…contd from My Trip to Nagapattinam – Part 2
I could see a lot of difference in the attitude and behavior of the people as compared to the people from the cities. As compared to the city dwellers, village folks are very loving. The children and teachers were all anxious to see what Vedic Mathematics is all about because they couldn’t get the knowledge easily from Nagapattinam. Even non-Math teachers attended the classes because of their yearning to learn something new. The children looked forward at the classes as a source of entertainment. They were far away from any negative influence that the kids in the cities are affected with. They were so shy that once when I uttered the word ‘Pair’ while explaining a topic in Math, they shied away their eyes. When they heard ‘Pair’ it reminded them of the word ‘couple’. And they were SHY! Which was a surprise for me. Because in the cities, we see children from lower classes exposed to all infatuations and school-love and relationships. But here, it was far beyond their imagination. I was told by Ganesh Sir that the total population of Nagapattinam itself was only 100,000. So, they could easily identify any outsider. If the children would be seen roaming on the roads after school hours, any onlooker would call up the school and inform about such an incident and the student would be warned. To them, internet was a taboo and talking of email ids and facebook was a hush-hush. All the while I enjoyed their village innocence and their love they showered over me. There would not be a single student who would pass by without greeting their teachers. The way of greeting in Chinmaya Vidyalayas was ‘Hari Om’ and I had to keep saying Hari Om as a return greeting every time I walked in school. The teachers too were very loving. Sometimes, if the lady peons who would serve me lunch would not be at the table, the teachers themselves (once even the vice-principal herself) would serve lunch for me despite my pleading requests of not to do so. In almost all alternate evenings, Saravanan Sir would call or come by the school just to ask me if I need anything from the market because he was going to the market. I experienced hospitality at its best over there. Their love gave me the spirit to take classes for long hours.
As usual, I enjoyed the classes very much. The children enjoyed too. We did techniques on faster subtraction, multiplication and squaring for all classes. For 9th & 10th, we did cubing and a few more techniques. For every batch, I enjoyed doing sessions where I could ask a lot of WHYs for everything they say. For example, while doing the concept of area they said, “Area of a square is side x side, area of a rectangle is length x breadth.” And I tried to bring all innocence to my face and asked them, “Why is it so?” They would reply, “It’s the formula Sir. If we don’t use that, then how will we get the answer?” I asked them again, “Who made these formulae? Why are they not different? Why area of a square is only side x side why not ½ x side x side?” They would give a puzzled look on their face. In every school where I’ve done workshops, I’ve faced the same reaction. I then have to lead them to get the thought of deriving a formula. Some would still say, “Area of a square is side x side because all sides are equal.” I then would ask them, “In that case area of a rhombus also has to be side x side because all sides of a rhombus are also equal.” Suddenly someone would come up with their logic saying, “Because in a square all sides are equal and all angles are right angles.” It is a strange thing how we derive a logic behind a statement. When our ‘mind’ is convinced on some idea (irrespective of the fact that it is backed by reasoning or not), it automatically tries to find logic behind the idea to satisfy the ‘intellect’. Say for example, for a person who is convinced that ghosts exist, he can come up with so many reasons to back his statement. These reasons may not sound logical for others. But for him, it is. Because he is sure of the idea and hence whatever reasons he finds is apt for his intellectual understanding. When others wonder and label him illogical, he must be thinking the same thing about others!
So, for children too, they are convinced by these formulae without even questioning its derivation to their teachers. Sadly, we do not get an opportunity to question or think and try to find the reason ourselves behind Mathematical formulae in school. Most of our teachers are taught to teach, not to make the minds to question. When I was in school, our Mathematics tuition teacher Sri P.P.Raman Sir would ask him so many questions which would make us think and derive solutions to problems. This enabled his students to get the exact reason and find the proper logic behind a proof. Unless and until students get an opportunity to think and discover the science behind every working in Mathematics, how are the supposedly to ‘understand’ mathematics? Many of them score, but very few understand mathematics.
While I was taking class here, it was raining outside. I said, “If I ask you why it is raining outside, then would you tell me – It is hot in Mumbai. Mumbai is 700 kms from here. And hence it is raining here!” They all laughed. I went on, “That is how it sounds to me when you say – All sides of a square are equal. All angles are right angles. Hence area of a square should be side x side.” There was complete silence in the class. They understood that their statements did not have logic behind it but still they thought it had logic. That was a thunderbolt to them. Till now they never thought that formulae have to be questioned or they can be derived. This was nothing new for me because in most of the schools I receive the same answers. Very few of them understand the concept of area. That when we say area of a figure is 50 square feet, it means the shape when divided into smaller squares of size 1 foot each, we will get exactly 50 squares.
Slowly, I had to take them to discover the formula for area of a square and rectangle. Once they have understood these two formulae, they gradually start thinking and deriving formulae for area of a triangle and parallelogram. That’s it! My objective is achieved if the slightest thinking process is set during the 8 – 10 hours workshops. In this school, there was one boy of 8th standard, Kamlesh. When I asked their class the derivation of formula for area of a rectangle, he thought for a while and said, “Sir, I can try proving it using an example. Suppose there are a certain number of bottles in a rectangular box, then I can get the total number of bottles when I multiply the number of bottles in a row by the number of columns.” That boy had got the idea. He could try proving a formula by associating it with another example which he might have (perhaps) solved or observed previously. This is a process that has to be cultivated in the children right from a young age – ‘how to get it solved?’ In his book How to Solve It, George Polya, a famous Mathematician says, “Look at the unknown (what is to be found out in a problem). And think of a similar problem having the same or similar unknown. This suggestion advises you to do whatever you would do anyhow, without any advice, if you were seriously concerned with the problem. Are you hungry? You wish to obtain food and you think of familiar ways of obtaining food. Have you a problem of any kind? You wish to find a certain unknown, and you think of familiar ways of finding such an unknown, or some similar unknown.” This is a very useful tip that can be used by teachers, parents or anyone for that matter, who wish to train children in problem-solving.
Two and a half weeks flew like anything. And it was the last day of the workshop. We took class-wise group photos and some casual photographs with the 10th standard students. The 10th standard students were asked to sit casually engaged in some conversation with me so that some candid photos could be taken. They were again shy. Finally I engaged them in another discussion over Pi and when they were engrossed in it, the photographer did his job.
Immediately after the photo session, I bid good-bye to all the students, teachers and staff and left for the railway station to catch my train. Two male teachers came to the railway station to bid me goodbye. For three weeks, with all the love I received from the village-folks I never felt I was away from my family. And there I was, on a train, continuing my journey back to place where I came from – my home, my family.