Frozen Turmoil

Frozen turmoil

I
Sometimes, your life puts you in situations where you find yourself torn apart -- there are some interactions that make you confront the reality of life’s extremes – this is when, pushed to a corner, you ask questions of a basic nature. This is what happened in my conversation with Rafiq a few hours ago. We will get to Rafiq finally, but not before I take you through this one night on platform one, of Gorakhpur’s railway station. In this waiting and watching, one gets to see many things that would normally be missed when we rush to board a train, and when we do not linger long enough on the platforms of railway stations. In this waiting, as I’m doing now, one gets to think of many things which otherwise lie buried in the depths of the sub conscious…we seldom allow them to surface.
II
It is eleven thirty and I’m now sitting on platform one of Gorakhpur’s crowded railway station waiting for my Gwalior Mail, scheduled to arrive at half past midnight, but already running two hours late. Another late night beckons me, but with these questions and confusions in my mind, and with Michael Oakeshott’s ‘Education – the engagement and the frustrations’ for company -- remember, I’m supposed to be doing what they call the Master of Arts in Elementary Education, or MAEE for short? After thirteen years of working for children’s education, trying to do all kinds of things, I chose to do this course, as I wanted to engage in some serious reading and writing. Who knows, the act of writing this article may also be part of this thinking, though what you will read here is not related to the course as such. I’m woefully off target in submitting course assignments on time, and may face the prospect of getting rusticated from the course!
I guess my night here will be pretty occupied with lofty thoughts on education, oblivious to the happenings on the platform.
At this late and humid hour, hundreds of men, women and children are sitting, sleeping, or talking with each other on platform one. Pillows, suitcases, gunny bags and the like are used as head rests. These men, women and children are mostly from the villages near Gorakhpur (or so I think), waiting like me to go on their various journeys. How many have a reserved ticket, I wonder…Where are they all going?
As I write this, a blind man walks dangerously close to the edge of the platform; another, having just woken up from his slumber, relieves himself at the edge of the platform. Two others follow suit.
III
An hour ago, I was on my way to Gorakhpur from Belahiya, in Nepal. Rafiq was the young driver, and we kept talking. I wanted to keep him awake, as I had learnt that he had driven all of last night, all the way to Ballia and back (a good 600 kilometers), and hadn’t slept a wink. Drivers who haven’t slept a wink scare me, like the one I had last time I traveled from Gorakhpur to Lucknow in June. Since train tickets were not available at short notice, I had to take the taxi up to Lucknow, and wait the night before boarding the morning Shatabdi Express to Delhi. The driver was a young, smart looking chap who hadn’t slept the previous night. As if this was not enough, he drove the entire night journey with his cell phone in his hand. He looked very disturbed, and kept making calls to his Gorakhpur girlfriend – he was upset that she had started talking to another man who, according to him, was a criminal, and who he resolved, in the course of our journey, to kill one day.
‘So, do you want to go around with him?’ He kept asking his girlfriend. In between, when he was not on the phone, he played loud music. Once, when I asked him to reduce the volume, he almost threatened me, ‘Lucknow jana hai ki nahi? Gana jor se sun ne ka shaukh hai mujhe…neend aa jayegi nahi to…Aap aagey baitho mere saath.’ I had to shut up, switch my seats and sit next to him. The songs he played nearly made me deaf.
Once, when I told him that he looked very disturbed, he gravely nodded, and looked lost. I could empathize with him, for, I have been there before. I continue to be there sometimes, for, the desire to possess and latch on to pleasurable moments, is difficult to overcome. Should it be overcome?
IV
At 1210 AM, I decide to get up and walk along the length of this more than one kilometer long platform of Gorakhpur. Besides wanting to find out the status of my train, I want to stretch my stiff limbs a little.
