which was attacked (actually, negatively resolved) by the great Euler in 1736 was to walk through the entire town of Konigsberg in such a manner that one would have to cross <i style="mso-bidi-font-style: normal;">each </i>bridge <i style="mso-bidi-font-style: normal;">once and only once </i>and finish at the starting point<i style="mso-bidi-font-style: normal;">. </i>The story goes that when people of <place w:st="on">Konigsberg</place> took their leisurely walks on Sundays and used the bridges to reach different points in the town it occurred to them that they could actually generate a puzzle based on the bridges. Thus, the above problem was posed.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">What an introduction this was to the topic of matrices! We spent two classes on the <place w:st="on">Konigsberg</place> problem, trying to draw our myriad routes across the seven bridges only to be stumped in the end. And then, CK told us that Euler stated that the <place w:st="on">Konigsberg</place> problem could <i style="mso-bidi-font-style: normal;">never</i> be solved. The actual proof came much later, in 1873 by one Carl Hierholzer. But the thinking that went into Euler’s reasoning spawned an entire new branch of mathematics called Graph Theory which was in turn intimately connected with the idea of Matrices. It also preceded the development of another branch of mathematics called Topology, Channa said. He did not of course go into details and enlighten us about these connections, nor did we have the time to actually see how Euler resolved the problem (the proof is not <i style="mso-bidi-font-style: normal;">so</i> difficult to understand, as I discovered later, but during Euler’s time, it must have been breaking news!). When I look back today, it amazes me to even think that a math teacher could have thought so much in depth, to present just one of the myriad topics we studied at school. How much he must have read and reflected, before presenting us the problem, and linking it to what we had to study as part of our course!</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Likewise, we had a fascinating discussion about the Barber’s Paradox, when Channa generally talked about paradoxes in mathematics. At that stage, I remember that we were beginning to discuss the idea of Sets. Channa walked in one day and asked if we knew what a paradox was. When there was silence in the room, he went on to explain that a paradox in mathematics occurs when we encounter a statement that contains ideas or thoughts that are conflicting (in any case, this is a simplistic way of understanding paradoxes and we will not get into a deeper discussion here). The Barber’s Paradox, of which there are many variations and which is also called a paradox of ‘self reference’, perfectly illustrates this. I remember the loud arguments and counter arguments in class when this paradox, first proposed by the mathematician and philosopher Bertrand Russell, was discussed. This is how it goes.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Suppose there is a village which has a barber who shaves only those who do not shave themselves, and no one else…the question is: who shaves him (the barber)? It looks simple at first sight but when you grapple with it, you get tied in knots. Now, if the barber shaves himself, he actually mustn’t, since he does not shave those men who shave themselves. However, if he does not shave himself, then he must, since he shaves those who do not shave themselves! So, we encounter contradictions in both cases. In the class as the paradox kept getting discussed, I actually remember imagining an unshaven barber whose beard kept growing and growing infinitely (actually, beards don’t grow that way!). Anyway, we had fun with this paradox. CK then mentioned that this paradox actually exposed a contradiction at the heart of set theory. In simple terms, this would mean that there is a statement ‘S’ such that ‘S’ and its negation (not S) are both true. Such inconsistencies would make the foundations of mathematics very shaky, since we would then have no basis for trusting any mathematical proof (remember, we discussed the angles of a triangle theorem and its proof earlier, where we remembered Channa’s insisting that proof must be solid and robust, no matter what kind of triangle one considered?).<span style="mso-spacerun: yes;"> </span></span></div>
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Just to illustrate paradoxes that are like the Barber’s Paradox, reflect on what is famously known as the ‘Liar Paradox’ (which, I remember, we also discussed in CK’s class) below:</div>
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<span style="font-family: "Batang", "serif"; font-size: 10pt;">“All Cretans are liars.” <i style="mso-bidi-font-style: normal;">(attributed to Epimenides the Cretan)<span style="mso-spacerun: yes;"> </span></i></span></div>
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Like the Barber’s paradox, the above statement results in contradictions. Think about it.</div>
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Again when I look back, I wonder and marvel at the depth of CK’s understanding of the subject, which he used so effortlessly to help us appreciate the pillars around which mathematical thought has been built over the millennia. I remember the fascination, and it still gives me goose bumps when I recall those few classes which enabled us a deeper glimpse of mathematical reality. It is only when one loves the subject and when one <i style="mso-bidi-font-style: normal;">cares enough</i> for the learner when teaching it, that will make you take the trouble to go the root of that discipline, and expose it to the learner. This can bring real joy. Joyful learning, unfortunately, is a much misused term in the lexicon of education – instead of connoting that joy can arise from struggle and insight as well, we are talking of making things easier for the child through fun and play. This trivializes the struggle and achievement that is part of the process of learning. </div>
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<span style="mso-tab-count: 1;"> </span>I’m not sure about the context in which the ‘Four Colour Problem’ (FCP) was presented and discussed by CK. May be it had to do with the <place w:st="on">Konigsberg</place> problem, before we got on with matrices. Maybe CK did say that it informed the development of new areas in mathematics like Graph Theory, Topology etc. The FCP was, till the 90’s a great unsolved problem of mathematics (originating in map making and cartography) which stumped the best brains. Finally, supercomputers had to be called in (for the first time, literally, to establish a major theorem) to process the huge amounts of data required to establish the proof way back in the 70’s. Even then, there was debate within the mathematical community – would <i style="mso-bidi-font-style: normal;">this</i> constitute proof? Did this not sound like an experimental proof which the natural sciences use routinely? Remember, in mathematics we are all used to deductive proof, Euclidean style! Anyway, a typical statement of the FCP might look like this: </div>
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<span style="font-family: "Batang", "serif"; font-size: 10pt;">“Given any separation of a plane into <a href="http://en.wikipedia.org/wiki/Contiguity#Geography" title="Contiguity"><span style="color: blue;">contiguous</span></a> regions, producing a figure called a <i>map</i>, no more than four colours are required to colour the regions of the map so that no two adjacent regions have the same colour.”</span></div>
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To put things simply, it is like saying that one does not need more than four colours to colour a map such that adjacent countries or regions do not have the same colour. While mathematicians were able to show/prove the case with five colours, the four colour problem stubbornly resisted a solution for well over a century. Interesting, isn’t it? One can never be sure which area of human activity can actually spawn a new area of knowledge which people keep pursuing even hundreds of years later! </div>
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And finally, who can forget Fermat’s last theorem? We were discussing the theorem of Pythagoras, that the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides: a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup>, where ‘a’ and ‘b’ are the two sides of the right angled triangle and ‘c’ is the hypotenuse. Every high school kid knows this, but few teachers would take the discussions forward beyond stating the theorem and one of its proofs (I have heard that there are approx. 370 ways of proving the above result!). CK went on where most teachers wouldn’t tread, and we were treated to the then 348 year old Fermat’s ‘Last Theorem’, which states that no three <a href="http://en.wikipedia.org/wiki/Positive_number" title="Positive number"><span style="color: blue;">positive</span></a> <a href="http://en.wikipedia.org/wiki/Integer" title="Integer"><span style="color: blue;">integers</span></a> <i>a</i>, <i>b</i>, and <i>c</i> can satisfy the equation <span style="mso-bidi-font-style: italic;">a<sup>n</sup></span> + <span style="mso-bidi-font-style: italic;">b<sup>n</sup></span> = <span style="mso-bidi-font-style: italic;">c<sup>n</sup></span> for any integer value of <i>n</i> greater than two. This, the French amateur mathematician Pierre de Fermat had asserted way back in 1637 in his famous notebook on the margins. As we can see above, the Pythagorean case is a special case of Fermat’s Theorem. To quote some examples, 3<sup>2 </sup>+ 4<sup>2</sup> = 5<sup>2</sup>; 12<sup>2</sup> + 5<sup>2</sup> = 13<sup>2</sup>, and there are various ways in which we can keep generating these ‘Pythagorean Triples’. Channa treated us to a history of this problem and said, rather sombrely, that the Fermat problem was one of the famous all time unresolved problems of mathematics. ‘Maybe one of you will solve it one day!’ he said, with a twinkle in his eye.</div>
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The mid 80’s were exciting times for Fermat’s Last Theorem (FLT). Countless mathematicians had by then grappled with it, and proofs had been presented for specific cases, and for ‘n’ running into several million. But there was no general proof. Little did we realize then (in 1985) that Andrew Wiles, the British mathematician was very close to deciding that he would spend the next seven or eight years in his attic in complete secrecy to crack the problem. Finally, in 1994, when the problem was declared as solved, I’m not sure if Channakeshava was still teaching at <place w:st="on">Baldwin</place>’s to make this announcement to students of the 9<sup>th</sup> or 10<sup>th</sup> grades. Wiles’ story is fascinating and if I talk about it here, we will move away from CK. There are popular books written on FLT which explain the story of the struggle behind its proof.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><sup><span style="mso-spacerun: yes;"> </span></sup></div>
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As I mentioned at the beginning, we were treated to these mathematical gems by CK for three years. I have mentioned only a few, but I must mention my consternation when we encountered the number Pi (<sup><span style="font-size: 10pt;">∏</span></sup>), which belonged to a class of numbers called ‘Irrational’ numbers – simply, as I have mentioned earlier, numbers that didn’t behave ‘rationally’, whose fractional parts went on and on and on in a never ending stream of decimal digits. We also discussed about the mathematics of the infinite, though I do not remember any specific instance that caught my attention. There was one argument about whether the number of sand particles on a beach was finite or infinite. It was also interesting to note that there were ‘different orders of infinity’. These days, I have revived my interest in the mathematics of the infinite.<span style="mso-spacerun: yes;"> </span></div>
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<b style="mso-bidi-font-weight: normal;">History of mathematics</b></div>
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These forays into mathematics were fascinating, no doubt, for a fortunate few. That mathematics even had a history like this was beyond our imagination as students, used as we were to rote learning methods by and large. None of my other teachers exhibited this in-depth understanding of the discipline that Channa did. He would tempt you by showing little by little, the intriguing life worlds of mathematics. After a while, we would be on to our usual exercises from the text (the more boring part!) but the stories remained with us.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span lang="EN-IN" style="mso-ansi-language: EN-IN; mso-fareast-language: EN-IN;"></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Another topic that caught my attention in school was the discovery about Indian mathematicians. When we discussed Pythagoras’s theorem and did quadratic equations in algebra, Channa posed questions that Indian mathematicians attempted more than a thousand years ago. I clearly remember CK discussing the 12th century mathematician Bhaskaracharya II. In fact, what was fascinating was that he had picked up a problem from Bhaskara’s <i style="mso-bidi-font-style: normal;">Lilavati. </i>This is Bhaskara’s treatise on mathematics (written when he was in his thirties), and as the fascinating story goes, is dedicated to his daughter Lilavati. If I remember correctly, Channa picked up the following problem from <i style="mso-bidi-font-style: normal;">Lilavati:</i></span></div>
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<span lang="EN-GB" style="font-family: "Batang", "serif"; font-size: 10pt;">“A bamboo 18 cubits high was broken by the wind. Its top touched the ground 6 cubits from the root. Tell the lengths of segments of the bamboo.”<span style="mso-spacerun: yes;"> </span><i style="mso-bidi-font-style: normal;"><span style="mso-spacerun: yes;"> </span></i></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">It takes the simple application of the Pythagorean Theorem to find out that the lengths of segments of the broken bamboo are 8 and 10 cubits respectively. While we all enjoyed doing this problem and the class was greatly enlivened as a result, the fascinating part for me was the travelling back in time that we did and the realization at the time that there were Indian mathematicians going back a thousand years and beyond who had worked on what we were learning in school. While we had only touched upon the ‘great’ discoveries of Indian scientists and mathematicians in the history class, CK’s treatment of the subject brought things alive, and history was no longer restricted to boring dates and events and the mugging up of occurrences of the past. He would have been a very good history teacher as well! Incidentally, the above problem also appears in the history of Chinese mathematics and is known as the <i style="mso-bidi-font-style: normal;">Kou Ku </i>theorem. It appears prominently in the 13<sup>th</sup> century text known as <i style="mso-bidi-font-style: normal;">Hsiang Chieh Chiu Chang Suan Fa Tsuan Lei</i>.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">In 1993, when I took to teaching at the <placetype w:st="on">Valley</placetype> <placetype w:st="on">School</placetype> in <city w:st="on"><place w:st="on">Bangalore</place></city> after I had had enough of manufacturing tractors, I learnt something more about the history of mathematics and took off from where we had left with CK. A senior colleague of mine, who was also interested in understanding how mathematics was produced across cultures, came to know that someone called George Gheverghese Joseph, a scholar from the <place w:st="on"><placename w:st="on">Manchester</placename> <placetype w:st="on">University</placetype></place> was in town. Joseph had researched extensively the ‘Non-European Roots’ of mathematics. We went to meet him and invite him to a lecture at the school. To our delight, he readily agreed. His lecture was gripping, and covered a vast canvas. He showed how ‘Eurocentric’ the entire enterprise of mathematics and science was – indeed, this is what we are taught in schools to this day – that <place w:st="on">Europe</place> was the centre of global mathematical and scientific development since the days of antiquity. Such a blinkered view ignores the fact that other ancient cultures also did a lot of mathematics, often predating the discoveries of <place w:st="on">Europe</place> by at least hundreds of years. A lot of this took place during <place w:st="on">Europe</place>’s great slumber, the Dark Ages. In this context and in particular, Joseph talked about his pet research project -- the discovery of mathematics of the ‘Kerala School’ which flourished between the 14<sup>th</sup> and 16<sup>th</sup> centuries most notably through the work of mathematicians such as Madhava of Sangamagrama and Nilakantha of Tirur, in Kerala. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Research on this alternative history of mathematics has conclusively shown that the work of the <place w:st="on"><placename w:st="on">Kerala</placename> <placetype w:st="on">School</placetype></place> predates the discovery of that great mathematical tool, the Calculus, by at least two centuries! While <city w:st="on"><place w:st="on">Newton</place></city> and Leibnitz, generally acknowledged as the founders of the Calculus must be given their due for combining a range of disparate ideas into a coherent discipline of the Calculus, the discoveries of the Indian, Chinese and Arab mathematicians cannot be disregarded. In fact, as Joseph pointed out, we cannot overlook the transmission of mathematical ideas from <country-region w:st="on">Egypt</country-region>, <city w:st="on">Babylon</city>, <country-region w:st="on">China</country-region> and <country-region w:st="on">India</country-region> through the Arab world to <place w:st="on">Europe</place>. Research in this area has thrown up compelling evidence that this mathematical transmission, right from the days of Pythagoras of antiquity, had informed the development of European mathematics (Pythagoras knew that the Egyptians knew his theorem, though he also knew they hadn’t proved it).<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>Anyway, the seed of curiosity that CK had sown in the mid eighties was further explored by me as a teacher, thanks to that chance encounter with Joseph in the mid nineties! Faithfully, I shared these exciting discoveries with the children I taught. Also, I ended up buying his book <i style="mso-bidi-font-style: normal;">Crest of the Peacock, </i>in which Joseph elaborates the theme of mathematics as it was done and discovered outside Europe, starting with the mathematics of the ‘Ishango bone’ (actually, a lunar calendar) from the mountains of Central Equatorial Africa 20000 years ago! It is a fascinating read and will certainly open your eyes. I’m sure CK knew about the alternative perspective on global mathematical development, but we didn’t discuss it in school.<span style="mso-spacerun: yes;"> </span></span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">The <place w:st="on"><placetype w:st="on">Valley</placetype> <placetype w:st="on">School</placetype></place></span></b></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>I graduated from <place w:st="on">Baldwins</place> in 1985 and became an engineer by 1991. After a two year boring stint in the industry in which I was a production engineer in a company that manufactured tractors, I decided to become a teacher. One reason most certainly was that I wanted to keep on learning, and I wanted to share the joy that comes with discovery and insight with children. Also, I was angry with our insipid educational system consisting mostly of de-motivated teachers most of whom were just doing their jobs. In that surge of idealism that I felt as a young man, I wanted to change the world by becoming a teacher.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>I attribute my reasonable success as a mathematics teacher to the fact that I learnt from what CK did with us in school. I made it a point, for instance, to discuss the history of mathematics in my classes. The <place w:st="on"><placetype w:st="on">Valley</placetype> <placetype w:st="on">School</placetype></place> library offered me good resources. I dabbled in ‘Vedic mathematics’ (VM), demonstrated some of its methods, got children excited and got involved in the debates around its veracity as a system of mathematical system. Joseph does talk about Vedic mathematics in his book but there are questions about whether Vedic mathematics actually originated from the Vedas, or, as I said, if the system is robust enough to be called mathematics. I remember attending a workshop organized on VM by the local RSS Shakha in Chamarajapet in <city w:st="on"><place w:st="on">Bangalore</place></city>. We were trying to solve cubic equations, and the ‘magical shortcuts’ of VM were on full view. But when we slightly changed the coefficients of ‘x’ in a cubic equation, the Vedic methods failed. Anyway, the children lapped up whatever I could teach. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>Wherever possible, I took children on a historical trajectory. We solved ancient problems based on the Pythagorean Theorem, in Trigonometry, Analytical Geometry, Logarithms and we widely debated paradoxes in mathematics. I included many of these discussions in worksheets and even managed to give problems based on these discussions in the various test papers that I set. Further, most of what I did with the blackboard as a teaching aid was from what I learnt from observing CK. </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>There were several ‘Aha!’ moments that the children and I experienced. I still remember how awestruck they all were (class IX students) when I showed them, through a small table I had prepared, how the idea of a logarithm actually works and simplifies the operations of multiplication and division, by converting them to the easier processes of addition and subtraction, respectively. Imagine, instead, if I had begun by saying: ‘If a<sup>x</sup> = y, then ‘x’ is called the logarithm of ‘y’ to base ‘a’! This is why children run away from mathematics. Well, we talked about the historical context in which logarithms were invented, and then I told them the story of the Scotsman John Napier who is generally credited with the invention of the logarithm. It is interesting that Napier indulged in mathematics as a hobby.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;">As you can see, CK’s legacy lived on in my life as a when I became a teacher. It still does, nearly three decades later. See, that’s what a good math teacher can do to you! </span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>I met CK at his residence again in March 2000, just before my marriage. He was happy to see me and was curious to know what I was doing. We discussed the strengths and ills of our education system and he listened quietly to the many things I shared about my work in education. He had retired from <place w:st="on">Baldwins</place> by then, but went to school everyday to leave his grandson. He couldn’t make it to my marriage reception and I learnt later that he was not keeping well that day.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>For me, CK will always remain the model math teacher. I have not seen a better math teacher since. He perfectly straddled the discipline of mathematics and its teaching – he was its passionate and eternal student and at the same time he loved teaching the subject. It is widely recognized in educational theory that the teacher’s knowledge consists of both subject matter knowledge and the knowledge of teaching (pedagogic content knowledge) among other aspects of knowledge that are needed to become a good teacher (if one views the teacher’s problem as a knowledge problem, that is). In a class of nearly 50 students and in a school that was traditional at best, CK struck a great balance. If I remember his teaching nearly thirty years later, it is because what he taught was internalized – forever! The teaching of procedures in mathematics (procedural knowledge) is a small part of mathematics education. It is the understanding of deeper conceptual underpinnings that is important. If one develops insights here, these insights are likely to stay throughout one’s life. And CK was constantly chipping away at the deeper and mysterious structures of the mathematical world, inviting us to explore and savour its beauty.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>As I write this, I have taken easy recourse to the internet to check if what I remember from Channa’s classes is correct. The World Wide Web is a place where everything we discussed in school with Channa is easily available, in print, in videos and in all sorts of forms. You can access all the fascinating stuff and it will keep you occupied for a lifetime. At the same time, the internet can dumb you down – it provides many things on a platter and you are tempted to copy paste from the myriad notes and articles and call them your own! No wonder then, that there is software developed to detect plagiarism. But in the eighties when CK taught us, the ‘<i style="mso-bidi-font-style: normal;">www’</i> was not even in our wildest fantasies of the future. He must have therefore read a lot, sitting in libraries and looking for his favourite books in bookshops. When some of us got a glimpse of his private library, we knew he was a serious reader of mathematics and science. His study was filled with hundreds of books then.</span></div>
