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PASSION FOR NUMBERS



Numbers were never the same: P.K. S. in action.

 

P.K. Srinivasan (November 4, 1924-June 20, 2005) was an extraordinary person in the world of math education. I met him in 1998, while making a set of videotapes on innovative teaching methods in mathematics for the DPEP, the distance education cell o f the Education Department, Government of India. PKS became the chief protagonist of those tapes.

He had retired from the Muthialpet High School, Chennai but continued to work as consultant for schools as diverse as Rishi Valley, the TVS school in Mysore, and Corporation schools all over Chennai. I attended a conference with him at Rishi Valley and heard his exquisite clarity on concepts ranging from fractals to the Fibonacci sequence. But my favourite memory of him is teaching the Narikuravar (gypsy) children at the Corporation School in Saidapet, Chennai.

Unique way

He had a unique way of introducing numbers to Kindergarten children. He felt that because they learnt numbers mainly in sequence — as 1,2,3,4 etc. they never really grasped the concept of discrete quantities. So after first letting them rattle off the sequence, he would intercept by asking, “Now show me 3 in as many ways as you can”. Initially there would be consternation among the kids and he would smile, his eyes gleaming with a fiery excitement. Putting up one gnarled hand he would first show 3 fingers, and they would all chime “3”. Then he’d bend his fingers, put out 2 first, then one more and say “2 +1” and they would repeat, “3”. Next he’d put up four fingers and bend one – “4-1 = 3”. Then “2+2”, “5–2”, and so it would go on.

I have seen the excitement that erupted among those toddlers for whom numbers would never be the same again; nothing like the anonymous sequence that they began with. Soon all kinds of finger play broke out and PKS just stood smiling toothlessly, infinitely careful not to disturb that first moment of epiphany. Quite unobtrusively he’d introduced the concept of quantity, and also laid the foundation for the primary functions of addition and subtraction.

He had a vast collection of books in his house at Nanganallur, and once he showed me a World Encyclopedia on Mathematics to prove that it was not just the zero that India invented, but also the fraction. The world was afraid to break up numbers, he said, for fear the whole edifice would collapse, but Indian mathematicians proved that the concept of the ‘Whole’ was in itself quite relative.

Later, in the same school I was to see a wonderfully concrete demonstration of this abstract concept. Taking a long strip of paper he first folded it into eight equal parts. Then opening it out with the creases clearly visible, he pointed to the first part and asked the children, this time of 3rd standard, to name it. “1 by 8”. Yes, that was fairly simple. And so it would proceed till he reached the last part, to which in predictable sequence, the children would intone “8 by 8” and then like a magician he would close the paper and re-open it, pointing to the same whole again to which they would now exclaim, but with some thoughtfulness, “ 1” . And slowly the concept would sink in, that every number is merely a complete fraction of itself. From here, it was a small step to simultaneous fractions. Concept always came first for him, and only then the function.

However complex the concept he never prodded the students. Just waited patiently till they discovered it for themselves, and it seemed to me that they all did. I could barely shoot from excitement myself. Infinity lay right there within the interstices of the feeble chalk points on that faded blackboard and PKS helped us all to see it.

In the interview I recorded then he spoke passionately about his faith in education. “If a child falls sick, the doctor cannot blame him. It is his duty to heal the sickness. Similarly, the teacher has to find a way to clarify misunderstandings and release mental blocks about maths. He cannot blame the student.”

Committed

He had visited the U.S. on a Fulbright scholarship and Africa on a teaching deputation. He also travelled frequently to Delhi and other parts of India to attend conferences and workshops. But his real commitment lay with the under privileged. His son, Kannan Srinivas, explained recently that, to PKS, this was his personal form of patriotism, this abiding faith in children to “develop themselves under proper exposure”.

Another great area of fascination for PKS was the life of Srinivas Ramanujan. PKS was his first biographer, travelling every weekend after school closed for many years to Kumbakonam, in search of details of Ramanujan’s life. He discovered the house where he was born, the temple he frequented and the letters he wrote to his father from Cambridge. All later biographers from the West were to use these primary sources and acknowledge PKS in their works.

Here again the interesting insight from his son was that this interest in Ramanujan fed into his passion for math education. Rather than simply celebrating a genius, PKS strove to create a climate where more Ramanujans could flower. PKS will remain one of the most inspiring individuals of his generation.

– SOUDHAMINI ( Chennai based documentary film-maker)

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1. This is one more reason why I shouldn’t read the newspaper ( Otherwise I will take these stories seriously and force them upon readers).

2. Who titles paragraphs  ‘Commited’ and ‘Unique way’? The rest of the article is really well-written and all, but seriously.

3. I had a teacher like that in my last year of school. I think I’ve mentioned him earlier, too. Anyway, he was awesome. Appreciating that even more now that I’ve a set of  utterly disinterested ‘teachers’ in The  Reputed College ( Just how this turned into a rant about college, I’ve no idea!) that I attend.

4. Sorry, I’m a Math-nerd.And a word-nerd.

Update on our lives: Lucid and I are miserable ( Because of college, in case any newer readers haven’t already heard). In addition to this, Lucid is also a Loser because she doesn’t go on the internet ( The  Internet! Where the normal people are!) anymore (also why she hasn’t been posting). Fuzzy’s college sucks less and she has Happy things to say, so we’re not talking to her.wakin-dream

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OMG, I’m a Cyber-klepto.

OK, let’s face it. Other people have better things to say than we ever will, so why not just steal their stuff, right? Right.