‘Your attention please…train number 1123, from Barauni via Sivan, to Gwalior via Kanpur, is reportedly running late by fours, and is expected to arrive on platform one at 0420 hours…the inconvenience caused is deeply regretted…krupya dhyaan de…’ Cold sounding, pre-recorded statement, condemning me to wait longer!
In my walking, I come to the end of platform one. There is an empty bench in a portion of the platform which is not very well lit. Next to it, on the ground, is a marvel of mobile creativity. A family of five – three children and their parents, lie fast asleep under a makeshift mosquito net, anchored by sticks from four corners, the sticks themselves anchored to four gunny bags which contain their belongings. Where are they from, and where are they going?
As I settle down for a long wait on this humid, mosquito infested platform, the Lucknow Barauni Express comes in. Most compartments are of the ‘unreserved’ variety, and in this crowded country, they are packed with humans at all conceivable angles. In some of these compartments, I see men and women sleeping at the door. Even the luggage van is not spared – today, it is filled with pilgrims, Shiva devotees, on their way to the Baijnath Dham in Deogarh district. The men are all attired in red shirts and dhotis. Suddenly, this quiet corner is filled with activity. Kids, who live on this platform, appear from nowhere, selling refilled water bottles for two rupees. That is how they make their living at this late hour. The chai wallahs are running around, so is the puri sabzi chap. The family of five sleeps peacefully. Many men relieve themselves on the edge of the platform. Suddenly, the place is filled with the stench of urine that rises from the railway tracks below and mixes above with the odor of chai.
V
Where are all these people from and where are they all going?
I see peaceful faces, and I see contorted faces. There are those who are sleeping with their mouths wide open and there are those whose eyes are not completely shut. They are all fast asleep. Then there are those who are staring blankly into space. They are all lying down in all sorts of positions. Will they wake up in time for their trains?
Where are all these people from and where are they all going? The Great Indian Mobile Adventure! Below poverty line (BPL), mobile…no, no, we are not talking about the company BPL that manufactures TVs and the like.
I am what they call a ‘freelancer’, as free as can be (or so I think). I travel the country, doing my ‘assignments’. Till a few months ago, I worked with an organization that did education for children in different parts of the country. I started off as an engineer, but pretty soon left my job of manufacturing tractors for farmers who could afford them. Then, by some quirk of fate, and aided by some thinking and visions of a ‘better’ life, I became a schoolteacher in 1993. Since then, I’ve been around, doing this and that. Finally, I decided this year that I had to work on my own – being in an organization has its own constraints as well. ‘Oh, this is not possible, that is not possible’, your colleagues or seniors will often tell you, just when you think you have come up with a smart idea. Organizational mandates are anyway pretty limited, and I have always wanted to do so many different things…so, let us see where this decision will take me. Like the decision I took in 1993, when I became a schoolteacher, I consider this to be second major one in my life. The decision to marry is probably the third! All such decisions are fraught with risk.
Here I am, doing a study for a local NGO called ‘Gram Niyojan Kendra’, on teachers called the ‘Shiksha Mitras’ of UP. Oh, by the way, there are so many ‘types’ of teachers today in UP and in other states. They have been given fanciful names by the Indian state, like Guruji, Shiksha Mitra and so on. Some even call them ‘contract’ teachers. Theirs is a different story altogether, and we must talk about what the Indian state is doing to its teachers someday. Not now. That’s a sad story anyway.
I travel the country for these assignments, writing, reading, researching, meeting men, women and children, learning, asking questions, trying to do something to ‘change’ our education system. I earn a living for doing this sort of thing. I sell my wares much like a farmer sells his produce, except that in many cases, unlike the poor farmer, I have much better access to people and institutions – they believe that I can deliver a good piece of work. I also get paid much more. In the farmer’s case, somebody else fixes prices in the local market. Very often, the farmer does not get his due. In extreme cases, he is forced to take his life. Remember what’s happening in Vidarbha?