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<span lang="EN-GB" style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span>I cannot help but reflect upon the status of the teacher now and wonder what it would mean to take a leaf or two from CK’s book. Can training make great teachers? Or, are teachers made even before that? I would tend to believe that one should love teaching and I’m not sure if this can alone come from teacher preparation. At the same time, I’m not discounting this preparation, both before and after, one becomes a teacher. This learning is an eternal journey. But it saddens me to see how teachers are treated within the educational system. We have created a system where we see the teacher as a contract worker who is often paid a pittance, who is made to do all kinds of things other than teaching and whose support systems are non-existent. Yet, we expect a lot from the teacher and somehow expect the teacher to be ‘different’ from the rest of the human species. How then can we expect children to glimpse that wonderful world that CK showed us, that I continue to see and marvel to this day?<span style="mso-spacerun: yes;"> </span></span></div>
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<span style="font-family: "Times New Roman", "serif"; font-size: 12pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">March 2012</span></div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com1tag:blogger.com,1999:blog-1233351832092294149.post-46693180682098513272012-03-31T14:04:00.000-07:002012-03-31T14:05:41.944-07:00Small steps towards science in HaryanaSmall steps towards Science in Haryana<br /><br />In April’99, DPEP Haryana organized a state level ‘Materials Mela’ with support from the Pedagogy Unit, TSG-EdCil and the DPEP bureau. There were extensive preparations in the run up to the mela. ‘Nanhe Kadam Vigyan Ki Or’ (literally translated as ‘Small Steps towards Science’), a handbook of Science teaching for teachers, had its roots in this experience. Tushar Tamhane and Sheshagiri provided resource inputs into the making of this book. What follows is a brief report of the process that led to this interesting book.<br /><br />In the beginning, we asked some basic questions – what are the various ways by which Science can be made enjoyable and meaningful for teachers and children in the primary years? Where should we begin? How should the handbook be written? Quickly, we realized that if new ideas in Science teaching had to be introduced, they would have to be related to that ‘Bible’, the textbook. Whether one likes it or not, most primary school teachers in our country still swear by the textbook. Any idea that cannot be linked with what the textbook is saying is considered ‘extra’; the usual refrain is that “We have to ‘cover’ the syllabus!” Therefore, the more specific the linkage with the text, the greater the degree of acceptance by the teachers, a maxim we realized in the early days itself. Not a very pleasant way to begin, but there was no choice! Ideally, however, we would have liked to rethink the Science curriculum, but there was no space and time for this to happen.<br /><br />So, with a ‘core’ group of teachers, resource persons from BRCs, CRCs DPO and DIETs, we began! Like hawks, we studied the existing science textbooks of each of the primary grades, looking for statements that provided even vague possibilities for experiments and demonstration. You see, we had to ‘equip’ ourselves with these ideas to provoke the teachers into thinking that they could do these things in the classroom. Our textbook search rewarded us with cryptic statements like ‘Hot air will rise’, or ‘Air exerts pressure’, or the ubiquitous ‘Air occupies space’. We grabbed these possibilities and brainstormed the possible range of experiments that could be set up to explore these ‘facts’. To help ourselves in this task, we had collected a wide range of science activity books from here and there – why reinvent the wheel when so many ideas exist? They had only to be adapted to our needs.<br /><br />As we moved along, we collected many interesting ideas for experimentation. Small task groups were set up on ‘Air, water, forces’ and so on. We resolved that we would follow the philosophy of ‘local context, local materials’ in our work. Arvind Gupta’s presentation on one of those days on using bottle caps, water bottles, ice cream sticks, used plastic bags, etc., spurred the group onto greater efforts. For the group, the dream of writing a book for thousands of teachers across the state was itself awe inspiring, and it kept them going. Another slogan that we established in the early days in the name of enquiry and exploration, was, ‘Karo! Vichaar Karo! Dubara Karo!’ (Try! Think! Try again!)<br /><br />As the mela approached nearer, we shifted base from TSG to SCERT Gurgaon, Haryana. The conference room was soon littered with materials which otherwise would have been termed as ‘junk’. Slowly, this junk was being converted into exciting experiments. Water bottles with balloons showed that air indeed occupies space. Plastic milk bags showed that pressurized air could even lift a person. Dry pieces of cloth could act as siphons, camera film containers acted as pumps, balloons could be stuck to the walls, marbles were used like bearings, matchboxes jumped up like frogs…each of these activities had a wealth of fascinating science to be explored and understood. We managed to link all of these to those cryptic textbook statements!<br /><br />Two incidents can never be erased from my mind – the first had to do with a curious professor of mathematics education at the SCERT who had walked in to see what we were up to. He was given a mineral water bottle, with a balloon fixed across its opening, hanging inside the bottle. When asked to blow the balloon inside the bottle, he found to his consternation that it wouldn’t expand. He went away, muttering that there was some ‘problem’ with the bottle or the balloon! He came back later to realize with a shock that the balloon could not be blown inside the bottle because there was something inside the bottle that occupied space – air! Despite their best efforts, some members of the group who were trying to ‘prove that 20% of the atmospheric air is made up of oxygen’, failed. In the classic experiment of the burning candle in the water container with an upturned glass tumbler, the water always rose to occupy much more than a fifth of the glass tumbler much to everybody’s frustration, thereby violating the ‘facts’ as presented in most textbooks! So, there was a great deal of discovery, learning, and more importantly, unlearning for many of us.<br /><br />The process of writing the handbook was equally interesting and challenging. There was a debate on including the ‘explanation’ for each experiment. Some favored the easy way, suggesting that we write the explanation at the end of each experiment. How would the teachers know otherwise? Others, who were a bit more adventurous, felt that the teachers and children should themselves discover the meaning behind each experiment. We would only write about the materials required and indicate the basic instructions to be followed. Eventually, the latter view prevailed. So we left an empty box on each page for the teacher to fill. Similarly, another box was left empty for the teachers and children to write about phenomena that they saw or experienced in their environment that illustrated an interesting principle. It would not be an exaggeration to state that this is perhaps the only Govt. primary school handbook with spaces for the teachers to fill! We chose catchy names for each experiment like “Are, Ye Pani kahan se!” (Hey! Where has this water come from?”) We even gave a list of references at the end of the book. There was another list of locally available materials that could be used for the experiments. All in all, we gave our imagination the best shot in the making of this book. Last, but not the least, the naming of the book – Tushar suggested Nanhe kadam Vigyan Ke (Small steps of Science), but the group felt that Nanhe Kadam Vigyan Ki Or (Small steps towards science) was better. So we left it there, enriched by all the small steps that we had taken towards that effort.<br /><br />The mela itself was lively; there were hundreds of participants from all over the state. The science group did a commendable job. <br /> <br />As I write this, I wonder – how far has this book reached? Has it made the life of the child and her teacher in DPEP Haryana more exciting and filled with a joy of discovery? It is one thing to write an interesting book, but quite another to make that book work in the harsh and complex reality of our schooling system. We can only hope that it has made some difference. We do realize however that many more Nanhe Kadams will have to be taken…<br /><br />Giri<br />July 2001Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com1tag:blogger.com,1999:blog-1233351832092294149.post-7368325710410458752011-10-23T01:39:00.000-07:002011-10-23T02:14:11.872-07:00Creating your own mathematicsWanting to do something different for a change a few days ago, I amused myself with a little bit of mathematics. In our work, we are always trying to make the life of the teachers and children much better in the primary school classroom. Any mathematical activity which we undertake is with this objective. <br /><br />I was playing around with a seemingly innocent problem of subtracting 169 from 637. However, I did it “my” way which was different from the “normal” and “accepted” method taught in school. Here goes:<br /> <br />100 + 100 + 100 + 100 + 31 + 37 = 468 (answer)<br /> <br />169 --- 269 --- 369 --- 469 --- 569 --- 600 --- 637 <br /><br />As you can see, we start with 169 and then progressively keep adding hundred. Why add hundred? Because it is easier to add hundred at a time. You are correcting an annual examination paper, and one of your children has come out with a working process with the answer as written above – what would your reaction be? Without being harsh on the teacher community, I would be tempted to say that this would invoke the much dreaded red cross against (and across) the answer. Not only that, the child would be pulled up with “This kind of an answer will not get you anywhere. No marks for this! Where is your working?” This would be followed by a “recapitulation” (torture) of the method:<br /> <br /> 637<br />- 169 <br />-------------<br /> 468 <br />-------------<br /><br />Of course, you’ll have to remember how to “carry one”, “borrow one”, and “pay it back”. <br /><br />Have you noticed how bus conductors deal with cash and return change? Suppose you have bought a ticket for Rs.5/-, and you hand over a Rs.50/- note. Many conductors, who have the habit being vocal about how they return the change, will be heard to say, “Ten, twenty, thirty, forty, fifty”. When “ten” is being said, the conductor actually gives you Rs.5/-, and then successively gives ten rupee notes till he comes to 50. In the process, you’ll have been given <br /><br />5 + 10 + 10 + 10 + 10 = 45<br /><br />Sabjiwalas use this method every minute. Where do the conductors and sabjiwalas have the time to “carry, borrow and pay it back?” Some of the sabjiwalas may not be even “numerate” in our definition. How are they able to manage?<br /> <br />Inspired with this discovery, I continued playing around with more problems. Consider the product: 17 X 14. This is how we normally do it in school:<br /><br />17 X 14<br />----------<br /> 68<br /> 170<br />----------<br /> 238<br /><br />There are other ways of doing this problem. One way would be:<br /> <br /> (10 + 7) X 10 + 4)<br />= (10 X 10) + (10 X 4) + (7 X 10) + (7 X 4)<br />= 100 + 40 + 0 + 28<br />= 238<br /><br />Can you think of other ways? How many of us wonder what takes place in the mind of the child when given a problem like <br /><br />56 + 27. Answer?<br /><br />There is something about the ease with which we use a ready made algorithm (an algorithm is a set of rules or procedures) whose logic we may not even understand, which stops us thinking about how we would approach a problem like 56 + 27. Mechanically, we follow the rule of “carrying over”. As teachers, we do not take the trouble to find out what happens in the mind of a child when it sees the problem. It may be more natural for many children to add 50 and 20 to get 70, and then add 7 and 6 to obtain 13. The final answer can then be got by adding 70 and 13. No wonder, we then let the children fall into a set of habits which, in the long run, close their minds to other possibilities. Our associations with particular procedures and our rigidity with particular symbols are so often tight that a child of eight may not know the answer to 7 multiplied by 5 but know straight away what 7 times 5 gives!<br /><br />To subtract 169 from 639, it is surprising how many personal procedures (or algorithms) there are, and yet, we are often stuck with the method we have learned in school. Algorithms may help us to ease the problem of writing procedures in a symbolic way, but that is not the end in itself. Consider another personal procedure for the same problem (i.e., 637 – 169):<br /><br /> 169:31<br /> 31 and 37 is 68<br /> and there are 6-less-2 hundreds <br /> 468 (answer)<br /><br />Here is a final example:<br />Since 637 = 100 + 100 +100 +100 + 100 +100 + 30 + 7, and <br /> 169 = 100 + 60 + 9, it follows that 637 – 169 can be written as<br /> <br /> 100 + 100 + 100 + 100 + 100 + 100 + 30 + 7 <br />-- 100 + 60 + 9)<br />------------------------------------------------------------<br /> 0 + 40 + 91 + 100 + 100 + 100 + 30 + 7 <br />------------------------------------------------------------<br />The reader is left to obtain the answer in whichever way is convenient. Notice how the above approach also helps in understanding the idea of the expanded notation. Notice also, that, in this case, “borrowing” as we would do it normally in a subtraction problem, is not required at all! After enough practice has been provided in the use of the expanded notation, the same problem could be now written as:<br /> <br /> 600 + 30 + 7<br />-- (100 + 60 + 9) <br />---------------------<br /> 468 + 0 + 0<br />--------------------- <br /><br />The process would be: Nine is greater than 7. Therefore we would need to borrow at least 2 from 30, and add it to 7. 9 – 9 is now equal to 0. By taking 2 from 30, we have made it 28. To subtract 60, we would need to take at least 32 from 600. Similarly, 60 – 60 is 0. Since we have removed 32 from 600, we are left with 568. 568 – 100 is therefore 468, the answer. <br /><br />Another typical way of solving this problem would be – starting from the left, i.e., from 600, we could begin by removing 100. We are now left with 500. But we see that 30 is lesser than 60, and 7 is lesser than 9. Therefore, how much would we need to borrow from 500 to subtract 60 and 9? First, take away 30, and add this to the 30 we already have. 60 – 60 is zero, and 500 – 30 is 470. We need to add 2 to 7, so that 9 is also cancelled in the same manner. Finally, we are left with 470 – 2, which is 468. <br /><br />Notice how the expanded notation is used, and how this gradually gives way to the illustration and use of the place value. The procedure of “borrowing” is very clearly shown. You don’t always have to borrow 10 or 100. On the other hand, the amount that you need to borrow is flexible, and depends on what is required to be borrowed. Borrowing can also be done in many different ways. By admitting this idea, we are allowing enough scope for the child to think and explore to find out how to go about a particular problem. And each problem brings with it a new experience and challenge. Often, the tendency is to teach expanded notation, place value and operations on numbers separately. This piece meal approach prevents one from seeing the connections.<br /><br />The methods explained so far do not destroy for me the other ways of subtracting that I know. Very often, the procedures we follow in our minds when doing a problem cannot be put on paper without making them to appear clumsy and chaotic to the reader. The above examples are sufficient to illustrate this. This does not mean that these methods are not correct, are ‘slow’, and therefore should not be followed. The only advantage of following the method learned in school is that it can be put down on paper without the need for elaboration. Secondly, these methods help us to compute quickly. This brings us to the next question… <br /><br />“What is the best method?” I do not want to ask this question without counter-demanding, “For what purpose?” There is nothing sacred about a particular method. In fact, the popular perception which tremendously influences our attitudes as teachers and parents towards children is that:<br /><br /><span style="font-weight:bold;">Speed = Brilliance,<br />Slowness = Dullness<br /></span><br />There are certain misplaced notions about what about the ‘qualities’ of a ‘good’ student of mathematics - the ability to compute fast, and the ability to handle big numbers. Shakuntala Devi is often referred to as a great mathematician (which she’s not!), because she can multiply two twelve digit numbers with ease, or obtain the square root of a ten digit number faster than the computer. Often, parents and teachers take pride in such skills that their children may have developed. Pray, what purpose will this serve to a child in an ordinary school classroom and later on in life? As adults, we can only pretend to understand the value of, say, 1 light year (the distance covered by light in one year, at the speed of 3,00,000 km/sec) which is 9460800000000 Km. Why should we torture our children then? <br /><br />Mathematics is not just about how fast you can calculate, or your ability to play around with big numbers which may mean little to you in everyday life. It is not limited to the application of ready made, uniform procedures to the solution of problems. It is about cultivating the ability to create and explore paths which we can identify with. It is often said that in order to learn mathematics, one needs to create (re-create) it for oneself. The examples discussed so far clearly illustrate this. What we consider to be the “fundamental” or “basic” principles of mathematics at the school level have taken thousands of years to develop. It necessarily follows that we cannot force the learning pace with children. Yet, how easily frustrated we become when we see a “wrong” answer! The truth may be that this wrong answer represents a genuine exploration on the part of the child, a struggle to comprehend.<br /><br />Most often, we do not let out children explore different ways to arrive at an answer with the argument that forming habits (in my words, the ability to mindlessly repeat) are a protection against the confusion that could take over if the mind began to charge off in too many directions. This uncertainty of not knowing what will happen makes us hold our cards close to our chests, and “protect” the interests of the child.<br /><br />The truth is that, as parents and teachers, we would like our children to cultivate and perfect these skills and habits so that they can ‘do well’ in the examinations and score high marks. Remember, the competition is tough out there! But, in the name of this competition, are we not inhibiting the natural ways of learning in our children? You decide… <br /><br />How can we have an environment where both experiences, i.e., formalized procedures and treatment of topics, are reconciled with exploration, imagination and the 'freeness' to think? While it is possible to go in all kinds of directions without necessarily having the ability to be able to compute fast, or be precise, this imagination would be useless without care in developing appropriate skills. On the other hand, these skills (of calculation, of being able to apply procedures, etc.) cannot be developed in isolation of the ability to be able to explore, imagine and think freely.<br /><br />New Delhi<br />26th April <br />1998Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com1tag:blogger.com,1999:blog-1233351832092294149.post-47408078127397856532011-10-23T00:59:00.000-07:002011-10-23T01:06:18.848-07:00Frozen Education -- a study of obstacles to children's education in Jammu and Kashmir<span style="font-style:italic;">(The detailed study is not attached here. If you are interested in reading it, send me an e-mail. I will get back with a copy.)</span><br /><br />A number of people and numerous conversations that we all had together are all responsible for this study. I will begin by mentioning Renu Singh from the Delhi office of Save the Children (SC), who first invited me to undertake the exercise of finding out the obstacles to the education of all children in Jammu and Kashmir. We began talking about it in the second half of 2009, but it was not until February 2010 that discussions on developing the tools for the study began. Sharif Bhat and Mufti Riyaz from SC’s office in Srinagar, and Neha Gandotra based out of Jammu were of tremendous help, particularly in identifying an enthusiastic group of young people who were willing co-learners and travelers and who did all the hard work of walking up and down the beautiful mountains, seeking to meet teachers, children, parents, and community leaders to understand what stops children from going to school. This list is long, but I must mention everyone -- Ufera, Soliha, Huzaifa, Umer, Shahid, Saleem, Wasim, Muzaffar, Tahir, Neelofar, Sharika, Rashida, Fayaz, Sheikh Ali, Mohd Ali, and Farrukh. I’m sure they enjoyed all the hard work and I hope they will eventually develop into the next generation of education activists that our society badly needs. <br /><br />Bashir, Gulzar and Targez drove us across the seven districts and helped us unearth many a story whose hints we can only give in this document.<br /><br />Save the Children’s local NGO Partners also deserve mention, especially for their support for the logistical arrangements in all the districts. The study would have been enriched further had they played a bigger role. Many thanks therefore to Yateem Tust, Yateem Foundation, Jay Kay Women’s Welfare Society (JKWWS), Modern Culture Club (MCC), and Kargil Development Project (KDP).<br /><br />Representatives from the educational departments told us much and helped us develop insights regarding the way their departments function (well, in many cases, how they do not function!). While some were wary of us, many opened up in the hope that their voices would reach far and remove the constraints in educating all children. In the same vein, Renu Nanda from Jammu University, Javed Rahi from the Tribal Research and Cultural Foundation, J & K, Prof. Madhosh (retired from the Kashmir University), and Mohd Rafi, District Collector, Budgam, need to be thanked in particular for enriching us. <br /><br />Finally, my deepest gratitude goes to the hundreds of parents, children and teachers who spent many hours with us, understanding patiently our incessant questions before responding to them, and allowing us to share their spaces at home, in the school and in their communities. Their spontaneous warmth and affection helped us to carry on. We learnt much in those hundreds of conversations, but I’m not sure if we have done enough justice in documenting the multitude of experiences in this document.