Poetry

(I’ve stolen this from here.)wakin-dream

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wakin-dreamSeeing as we received no hate mail and found no identifiable drop in the number of viewers since my last post -which I stole- I figured, hey, stealing from myself can do no harm!

This is why, even though I’d promised to take my pictures elsewhere and write REAL posts on here, you get this instead:

Blueness

"Not Sunflowers"

piano

"Piano" in HB pencil.

Yes.Piano.I have often been commended on my abundant creativity.

Cecilia (Atonement)

"Cecilia (Atonement)"

One of those I actually like.So of course, it would be the one that my scanner wants to ruin most.Sigh.Life. Etc..

fireplace

And, at last, my old friend- The Fireplace.

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wakin-dreamFor anyone whose predominent thoughts on the title run along the lines “Erm, WHAT?!”, I have two things to say

1. Bear with me.Please (Magic word and all..!).

2. Addressing the ” No, I really don’t know what you’re talking about” -section of readers (The former was aimed at the “Have you lost it?!” -group), here’s what Wiki has to say:

A fallacy is an argument which provides poor reasoning in support of its conclusion. Fallacies differ from other bad arguments in that many people find them psychologically persuasive. That is, people will mistakenly take a fallacious argument to provide good reasons to believe its conclusion. An argument can be fallacious whether or not its conclusion is true.

Anyway, I found this very interesting post on Geekpress that I have based this on stolen :

List of logical fallacies

Ad Hominem:
This is the best logical fallacy, and if you disagree with me, well, you suck.

Appeal To False Authority*:
Your logical fallacies aren’t logical fallacies at all because Einstein said so. Einstein also said that this one is better.

Appeal To Emotion:
See, my mom, she had to work three jobs on account of my dad leaving and refusing to support us, and me with my elephantitis and all, all our money went to doctor’s bills so I never was able to get proper schooling. So really, if you look deep down inside yourself, you’ll see that my fallacy here is the best.

Appeal to Fear:
If you don’t accept Appeal to Fear as the greatest fallacy, then THE TERRORISTS WILL HAVE WON. Do you want that on your conscience, that THE TERRORISTS WILL HAVE WON because you were a pansy who didn’t really think that Appeal to Fear was worth voting for, and you wanted to vote for something else? Of course not, and neither would the people you let die because THE TERRORISTS WILL HAVE WON.

Appeal To Force:

If you don’t agree that Appeal to Force is the greatest logical fallacy, I will kick your ass.

Appeal To Majority:
Most people think that this fallacy is the best, so clearly it is.

Appeal To Novelty:
The Appeal to Novelty’s a new fallacy, and it blows all your crappy old fallacies out the water! All the cool kids are using it: it’s OBVIOUSLY the best.

Appeal To Numbers:

Millions think that this fallacy is the best, so clearly it is.

Appeal To Tradition:
We’ve used Appeal to Tradition for centuries: how can it possibly be wrong?

Argumentum Ad Nauseam**:
Argumentum ad nauseam is the best logical fallacy.
Argumentum ad nauseam is the best logical fallacy.
Argumentum ad nauseam is the best logical fallacy.
Argumentum ad nauseam is the best logical fallacy.
Argumentum ad nauseam is the best logical fallacy.
Argumentum ad nauseam is the best logical fallacy.
Argumentum ad nauseam is the best logical fallacy.

Begging The Question:
Circular reasoning is the best fallacy and is capable of proving anything.
Since it can prove anything, it can obviously prove the above statement.
Since it can prove the first statement, it must be true.
Therefore, circular reasoning is the best fallacy and is capable of proving anything.

Burden Of Proof:

Can you prove that Burden of Proof isn’t the best logical fallacy?

Complex Question:
Have you stopped beating your wife and saying Complex Question isn’t the best fallacy?

False Dilemma:
I’ve found that either you think False Dilemma is the best fallacy, or you’re a terrorist.

False Premise:
All of the other fallacies are decent, but clearly not the best as they didn’t come from my incredibly large and sexy brain.

Gambler’s Fallacy:
In all the previous talks about this subject, Gambler’s Fallacy won, so I just know the Gambler’s Fallacy is going to win this time!

Guilt By Association:
You know who else preferred those other logical fallacies?
(insert pictures of Hitler, Stalin, and Pol Pot here)

Non Sequitur:
Non Sequitur is the best fallacy because none of my meals so far today have involved asparagus.

Post Hoc/False Cause:
Since I’ve started presuming that correlation equals causation, violent crime has gone down 54%.

Red Herring:
They say that to prove your fallacy is the best requires extraordinary evidence, because it’s an extraordinary claim. Well, I’d like to note that “Extraordinary claims demand extraordinary evidence” is itself an extraordinary claim.

Relativism:
Well maybe all those other fallacies are the best for you, but to me, the relativist fallacy is the greatest logical fallacy ever.

Slippery Slope:

If you don’t like Slippery Slope arguments, you will do poorly in class, drop out of school, commit crimes, go to prison, and die of AIDS.

Special Pleading:

I know that everyone is posting about their favorite fallacies, but Special Pleading is out-and-out the best, so it should just win with no contest.

Note:

*Replace ‘Einstein’ with ‘BWC’ and you have a legit reason folks.No fallacy there!

**Lucid is under the impression that I use this one a lot. Her new approach to arguments with me is, well, not to argue at all. Hehe. Growing smarter from all the time spent around me, that girl.

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