And these hundreds sleeping out here are in many ways no different from me. They are all out to survive, search, make meaning, love, even if it all means leaving home, never to come back in some cases. The Great Indian mobile adventure! It uproots millions, including me. My friend tells me that I have a greater degree of choice and freedom than the farmer, or those who do not even own a piece of land, and are forced to be mobile all the time. I agree. But there are similarities as well. I too came to Delhi, 2500 kilometers from Bangalore, in search of work, leaving my family behind. That’s an important price to pay, isn’t it? I do not know how much choice I had in taking this decision – something had to give in, to make place for something else. It is like this always. This freedom thing is complex to understand. I am not free to do anything I want, perhaps, because I have to make choices, being fully aware of the implications of each choice I make. Doesn’t choice cut down many other possibilities? Or is my understanding of freedom and choice all wrong?
VI
At 1:15 AM, tired of walking up and down, I enter a crowded waiting room on the first floor. There is this sole empty bucket seat, next to a large table in the middle of the room. Two men are sleeping on this table, while another twenty are sleeping around it, in various directions. Inside, there is a toilet, and it smells. Carefully, I make my way to occupy this red colored bucket seat. One of the snoring men on the table is a pot bellied Railway Police Constable. As I occupy my seat, he turns over to face me. His right, bloodshot eye is open, as if watching my exercise of writing with suspicion and derision. He snores, fidgets, and then snores again. The pre-recorded announcements continue, and there are trains rumbling in and out all night. I continue writing. At 2 AM, pangs of hunger set in.
VII
We mentioned Rafiq, didn’t we? I had to sit next to him, in the front seat, to stop him from falling asleep. A conversation was anyway in the offing…and this conversation triggered off some uncomfortable thoughts. Frozen turmoil!
Rafiq too is smart looking, like the other cell phone crazy and girlfriend disturbed driver of June. He looks tired after a sleepless night.
Rafiq, the eldest of all of nine children, stopped going to school after grade 8 and ran away from home, unable to bear the pressure of attending school any longer. He came to Nautanwa, a dusty town on the Nepal border (the place where Gram Niyojan Kendra has its office). Since 1997, he has been working as a driver.
‘My first Malik (master) was a customs man, who had made a lot of money. He was good to me, and paid me Rs.4500/- per month. Some years ago, he was transferred to Lucknow. Since then, I’ve been stuck with this man who is out to suck my blood.’
‘How much does he pay you?’
‘Rs.1500/-, that’s all. It’s a bloody 24 hour job. I told him I couldn’t go with you today…he threatened me and said that he would not pay my salary if I didn’t go. Is this the way to live? Garibi…’ he pauses, his voice choked. I can sense the lump forming in his throat. Silence.
Just then, Savitha my wife calls me from three thousand kilometers away on my cell, which has suddenly entered coverage area. Nikhil wants to speak. ‘Papa, get me the latest Power Ranger. It is called SPD Delta Morpher…’
Aha! The impact of the cartoon network, I think. Before I can recover, there is another demand. ‘I need another new Bey Blade Stadium’. That also reminds me – I’m supposed to write an article about the Bey Blade and how it has taken over the kids in urban homes of India.
‘Will you get him some clothes?’ That’s my wife again. ‘And…’ Snap! Out we go, out of the coverage area…
‘Why don’t you study further, Rafiq? You might get a better job.’ I return to the conversation with my new found driver friend. I’m not very sure if my suggestion would mean anything to him. He laughs bitterly, ‘Of what use will it be Saheb? Will it fill my stomach? There are so many who have studied, who are roaming without any work.’ This is Rafiq’s challenge to the human capital theory.
Like a good father, I will get things that my son desires. Like a good father, I will buy him books as well, hoping that he will pick up the reading habit. If he can learn to decode text, he can perhaps decode the world…and if he can do that, with a little bit of sensitivity, he can perhaps change many things for himself and for others.