<br /><br />We have tried to map the kinds of obstacles that prevent children from going to school in the state of Jammu and Kashmir, enjoying school and learning something meaningful and relevant that they can use on their lives. These obstacles are quite complex, and our observations show that they are often rooted within the families, local communities and the functioning of the schooling system itself. They may arise due to the phenomenon of Gurbat (the Kashmiri word for poverty, which goes beyond income related poverty), or may still be affected due to civil unrest (as in the case of the Kashmir Valley, when many teachers happily do not attend school whenever there is a hartal). In many cases, it is in the nature of human behavior that the greatest obstacles arise – an insensitive parent, family member, an abusive teacher or a corrupt and complacent worker in the education department – all of them play significant roles in making or breaking the educational cycle of many a promising boy or girl. We have seen all these examples in the course of this study. I still remember interviewing this teacher in a Poonch village for over an hour. He was very articulate and gave me the impression that he was one of those hard working and conscientious teachers. Happy that the interview went off well, I then walked into the next room where children from that school were waiting for me to initiate a discussion. The first thing they said was “Jis teacher ke saath aap baath kar rahe the, woh ek mahiney ke baad school aa raha hai…mahiney mein ek ya do din aata hai bas…” This put me in deep thought. Isn’t this one of the biggest obstacles, I wondered? Coupled with this, when one heard stories of how corrupt the system of governance (including the educational system) has become, one wonders which obstacle is the biggest of them all – the family, the teacher, the education department, civil unrest, or political instability, among others? <br /><br />Perhaps the answer lies in creating an environment where everyone concerned -- parent, teacher, politician, policy maker or administrator or child, is able to overcome one’s own limitations, develop deeper understanding and sensitivity to the child’s needs, and bring all the resources at his or her command to make the difference. The energy for this has to come from within the government, from that conscientious minority pegging away, trying to reach the poorest of the poor. Still, this may not be enough, and we will need to involve external agency to mobilize the constituencies to develop a mass of critical consciousness that can make a difference. <br /><br />2011Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-49866790431854711422011-10-23T00:40:00.001-07:002011-10-23T00:40:32.491-07:00KuniI<br /><br />My son liked this story so much that I had to tell it to him many times over, Ditto, with my daughter. I still tell them Kuni’s story if I do not have any other story to tell. Little did I realise that my childhood tryst with Kuni would mean a lot to my children. At some point, as I realised how much they liked this story, I decided to write it for children. That day is not far off.<br /><br />The year was 1978 – thirty three years ago! ‘Thirty three years ago…’ sounds nice when one tells a story, especially to those much younger than you. It feels as if you have accumulated so much experience! Anyway, let me get on with the story. My granny’s ancestral home in Bengalooru’s Cantonment, off Queen’s Road, was about to be sold for rupees seventy nine thousand. There are conflicting versions of how it happened. My parents always maintained that my uncles – three of them – were very keen on getting that house sold. Nobody wanted to stay together, and they had their own lives. So the question of keeping that property for everyone to live together one fine day didn’t arise. Often, they talked to my granny about selling the house and getting their share of the little booty. Left with no other option, the old woman gave in. Since she was staying with us, it was agreed that my father would get a substantial share of the proceeds. <br /><br />I don’t remember the many details of what it took to sell our home, but there is this vivid picture of a discussion the entire family had in our small living room with a chap called Samiullah who finally bought the house. I was allowed to sit on a wooden stool somewhere in between two adults as they all haggled over the final price. The other piece of memory is that of my father and uncles counting seventy nine thousand rupees! I marvelled at their speed, as I always do when I stand at the bank counter sometimes to see money getting counted. No cheques, no electronic transfers. We didn’t even imagine that there could be something called electronic money those days. I’m pretty sure that my father didn’t have a bank account. He brought home his meagre few hundred rupees salary in cash and handed it to my granny who managed the household with my mother. Life was simple those days, and I didn’t even realise as a child that I missed out on anything.<br /><br />Years later, when I could understand life’s nuances better, I was told by my older cousins and some aunts that my father had committed a Himalayan real estate blunder. I was told that that the Muniswamy Road house was worth crores! Had it been sold later, everybody would have become ‘lakhpatis’, at least – so went the argument. I had several such conversations and everyone seemed to point fingers at my father for his lack of foresight. My parents always thought otherwise and said ‘Look, they needed money, that’s why they sat on your granny’s head and made her agree.’ These arguments mattered little when I was young. <br /><br />Anyway, we left 14, Muniswamy Road one day in 1978 from my childhood home, never to go back again. It was the first time that I moved from one home to another. My father called my childhood home an ‘outhouse’ meaning that all the rooms of the house were built in a line at one end of the plot of land leaving a large compound space in which we had the Tulsi katte, several flowering plants, a huge coconut tree (which my mother said was planted on the day I was born) and a big tree that gave the fragrant Sampangi flowers which were in great demand in the Shivaji Nagar market nearby. My friends and I played and pranced around in the large compound. I remember tri cycling, playing hide and seek, watering the coconut tree and climbing the Sampangi Mara. There are other memories, such as pissing out by standing at the room window holding its railings, when it was raining. Bahadur, our tenant who had rented one room at the corner of the plot, ran past and, when he saw this parabolic stream coming out of the window ducked underneath and carried on!<br /><br />II<br /><br />We shifted southwards to a place called Jayanagar 9th block. For one year, my father said, we would have to stay in a rented place while our new house was getting built in a new residential area called J. P Nagar. The roads were just getting laid out, and my mother would often walk from 9th block to J. P Nagar 2nd phase to supervise construction. Later, our house would appear as a white speck from the end of 9th block Jayanagar. It was only the second house in all of J. P Nagar!<br /><br />Our rented home in 9th block was very small and I remember the difficulty I had adjusting in this space after 14, Muniswamy Road. Anyway, I quickly made many friends in the neighbourhood and spent most of my time on the streets of 9th block, playing lagori, marbles, flying kites, spinning the tops and playing cricket – all on the street. I keep telling my son that these games have more or less disappeared from our cities nowadays. I can vouch that kite flying in Bangalore has all but disappeared. Kids spend a lot of time playing virtual games on the cell or computer. And then there are these malls, which have mushroomed all over the city, where you pay through your nose to satisfy your child’s desire to play. Gone is that spontaneity which we enjoyed as children. <br /><br />Kuni quickly became a dear friend. At that time, I didn’t know that ‘Kuni’ in Kannada actually meant dog! This only dawned several years later. There she was, simply called ‘dog’ by all of us. For a dog that spent most of her time on the streets, she looked quite big and brown, almost like an Alsatian. I discovered from my friends that she had quite a few children who, like her, inhabited 9th block’s lanes. They all looked quite different. She must have had several lovers! I would feel strange but curious and excited nonetheless at the sight of her mating with another dog -- the famous ‘doggie position’, as I learnt some years later! Other dogs would wait to mount her, in heat, often snarling at each other and mounting her even if she was stuck with another dog. Some of my friends threw stones at dogs who had coupled. They enjoyed doing this and didn’t think much about the hurt they inflicted on other living beings. Children can be violent, too. I wondered why dogs had to get stuck that way… <br /><br />Once I fed Kuni with some chapathis, she expected some titbit or the other from me all the time. My mother and granny readily obliged and we usually fed her food that we ate – rice, dal, chapathi, biscuits. Pretty soon, she started spending a lot of time in the vicinity of our new home. To escape the heat, she would just jump over the gate, come in and lie down in front of our door. The small plot of land on which we lived was partitioned into three separate houses, two of which were rented out. Subbamma, our landlord, lived in one of these houses opposite ours. She didn’t seem to mind Kuni.<br /><br />As the days passed, Kuni started waiting for me to return from school. I usually walked home from the 9th block bus stand and as I entered the last stretch every day, I would often find my mother standing at the gate, waiting for me. Seeing me, she would look back and say something to Kuni, who often waited inside. Kuni would then charge across a very short stretch of compound, leap over the gate and come charging towards me, her tail wagging madly, joy written all over her face. Our evening meeting usually had the same script – she would stop just in time to avoid a collision and then would kneel in front, straightening her front legs, wagging her tail, waiting for me to initiate some affection. I would go close to her, pat her head, and ask her how she was. She would then pounce on me, and I would hold her forelegs as she walked on the other two, and that’s how we often covered some distance. Then she would run away, only to return after a few minutes. I fed her the biscuits I was given along with a glass of milk.<br /> <br />Every evening, as my friends and I played on the streets, Kuni hung around. Sometimes, she would go away for an hour two, but always came home for dinner. She would stay the night in the compound. Winters in Bangalore were quite nippy in the late seventies. I still remember how misty it would get in the mornings and how our skins would crack during those months. We all liked to ‘smoke’ in the mist then! To make Kuni comfortable at night, we spread out a gunny bag in front of our door. My parents and granny would not let Kuni in. I often tried very hard to cover her with another gunny bag, but she would usually come out of it and was not comfortable being covered.<br /><br />Once, our neighbours had a social function and there were many people who had come for lunch. It was some festival and I remember being home that day. Lunch was spread out on banana leaves, which were all later neatly rolled out and thrown outside a little away from our house. There was no public dustbin. It was all left to the cows to eat the banana leaves. Before the cows came, Kuni and her friends appeared and rushed madly towards the banana leaves, hoping to find some morsels of food. There were many dogs fighting for very little food. Kuni was getting side lined by the other dogs and I didn’t like it one bit. I scared away the other dogs with a stick, and this gave Kuni a chance to eat some food all by herself. The other dogs kept growling, but they did not dare to come near me. I think Kuni became more close to me after that – at least, that’s what I thought then.<br /><br />One day, as I walked towards 9th block bus stand to board my school bus, Kuni started trailing me, much to my surprise. She had not done this before. I kept asking her to go back but she wouldn’t listen. So she walked behind me, all the way till the 9th block bus stand. The school bus was ready and would leave in a few minutes. I got in, and Kuni followed! She didn’t want to let me go. What I did, I tried to tell her to get down and when that didn’t work she had to be pushed out by the bus conductor. I kept worrying about her all day and was relieved to find her fine in the evening.<br /><br />As the days passed, Kuni and I only got closer. She would spend most of her time at our place, or somewhere nearby. She went with me whenever I set out of the house, to play or visit a friend’s place. On my part, I looked after her as best as I could. I became friends with her children too.<br /> <br />Finally, she didn’t come home in the morning over a weekend. I remember going out and looking for her. I enquired about her with a few friends, but they didn’t have an answer. So we started searching in the lanes of 9th block. ‘Go to the main road, there’s a dog lying there’, said one of our neighbours. We found Kuni lying inert in the middle of the main road, the one that connects the Bannerghatta road with Kanakapura road. Why is she lying down in the middle of the road? I thought. She would be run over by the Gaadis. I didn’t understand, till my friend pointed out to blood beneath her head. With a heavy heart, I realised that she had been run over by a callous driver. I couldn’t believe it. ‘Can’t we take her to a doctor?’ Nobody answered. <br /><br />I came home crying. I looked back -- Kuni was surrounded by her children, all with sad looks on their faces, their tails down, sniffing her on that fateful main road.<br /><br />Raipur<br />October 2011Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-81828916960945390822010-02-10T07:05:00.000-08:002010-04-16T21:48:46.243-07:00Quotations from Kargil on Education<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDDNkz_XIAQLjqaT4s5iuklc1daWDo0gtoc0UF2prVHD-fXAaAwEciF5Ss6p0x0toxh3ax1vwY-wFK7n4C_4TB8Sx-ohNAxxQVMVoHoocKj2qKV6bP0VWwkxf7haVgpWKgpAJ95ped5GQ/s1600-h/P1000695.JPG"><img style="margin: 0px auto 10px; text-align: center; width: 458px; display: block; height: 240px;" id="BLOGGER_PHOTO_ID_5436696158969894146" alt="" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDDNkz_XIAQLjqaT4s5iuklc1daWDo0gtoc0UF2prVHD-fXAaAwEciF5Ss6p0x0toxh3ax1vwY-wFK7n4C_4TB8Sx-ohNAxxQVMVoHoocKj2qKV6bP0VWwkxf7haVgpWKgpAJ95ped5GQ/s320/P1000695.JPG" border="0" /></a> <div></div><div></div><div align="justify"><span style="font-size:180%;"><strong>B</strong></span>etween January 2007 and March 2008, I had the opportunity to work on the theme of education of children in the remote, harsh and beautiful district of Kargil in the Ladakh region of Jammu and Kashmir. To begin with, I was invited by Save the Children to work closely with its NGO Partner, the <em>Kargil Development Project</em>, and the <em>Ladakh Autonomous Hill Development Council,</em> Kargil, to help develop a long term educational strategy for the district. Later, as my work progressed, the Hill Council extended my association for another year to enable me to complete my work. Working on this assignment with a group of people identified by the Council as the 'core team' was truly an enriching experience <em></em>-- I spent much time in Kargil, traveling almost every month to work with this core team, preparing them to do a systematic study of he ground situation, as well as develop an appropriate plan of action. In this process, we asked: 'What kind of education could be considered relevant, meaningful and useful for the children of Kargil? What is wrong with the education that children get today? What needs to be done?' To get answers to these questions, we met hundreds of children, parents, teachers and others from many local communities spread across the entire district. We had many beautiful and enriching conversations in the middle of the semi arctic winter, when temperatures would often drop to minus 25 degrees, when it would snow heavily for days, blocking all routes to remote villages in the mountain side. Sipping <em>namkeen chai,</em> I often shared the dreams, aspirations and frustrations of beautiful people from a forgotten land. I still haven't been able to share the story of this journey. But what I have with me is a collection of statements which were made to us by children, parents, teachers and community members in the course of many conversations spread over a few months. I have great pleasure in sharing them with you. Many more statements lie hidden in the interview notes that were made, but for lack of time, I was unable to dig them all up from the Hill Council's office in Kargil. Perhaps that is another project, which I will need to undertake another day...meanwhile, happy reading, and a warm welcome to Kargil!</div><div align="justify"></div><div align="justify"><u></u></div><div align="justify"></div><div align="justify">__________________________</div><div style="font-family: times new roman;" align="justify"><span style="font-size:130%;"><strong>
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<br />“Duniyavi ilm raastha dikhatha hai aur mazhabi ilm usey mukam deta hai.”
<br /><span style="font-weight:bold;">Haji Mohd Yakub, Teacher, PS Shimsha, Drass</span>
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<br />“Education is like a candle in everybody’s life. It shows the way of good life.”
<br /><span style="font-weight:bold;">Asghar Ali, Teacher, PS Shimsha, Drass</span>
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<br />“Waqt ke saath chalna chahiye. Jo zubaan zyada isthemaal ho, usey hi padhana chahiye.”
<br /><span style="font-weight:bold;">Bashir Ahmed, Teacher, MS Shimsha, Drass</span>
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<br />“Talim saaj mey sar uthake jeene ke laayak banayega.”
<br /><span style="font-weight:bold;">Abdul Qayoom, Teacher, MS Shimsha, Drass</span>
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<br />“Private schools have 100% results because they bribe the board of school education. All the parents of children who study in government schools, are poor. They do not have enough money to bribe the board. So the teachers are not ‘effective’”.
<br /><span style="font-weight:bold;">Mohd. Raza, Parent, Shimsha, Drass</span>
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<br />“Ek aisa school ho, jisme accha teacher ho jo kabhi na mare…”
<br /><span style="font-weight:bold;">Safia Bano, Class 5, MS Shimsha, Drass</span>
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<br />“Jab mei padhti hoon, to mujhe lakdi gobar laane ko kehte hain…”
<br /><span style="font-weight:bold;">Hakima Bano, Class, HS Moradbagh, Drass</span>
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<br />“Parents send children to school and forget them after that.”
<br /><span style="font-weight:bold;">Ghulam Mohi-ud-din, Teacher, MS Matayen, Drass</span>
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<br />“If he does not go to school, I will teach him.”
<br /><span style="font-weight:bold;">Sidiqa, Parent, Shimsha, Drass</span>
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<br />“Hamaare yehaan gorbat hain. Hamaare yehaan ladkon ko bhi ladkiyon ki tarah vazifa diya jaye, taaki ladke bhi apni zaruriyat poori kar saken.”
<br /><span style="font-weight:bold;">Shabir Ahmed, Parent, Matayen, Drass</span>
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<br />“The child is like the branch of a tree. Whether we point the branch in the right or wrong direction depends on us.”
<br /><span style="font-weight:bold;">Haji Mohd. Yakub, Parent, Shimsha, Drass</span>
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<br />“…good community, a big playground and water…”
<br /><span style="font-weight:bold;">Basharat Ali, Student, Class III, Shargol</span>
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<br />“I want to become a teacher. I will teach my family…this, they need.”
<br /><span style="font-weight:bold;">Mohd Ali, Student, Class VIII, Pashkum, Shargol </span>
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<br />“Phool ke saath baitna aur paani dena…”
<br /><span style="font-weight:bold;">Mehmooda, Class X, HS Sangrah, Sankoo</span>
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<br />“Jeene se marne tak training zaroori hai…”
<br /><span style="font-weight:bold;">Sayeed Masood Ahmed, Teacher, Sankoo</span>
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<br />“Do saal se is school mei koi inspection ke liye nahi aaya hai.”
<br /><span style="font-weight:bold;">Teacher, HS Sangrah, Sankoo</span>
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<br />“It depends on the learner’s personality. Some children need chocolates, and some children need the stick.”
<br /><span style="font-weight:bold;">Syed Allahuddin, Teacher, MS Taikat, Sankoo</span>
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<br />“Agar rishvat na khaayein to local theek hai, varna non-local theek hain.”
<br /><span style="font-weight:bold;">Haji Mehdi, Parent, Sangrah, Sankoo</span>
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<br />“Talim azhat zaruri hai, garibon ke liye taaki woh kumba chala sakein. Kyon ki, iska ghar garib hota hai, iska ilm garib nahi hota.”
<br /><span style="font-weight:bold;">Ahmed Husain, Parent, Sangrah, Sankoo</span>
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<br />“Ladkon ko talim zyada zaruri hai kyon ki ladkiyon ko doosre ghar le jayenge jahan uska pati zimmedar hoga.”
<br /><span style="font-weight:bold;">Ameena Bano, Parent, Faroona, Sankoo</span>
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<br />“Local teachers chaalaak hotey hain. Aadmi ke hisaab se kaam karte hain.”
<br /><span style="font-weight:bold;">Fiza Bano, Parent, Faroona, Sankoo</span>
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<br />“Talim agar seekhein, to shayad bade hokar doctor ya engineer ban jaaye. Agar na seekhein, to kam se kam, Thekedaar ban jaaye.”
<br /><span style="font-weight:bold;">Mirza Mehdi, Parent, Faroona, Sankoo</span>
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<br />“Jin bacchon ko padhayi na ho wo kuch bhi nahi kar sakenge, chahe zamindari ho ya naukri.”
<br /><span style="font-weight:bold;">Tewang Dorjay, Teacher, MS Phey, Zanskar</span>
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<br />“In the coming days/years, parents should also be trained along with teachers.”
<br /><span style="font-weight:bold;">Rigzin Namgyal, Teacher, LHS, Icher, Zanskar</span>
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<br />“This is what I would like to say – if I get the opportunity, I would like to share information about my profession, i.e. agriculture in school.”
<br /><span style="font-weight:bold;">Tsering Raftan, Parent, Icher, Zanskar</span>
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<br />“If children are taught some arts and crafts and other such skills apart from the subjects they study in school, it will be nice. When children leave school, even if they can’t get a job, they can still earn a livelihood with these skills.”
<br /><span style="font-weight:bold;">Sonam Tsewang, Parent, Kumie, Zanskar</span>
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<br />“Papa kehte hain, ki padh likh kar mujhe jahaaz udhana hai.”
<br /><span style="font-weight:bold;">Divya Bharati, Class 3, Padum, Zanskar</span>
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<br />“Aisa badlao hona chahiye ki har tarah jadeed talim milay aur duniya ke saath chal sakay. Agar buniyaad sahi na ho to aage fail hona laazmi hai.”
<br /><span style="font-weight:bold;">Tsewang Mutup, Teacher, HS Phey, Zanskar</span>
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<br />“Talim aisa milay ki unhe sarkai naukri ke peeche na bhagna paday. Har doosre tarike se apna rozgaar khud paida kar sakay, jaise tourist guide.”
<br /><span style="font-weight:bold;">Sangis Chosphel, Parent, Icher, Zanskar</span>
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<br />“School grant se sheesha aur taat kharidkar laya aur school mey ghar jaisa mahoul paida kardiya. Bacche ab school mey ghar jaisa mehsoos karte hain.”
<br /><span style="font-weight:bold;">Tashi Stopden, Teacher, PS Kumie, Zanskar</span>
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<br />***********************************
<br />Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com2tag:blogger.com,1999:blog-1233351832092294149.post-49379831784553526662010-01-19T03:08:00.000-08:002010-02-18T23:01:11.121-08:00Notion of Quality in the Right to Education Act, 2009<span style="font-size:180%;">T</span>he first of its kind Right to Free and Compulsory Education Act, which was finally realized 62 years following India’s independence in August 2009, is intertwined with a long history of debates about the provision of education to all children in this country. Sadgopal (2008) in his documentation of the history of these debates, notes that the debate goes as far back as 1882, when Mahatma Jotirao Phule’s memorandum presented to the Indian Education Commission (the Hunter Commission) talked about how the British government’s funding of education ‘tended to benefit the Brahmins and higher classes’, leaving the ‘masses wallowing in ignorance and poverty.’ The next important event was when Gopal Krishna Gokhale moved the Free and Compulsory education Bill in the Imperial Legislative Assembly in 1911. This met with much resistance, on the argument that resources were not enough and also on the concern that if all children were to attend schools, there would be nobody to work on the farms of the landlords! The argument of lack of resources was repeated in 1937, during the National Education Conference at Wardha, where Mahatma Gandhi talked about giving priority to Basic Education (Nai Talim). Debates again featured quite prominently in the constituent Assembly (1948-49), when the idea of ‘Universal Free and Compulsory Education’ was discussed. It was only after much effort that Article 45 went through, promising free education for children up to 14 years. However, since it was under the directive principles of state policy (Part IV of the constitution and not Part III, where it would have acquired the status of a Fundamental Right in Independent India) the article was deprived of the status of a fundamental right. It was not until 1993 (the famous Unnikrishnan Judgment) that the Supreme Court, in a radical interpretation of the constitution, conferred on Article 45 the status of a right, by linking it with Article 21, the Right to Life, which the court stated would be meaningless if it did not come with Right to Knowledge. This led to the introduction of Article 21 A.<br /><br />To cut a story short, eight years later (in November 2001) the 86th Amendment Bill was presented to the Lok Sabha, but with serious flaws (such as the exclusion of the under six age group, among other equally important concerns such as inadequate budgetary allocations etc) as expressed by many civil society groups. The bill was passed by parliament in December 2002, without these concerns being addressed. It later became the ‘model bill’ or the Draft Right to Education Bill sent to the UTs and states. In 2009, this bill has now become the Right to Free and Compulsory Education Act, still with its many concerns intact.<br /><br />What does the Education Act document have to tell us about educational quality? It must first be noted that the Education Act is a legal document, which means that education is justiciable, and as such, a court of law can be approached to address/resolve any grievance or complaint. In a legal document, we cannot expect detailed discussions or reflections of a conceptual nature, as we can in the case of academic documents like the NCF or even articulations made under large scale programs like the DPEP and SSA. Yet, nothing in the Act prevents anybody from referring to or using these other articulations of the government as a source of direction. The point however is: which articulation is to be used? How are these articulations to be interpreted? We have already seen the difference between articulations presented in the DPEP/SSA documents compared with another important government document, the NCF 2005, which propounds a different notion of quality. What is the relation between these documents and the Act? This would need examination. Should the Act have referred to these earlier documents for the purpose of interpretation? The Act does refer, in Chapter III, point 6(a): ‘The Central Government shall develop a framework of national curriculum with the help of academic authority specified under section 29.’ National Curriculum Frameworks can change from time to time, and are as such not immutable. This would allow for the predominant version of quality that has been negotiated at any given point in time.<br /><br />As a legal document, the Act outlines certain conditions that have to be met by those involved in the provisioning of education – these could involve the government, parents, teachers, private school managements etc. If the conditions as stipulated in the Act are not followed, they are bound to invite punitive action in many cases. For instance, if the Headmaster of a school does not issue a transfer certificate to an out going student (Chapter II, under point 5.3), he/she is liable for disciplinary action under the service rules applicable. Another example is that of school provisioning (Chapter III, under point 6). Within three years from the commencement of the Act, the government should provide a school with the limits of the neighborhood if a school is already not available. Another assertion of a non-negotiable condition is the following (Chapter IV, point 14.2): ‘No child shall be denied admission in a school for lack of age proof.’ This is one way of ensuring access to a school. Many more such examples can be given. The point to be made is that by specifying certain conditions, the document hopes to put in place certain ‘minimums’ or ‘non-negotiables’ that are presumed to ensure quality. Are these minimums enough? Do they reflect what one would like to see as quality, the essential character of education about which we have been discussing? Further, are they clear and comprehensive? Let us take one example. Who is the teacher, if we are to implement the provisions in the Act effectively? Chapter IV (titled ‘Responsibilities of Schools and Teachers’), points 23.1 and 23.2 have to say something in this regard (P.8, Part II of the Act).<br /><br />“23.1 Any person possessing such minimum qualifications, as laid down by an academic authority, authorized by the Central government, by notification, shall be eligible for appointment as a teacher.<br /><br />23.2 Where a state does not have adequate institutions offering courses or training in teacher education, or teachers possessing minimum qualifications as laid down under sub-section 1 are not available in sufficient numbers, the Central Government may, if it deems necessary, by notification, relax the minimum qualifications for appointment as a teacher, for such period, not exceeding five years, as may be specified in that notification.<br /><br />Provided that a teacher who, at the commencement of this Act, does not possess minimum qualifications as laid down under sub section 1, shall acquire such minimum qualifications within a period of five years.”<br /><br />These points are vague, at best, and open to multiple interpretations. For instance, the Act is silent on the phenomenon of ‘para teachers’, which is argued by many as a dilution in the idea of a teacher, and as a cheap and economically effective way of filling teacher vacancies in many states, and as a logic that will be used to ultimately phase out all the regular government teachers with contract teachers (Kumar, 2001). What position does the Act take on this issue? Further, what about teacher preparation, another area which has been put into grave danger with the unregulated and unbridled expansion of private teacher preparation institutions all over the country in the last 8-10 years? Any person can possess ‘minimum qualifications’, but where these qualifications have been obtained from an institution whose quality is highly suspect, we have a serious problem. Thus, on the whole, the ambiguity regarding the teacher, a key determinant of quality is one among several such, in connection with the notion of educational quality that the Act seems to propound.<br /><br />Should the Act even specify any conception of quality? This question needs to be discussed. As mentioned, by specifying certain ‘overall boundary conditions’, the Act hopes to ensure certain non-negotiable aspects of providing all children with a free and compulsory. In Chapter V (P.9, titled ‘Curriculum and Completion of Elementary Education), the Act specifies certain parameters which can be seen as intimately related to the idea of quality. It would be worth reproducing them here in full:<br /><br />29 (1) The curriculum and he evaluation procedure for elementary education shall be laid down by an academic authority to be specified by the appropriate government, by notification.<br /><br />29 (2) The academic authority, while laying down the curriculum and the evaluation procedure under sub-section (1), shall take into considerations the following, namely:<br /><br />(a) conformity with the values enshrined in the constitution<br />(b) all round development of the child<br />(c) building up child’s knowledge, potentiality and talent<br />(d) development of physical and mental abilities to the fullest<br />(e) learning through activities, discovery and exploration in a child friendly and child-centered manner<br />(f) medium of instruction shall, as far as practicable, be in the child’s mother tongue<br />(g) making the child free of fear, trauma and anxiety and helping the child to express views freely<br />(h) comprehensive and continuous evaluation of child’s understanding of knowledge and his or her ability to apply the same<br /><br />For a law to be enforceable or justiciable, it has to be precise, with no two meanings, since ultimately it has to be interpreted unambiguously by the judiciary. With the abovementioned points, there is much scope for subjectivity. For instance, how are we to understand points (b) and (d) above? In the context of schooling, developing mental abilities can involve a range of aspects Similarly, for point (e), where Child Centered again gives scope for much debate, and point (g), where ‘helping the child to express views freely’ finds mention. It can be claimed that a school is not child centered, or is not allowing children to express themselves freely. In the arguments that will follow, the school can defend itself on certain parameters, while the litigant can offer another set of reasons to suppose that the school is not child centered. How is the judiciary to make a judgment, when there is no precise definition of these terms? Further, in point (g), the inclusion of terms ‘fear, trauma and anxiety’ can similarly give rise to different interpretations, but it is argued by some that the judiciary is well versed with the ‘negatives’ – there is a history of litigation involving the negatives, and it therefore should be relatively easier to deal with them with some clarity. It is the positives which need to be sorted out. It can also be argued that if there had been precise definitions of ‘child friendly, child centered’ etc, these definitions could limit or ‘lock’ or ‘seal’ the notion of child-centeredness in education, which is essentially an open ended idea or notion that can be subjected to continuous reflection and debate. Indeed, in a larger sense, it can be argued that the notion of education cannot be laid out in a definite sense, for the very nature of the concept and the contemporary demands on it suggest that it be kept open for scrutiny.<br />Given the complexities that could arise in litigation involving the above aspects, one argument is that this loose description should not have been there in the first place as it can lead to much ambiguity. However, the question that will arise then is what notion of quality informs the Act. The only way out is for the judiciary to do its own systematic research and understanding of core concepts in education, which will enable it to provide an informed and fair judgment to resolve disputes. Where the disputes concern issues like infrastructure and basic facilities (as outlined in ‘The Schedule’ titled ‘Norms and Standards for a School, P.12 of the Act), they need not be complex. It is in the intangibles that a far more nuanced and refined understanding will be needed. Our initial reading of the Act has shown therefore that there is much to be discussed regarding the issue of educational quality.<br /><blockquote></blockquote><blockquote></blockquote>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com1tag:blogger.com,1999:blog-1233351832092294149.post-7005076933486747522009-10-14T22:23:00.000-07:002009-10-14T22:28:02.181-07:00Does language teaching need a study of language?<div align="justify">In my opinion, the issue or question of the relevance of the study of language in language teaching is very similar to the question ‘Does one need to study mathematics or science in order to be able to teach these subjects better?’ Though it might seem like a short aside, I would like to first explore this question before coming to the language issue.<br /><br />Two years back, I had the opportunity to undertake a study of teacher’s views and understanding about the subject matter of mathematics and its pedagogy. In the course of doing this study, I came across literature that explored the place of discipline or subject specific knowledge (in this case, mathematics) in classroom teaching. For instance, Skemp (1971 and later) highlighted the frustration of children who are mainly taught the ‘how’ when they actually want answers to the ‘why’. Liping Ma’s landmark comparative study (1999) of Chinese and American elementary school teachers brought the dimension of teacher preparation centre stage. Ma compared the situation of mathematics teachers in China and the United States. Using data from her study, she developed the notion of ‘profound mathematical understanding’ in teachers and stressed that this understanding is crucial to how they perceive mathematics and teach it. Based on her analysis, Ma then argued for ‘a connected, structured and longitudinally coherent knowledge of core mathematical ideas as an essential pre-requisite for any teacher’. In a similar vein, Deborah Ball et al (2005) state that ‘classroom problems are also mathematical problems’. This leads to the question: ‘What kinds of mathematical reasoning, insight, understanding and skill are required in the teaching of mathematics?’ The position taken by Ball is that the interactive work of teaching itself involves ‘knowledge of mathematical ideas skills of mathematical reasoning and communication, fluency with examples and terms…’ This requires additional mathematical insight and reasoning which involves ‘a kind of depth and detail that goes well beyond what is needed to carry out the algorithm reliably.’ This correlation was shown to exist on the basis of data collected for more than 700 teachers and 3000 students.<br /><br />It is quite clear from the above examples that subject matter or disciplinary knowledge is considered to be critical for deeper more meaningful teaching leading to understanding. Along with this knowledge is the knowledge of how children learn. Together, these two aspects are integral to the preparation of the teacher. We can extend this case to the study of language and language teaching as well. In the case of teachers, this aspect would be considered to be an integral part of their education and preparation as teachers. For teacher educators and practitioners in general, this would mean developing sensitivity to how language works. For children, a teaching-learning process grounded in the principles of language learning may offer many possibilities for deepening their learning experience as well as for creative expression, among others. Just why is this kind of knowledge necessary in the case of language teaching and learning? I have tried to present some arguments below.<br /><br />Much of what passes for as learning in primary and elementary school is traditionally measured in terms of the 3R’s (reading, writing and arithmetic). In educational practice, there is no dearth of small, medium and large scale quantitative surveys to ascertain whether children have acquired the 3R’s after, say five years, of schooling. Testing of children has almost become an obsession. Furthermore, with regard to language learning, in many cases the conventional practice is to break it up into ‘listening, speaking, reading and writing skills’ (the so-called L-S-R-W model) almost as if these skills are picked up in isolation of each other! This pre-occupation with measuring outputs, without paying sufficient attention to the processes of learning and other important aspects such as the resources children bring, their diverse backgrounds and narratives, reduces much of language learning to a mechanical ‘input-output’ model. We have seen this positivist, reductionistic approach since the ‘Minimum Levels of Learning’ (MLL) days of the nineties. The approach has continued in some form or the other to this day, though the term MLL itself may not be used as widely as before. It is in this larger context we must view the question of the relevance (or need) of the study of language to language teaching. <br /><br />There are other issues that deserve attention as well. First, we tend to look at language as ‘another subject to be learnt’. I suppose this view reduces or even negates the potential that language learning offers for learning in general. Like in mathematics, where procedural knowledge is often emphasized at the cost of developing understanding, language teaching too suffers from a narrow view that places correctness of grammar and pronunciation above creative expression. This leads to a kind of mechanical classroom practice where error correction is given undue emphasis. The fact that children have mastered grammar long before they enter school is lost on teachers and also in the process of their preparation. Other notions (already pointed out in the reading provided for this assignment) include the myth of language purity, dialect inferiority, pride of place for certain ‘mother of all’ languages, multilingualism as a problem, etc. These notions are so deeply ingrained that they are rarely problematized as issues during teacher preparation.<br /><br />The above observations may be categorized as those belonging to the realm of pedagogy on the one hand and on the other, larger (often unexamined) worldviews about people, language, culture, power, politics, and so on. Of course, these worldviews in turn influence education policy, teacher policy and classroom practice.<br /><br />Given these observations, we must ask: What is the value in a study of language as part of a program on education? The first value addition is that such an endeavor may contribute in important ways to developing sensitivity and awareness in teachers and teacher educators as regards the equality and structural unity of languages. This might then lead to a respect for the diversity of languages. In turn, we could then start looking at multi-linguality and multiple socio-economic and cultural contexts as resources instead of considering them as burdensome problems to be dealt with through imposition of uniformity. Further, such a study could contribute to a deeper and informed understanding regarding the history and politics of language, and how language has been used as a tool for promoting vested interests. Also, in this regard, teachers and others could appreciate the rich and varied cultural history and resources that a country like India possesses.<br /><br />In offering arguments for a study of language as part of language teaching or for a program on education, it may be important to ask: Is language to be treated as a separate subject? Does language development not have something fundamental to do with cognition itself? This view is articulated by Halliday (1994) that ‘When children learn language, they are not simply engaging in one kind of learning among many; rather they are learning the foundation of learning itself.’ If one wishes to take this position, then there is no escape from a study of language in any program of teaching or education. <br /><br /><strong>References<br /></strong><em>Towards a language based theory of learning</em> (M.A.K Halliday, 1994, source not specified)<br /><em>The Psychology of Learning Mathematics</em> (Richard Skemp, Penguin Publishers, London 1971)<br /><em>Knowing and Teaching Elementary Mathematics – Teachers’ understanding of Fundamental Mathematics in China and the United States</em> (Liping Ma, LEA Publishers, London 1999)<br /><em>Knowing Mathematics for Teaching – Who knows mathematics well enough to teach third grade, and how can we decide?</em> (Deborah Ball et al, American Educator, 2005)<br /><em>Knowing mathematics for teaching – baseline study of practicing mathematics teachers</em> (Sheshagiri K.M, 2007, Supported by Sir Ratan Tata Trust)</div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-3727287233372680542009-09-09T10:51:00.000-07:002009-09-09T11:01:45.012-07:00What the Karnataka textbooks say on things that matterRecently, I had the opportunity to do a quick study of the Karnataka State Social Studies textbooks to see how the idea of the modern nation is represented. Specifically, I looked at the construction of values and ideals of 'national progress,’ ‘democracy,’ and the 'ideal' citizen. Inclusions and exclusions in terms of gender, caste, class, religion, ethnicity and location (rural/urban) were also noted, along with the role the textbook content explicitly/implicitly assigns to education in national development. The study was an eye opener in many ways, and I ended up asking more questions than I have been able to answer!<br /><strong></strong><br /><strong>Brief description of the textbooks studied</strong><br />The books studied are the two Social Science textbooks of Class V used by the government schools in Karnataka. The books have been published by the Karnataka Textbook Society. The core curricular areas for Class V have been represented through the textbooks in the following manner – barring language, which has dedicated textbooks for each language (Kannada, English, Urdu, etc), the other subjects are all clubbed together in two textbooks, one for each semester (the academic year is divided into two semesters at the primary and middle school levels). Thus, semester 1 has a combined textbook for Social Science, General Science, Environmental Studies and Mathematics. The same is the case with the semester 2 textbook. The reason why this is so, is not clear. However, what is clear is that curricular or pedagogical concerns have not informed the production of these ‘all in one’ textbooks – for instance, there is no integration of content across disciplines. There are merely separate sections for each subject. It is quite possible that the effort has been to reduce the total number of textbooks that children need to carry (and hence reduce the load of the school bag)! Another reason would be to economize textbook printing.<br /><br />The Social Science part/section of the composite textbooks is further divided into the areas of History, Civics and Geography. The topics dealt with each of these areas are described below.<br /><br /><strong>Semester 1 topics</strong> <strong>(History)</strong> -- History of India – land and people; pre-historic India; Indus Valley Civilization; Vedic Age; Jainism and Buddhism<br /><strong>Semester 2 topics</strong> <strong>(History)</strong> -- Ancient North India; Mauryan Empire; The Kushans; The Gupta Empire; India after the Guptas; Ancient South India<br /><strong>Semester 1 topics (Civics)</strong> -- Civics and its importance; Public Property<br /><strong>Semester 2 topics (Civics)</strong> -- Rural Communities; Urban Communities; Panchayati Raj; Civic and District Administration<br /><strong>Semester 1 topics (Geography)</strong> -- The Solar system; Latitude and Longitude; Weather and Climate; Effect on daily life of weather and climate<br /><strong>Semester 2 topics (Geography)</strong> -- Physical features and climate of India; Agriculture and Industry; Population of India<br /><br />Aspects of the ‘modern nation’, such as values and ideals of 'national progress', democracy, the notion of the 'ideal' citizen, inclusions and exclusions in terms of gender, caste, class, religion, ethnicity and location (rural/urban), and the role of education in national development, are all implicitly or explicitly addressed in both the Class V textbooks. They are not situated in any particular chapter, but are spread across the entire text. In particular, the strongest linkages/references are seen in the sections that deal with the subject of Civics. In the coming paragraphs, we will look at examples of how the textbooks approach the above mentioned aspects of the modern nation.<br /><strong></strong><br /><strong>The ‘ideal’ or ‘good’ citizen<br /></strong>Lesson 6 of the semester 1 textbook (P.39) begins with a statement about citizenry. A citizen is referred to as somebody ‘who is a member of the country or nation and who abides by the rules and regulations of that country.’ Further, ‘A Good citizen loves and respects his country. Every citizen has certain rights and duties.’ Civics, it is stated, ‘tells us about the role of the citizen in society and in the government.’ Conducting oneself in a disciplined manner and respecting the needs of others is identified as one of the key aspects of a ‘good civic life’.<br /><br />On page 40 of the above book, the ‘Characteristics of a good citizen’ along with those of the ‘good civic life’ are outlined thus:<br /><br />• Keeping the school premises clean<br />• Keeping the house and street clean<br />• Helping children and old people<br />• Following a queue system<br />• To respect national flag and national anthem<br />• To protect public property etc<br />• To defend the country in times of need<br />• To pay taxes without fail<br />• To cast vote during elections<br />• Not to participate in anti-social activities<br />• Understand that giving or taking bribe is an offence<br /><br />The second semester book also (on P.60, 61 in the chapter on urban communities, and further on P.96 in the chapter on Population of India) outlines certain duties of citizens (interestingly, these or any other duties do not feature in the chapter on rural communities):<br /><br />• To keep surroundings clean<br />• Not to smoke in public places<br />• To dispose waste materials<br />• To reduce the use of plastic bags<br />• To use electricity and water sparingly<br />• To develop the habit of working hard and live by earning<br />• To obey the law and lead a peaceful life<br />• To control population explosion<br /><br />From this description, one cannot help but get the impression that the good or ideal citizen is a passive person one who has to ‘obey’ or follow a range of rules set by/in his nation so as to preserve order (whose order?) in society. This almost sounds like a mechanical list of ‘things to do’ in order to qualify for the tag of a good or ideal citizen. While sensitivity to the needs of others is mentioned, the rest of the items listed above seem to require an almost blind belief in the following of rules set out by the powers that be. Neither the textbook content nor the questions that follow provide much space for exploration by the teacher and children. For instance, what could respect for the national flag and anthem mean? Why should standing up when the national anthem is played be construed as good citizenry, and not otherwise? In the same vein, what could ‘anti-social’ activities mean? Would participating in a meeting/dharna/procession that critiques government policy be considered anti-social?