Back to coverage area. ‘Listen, get me some clothes.’ Oh, I need to buy a printer, a scanner, a flat screen and speakers for my computer. Am I not supposed to set up an office, now that I’m on my own? However, money from my last assignment is yet to come! Our needs are endless.
The Great Indian Mobile adventure! Wherever you go, the network follows…
VIII
Something snapped, and I cried within, silently…how many different worlds humans inhabit. What an incredible variety of human experience there is! What pain, suffering and despair must we all undergo…
Some have everything they might desire, yet they are not happy. Many do not have much, and they wonder why they are that way. Like Rafiq who keeps asking perhaps. He is only painfully aware of the differences.
For a few moments, I was torn asunder, painfully aware of this schism, this chasm…I cried again, and my breathing quickened. I tried not to show it. We drove silently.
IX
My train arrived at 0815. I saw it come in on platform 2, as the other train I was in, rumbled out of Gorakhpur. I was advised by the ticket collector not to trust train number 1123. ‘Instead’, he said, ‘Book the one that comes at 0745. It’ll take you to Kanpur faster, and you will get your Shatabdi from there.’ So I had to cancel this ticket that would have entitled me to a journey in an air conditioned compartment, and purchased another which would entitle me to get into what they call the ‘Jan Sadharan’ express which does not have any reserved compartments. This one was going all the way to Ahmedabad.
After walking up and down for 15 minutes, I found a compartment in which I could stand. Eventually, I pushed myself inside and sat on the edge of a seat. After an hour, I was a little more comfortable. In this packed train, I could have observed many more things about how people live. I chose not to.
Meanwhile, many more events had occurred on platform one. By 0600, almost everyone had woken up, and left in this or that train, all over UP, Bihar and beyond. The platform was cleaned. First, they swept it, and then, they poured water to wipe it clean from one end to the other. Only one thin man remained, about who I have not written so far. He was still lying on the ground, legs spread out, eyelids popping out, breathing deeply. Flies covered him from head to toe on Gorakhpur’s platform one.
X
There are those moments, as I wrote in the beginning, which make you think, which remind you that all is not well with the way we humans live and treat each other. This was one such moment.
Shesh
August 2006
Gorakhpur, UP

Creating your own mathematics...

I was ploughing through my old writings today and came across this interesting article on 'creating our own mathematics which I had written almost ten years ago, in 1998. Happy reading!

When I was experimenting…
Wanting 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.
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:
100 + 100 + 100 + 100 + 31 + 37 = 468 (answer)
169 --- 269 --- 369 --- 469 --- 569 --- 600 --- 637
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:
637
-- 169
-------------
468
-------------
Of course, you’ll have to remember how to “carry one”, “borrow one”, and “pay it back”.
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
5 + 10 + 10 + 10 + 10 = 45
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?
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:
17 X 14
----------
68
170
----------
238
There are other ways of doing this problem:
One way would be…
(10 + 7) X (10 + 4)
= (10 X 10) + (10 X 4) + (7 X 10) + (7 X 4)
= 100 + 40 + 70 + 28
= 238
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, say,
56 + 27
Answer?
There is something about the ease with which we use a readymade 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!
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 learnt 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):

169:31
31 and 37 is 68
and there are 6-less-2 hundreds
Answer: 468
Here is a final example:
Since 637 = 100 + 100 +100 +100 + 100 +100 + 30 + 7, and
169 = 100 + 60 + 9, it follows that 637 – 169 can be written as
100 + 100 + 100 + 100 + 100 + 100 + 30 + 7
-- (100 + 60 + 9)
------------------------------------------------------------
0 + 40 + 91 + 100 + 100 + 100 + 30 + 7
------------------------------------------------------------
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:
600 + 30 + 7
-- (100 + 60 + 9)
---------------------
468 + 0 + 0
---------------------
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.
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.
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.
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 learnt 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…
“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
Speed = Brilliance,
Slowness = Dullness
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?
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 readymade, 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.
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.
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…
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.
26th April, 1998