<br /><br />It is interesting that the characteristics listed above of a good/ideal citizen do not seem to include a critical element or faculty, such as the ability to question a given phenomenon, or form a strong civil society to struggle for people’s rights, or engage political representatives in serious discussions about a range of issues that affect people’s lives. Further, there is absolutely no discussion about why the abovementioned list of characteristics are so often in short supply in everyday life, ranging from motorists who routinely break traffic rules, to the more complex phenomenon of how the state itself can perpetrate acts of violence against its own people (several examples can be given here). Perhaps it is too much to expect a state sponsored textbook to be critical of the state! But the point here is that the text does not problematize the notion of the good/ideal citizen, thus cutting out the possibility of critical engagement by the teacher and students. On the other hand, what comes across implicitly is that the country or the government is always right, and works in the interest of all people. Therefore, it is the duty of a good citizen to always obey the rules and laws of this country.<br /><br /><strong>Descriptions of ‘rural’ and ‘urban’<br />Rural communities<br /></strong>There are interesting ways in which ‘Rural Communities’ and ‘Urban Communities’ have been described in two separate chapters of the semester 2 textbook. The competencies children are expected to pick up after the rural communities chapter are the following:<br /><br />• Know the important occupations of the villagers<br />• Understand the problems of villages, measures taken by the government to improve their conditions and get themselves involved in development programs<br /><br />After acknowledging the importance of the rural community in general and the farmer in particular for national progress, the textbook presents a rather idealized view of the village. It states that ‘Villagers fulfill their needs among themselves. They work together to form a village community.’ This is an oversimplified description of the village, perhaps even a distorted image! To this is added another idyllic image: ‘In villages there are rivulets, ponds, tanks, pastures and sacred groves. Villagers celebrate festivals and worship gods and goddesses.’ Almost immediately, as if to correct this description, the idealized pictures are replaced with a section on the ‘Problems of Rural Communities’ – these problems are either ‘Economic, Social’ or of illiteracy (due to lack of education). The few sentences under ‘Social Problems’ are vague and do no justice to the intricacies and complexities of rural life (italics mine): ‘Some rural communities still practice untouchability. People of some castes are not allowed to enter temples, use public wells and participate in public functions. Further, some people are superstitious.’<br /><br />It is not clear why there is so much vagueness in this description. Who is referred by the word ‘some’? Why are the identities of people termed as ‘some’, hidden and why are they made faceless? Where do these people stay? Why are things like this? These questions beg for explanations in the book. It looks as if the textbook authors are hesitating to discuss upfront the real problems of Indian society, such as the divisive and discriminatory caste system that has existed for thousands of years. What is therefore clear is that there is a downplaying of the deeply hierarchical and divisive nature of Indian society, which has historically led to discrimination and exclusion of groups of people labeled/classified as the Scheduled Castes/Scheduled Tribes etc. By skirting this discussion altogether, the 2nd semester textbook of Class V in many ways actually excludes, from the learning experience of the child, the very existence of these marginalized communities. Thus, an opportunity to critically examine and understand important features of Indian society is lost. However, we may note that the terms SC/ST are freely used in a following chapter on Panchayat Raj, which is mainly a factual account the three tier system of local governance both in the rural and urban contexts.<br /><br />If the issues such as caste find such casual and careless treatment, the aspect of gender, class and religion (again factors that contribute to Indian society’s stratification and division) do not find mention either, anywhere in the body of the text of the class V books. There is a passing mention that (P.52) ‘…farmers take up other occupations like rearing cattle, sheep, poultry farming and making baskets. There are blacksmiths, potters, barbers, stone cutters, weavers, cobblers, goldsmiths, tailors, oil millers and washer-men in our villages.’ This long list does not educate us about the structure of Indian society—it is just that there are different people doing different things.<br /><br />Having identified the ‘problems’ of rural communities, the lesson goes on to state that the government provides, through development programs ‘…drinking water, education, employment and medical facilities’ to improve the standards of their lives.<br /><br />There is one full page illustration (in the form of a collage) of ‘rural life’ in the chapter on rural communities with the caption ‘Development is the fruit of hard work’. One part of the illustration shows a village scene in which a woman walking away from the hand pump, carrying two or three pots of water on her head, while another is filling hers. Another part shows a big dam with the power grid in the background of a village with tiled houses (actually, the power grid leads away from the village, and we have no way of knowing if the village is supplied with electricity!). There is mechanized farming in this village, for we see a tractor in the foreground. Also is shown a woman serving a man with food. The third part of the illustration in the collage shows a train in the background passing by the village, while in the foreground, there is a postman delivering a letter to a woman. In the distance, a group of women are seated in a circle in front of their houses, doing some domestic work.<br /><br />From the illustrations, one can make out that women manage the house while men seem to be the more mobile of the two (this is of course based on only two or three examples). The distinct aspect however concerns the technology – the big dam, the power grid, the tractor and the train, are the technologies that are expected to improve the living conditions of rural communities. Of course, the hand pump provides clean water. All of these are seen to be contributing to the development and modernization of rural communities. Again, this appears to be idealized and simple.<br /><br /><strong>Urban communities </strong><br />The rural/urban distinction is first established in terms of population (high in urban areas) and occupation of people (‘productive’ like agriculture in case of rural folk, and ‘services’ like offices, factories etc in case of urban folks). Another distinction is that urban areas have factories, which rural areas do not. Urban problems revolve around (a) Pressure of population, (b) Problem of housing, (c) Environmental pollution and (d) Social problems. Again, these are not problematized. Why, for instance, is there a population problem? The textbook answers this by stating that ‘people go from villages to cities and towns in search of jobs’, which in turn creates problems for housing. Further, this results in lakhs of people not even having basic facilities. Slums thus get created, and their ‘clearance’ becomes a ‘great problem in urban areas’.<br /><br />The above description of the population problem directly contradicts what the earlier chapter on rural communities states (‘Villagers fulfill their needs among themselves…’)! Further, there is no hint regarding who these migrants are, and why they may be forced to migrate. There is not even one example to illustrate a point or argument in a deeper manner. Again, these people are faceless. In one sense, this is like using the word ‘some’ in the earlier chapter. Thus, voices and representations of those who are excluded (and who invariably become the migrants searching desperately for livelihood of any kind) do not find any expression again, as in the earlier chapter.<br /><br />The text attempts to create or show other distinctions between rural and urban communities, but these distinctions are problematic and are not explored deeply enough. For instance, under ‘Social Problems’ (P.60), ‘poverty, unemployment, stealing, violence, exploitation of children and women’ find mention. Interestingly, unemployment, violence, and exploitation of children and women do not feature as problems of rural life. Also, environmental pollution and housing appear to be exclusive problems of urban communities.<br /><br />One gets the sense from the rural and urban chapters that urban problems are numerous and are more complex than rural ones. This is why the authors perhaps felt that it was important to talk about the duties of citizens in the urban case, which they did not deem fit for the chapter on rural communities!<br /><br />Values and ideals of national progress; democracy; role of education in national development<br /><br />Moving on, the idea of ‘National Progress’ in the class V textbooks is linked to the notion of a ‘good citizen’ and his or her duties. In the chapter on urban communities (P.61, semester 2), it is stated that ‘If the citizens imbibe these qualities in their daily life, many problems that we are facing today will disappear. Our life will become golden. The country will progress.’ Thus, ‘good and obedient’ citizens are wanted and the authors seem to bemoan the fact that such citizens are in short supply! The fact that these long lists of qualities of a good citizen are included in the textbook suggests that school education is expected to play a critical role in the formation of good citizenry. Of course, this is implicit. Despite these safeguards, why is it that we continue to have so many civic problems? This is nowhere reflected upon. Has education failed then?<br /><br />Another place where national progress finds mention is in relation with the farmer (P.51, 52, Semester 2) who is the ‘…backbone of our country. The country cannot progress unless the villages are developed.’ So, this is the second strand in the thinking on the values and ideals of national progress. There are some more observations in a later chapter (Lesson 12) titled ‘Agriculture and Industry’. In this chapter, it is acknowledged in the beginning that ‘India is a land of agriculture. Seventy percent of the population depends on agriculture for their living. India is self sufficient in food production.’ This, it is claimed, is as a result of the Green Revolution which adopted new agricultural technology for growth in production. Thus, the role of technology is central to national progress. It is also stated in this regard that: ‘By this (the green revolution) the country has achieved self-sufficiency in agricultural production and economic progress.’ This is a one sided view which completely ignores the ground realities (survey after survey shows alarming levels of malnutrition among more than half of India’s young children, women, for instance). It also contradicts what the same textbook says earlier in the rural communities’ chapter (P.52): ‘Most of the farmers have very small plots of land. The yield is not enough for the needs of the family.’ How can we then say that we have achieved self sufficiency in agricultural production and economic progress?<br /><br />Technology is seen as an ideal force for national development. Industries, which use this technology (P.92, Semester 2) ‘…Play a great role in the development of the country’s economy.’<br />The word ‘democracy does not feature in the Class V textbooks on social science. Since I have not studied the Class VI and VII books, it is not possible to state if this topic has found treatment there or not. The topic could have been discussed in the chapter on Panchayati Raj, but the authors have chosen instead to present factual information on Panchayats without for a moment reflecting on the possible links between Panchayats and local democracy and governance. Perhaps the other place where democracy is implicit is the notion of good citizenry, which we have discussed in some detail earlier.<br /><br /><strong>Summing up<br /></strong>This quick study/review of the fifth standard social science textbooks of the Karnataka government in connection with notions of national development, citizenry, democracy, inclusion/exclusion etc has thrown up some interesting observations, as I have already noted. One limitation of this review must be acknowledged upfront – that the review has confined itself only to Class V textbooks. It is possible that the missing pieces may find some treatment in books for Classes VI and VII. However, given the approach seen so far, it is likely that the treatment is going to be problematic from a pedagogical as well as curricular point of view. Issues such as the above, which might require an ‘open ended’ approach are instead presented factually and in an oversimplified manner, ignoring complexities and conflicts. In all cases, the government is seen as doing the right thing all the time. It is the citizens who have to buck up and play their constructive roles.<br /><br />By presenting content in a factual manner and by not problematizing the study of Indian society, the opportunity for deeper, critical reflection has been greatly limited both for the teacher and the student. A word must be said about the questions and other exercises after each chapter – they merely promote memory recall. This effectively shuts out any possibility that may exist for developing a critical outlook. Only if the teacher rejects such content (or looks at it as open to debate and interpretation) will there be a possibility of rethinking fundamental assumptions that underlie the structures and processes in Indian society. This in turn can make the learning experience very enriching for every child. But how many teachers are likely to embark on this more difficult but rewarding journey?<br /><br />One may argue that for children as young as ten years, it is not advisable to present the conflicts and contradictions of a society as complex as India. If this indeed is the case, we are undermining the intelligence and capability of children to grapple with complexity, diversity and conflict.<br /><br /><strong>July 2009<br /></strong>BengalooruSheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com4tag:blogger.com,1999:blog-1233351832092294149.post-79025131214688565602009-08-24T11:16:00.000-07:002012-06-01T06:20:43.912-07:00The White Matter Problem<div dir="ltr" style="text-align: left;" trbidi="on">
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<strong><span style="font-size: large;">S</span></strong>ince the last twenty five years, I have been confronted by the ‘white matter problem’. No, this has nothing to do with the visible white matter in the universe through the astronomer’s telescope. Nor has it anything to do with the other problem that has puzzled cosmologists – the ‘dark matter’ problem – the mysterious invisible matter which might eventually decide if the universe will go on expanding forever, or contract back into a singularity after what might seem to be an eternity. Now, a singularity is a kind of entity that is difficult to understand – imagine all the matter in the universe squeezed into a point that has no dimensions! Further, imagine that the universe began from a singularity, at which point time actually = zero! I must return to this strange and perplexing discussion another day! I must understand it before I pass on into that singularity!<br />
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I’m not even talking about the grey matter inside our heads. The white matter above my head, but rooted in it is the issue that has caused consternation to certain people over the years. So, let me tell you that story.<br />
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In the midst of thick, jet black hair, the first white strands grew. I noticed it when I was thirteen I guess. I remember commenting about it to my mother, standing in front of a big mirror in the small living room of our Koramangala house. I’m not sure if she worried about it then. I didn’t, too – it was easy to hide the few white strands by pushing and patting them carefully below the black majority after oiling my hair with coconut oil every morning. <br />
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The years passed. There was no appreciable change in the quantity of white matter with its roots in my head. In 1987, the year I got into engineering, it hadn’t attracted much attention. Even if it did, I don’t remember it. Ditto in 1991, the year I graduated, least interested in the enterprise of designing, making and fixing machines In a couple of years, I got disgusted with the experiences of shouting every day at men on the shop floor, egging them on to produce more and more in less and less time. From that point on, more strands of white started sprouting, and people I knew began noticing. Still, the thick and jet black majority managed to obscure this fresh growth. However, it required some effort at combing time every morning. After a while, I began to wonder if this hiding business was worth it. As the days passed, I managed to ignore it altogether.<br />
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In 1993, the year I became a schoolteacher, the kids I taught, noticed. So did my fellow teachers. There were not too many direct comments, though. May be no one wanted to offend me. I even suspected that some of my colleagues liked what they saw, especially some female colleagues. This hunch was only based on their appreciative but cryptic comments such as ‘It looks good’, for instance. On second thoughts, I wondered if it was a case of dripping sarcasm. In the hope that I could attract more female attention, I began conjuring theories of male-female attraction based on white matter – ‘older women get attracted to younger men with white hair because it makes them look matured; younger women also get attracted to young men with white hair because they are looking for someone wise to spend their time with’. Of course, these theories were hopelessly out of sync with the times and I didn’t land up any girlfriends young or old based on my white matter alone. To this day, I fervently believe in these theories, waiting for a miracle to happen! <br />
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In the mid-nineties, when I left the school to move to Raichur in North Karnataka to do some work in the village schools, I did business with the barbers with their open roadside parlors in the small and remote town of Deodurg. They started noticing, first thing. <br />
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Getting a haircut done in Deodurg was a different experience – unlike Bangalore, where you could sit for the haircut inside a reasonably well kept room with its large mirrors in the front and back, the Deodurg open barber usually had his shop under the sky – some had the mirrors usually fixed to a tree on one side of the road, and those seeking a haircut usually had to sit on an old wooden chair facing the mirror, propped up on carefully arranged stones that were flat. It was a bit of a circus in every sense of the word. What made it different was it felt very public. When I sat on one of those chairs for the very first time, I felt that everyone on the road – humans, dogs and pigs were watching me. Of course, they were only minding their business. The roadside tree barber would engage you in small talk, and if you were curious enough, you could get a colorful account of life in Deodurg town. They say that a barber is one of the best informants if you are doing some social research anywhere.<br />
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Anyway, the barbers got interested in my white strands because it had a direct business implication for them – the profits to be made from dyeing! Barber after barber wanted me to dye my hair and wanted me to look young and dashing again, with jet black hair. With fervent hope, they would always ask ‘Sir, shall I dye your hair this time? Sir it has spread Sir, all over the sides…that too at such a young age, Sir!’ Some of them indeed looked concerned. But I would generally remain unmoved, determined not to yield to their devious business suggestions. By then, I had developed a couple of stock replies: ‘Why should we hide anything?’ I would retort as if I was an open book for everyone to see and write on. And then assert, ‘Let me age naturally! Life will go on!’ This philosophical invective would result in an amused smile from the barber: ‘Ok sir, your wish.’ The next month he would repeat the same questions as if nothing had happened. Great triers, these barbers were! <br />
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In the late nineties when I moved to Delhi the white strands were no longer the minority. They were noticed often, comments were passed and I carried on, unfazed. To tempt me further, the East Delhi barber whose shop I frequented tempted me with a ‘package’ consisting of a haircut, head massage and dyeing. ‘But if I dye it will it not turn brown?’ I protested, based on my observations of those who wanted their hair to appear eternally black. I thought that would keep him quiet. But he replied easily. ‘Nowadays there are dyes which will not allow your hair to turn red or brown.’ Of course, I didn’t believe him. Such exchanges would generally end with my stock replies. The barber would then quietly go about his job. A haircut usually resulted in exposing more white matter. Given that I went in for short ‘crew’ cuts, the short, white hair would stand up straight for a few weeks – combing didn’t make any difference a few weeks after every cut. <br />
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In North India, they liken marriage to a laddoo. You are told that it is that kind of laddoo which you will regret not eating. And if you do bite into it, you would regret as well! It’s a bit like saying ‘Heads I win, tails you lose.’ Strange laddoo! Anyway, I swallowed this laddoo in 2000 after Herculean efforts by my father to find me a bride. The passport sized photo of mine which was shared as part of the correspondence still hid the white strands that were threatening to come out. I passed the bridegroom test just as she passed hers and we decided to eat the laddoo. I don’t think she noticed that much white matter – in any case, she didn’t look scared or put off. We didn’t get too close for her to notice the defiant white. She later said that she might have reconsidered her decision to bite the laddoo with me. I thought the coconut oil had done the trick!<br />
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In a workshop where we were attempting to develop a Country Strategic Plan (CSP) for five years based on what was touted as the ‘Security Framework’ (because we thought everyone was feeling so insecure in the rural communities where we worked!), my colleagues from this new organization I had joined in Delhi noticed the many white strands. It was two weeks before the D-day. During the tea break, I heard ‘Are you not going to dye it before you go to Bangalore?’ for the nth time. The others nodded in agreement. ‘No’. I said as a matter of fact. No explanations were given or asked for. ‘…salt and peppery hair…!’ One of them said as we went back to develop that CSP. I’m not sure if that CSP made much difference anyway in the lives of people. We are often very good at producing lofty sounding documents and think we are doing a great job of bringing ‘development’ to poor communities. And most of the time we spend writing these documents.<br />
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Post marriage, when we returned to Delhi, the white secret was out. She felt distinctly uncomfortable about it. I suppose there is this tendency among girls to compare their husbands with their fathers especially where they have enjoyed good relationships with each other. Her advocate father, I was made to believe, had few white strands at sixty. ‘No dyeing-wyeing for him!’ I felt myself shrink and felt like hiding somewhere when I heard things like ‘You look fifty!’ as a matter of fact. ‘You look like my uncle’. Even he looks younger. <br />
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Theirs must have been a family of jet black hair owners! Or so I thought, amused and angry. For some years after marriage, she tried hard to get me to dye, but I didn’t budge. Ego problem, some people said. Can’t you just please her? I let it be. Colleagues, friends and anxious sounding relatives kept reminding me now and then. By then, I had developed another stock reply: ‘Accept me as I am. Haven’t I accepted you as you are? The essence of any marital relationship, as I would realize later, is this acceptance. It reduces stress and unnecessary expectations. This argument, however, cannot be stretched too much – there will be cases where one is required to change if the relationship is falling apart or if there are serious problems of relating itself. But that is a discussion I do not want to enter into right now. <br />
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In 2001, we had a baby boy. My wife resolved to win him over to her side in her battle against the pure whites. ‘A good four to five years, before he starts pestering me’, I pointed out one day. ‘So what?’ She retorted. ‘At least then you will have no choice. You can’t afford to see him embarrassed in front of his friends by your white hair. He will not even call you his father.’<br />
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Till date, my son who’s just crossed eight has not bothered me with the question, except when he’s been pushed to do so. He loves his father as he is, white matter and all. Meanwhile, the proportion of whites has gone up significantly. It shows up in photographs. My wife still talks about it, though I guess she’s realized it’s a losing battle. We now have a darling daughter, all of two years. Perhaps she’s pinning her hopes on the little girl to win me over? After all, daddy’s girls wield tremendous power!<br />
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I must admire the barber’s patience, though. All barbers want better business. The dyeing bit brings in more moolah than the cutting bit. So they’ll keep asking the question. They now have a range of techniques and products designed to make you look eternally young. But I suspect it’s a losing battle. The whites, along with the wrinkles, are bound to appear sooner or later. As I write this, the whites have colonized newer areas. Pretty much like a tumor, they have spread to the moustache and the beard. Recently, I noticed a couple of stubborn sprouts on my right eye brow! <br />
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My relatives, who I do not meet often, appear surprised every time we get together. I’m sure they talk. Who cares anyway? Many of my cousins are into dyeing – I can easily make it out. Some six months back, at a social gathering, my cousin’s wife called me aside. After exchanging the usual pleasantries, she turned her attention to you know what. As we talked, there was not much eye contact – she was sizing up the white thingies. ‘Dye, dye, dye!’ seemed to be the message. I just had to look better.<br />
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There is this modern obsession to lose weight, look young, sexy and fair. ‘Eye candy’ is the term used to describe someone who’s just managed to look right after sweating it for hours in the gym. The industry behind this body manipulation is worth billions of dollars. It sends messages into our subconscious, and once these messages get there, they make damage, since we have been unable to filter them. <br />
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The white matter problem is only a small part of this industry, which promises much – smoothening skin wrinkles, whitening teeth, blackening and coloring hair, tucking the tummy in especially if you do not want to exercise, sculpting noses, buttocks and pulling up sagging breasts apart from growing hair on balding pates and god knows what. Approaches vary. In some cases, you are required to apply a cream which will have magical effects on your skin. In other cases, a dye will do the trick. The more complicated cases and desires get under the surgeon’s scalpel. The human body is seen as a commodity. The ads in the newspaper scream: Pay to lose 5 Kgs and lose the next 5 Kgs for free!’ The local barber I visit has a bewildering range of products that include massages and steam baths and so many things I cannot even remember. He is no longer the guy who mainly works with the razor, scissor and comb. <br />
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Nowadays my son attends a cricket camp nearby. A classmate of his also comes to this camp to hone his cricketing skills. The other day, we were playing a small game after their practice session. I was wicket keeping while my son’s classmate batted. In between he kept looking at me before taking his guard to face the next ball from my son. <br />
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‘You didn’t dye your hair?’ He asked. I reasoned, and if my wife could have heard me thinking, she’d have been delighted -- ‘Which boy would like to have an old looking father?’ But on second, stubborn thoughts, I asked: ‘What if this old looking father has a young heart, loads of questions about life, an insatiable curiosity and desire to live? What if this old looking father wants to stretch the limits and suck very drop from life? Wouldn’t that matter more? What if…?’ The temptation to yield to the dye was banished forever then. We worship the body so much that we forget the heart. The heart doesn’t grow old. And then, we want to live in zones of comfort. Does this not make us old already, even if we may look young? <br />
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The surest indicator to find out if you are young or old is to ask if you are child-like. There is a difference between this and being childish. Being child-like allows me to be young, white matter and all. It allows me to be alive to new possibilities every moment. The mind is not grooved in any one particular pattern of thinking and action. There are no self-limiting thoughts, and there is little fear of the unknown. Embracing uncertainty comes naturally in a child-like state. This is the state I aspire to be in, even as the whites conquer and colonize my body. My goal is to find that place inside my self where I am still a carefree child. This can be brought forth. I can therefore bring back my childhood – it is ready to be evoked and integrated into my being. The brilliant writer and therapist A. H Almaas says that this exercise of recapturing childhood is not merely a return to childhood but something more significant:<br />
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“When we look at a child,” writes Almaas, “we see that the sense of fullness, of intrinsic aliveness, of joy in being, is not the result of something else. There is value in just being oneself; it is not because of something one does or doesn’t do. It is there in the beginning, when we were children, but it slowly gets lost.”<br />
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As adults, it doesn’t quite matter whether one has white or dark matter on one’s head -- we usually lose track of that joy inside us, despite the numerous sources of pleasure and distractions that exist today. Even a very good looking adult with a toned body can still have very low levels of worthiness and satisfaction. The desire to be young again is a symbol of the deeper desire to remain new. Children take to this like a fish takes to water. By putting ourselves back in a childlike mindset, we open the way of learning. As Almaas puts it: “We are the pleasure, we are the joy, we are the most profound significance and the highest value.” <br />
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24th August 2009<br />
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Bengalooru<br />
<br /></div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-50089178769936401472009-08-17T23:12:00.000-07:002009-08-24T11:33:11.215-07:00Insect as metaphorThe insect kept struggling to stay afloat the dirty water standing on the side of the road. I stood on the footpath which was the bank, and watched its condition. From where had this insect come? It would have been happy and comfortable flying here and there, living its uncomplicated life. By some strange mix of circumstances, it had landed on this muddy bit of water. It certainly looked out of place. One can say that if the road had a proper system to drain the water, the puddle with the struggling insect would not have been there in the first place. The insect would have been elsewhere then, perhaps in a less hostile environment. But Kolkata is no different from any other Indian city, I guess. We keep spending crores of rupees every year on ‘maintenance’ but one good rain is enough to make the water stand and trap insects such the one I was watching.<br /><br />Was the insect used to this watery environment? It looked like the flying type, with its tiny, immobile wings. In that stagnant pool, it was desperately moving its jointed legs, trying to find surer ground. One bit of a solid surface would have been enough to get it airborne again. I saw a piece of cardboard jutting out of this stagnant pool, about three feet from the struggling insect. One stride at the most for me but for the insect in that condition, three feet was large.<br /><br />The notion of scale is relative, isn’t it? For instance, what distance would this insect travel all its life? What about an ant? A mosquito? Lice in the hair? Viruses? Many insects may travel within very limited boundaries all their lives when compared with humans. May be for them that distance is normal or even huge. From our anthropocentric view (we tend to follow the dictum that ‘man is the measure of all things’), the insect distance may be small. But what about the lice in the hair of a person who travels across continents? It has a great chance of seeing the earth. So does a cockroach that gets packed in your suitcase which is flown from Bangalore to Kolkata! Both in terms of scale and speed of travel, the oblivious cockroach has not seen anything like it before. The best example I can think of right now is the H1N1 virus which my friend thinks is the ‘Varaha avatar’, a reincarnation of God in his various forms. This virus has traveled all the way from Mexico, free of cost.<br /><br />For that matter, even those of us who do not travel much beyond the immediate confines of our home and community are all cosmic travelers, aren’t we? For one, the earth goes around the sun at an astonishing 18 miles per second, the sun completes one turn around the center of the Milky Way galaxy every 250 million years, while the galaxy itself (like millions or billions of other galaxies) is hurtling through space-time at this very moment, or so we are told. Nothing is resting then, everything moves. There is no absolute rest anywhere in this universe. No minus 273 degree Kelvin.<br /><br />The struggling insect was closer to the piece of the wet, jutting cardboard. It sparked off another set of thoughts. What about what happens in our schools? Children struggle day after day, year after year in this often hostile environment, searching for pattern, searching for meaning. That search is not fruitful, except in some cases. Like the struggling insect I saw in Kolkata, most children just manage to stay afloat. There are very few anchors in any case, very few wet cardboards jutting out of the muddy waters of the experience we call schooling. Last night, I was reading Margaret Donaldson who says ‘…that some of the skills which we value most highly in our educational system are thoroughly alien to the spontaneous modes of functioning of the human mind.’ This is one view.<br /><br />The other way of looking at the struggling insect is to ask: What is life without a struggle? Growing and becoming are all as a result of struggle. What is life without a scar, a deep imprint? Without an experience that brings you close to the edge and sometimes takes you over? A sense of achievement follows struggle. Once you reach the wet cardboard that juts out, you have a vantage point which helps you understand where you are. It also offers possibilities for where you want to go, and what you want to become. Genuine understanding perhaps develops like this. The ‘Aha!’ moment of understanding is the cardboard climbing moment which was preceded by struggle and engagement. That is joyful learning – the struggle for understanding, the understanding itself, the looking beyond. Not, on the other hand, the doing of an activity for the sake of doing it, to be followed by 'real' (actually, rote) learning, as many teachers thought when the wave of joyful learning swept all over us in the decade of the nineties.<br /><br />Schools are supposed to make children struggle to reach the cardboard and even go beyond. They can do it but end up not doing it. Instead, children struggle mindlessly. The human potential for meaningful struggle leading to achievement is lost on our teachers and educators. It is lost the moment the child steps into school.<br /><br />I didn’t wait long enough to see what happened to the insect. Had to get back to my workshop session where I narrated this story.<br /><br /><strong>18 August 2009</strong><br /><strong>Bengalooru</strong>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-42243834333400216272009-08-14T02:48:00.000-07:002009-08-14T02:50:30.183-07:00Classes versus the massesSometimes, all it needs is a few snatches of conversation to get us to explore deeper and fundamental aspects of our daily living. These thoughts remain with us for days as we mull over the issues that came up, explore them from various points of view and also look for resolution. I had this opportunity a couple of days back while I waited in the lobby of a Kolkata guesthouse.<br /><br />These days, I’m engaged in getting a group of people working with a well known Kolkata NGO to get into the act of writing – the idea is to use it as a tool to learn more about the self and also explore the possibility of writing about others, particularly children, parents, teachers, the educational system at large and so on. What does ‘writing on education’ mean? What does it involve? What place does writing have in our eternal quest for providing meaningful education to all children? Can everyone write? What sort of preparation is required? How do we address the issue of ‘personal and public’? These are some of the questions we are trying to grapple with in the course of the workshops I’m facilitating.<br /><br />Let me get back to what happened in the lobby. The quick exchange I had with the hotel wallah went like this, with the opening statement made by me.<br /><br />‘It is raining and the weather’s pleasant isn’t it? Much better than what it was in June.’<br />‘Yes’, he agreed. ‘It’s also pleasant because the old (pre-1993) vehicles are no longer running on the roads.’<br />‘I heard about it. This is a recent government decision, right? They did it in Delhi some years ago.’<br />‘Yes sir. I can feel the difference myself. Pollution has come down by 60%, they say.’<br />‘Oh…that’s nice.’<br />‘Sir, the problem is with the masses. They have spoilt our city. I’m a tax payer, but these people reap the benefits. They have polluted the city with their old gaadies.’<br />‘Ok,’ I nodded, waiting for him to go on. I was not sure if I agreed with him. This exchange was becoming interesting! The hotel wallah had begun taking certain positions which I wanted to examine further.<br /><br />‘What about their livelihoods then?’ I posed.<br />‘There are so many jobs in Kolkata, if they are really interested in doing them. We too have a couple of vacancies. When these people don’t come forward, we end up hiring Bangladeshis.’<br /><br />His masses bashing continued. ‘You know, I was recently reading the speech given by the ITC (Indian Tobacco Company) Chairman. He explains so clearly the steps for global warming – who causes it, how it happens…I’m now convinced it’s the masses and their dirty ways.’<br /><br />I wondered what wisdom Deveshwar, the ITC chairman had shared on global warming which had so impressed the hotel wallah. Later, I did get to read his 98th annual general body meeting speech of July 2009, in which he says makes all the right noises about global warming. Yet, when he presents the solutions that ITC has proposed or even undertaken in terms of green technology, one cannot help but see the unmistakable emphasis of maintaining soaring profit lines and margins. I wonder to what extent this meshes with issues like environmental sustainability. It certainly merits deeper examination<br />It’s amusing, isn’t it? One invokes the chairman of a company that manufactures cigarettes for profit when it comes to tackling global warming! Well, I actually do not have a problem with corporations who come forward to tackle issues of grave importance like global warming and climate change. However, from whatever little I know, I wonder if there is much to cheer about regarding their roles – are they actually serious about it? Is there sincere action? The green mantra is great if you want to build a ‘do-gooder’ image. Beneath the image, fundamentally little will have changed. It is indeed interesting that we look to corporate leaders whose sole aim is profit making at all costs, for direction! We can discuss many more examples like ITC, perhaps. My cursory observation shows that while ‘Corporate Social Responsibility’ is the tag used for undertaking a wide range of efforts (in education, health, agriculture, micro-finance and so on), the nature of the real businesses does not change – in the form of SEZs, big dams, power stations, mining, cutting of forests, software exports and a myriad other activities (often aided and abetted by lax government laws and even laxer implementation), corporations ‘Rule the World’, as David Korten puts it in his very disturbing book ‘When Corporations Rule the World’. <br /><br />Anyway, since Mr. Hotel wallah was keen on proving his point, he invoked another dubious example. ‘You’ve heard of Alyque Padamsee (the ad man)?’ Before I could nod my ‘Yes,’ he went on. ‘He has written about what is happening in Bombay. With all their hard earned money and their taxes, they try to clean the city. But these people come from all over the place and set up their jhuggi-jhopdies right next to the posh localities.’ I wondered if he wanted to complement Bal Thackeray and Raj Thackeray’s Bombay cleansing efforts. But he didn’t get that far. I wondered if Kolkata had their counterparts as well.<br /><br />I was convinced that a deeper engagement with this man was necessary. My first question was on the energy and pollution front. Quickly, I asked: ‘Do you know that using an A.C consumes about thirty times the power used by an ordinary fan?’ He looked as if he didn’t know. I went on: ‘People like us who use AC’s are also polluting the earth, much more than the masses.<br /><br />He didn’t quite understand, and countered: ‘But it doesn’t pollute the air, right, like the old taxis and auto-rickshaws?’<br /><br />‘That may be the case if you look at it superficially,’ I pointed out. ‘What about thermal pollution?’ That is also another form of pollution which we don’t discuss much about. The real damage these high energy devices cause is elsewhere, far away from our cushy homes and hotels. From where do we get so much power to run our ACs? From some coal powered or hydro powered plant. Running an AC means burning that much more coal. Putting up a giant hydro project means that much more displacement of people who we call the masses.’ I was trying hard to remember some post independence statistics quoted by Arundhati Roy in her article ‘For the Greater Common Good’. 33 million, if I remember right, by very conservative estimates are the number of people displaced by big dams (at 10000 people per dam X 3300 big dams) since Independence.<br /><br />‘But we cannot do without AC’s in this kind of weather’, he protested.<br />‘That’s a lifestyle issue as well’, I pointed out. ‘How can we blame the masses alone, when we are doing more damage?’<br /><br />Some silence. It brought us face to face with the unresolved conflicts and dilemmas of our own lives. When we choose to face these conflicts, silence is perhaps a good way to begin with. Beneath that silence, there is a cauldron of thoughts, reactions, justifications and counter reactions all of which need sorting out. But the truth stares at us in the face and we cannot afford to deflect it with a cacophony of arguments. Martin Lings, the Islamic scholar, has put it beautifully:<br /><br />‘If it can be said that man collectively shrinks back more and more from the truth, it can also be said that on all sides the truth is closing in more and more upon man. It might almost be said that, in order to receive a touch of It, which in the past required a lifetime of effort, all that is asked of him now is not to shrink back. And yet how difficult that is!”<br /><br />By then, my colleague arrived to pick me up. ‘And let’s think about why is it that the masses have come to the cities in the first place’, I managed to say on my way out. ‘Nobody wants to live in sub-human conditions in the cities, but many don’t have a choice…’<br /><br />I met the hotelier in the evening when I went to collect my room key. ‘I’ve been thinking about your AC point’, he said. Somewhere, I thought, a dent had been made even as we continued making our big carbon footprints for the day.<br /><br /><strong>August 2009<br />Krishnagiri</strong><br /><em>Tamilnadu <br /></em>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com3tag:blogger.com,1999:blog-1233351832092294149.post-22138924837406316302009-07-23T11:14:00.000-07:002009-07-23T11:26:07.002-07:00The Marriage Postulate<div align="justify"><em>Nearly twelve years ago, I wrote this piece. My marriage was a good two and half years away, but the thought had started bothering me a little. My parents were anxious to get me married off and 'settled'</em> <em>in life. Here I was, with so many questions and confused thoughts. I decided to make sense of that turmoil through this article. Writing about it made me feel somewhat more comfortable, I remember. Ultimately, I don't think I was guided by a 'rational' decision into marriage -- I just plunged into it, like everyone else!</em> </div><div align="justify"> </div><div align="justify">Having reached a “marriageable” age, it is only natural that the thought should now be consistently nagging my mind. My thinking has left me confused - clarity on the matter seems like the mirage. What does it mean to marry, after all? And why am I so bothered by the question?<br /><br />A friend of mine, who’s evidently happily married, said as a matter of fact, “You are needlessly being consumed by this question because you look at it as a major decision in your life. Why should it be so? Just marry!” If only it had been just as easy!<br /><br />To begin with, the thought of staying with somebody all your life is frightening. Suppose we get bored of each other? What if we begin to dislike each other intensely? In this sense, isn’t marriage some thing that “makes” or “breaks” our lives? The latter phenomenon is being observed with increasing regularity. The standard reply to this would be, “Well, everything depends on how you make it work, the extent of give and take, the ability to adjust...” I can only nod my head in vague, cerebral agreement.<br /><br />The institution of marriage is as old as the hills. It’ll be interesting to see how it began. Perhaps this will provide us with insights into the issue of why one should marry at all, or say, what the advantages may be, if one marries.<br /><br />Prehistoric people were primarily nomadic. They must have operated with some division of labour. Quite understandably, the men-folk would have done the roaming, hunting etc., while the women were relatively less mobile, rearing children and so on. With the advent of agriculture, the mobility of men must have reduced, as their work profiles changed.<br /><br />In the initial stages, I suppose there were no restrictions to mating freely within a particular community. The issue of pair bonding may have come about in relation to taking care of the young ones. Thus, it seems to me that, over a period of time, the bonding must have become “institutionalised” and ritualised because of this reason, i.e., proper care for the offspring, and the propagation of the species.<br /><br />I’m sure there was a realisation that this would be a socially stable arrangement. Also, it ensured some sort of security for the individuals involved, physically and emotionally.<br /><br />How were mates chosen? I do not know, but I believe that the process was more instinctual, and not governed as such by the intellect. There must have been the problem of separation, if “everything did not go well”. How did it operate then?<br /><br />Today, the essential argument for marriage being the same, the process has become vastly complicated. No longer does it cater only to the issue of species propagation - the central problem of marriage is the problem of compatibility.<br /><br />In this connection, the study of astrology is interesting. Scientific scepticism does not deter the astrologers who cling to the belief that our fate is linked to the movements of the stars and planets. This is somehow related to the psychological attributes of the person. Presumably, horoscope matching is nothing but the matching of these attributes.<br /><br />Well, this is one side of the story. While astrological predictions are considered to be important, marital harmony is seen to be very much linked to (that oft used word) compatibility. Physical, emotional and intellectual matching, to various degrees, is the crux of the matter. Add to this the matching of social and economic status. Nowadays, these two seem to have taken precedence over the others as necessary criteria for a “good” marriage. Marriages are increasingly beginning to look like business propositions. Thousands of years ago, the processes leading to a bonding for life must have been much simpler.<br /><br />What are the arguments for marriage? My supposition is that humans have to grapple with loneliness and insecurity - this is our fundamental predicament. Many are the efforts that are expended to overcome this condition. My own understanding is that this predicament invariably leads to, in all of us, a universal hunger and longing for love. Marriage is one of the ways by which this incompleteness can be filled. In this context, the essence of marriage is that it is a process of sharing our lives (with our husbands and wives…) -- joy, sorrow, pleasure, ideas, feelings, sunsets and sunrises, the trees, hills and vales, rivers, oceans, butterflies, babies and indeed, the entire gamut of existence. It is this sharing that helps us to transcend our aloneness and vulnerability and become stronger. The creator has perhaps intended in the cosmic scheme of things that man and woman be complementary to each other, like the pieces of a jigsaw puzzle. <br /><br />Having put forward my case for marriage, let’s look at the flip side of things. Marriage, in my opinion, is a ‘construct’ of the human mind. In this sense, it is artificial, perhaps unlike the natural theory of selection of Darwin. It is not ‘naturally’ intended as a process in nature. Barring the issue of insecurity and safe propagation of species, I do not see any other worthwhile reason for marriage. Custodians of marriage may reproach me for being ‘anti-marriage-establishment’. Let that be. This is precisely how I feel. There may be a few exceptions, where individuals have managed to live with each other for several years, and yet the experience is enriching and meaningful. By and large, many couples whom I have met indicate that their relationships have become routine. The rejoinder to this may be that it is entirely up to the individuals to “make it work”. But when I see a widespread breakdown of sorts – divorce, suicide, extra-marital pre-occupations, even couple ‘swapping’ and an overall lack of purpose and meaning in marriages, I am inclined to believe that a re-thinking is needed. These are manifestations of a ‘gross mismatch’ of the different compatibility criteria that contribute to a good marriage. Something is therefore wrong.<br /><br />I must address the issue of matching and compatibility in greater detail now, after having touched upon it so far in a somewhat casual manner. All conditions of compatibility operate as a whole, and not separately by themselves, and each condition is linked to the other. It is only because some (or few) of these criteria are met that people are looking elsewhere for fulfilment. The outlook is not holistic, and does not cater to the soul. The nourishment is only partial: “I’d like to marry somebody who’s earning at least 20,000/- per month (so that our combined earning is at least 30,000/-),” or, “My wife should preferably be a software engineer working in a multi-national corporation.” I do not wish to be unjustly critical, but these are statements indicative of a trend that doesn’t promise healthy, enriching marriages. While I do appreciate that there are practical difficulties especially in an age of spiralling costs, these parameters should not be allowed to take precedence over other, more important factors that will ultimately contribute to human wellbeing. If happiness in marriage is what one aspires for, it is puzzling that we’re choosing routes which will only take us there tangentially, or may not even take us there at all.<br /><br />Translated into simpler terms, one way of looking at marriages is that they are need-based. Every individual has many needs, apart from just finance – sexual needs and their fulfilment, for instance. Emotions need proper expression; their suppression only leads to frustration. Thus, it seems that need fulfilment is closely linked to compatibility, and comes before it. But how can needs get fulfilled when two individuals may have very different sets of needs, priorities and expectations?<br /><br />We finally then arrive at the matter of ‘compromise’ and ‘adjustment’. These are words that are used more than they are implemented. They essentially refer to the giving up of space in order to create space for the other. Its almost like saying, “Well, we may have several needs – can we learn to express them; can we also agree upon which of these needs can be met, how they can be met; can we agree upon what may not be possible, and why so?” This dialogue is necessary to keep the relationship going, and needs a considerable amount of time, effort and perseverance. <br /><br />I’m still not convinced that this is possible by and large throughout the human species. Is it humanly possible for men and women to stay meaningfully and purposefully with each other throughout their lives, rear children, and look after each other? To many this may be a redundant question. I ask it with all sincerity and passion, for it relates to the overall quality of life, and not, on the other hand, a mechanical, routine exercise of living.<br /><br />By nature, there are various impulses operating within us, which may not find an expression in marriage. What is to be done about them? Forget them, suppress them, or, find fulfilment and gratification for them discreetly elsewhere? How does one look at the issue of loyalty in a marriage?<br /><br />I’m still confused, but I’d rather believe that the creation of the institution of marriage might not be in consonance with certain fundamental, natural qualities and tendencies in human beings. It is only the fear of chaos that has ensured the endurance of the institution.<br /><br />My imagination recoils at the thought of the resultant disorder that would prevail in society if it not were for marriage. Perhaps, we can make it work if we set our own inner houses in order. <br /><br /><em>November ’97</em></div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com3tag:blogger.com,1999:blog-1233351832092294149.post-43532913390144306732009-07-20T21:15:00.000-07:002009-07-20T21:30:19.773-07:00Depression<div align="justify"><em>Here is another article from the winter of '89. As with many other articles that I wrote then, this is another example of one of my soliloquies. During bouts of depression, I often wondered what it was all about, and how to deal with it. Reading it twenty years later, I realize that the approach to dealing with it remains essentially the same, at least for me. Additionally, perhaps, my understanding is that if we chase depression to get rid of it, it comes back stronger! The best way then is to let it come, and pass...</em> </div><div align="justify"></div><div align="justify"></div><div align="justify"> </div><div align="justify">One thing is absolutely certain about depression – it makes one feel depressed! Surely, depression is one thing which everyone likes to get rid of before it sets in. Often the fact that depression can be got rid of by identifying its root causes is overlooked, further aggravating the condition.<br /><br />Now there are two ways by the help of which one can identify the root cause of depression. The first of these methods (which I will call the ‘biochemical-particulate’ view) will certainly sound crazy, but can be relied upon to yield satisfactory results! First of all, it is important that you assume a relaxed posture with your eyes closed. Try to imagine the various chemical reactions taking place in your brain, and also bear in mind that there is a physical basis for these chemical reactions, at a deeper level the end result of which is this state called depression. Now, whatever is causing this depression is the final result of an extremely complicated (and perhaps unfathomable) set of processes that are taking place in your brain. It should be borne in mind that the environment i.e. the surroundings have a profound influence on all these processes, because of the mutual interaction between the brain and the environment.<br /><br />The key to the solution of your problem lies here, in the labyrinthine complexity of your brain. By the time you ‘understand’ these reactions, and find your way out of the millions of neural networks in your brain, you will find that your depression has vanished, as your observation will show that in the ultimate analysis, your depression does not have any cause and that it is a part and parcel of life!<br /><br />The second method will help you to attack depression from a slightly different angle, with the same end results. Try and look at only the positive aspects of life. Identify the positive points of your character. Remember all the good moments of the past, when you were smiling with happiness and also remember the times when you, by your good deeds, brought a smile on the faces of your near and dear ones. Note that these good moments will come many more times in your life, and you have to carry on at least to experience these moments and derive joy from them.<br /><br />You are actually a very privileged person, because you are capable of reading whatever I have written…there are millions in this world who cannot even read. And there are millions of them who have seen the most horrible things in life, and whose plight is heart rending – yet, some of them are smiling always! Learn from them! You have to consider yourself to be very lucky, as you may not have experienced the cruelest aspects of life – even if you have, you are better placed than many others, as you can possibly learn a lot from these incidents and experiences.<br /><br />Are you still feeling depressed? Remember – you have been sent into this world because there was a very strong reason, a very special purpose – it is your responsibility that you achieve your goals while there is still much time. Look at the beggar on the street -- he is not in a position to help his own self, let alone help others. Is not your position better than his, that you are in a better position to help yourself, and others? Start now! It is important to realize that a genuine smile on your face is always welcome, and a good deed per day will not only make others smile, but will also make you smile, automatically.<br /><br />Where is your depression now?<br /><br />(November 1989) </div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-47502706942417335132009-07-04T02:32:00.000-07:002009-07-04T02:49:06.569-07:00On the nature of scientific enquiry<div align="justify"><em>Here is an article I wrote in the summer of 1989. Those were the days of fascination with disciplines like theretical physics and mathematics. My friends and I bunked classes to discuss quantum mechanics, relativity theory and other exciting developments that had revolutionized our understanding of the physical world. Yet, despite the power of these forms of knowledge to unravel the mysteries of the universe, I was distinctly uncomfortable as I felt that these disciplines did not admit certain types of questions. Some of that tension is reflected in this article.</em> </div><br /><div align="justify"><strong><span style="font-size:130%;">I</span></strong>n his Evolution of Scientific Thought, A.d’Abro says:<br /><em>“Consider the phenomenon of gravitation. Does any one really imagine that Newton or Einstein has ever attempted to explain gravitation? To say that gravitation is a property of matter or is the property of space-time in the neighbourhood of matter is just as much of an explanation as to say that sweetness is a property of sugar; for in the last analysis, what is matter – what is space-time…? (Scientists) content themselves with describing the properties and the relationships that appear to connect them. Clearly, those who seek explanations will find no comfort in science. They must turn to metaphysics. And yet, as a matter of fact, these rather gloomy conclusions are gloomy because we are expecting too much…we shall find that the descriptions of science are creative and fertile, and not sterile, as descriptions usually are.”</em><br /></div><div align="justify">As far as my opinion goes, I would like to point out that I wholeheartedly disagree with A.d’Abro’s point of view. To be just content with explanations or an understanding of the relationships between various parameters without really wanting to find out why these relationships exist (or, more appropriately, in the words of Stephen Hawking, “What breathes fire into these equations…?”), does not represent a complete enquiry as such.<br /><br />Till now, most scientists have been too occupied with the development of new theories that describe what the universe is than to ask the question why. On the other hand, the people whose business is to ask why, the philosophers have not been able to keep up with the advance of scientific theories. Scientists often ‘look down’ or dismiss philosophical speculations, though they may themselves be constantly suppressing such urges within themselves! <br /><br />Perhaps, as A.d’Abro says, those who seek explanations will find no comfort in science, and that they should turn to metaphysics. But can we really afford to be satisfied with just this ‘what’ kind of information and knowledge? We should be grateful (to whom, I wonder?!) because we are in a position to ask – what is matter, what is space-time, why is the universe…? Perhaps nature has ‘built’ us that way, so that we can ask these questions.<br /><br />Let me consider this problem from the ‘atomic’ viewpoint of science. ‘Life’ can be defined roughly as ‘atoms trying to understand more about atoms’. I am not in a position to explain what understand means. And if atoms can ‘ask’ why atoms should exist, for example, there should be a reason, the reason being that atoms have themselves felt the need for asking these questions, knowing fully well that they have ‘felt the need for asking these questions’, and also ‘knowing that they know fully well that they have felt the need for asking these questions…ad infinitum.<br /><br />When the need for asking these questions has been felt, the answers should be there – there cannot be questions without answers, however seemingly stupid or otherwise the questions may be (actually, no question is stupid as such). This is necessary to maintain some sort of ‘equilibrium’ or ‘balance’ in this universe…there should not be any ‘agitation’ which will disturb the ‘universal calm…’ In that sense, being content or jubilant that it is enough to understand relationships between various parameters without asking why those relationships exist, does not represent the highest product of the human intellect. The process of enquiry may go on forever, but that should not deter one from asking these questions. That is my sincere opinion. <br /></div><div align="justify"><strong>March’89 </strong></div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-38940254724558615232009-07-02T23:25:00.000-07:002009-07-02T23:28:28.044-07:00Musings on Cricket and Life<span style="font-size:130%;"><strong>S</strong></span>ome experiences can scar you for life. They leave a certain block in the mind which is difficult to overcome. Lifelong behaviour is influenced by these scars that just don’t go away. Just when we seem to think that we have dropped the baggage for good, some incident or the other allows that part of the memory to surface with a vengeance -- it recreates the experience and leaves us perplexed, angry and bitter for a while. It feels as if we have relived that experience. I suppose this is what happens when we try to suppress such experiences.<br /><br />The experiences that scar you for life can also lead to disastrous consequences. I still remember the scene in a Bharatpur village in Rajasthan more than three years ago. I was doing a classroom observation in a government school, sitting in the veranda. Overcrowding and lack of space had resulted in the veranda being converted into a classroom. It is still a common sight in many schools, despite massive investments in infrastructure over the last decade. I was sitting in one corner of the class, and could see the village beyond. Suddenly, a boy came running almost out of nowhere and jumped without hesitation into the well adjacent to the school. I was too horrified to react. Some of us, including the children who had seen the boy jump, instinctively got up and ran towards the well. The teacher followed suit. Soon, everyone from the school had gathered around the well. The boy’s brothers had come running after him within a minute. Quickly, to my amazement, a rope was tied in a crisscross manner round the elder brother’s shoulders and waist, and he was lowered into the well. Many villagers had turned up by then. The women were wailing, while the men could be seen arguing heatedly. The boy’s inert body was brought up after what seemed like an eternity. We had stationed our jeep just in case he had to be rushed to the hospital. Luckily, he survived. I learnt later that his elder brother had admonished him. Following an argument, the boy had decided to give it all up.<br /><br />I was left wondering how fragile human nature is, after all. Steely determination, focus, energy and strong will that we see and experience sometimes gives the strong impression that human nature can withstand much onslaught. What surprises me however, is its fragility. Nowadays, we hear more and more and see more and more of this fragility, through examination related suicides, relationship problems and all other kinds of human issues. A friend of mine had once looked at suicide differently. ‘Contrary to the notion that suicide is an escape from the misery of it all, it is an assertion’, she had said, adding that extreme human will is required to carry out the act. She is right in a way. But I would still maintain that the human will can assert in ways that can prevent self destruction. Perhaps this can happen if one sees meaning in life. When this sense of meaning collapses, it is difficult to carry on. I’m still reading that wonderful book by Victor Frankl titled Man’s Search for Meaning, which talks of hope and emancipation even in as harsh a place as the concentration camps of the second world war. What an amazing story it is! <br /><br />Then there are some experiences can leave you disturbed for a long time, till you find ways of dealing with them. Dealing usually involves looking at them in perspective, and in believing in oneself. What this essentially means is the development of a certain kind of detachment, and understanding the circumstances that led to those incidents. Subsequent accumulation of a wealth of experiences and wisdom as we grow up can help us appreciate why such a thing happened in the first place. I have usually found that ‘laughing it off’ (which often also involves laughing at oneself) is the best way to deal with the hurt that comes from such experiences. That is what I’m now able to do with my experiences on the cricket field almost thirty years ago.<br /><br />The year was 1980, and it was the hundredth year of our school. Imagine! I was in grade six. We were all busy preparing for the centenary celebrations. As such, the normal, monotonous routine of the school was broken because of this huge event for which we were getting ready. We were all happy, as we didn’t have to sit through class after class everyday. During that period, I was asked to report for practice in the junior cricket team of the school. Apparently, someone had seen me play in one of those myriad matches that we used to set up during lunch time in the big field, often stacking up our bags or big blocks of stone as the wickets at either end. At any given point during lunch time, there would be at least twenty matches played on our famous big field. I remember that I had somehow developed the skill for producing a prodigious amount of turn with my off breaks. This troubled almost any batsman who faced me.<br /><br />Iyer, an ex-student of our school, was our coach. He was probably 18 or 20. As soon as I reached for practice after school in the small field, he asked me to do a few rounds and then threw me the leather ball. Unlike the ‘cork’ ball, which was easier to turn, I was unable to turn the leather ball as sharply. But my good line and length and quick movement through the air was enough to still trouble most batsmen. Iyer seemed pleased and he said ‘You are pitching the ball in places that are difficult for the batsmen to play…’ I was pleased as hell and attended practice regularly. I don’t remember much about batting practice, but I remember bowling my heart out everyday. There were sixteen of us who were part of the junior team.<br /><br />There were my off days as well. After some time, I had more off days than good days at bowling practice. Something was wrong. This resulted in Iyer not interacting with me much. He would only expect me to field and fetch the ball. I would wait longingly for a bowling stint which didn’t come my way for a long time. However, my lunchtime matches continued, and I continued to trouble many batsmen. One fine day, Iyer threw me the ball again. How I troubled Sharath, one of our best batsmen and junior team captain, with my flight and spin! He would dance down the wicket and I would pitch it just a wee bit short. At other times, the trajectory of the ball would draw him forward full stretch. I thought I had rediscovered my lost art. Suddenly, everything looked good. But Iyer still decided not to operate with me everyday at practice. He wouldn’t tell me what was wrong and what I could do to change things. No feedback, no conversation. <br /><br />A few months later, we had the Cottonian shield. The matches were played in the small field of the Bishop Cotton School. We won the first two matches and suddenly found ourselves in the final. I didn’t get to play but got to watch from the sidelines. The final match against Cottons was a three day affair which we lost quite badly. Naturally, the team was dejected.<br /><br />I remember the prize ceremony and the distribution of certificates. They started calling out our names. I waited for my turn to go up on stage and collect that certificate of participation. That moment never came, and I was too shocked to come to terms with what had happened. The gathering dispersed even as I heard many hurrahs for the winners. All my junior team friends were carrying their certificates on which their names were written. We got into the school van. Sitting quietly in a corner, I tried very hard to suppress a tear. Some of my friends noticed my turmoil but didn’t say anything. I suppose they couldn’t. In a matter of fact way, Iyer told me that there were only 15 certificates prepared. My name had been deliberately left out of that list. Why? Why me? After all those months of practice, and cold shouldering!<br /><br />Tough times followed for some days. Eventually I got over the incident. Luckily, I didn’t give up cricket. The big field matches and the street matches near home continued as before. I loved the game too much to be bothered about Iyer. A couple of years later, Sharath asked me to report for practice in the senior team. Promptly, I got back to practice. We played many matches. We won some, we lost some. But we didn’t make it to the final of any tournament. I enjoyed the playing, though. I suppose that is what matters, ultimately.<br /><br />Our school football team was much better. They won the interschool shield in 1984, just a day before Indira Gandhi was assassinated. I remember the extended holiday!<br /><br />Looking back, I realise what a bad teacher and a bad coach can do. Only my self belief helped me to overcome those initial moments of despondency. Iyer was a bad and insensitive coach, who didn’t believe in open, honest communication, the hallmark of a good teacher. Perhaps he was too young to be one, in the first place! I wonder where he went.<br /><br />I sometimes worry for my son, who’s taken to practicing cricket in an academy near home. It is a sixty year old club, perhaps the oldest in Bangalore. He practices thrice a week and we play endlessly in our living room and in the backyard. He’s got a good front arm bowling action, and has all the potential to become a good bowler. His batting is improving too. I’m happy he’s pursuing a game of his choice, given that the school he currently goes to does not even have a playground! We’ll change his school next year. I want him to enjoy his game, and will not expect anything more from him.<br /><br />The beauty of cricket has very nearly been killed by the BCCI, which is run by a bunch of ruthless businessmen who want to milk from it the last drop of money. I don’t see much spontaneity in the way the game is played. We played cricket in every conceivable place without thinking where it would lead us. We enjoyed playing it. Period. Today, everyone seems to be making a plan to make it big. Parents want their children to get into the under 10 league and move up from there. The many different forms of the game have opened up avenues for raking in the moolah. Young children are exposed to it all through television. It is up to the parents and the coaches to tell their children, ‘Look just go out there and enjoy playing the game. It’s a game after all!’ As parents, we need to be careful not to thrust the burden of our expectations on our children. At the same time, we will need to prepare them to handle failure, through self belief. I can only hope that Iyer is doing well, if he is still a cricket coach. <br /><br /><em>July 2009</em>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-2513858009108830652008-12-12T03:05:00.000-08:002008-12-12T03:06:13.007-08:00A tail for Pi...<p class="MsoNormal" style="margin-right: -1.85pt; text-align: justify;">Sometime back, there was a discussion on one of the math e-mail groups I'm a part of, regarding the number Pi. This discussion brought back memories of what we did with Pi when I was a teacher at the Valley School (KFI) in <st1:city><st1:place>Bangalore</st1:place></st1:city> some 15 years ago. As part of preparations for our science day, we prepared a 'Pi tail'. I had with me a computer generated value of Pi up to 2500 decimal places. The idea was to write out all these decimal places in the form of a tail. So we made strips from newspapers, and using marker pens, wrote out the entire thing! Of course, children came to the math room whenever they were free (many a times, they even bunked classes to make the pi tail!).</p> <p class="MsoNormal" style="margin-right: -1.85pt; text-align: justify;"><o:p> </o:p></p> <p class="MsoNormal" style="margin-right: -1.85pt; text-align: justify;">On science day, we took out this long tail (which incidentally measured all of 850 feet long) and, starting from the notice board opposite the library, we literally bound the school complex with this tail! It went inside some classrooms, the toilets, and whatever was left of it, children climbed the tree at the jungle gym and let it hang from there! Everyone was curious, particularly the younger children. They were seen running along the length of this number tail. When a few children I taught came up to me and said 'Now we understand why one calls Pi an irrational number...it seems to go on and on without any end!' I knew the Pi tail had made a difference. So much for 'experiential learning'!</p> <span style="font-family:";font-size:130%;"><span style=""> </span><span style="font-family:times new roman;">Try this out and have fun with your children!</span></span><span style="font-size:85%;"><br /></span><br /><span style="font-weight: bold;font-size:85%;" >Shesh</span><br /><span style="font-style: italic;font-size:85%;" >July 2008</span>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com2tag:blogger.com,1999:blog-1233351832092294149.post-83011092289611544382008-11-03T08:49:00.000-08:002008-11-03T09:58:05.364-08:00Did you say 'Kid'?<span style="font-size:130%;">T</span>he other day, there were two surprises. One was an sms from an old classmate of mine, who was my best friend during my 11th and 12th standard days. Well, that was 22 years ago. The other was a call from another classmate, again from the same class. I was not too close to him, but we had been good friends nevertheless. They had got my number from yet another classmate who I had bumped into last year at the Hyderabad airport. Some of my friends from the class of '87 had kept in touch, and it was at one of these recent gatherings that they remembered me. This had resulted in the sms and the call. I went down memory lane. I had to...<br /><br />The friend who had called is a very enterprising chap, with very good social skills -- I still remember the ease with which he often interacted with people, young and old. He knew so many people and had friends from different colleges in town. He went on to do several things which required him to bring to the fore his people skills. For a long time, he became an event manager for the corporate sector. He was the organizer behind the famous 'Bangalore Habba' (festival) every year. It therefore came as a pleasant surprise for me to learn that the event manager somehow became interested in the education of children, particularly in the ideas of Maria Montessori. He even did a Montesorri course from one of the colleges in the city. With his wife, he then started a chain of Montessori pre-schools in Bangalore, called the 'Roots Montessori' schools. There are four of them now. I was happy to hear about his experiences, and his passion for Montessori's educational ideals engaged as I am, in the education of children since the last fifteen years . 'I believe in total freedom for the child...the heavy bag should be banned!' he proclaimed. Indeed, he was planning to get his five year old son in the well known Valley School which had been established by Jiddu Krishnamurti in the late seventies in a beautiful location some twenty kilometres from Bangalore.<br /><p>We kept talking abut our families and about our other friends, their families, their kids. I told him I had two kids, and asked him if he had any. He said he had one child. He had been in touch with many other friends from the class of '87. Does any of them have kids, I asked? He solemnly replied that so and so had one child, while so and so had no child...Finally, at one point, he had to cut me off. 'Did you notice that I have been using the word 'child' everytime you use the word 'kid'? I said I did. 'Do you know what 'kid' means'? Again, I replied in the affirmative. 'So, why do we label them as the young ones of a goat'? I explained that it was the first time that such a thought had even been put into my head. capricorn though I am, I had never imagind a goat when I had used 'kid' all these years. 'Let us call them children...let us give them their due', he said. 'Very well, point taken', I said. I knew what he meant, though I argued with him that a verbal shift is not enough. </p><p>His point was about semantics. Well, using the right words is perhaps the first step towards a clearer communication and understanding of meanings, without belittling the real nature of people or things. But does it change anything fundamentally, I wondered. The best example perhaps is the term 'differently abled', instead of 'disabled' when we are talking about some people who are in difficulty. 'Disabled' connotes a loss of ability. Yet, 'differently abled' brings back life, and points out that all is not lost, and that the person is able in many different ways. This is a powerful shift, provided it is accompanied by a paradigm shift in thinking, attitude and behaviour towards those who face disability of one kind or the other. Merely using politically correct words does not bring about this shift. It requires far deeper adjustments and changes on our part.</p><p>The same is the case with the term 'child'. Even if we were to use it, 'child' would mean different things to different people. To someone who is educated about children and their development, the term would evoke one set of images and meanings. To a parent who is hell bent on ensuring that his son or daughter gets great marks in the examination and always stays ahead of his class, the word will evoke an altogether different set of meanings and images. To use the word child and to appreciate what it means will require much harder work on the part of adults. Notions of child and childhood vary from culture to culture, and they keep changing with the times. Going by the middle class anxiety for performance in the examinations, and going by narrow definitions of what it means to succeed or fail in life, the problem is not so much about using the word kid or child, as long as we remain impervious to the potential of every child to grow as human beings in uniquely different ways.</p><p><em>November 2008</em><br /></p>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-88945046945965502322008-07-04T10:58:00.000-07:002012-06-29T02:39:56.248-07:00Biochemical Evolution: some questions<div dir="ltr" style="text-align: left;" trbidi="on">
<em>I'm today uploading an article I wrote 22 years ago, in 1986! I was in the 11th standard then, full of questions about what we were learning in science. We were studying evolution, which I found quite intriguing. Some questions I had then were: Why did evolution occur at all? What is it that was responsible for 'more advanced' life forms to emerge as the years went by? These and other reflections are part of this article. Our lecturers simply gave us information. They didn't have answers to these questions. I'm not sure if my understanding is better now, but I have read a little bit of Richard Dawkins, Stephen Jay Gould, James Lovelock and Lewis Thomas. These books, together with my own thinking, have helped me along the way...</em><br />
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<span lang="EN-GB" style="font-size: 14pt; font-style: normal;">Evolution</span></h2>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB" style="font-size: 18pt;">T</span></b><span lang="EN-GB">hese days, we are learning about evolution of life on earth. For me, this is a new topic and it surprises me a little that we did not encounter it in school. Anyway, I find the idea of evolution fascinating and I guess it will take some time for me to appreciate its complexity. The big question is: Why did it <i style="mso-bidi-font-style: normal;">happen</i> in the first place? And <i style="mso-bidi-font-style: normal;">how</i> did it give rise to such an incredible variety of organisms, small and big? The way we are discussing it in class, looks like have taken this mind boggling phenomenon for granted to be just read with the upcoming examinations in mind. The guy who is dealing with this topic is killing it, literally! I wonder why they don’t feel excited about it.</span></div>
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<span lang="EN-GB">Whether life originated on the earth, or came from outer space, piggy riding some asteroid or meteor a few billion years ago is still being debated but the former hypothesis is more widely established. It is generally accepted that the Viruses were the first ‘organisms’ on the earth, churned out by that process called evolution. It is a bit like magic – the magician keeps stirring this pot containing the ‘primordial soup’ containing air, water and some rag tag chemicals and suddenly, at some point in time, we have these really tiny weeny self-replicating organisms (discovered only in 1898 as microscopes became powerful enough to reveal them) popping out! How did this happen? </span></div>
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<span lang="EN-GB">The classification of viruses defies taxonomists (the people who classify living things, based on some criteria) till this day. They are ‘common’ to the plant and animal kingdoms (by the way, ‘kingdom’ is a kind of category that taxonomists use), and secondly, they exhibit both living and non-living characteristics! In the laboratory, you can put the virus in deep freeze and it will behave like its dead. When conditions become ‘favourable’ it will thrive and show the characteristics of living cells. Viruses possess the basic materials needed for life – proteins and nucleic acids. The proteins form a capsule or coat around the nucleic acids. The jargon given to us in the class recently is: ‘Viruses are obligate, intracellular parasites’, i.e., they can replicate themselves only in a host cell.</span></div>
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<span lang="EN-GB">This tiniest of the tiny living thing causes untold damage to the rest of the living species, whatever their pretensions to size and complexity and power may be – we have heard of the HIV which has already brought us much grief and then, I have read somewhere about an even more devastating virus called the Ebola virus which exists in some place in Africa. </span></div>
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<span lang="EN-GB">From what we have learnt so far, it seems that the evolution of various forms of life ‘began’ from the viruses and it took thousands of millions of years for evolution to ‘make’ us. Our textbooks tell us that Mycoplasmatales (also known as Mycoplasmas) were the next products of evolution after the viruses. This is the message I get because the Mycoplasmas chapter comes after the one on viruses! They look a little more intricate that the viruses. However, Mycoplasmas, like the viruses, cannot be classified definitely as belonging to the plant or animal kingdom.</span></div>
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<span lang="EN-GB">How did Mycoplasmas come on the scene? What were the factors that caused this change? It is tempting to think of a change in the environment which ‘forced’ the viruses to adapt themselves in order to ‘become’ mycoplasmas! It is difficult to think of any other reasons at this stage and I do not see the viruses ‘feeling’ something inside of themselves as a result of which they ‘evolved’ to give rise to the new, slightly more advanced organism. It is interesting to note that we humans also change when something external to us, changes. And I suppose that we ‘grow’ as a result of the things that we learn from these changes – in this sense, we too evolve. Or so I think! We cannot live alone.</span></div>
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<span lang="EN-GB">Let us take this further. The blue-green algae, which contain the bluish green pigment, came next. All the three forms of life mentioned so far – viruses, mycoplasmas and the algae -- are examples of very ‘primitive’ (or ‘prokaryotic’) organisms. They do not contain the specialized structures that a well-developed cell contains, and their metabolism is not very complicated. However, the algae are more intricate than the mycoplasmas which in turn look more complicated under the microscope than the viruses. We are given to understand that ‘animal like’ cells, like the Euglena, would have appeared next. These were followed by ‘proper’ animal cells, like the shapeless Amoeba and later, the Paramecium, which has a definite shape. </span></div>
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<span lang="EN-GB">Again, I come back to the question raised earlier – what changed in the environment for this diversification to occur along two well defined routes? And what was the distinction at that stage – that animal cells cannot make food like the plant cells do…?</span></div>
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<span lang="EN-GB">As we went along, we realized that the process of evolution witnessed a turning point of sorts, with the emergence of the Bacteria. Structurally and functionally, the bacterial cells are more complicated than the others discussed so far. The presence of different elements or parts in the bacterial cell -- the cell wall, protoplast, cell membrane, cytoplasm, nucleoid, ribosomes, etc. point out to a well organized cellular set-up. It is a bit like comparing the difference between nomadic man and the chap who settled down much later inside a home and started doing some agriculture. Life then became a little more organized and one didn’t have to live only on instinct. </span></div>
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<span lang="EN-GB">Now these Bacteria may also be ‘photosynthetic’ – that is, they can make food using a pigment called chlorophyll. There is general agreement that these organisms belong to the plant kingdom. Does this mean that plants appeared before the animals on earth? More specifically -- did ‘plant like’ characteristics appear first? What were the reasons for this to happen? Only more questions! We have been taught that plants and animals have to depend on each other for survival. Does this interdependence apply even to the most primitive organisms, perhaps extending to the furthest reaches of evolutionary time? It is then striking that the characteristics of plants appeared first.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB">It is indeed tempting to believe that these evolutionary processes (including the diversification along the two different paths – the plants and the animals) were the result of accident. I wonder how it can be explained. It is equally attractive to consider the proposition that everything was ‘pre-determined’ (by whom?!).<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB">The formation of the sexes was a very important event, for, it ensured species propagation. Prokaryotic cells can reproduce only asexually, whereas the more advanced (eukaryotic as they are called) cells can reproduce through conjugation. Humans do it this way! However, in the case of the earliest organisms, it is difficult to distinguish the sexes morphologically (meaning, it is not very obvious from physical appearance). As we climb the ladder of evolution, it is not difficult to differentiate between plants and animals. The identification of the sexes also becomes easier.</span></div>
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<span lang="EN-GB">We have very briefly touched upon this thing called evolution with these examples. The question that keeps coming back to us is about the role of the environment, and the interaction between changes in this environment and the living organisms, which over a period of time actually resulted in more diversity, intricacy and complication of forms – and, I would also like to add, abilities as well. This seems to be a dynamic process which I do not think has stopped to this day. Why was diversity important? In addition to diversity, we also see a progressive complication of living forms from the tiniest, most primitive organisms, to this human who is self aware and conscious, who is in a position to ask such questions and probe into the nature of things. How did this happen? </span></div>
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<span lang="EN-GB">I asked this question in class today but our lecturer did not have any satisfactory answer. He mumbled something about ‘survival of the fittest’ (that famous Darwinian slogan of sorts!) but I couldn’t make out who was fitter – the viruses, the mycoplasmas or the bacteria? All the three organisms exist even today! If one of them had been fitter and more powerful, the others may not have existed. The issue, therefore, cannot be explained away as easily.<span style="mso-spacerun: yes;"> </span></span></div>
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<span lang="EN-GB">My answer would be – the earth has been continuously changing since the time it was formed 5 billion years ago. Its surface has undergone major upheavals through earthquakes, volcanic eruptions, etc. and temperatures have kept changing, becoming progressively cooler. It is quite possible that the molecules of life must have felt (what does this mean though?!) these changes. Through complex chemical reactions, these molecules would have adapted to these changes. And adaptation is perhaps the basis for complex forms to get generated as the aeons go by.</span></div>
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<span lang="EN-GB">The central question which I never tire of asking, is why did evolution take place at all? Was it inevitable, given the conditions available as the earth passed through different stages after its formation? And again -- why would changes in the environment necessarily lead to the formation of ‘better’, or ‘more advanced’ organisms? Why, for instance, should the Paramecium evolve as the next organism in the evolutionary ladder after the amoeba? </span></div>
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<span lang="EN-GB">There ends my quest for answers at present. It is possible that if evolution is viewed from a different perspective, these questions can be answered. Who knows, I may be the one who will do it at a later stage… </span></div>
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<b style="mso-bidi-font-weight: normal;"><span lang="EN-GB">May 1986</span></b></div>
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<i style="mso-bidi-font-style: normal;"><span lang="EN-GB">Bangalore</span></i><span lang="EN-GB"></span></div>
</div>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-43994397671993568162008-06-09T23:11:00.000-07:002008-06-09T23:37:23.859-07:00History of Teacher Development in TamilnaduMy current research interests are focused on writing up the History of Teacher Development in India. This is a multi-state study commissioned by the Azim Premji Foundation, and I'm part of the research team, writing up on the subject for Tamilnadu and Kerala (and a small note on Jammu and Kashmir, with special reference to my experiences of working in Kargil in the past one and a half years). Our cut off point is the National Policy on Education (NPE, 1986). So, for all the states chosen for the study (Tamilnadu, Kerala, Maharashtra, West Bengal, Rajasthan and to a limited extent, J&K), we are doing a fairly detailed documentation of efforts in the last 20-25 years. Such a comprehensive documentation does not exist at present.<br />I have finished writing the Tamilnadu chapter and thought of sharing this with those of you who would be interested in knowing what has been happening with teachers there.<br />Researching Tamilnadu and its teachers has definitely been an eye opener. Though I have been<br />working in education for 15 years now, I have realized that it is only when one examines a theme or subject in greater detail that one begins to appreciate its various dimensions. Historical research is a powerful tool that enables us to go down to root causes and determine the complex interconnected factors that influence many a development in policy and practice.<br />Without getting into details here, all that I would to state is that the Tanilnadu study made me sit up in alarm, for what the state is doing to its teachers is not in their interest, and icertainly not in the interest of children, if one goes by current trends and developments. There is hope, for sure, but the gains made can very quickly be negated by retrogressive measures...<br />To obtain the full textof what we have found in Tamilnadu, e-mail me at <a href="mailto:giri.shesh@gmail.com">giri.shesh@gmail.com</a><br />By the month end, I hope to write the Kerala chapter as well...Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-76295924905092545452008-04-24T04:47:00.000-07:002008-04-24T04:52:09.309-07:00The Dance of Life...Years ago, when I was in school, I was often asked by elders in the family about what I wanted to become after growing up. I remember that my answer always unhesitatingly was ‘astronomer’, much to their surprise. Then, on one occasion, when there was a family function at a temple in some congested street of Bangalore, my cousin’s husband, who had a ‘good career’ going as an engineer, told me in no uncertain terms that astronomy wouldn’t do as a career. At best, he said, I could get into some unknown college or university and remain a lecturer all my life! The ‘lecturership’ didn’t sound perturbing at all, as did his admonishing tone. Little did I realize then the harsh realities of the world, and of growing up in it -- the constant pressure to perform, be ‘molded’ as the adults around us wished, and take up careers ‘approved’ in society. Little did my cousin’s husband realize the joys of peering through the telescope and asking – how big is the universe? Where did it come from? Was it always there? Is there life elsewhere…? He perhaps thought that all of this would be best done after retirement!<br />Twenty years hence, I’ve missed my astronomy bus, and, working in the social development sector, I still ask these questions. My cousin’s husband has retired, and is now looking to marry off his daughters to ‘US-based’ grooms. My guess is that he still hasn’t peered through a telescope.Some questions though, remain. To begin with, thanks to my exposure in the field of education, I constantly ask – what should the purpose of education be? Gandhi had said, ‘By education I mean an all round drawing out of the best in child and man – body, mind and spirit.’ That does sound vague and distant doesn’t it, if one goes by what one sees today in the name of education?<br />Let me not get stuck with definitions at this stage, and instead move on to a more complex issue – the relationships between the development of our potential as human beings, our upbringing, the education system, the work we do in our lives, and our ability to be happy. What are the mechanisms available for each of us to realize our innate potential through work that pays, and makes us happy? One of the organization’s that I worked for has a laudable vision of ‘…a world in which children realize their full potential…in societies that respect people’s rights and dignities…’ I do believe, however, that we haven’t reflected what this vision means as regards action. What does ‘development of full potential’ mean? When do we know if someone has developed his/her full potential? What are the links with schools and education, for instance?<br />In my own case, these links are not straightforward. I graduated as a mechanical engineer, worked in the corporate sector, then became a schoolteacher with the Valley School, Bangalore (as part of the J. Krishnamurti Foundation, India), then entered the social development arena with ‘Samuha’, an NGO in Northern Karnataka, became a ‘consultant’ with the Govt. of India for a large primary education program, then ‘advised’ three funding agencies regarding their investments in education. I’m now a freelancer and a wanderlust, journeying in education, and through life. That’s longwinded, isn’t it? I may get back to teaching next. I’m not sure if my potential is being fully used, but I do feel strongly that this is one of the things I would like to be doing. The mechanisms in society were not enabling, and one had to work one’s way around. Then there were those who tirelessly pointed out that I had ‘got it all wrong, that I was an escapist…’, but this didn’t deter me from carrying on.<br />We may find some answers in the field of economics. The economy, it is said, is the ‘happening’ thing that defines peoples’ lives – how we live, what we wear, what we think and so on...Perhaps it may enlighten us if we understand it better. Large amounts of money, including those in mega scams, exchange hands; large volumes of goods move from one part of the world to the other…all these activities are supposed to bring more comforts, make more people happy, generate jobs, and ‘uplift’ people. Or so we believe.The ‘state of the economy’ is often talked about, and I wonder what that means. This is a funny way of capturing the quality of people’s lives through some numbers. As an aside, what puzzles me, however, is that we have business leaders and politicians patting each other’s backs for ‘low inflation’ and India as a ‘knowledge superpower’, while millions sleep hungry every night…<br />Economy or not, I see many persons unemployed around me. The connections are indeed intriguing, if they are examined further. Our education system creates round pegs that have to fit in square holes – there are graduates and postgraduates who ride motorcycles and deliver Mc Donald’s pizzas at your door step; mad caps like me; business executives who earn six figure salaries every month and still cannot be happy. And don’t forget the hundreds that Osama Bin Laden, George Bush and the RSS/VHP have managed to inspire… It takes, as they say, all kinds of persons to make this world, to produce all kinds of goods and services. You give something (your understanding, skills…), and take something back…I’m not sure if that maximizes our potential, keeps us and others around us happy, and pays reasonably. A quick look around at a world in which there are gross inequalities, violence, large-scale environmental degradation…leaves you with a feeling that something is terribly wrong, somewhere. I’m sure all of this is connected with the questions I have raised earlier about the ‘relationships between the development of our potential as human beings, our upbringing, the education system, the work we do in our lives, and our ability to be happy...’ As an afterthought, I also wonder if the business of happiness is connected to these things, or, as they say, ‘is in the mind.’ You decide.<br /><strong>Shesh</strong> <em>(November 2003)</em><br /><em>Updated: April 2008 </em>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0tag:blogger.com,1999:blog-1233351832092294149.post-22422220858459904442008-04-19T03:17:00.000-07:002008-04-19T03:20:48.583-07:00A bus with a view<p><strong>I</strong></p><p>The little boy and his father finally got a chance to get on to a bus together one evening. It was one of those days when their car was at the service station. In fact, the boy and his father were going to fetch the car from the service station that evening.<br />For a long time, the father had told himself: “I must take the little fellow for bus rides in the city. It will be a different experience all together…” For a long time, the city bus ride remained just that – a thought that sometimes nagged and reminded. Partly because the boy’s father travelled so much on work (which left him with less time to spend with the family), and partly because the boy’s mother was not happy with the idea (that it was not safe for her young son to travel by the local bus), the practice of using buses by the family had dwindled. She could not understand why bus travel was on her husband’s mind, when he and her son could have travelled by the auto-rickshaw. When middle class families are upwardly mobile, and are on an acquiring and consuming spree, they would like to show that ‘they have arrived’. Bus travel then, among other frugal practices of living, is one of the casualties. It is even considered to be ‘below one’s status level.’<br />That evening, all of this changed for a few hours.<br />They would have to travel by at least two buses to reach the service station located at the other end of the city. The city itself had grown in size, and travelling to the other end took a much longer time than before. It was that much more difficult as well. The boy’s father has seen a smaller, greener city with less people, less noise, less vehicles and more lakes. The city was often called ‘The Air Conditioned City’. It was also called the ‘Pensioner’s Paradise’. You could retire here, and hope to lead a peaceful life.<br />The boy’s father had often noted, “Not only is this city expanding horizontally, it is growing vertically too!” The flat system was largely unknown in the early 80’s. Like a plague, it dominated the city’s landscape now. There were flats of all shapes and sizes – they came at all costs, catering to many tastes and fantasies. They were fancily named, too – the names suggested a longing for all things European. From a distance, the boy’s father had recently been shown an ‘ultra-modern’ flat adjacent to the city’s famous cricket stadium. He had learnt that it had a swimming pool on every floor! He had then thought, “So, this is what we mean by modernity, eh? The more modern you are, the more you consume. The more you flaunt. They drain all the water from the ground and pump it up for these people to live their lifestyles!” Not far away, people queued for water everyday and had to wait for hours.<br />The flat system also stimulated his imagination. He found the practice of ‘living on top of each other’ (as he called it) amusing, and did not like it much. He was used to living and growing up in houses that were independent, small or big. Many times he had worn his X-ray glasses, and looked at the first flat that came his way. Shorn of the arrogance of these structures and their names, he witnessed a variety of human experience, the eternal drama of everyday living – men, women and children going about their daily chores in their living rooms, bedrooms, kitchens, toilets; fornicating men and women, making guttural sounds; crying and playing children; bedridden old men and women; snatches, of conversations, arguments and fights; women being abused by their men; men being shouted at by their women; clothes on the clotheslines in the balcony; audacious looking dresses, both inner and outer; people meditating and praying.<br />All on top of each other, at right angles, in boxes of various shapes and sizes, people led their lives.<br /><strong>II</strong><br />The little boy and his father excitedly got into the first bus that would take them part of the way, till the main city bus terminus in a place called ‘Majestic’. Not too many passengers were around, so the boy got a seat next to the window. This is what his father had wanted for him.<br />Just two minutes into the bus ride, the boy exclaimed, “I can see so much!” The bus was stuck in a traffic snarl and was slowly winding its way through some by-lanes of Malleshwaram, the crowded, bustling area in the Northern part of the city. A year ago, these lanes had not seen buses and much traffic. People who lived here had led quieter and less smoke filled lives then. Thanks to an explosion in vehicular population, the Pensioner’s Paradise struggled to keep up pace. Flyovers, ‘Fly-unders’, expressways, widening of roads…these had become a common sight. In an effort to provide a ‘Mass Rapid Transport System’, the city’s planners and politicians had embarked on the ambitious metro rail project. As a result, bus routes had changed, and regular commuters got to see parts of the city they had never seen before.<br />Trees were the first casualty, and tree lovers routinely held protests. Shop keepers too protested, when they were told that their shops would be demolished to make way for the metro. For the rest of the city dwellers, it was a saga of endless traffic jams and dust. Two ways became one ways, and one ways became two ways overnight.<br />“Look at that man -- he is changing his clothes!” The window seat afforded the little boy a peep into a bedroom off the narrow road.<br />“Why has the bus stopped?” the boy wondered. “Hey, look! They are playing a game on the laptop!” The man stretched to look out of the window and saw a car standing adjacent to the bus. Two boys in the backseat were oblivious to the din and smoke outside. Immediately, he was reminded of a bus ride he had had in Delhi some months ago on his way to Jaipur. Three boys were watching a blue movie in the backseat of an air conditioned car. He even remembered the scene in which the woman was on top. The car gradually drew away with its lustful spectacle inside. “Isn’t it strange?” The man wondered. Technology can do all kinds of things for us, yet in most cases we seem to be using it to sate our carnal instincts.” He had read somewhere that a significant amount of traffic on the internet was to access all kinds of porn material. <br />“So, are you enjoying the ride?” asked the father. “Yes, I can see so much! We can’t see all this when we drive in our car, right? I am sitting so high above the road.”<br />The bus moved ever so slowly and they passed a line of shops in a narrow road that had not seen so much traffic. The boy looked on intently, through the window. His father knew that he was absorbed in the new spectacle his bus seat offered him. Position changes perspective, right? A few minutes later, the boy dozed off.<br /><strong>III</strong><br />They had to change buses at the central bus station in Majestic. The next bus ride was longer, as the distance covered was more. Since everyone had poured out of their offices, schools and colleges by then, there were traffic snarls everywhere. Nice word, this. In a traffic jam, everyone ends up snarling at everyone else.<br />In the second bus which they boarded at Majestic, some one sitting behind started talking with the little boy. ‘What’s your name? Which school do you go to?’ Then he was tickled! After a while, this interaction ceased. By then, they were passing by the city’s horse racing course. Thanks to a flyover constructed right next to the course, the boy was able to see the outline of the course, but not much was visible, as it had become dark. Throughout the ride, the boy’s father kept pointing out various landmarks in the city. The famous Town Hall, the Botanical Gardens…a discussion about these spaces followed. <br />A few minutes later, a woman in a black gown got into the box. Her face was covered as well. The boy asked, ‘Who is she and why is she wearing a dress like that?’ Asking a question like that was easy, but answering it was not! His father had to explain the background of that dress worn specifically by women in Muslim communities. It was called the ‘Burqa’ and the practice of wearing it to prevent men from seeing women, was called ‘Purdah’. ‘But why should she wear that, and why can’t men see her…?’ was the next question. The man wondered: ‘Is this what a bus ride can do to my son’s curiosity?’ He began to realize how much of the real world is blocked when one travels in a car.<br />Ultimately, everything depends upon one’s vantage point. Like the car, the bus is a bigger box which we inhabit for a limited time when we travel from one place to another. Unlike the car, the bus allows us to socialise and interact with other human beings. This changes our perspectives about others and about living, if we allow ourselves to learn. Economic mobility is fine, but it tends to isolate and segregate people from each other. Not only that – more importantly, it cuts you off from nature – we begin to live inside boxes. It makes you consume more, without regenerating nature.<br />The other point is this: one’s vantage point also helps to decide how much one wants to get out of life. Limitless living is possible when, through exploration, we keep shifting vantage points, each point offering us a broader yet in depth experience of life itself.<br />All these points were not lost on the boy’s father as they headed home after collecting their car.<br /><strong>April 2008<br />Bangalore</strong> <br /> <br /> </p>Sheshhttp://www.blogger.com/profile/17106190578475778162noreply@blogger.com0