# SWAMI VIVEKANANDA | 150th Birth Anniversary (1863 – 2013)

Everyone born will die some day…except for a few who are born to live Forever.
Om Nityaya Namah! Salutations to the Eternal One!

SWAMI VIVEKANANDA | 150th Birth Anniversary (1863 – 2013)

# Experiences at National Conference of AMTI 2013 | Day 3

Day 3: 8th Jan 2013

The day started with a few students’ presentations followed by the much awaited Final Quiz. Sixteen finalists from the written test paper on Mathematics (which happened the earlier day) were selected and formed into four teams. The rules were explained to all the team members by the Quiz Master – Sadagopan Rajesh, who happened to be a trainer for Olympiad kind of exams. The quiz was very well-organized and conducted by him. Once I started seeing the questions, I was glad that I wasn’t selected for the finals or else my team would have got almost zero contribution from me. The questions were very tough and the maximum time to think was 45 seconds where they got questions like – If you add 2 at the beginning and at the end of a natural number and subtract it from the original number, then you will get the difference as 2317. Find the number. Another question was – ‘n’ is a natural number such that 2^n divides 2013! (2013 factorial) exactly. What is the hightest power of ‘n’? And the answer was 2004, i.e., 2^2004 divided 2013! exactly. I had no clue how the kids got the answer in JUST 45 SECONDS!!!!!!!!!

To teach a child, many a times it calls for going down to his level. He gave a very good example which he used to teach the concept of Mathematical Limits when children found it difficult. He said, “A movie actress told the director that I will act in your movie only on one condition: Nobody should touch my body. And there was a kissing scene in the movie. So, the actor and the cameraman had to take the shot in such a way that both the actor’s and the actress’ faces came very near but the lips never touched. That is how a Limit in Mathematics is!” The audience burst into laughter. He continued, “Don’t think that why this old man is coming here and saying such things to the young audience. If you have to teach something to a teenager, try getting down to their level and see how fast they pick up the concept. I could see no better example to explain the concept of Limits to a 11th grader.

He also added that we should give the children an opportunity to come up with new questions. A person who is able to ‘spit questions’, he can have a Creative Thinking, which is very important in Mathematics. From the question that we pose to the students, they should be able to come up with more doubts and form more questions. One should also see to it that in a child a Critical Thinking is also inculcated. These qualities of Creative and Critical Thinking, can go a long way in Mathematics. He also requested bodies like AMTI to reach out to Govt. schools where the talents are not much recognized. All these students who had come for the National Seminar were from well-to-do schools and that’s not where the majority of students lie.

His talk was equally inspiring for the mixed age group in the audience and the applause after his talk lasted for a long time. One could see how much he was involved in his talk and how the words were coming out of his heart. He belonged to a rare class of teachers who could teach any student right from primary to University students. I saluted him from the bottom of my heart! I took the opportunity to follow him after the talk and present him a copy of my book – The Teacher Who Taught Us To Think that I had written about my Mathematics teacher. He was happy to know about the content of the book and gave a small pat on my face. It was a great feeling to have got even a touch of such a great teacher!

We all went to have lunch and came back to the hall for a ‘Short-Talk’ session where anyone could speak about the programme or anything on Mathematics, for 3-5 minutes. I took that opportunity to share couple of my thoughts. One – to have an Olympiad kind of test, like the one we had the previous day, for teachers so that we can equip ourselves with better thinking and facilitate better teaching to our students. Second – few students who presented papers were not trained properly. In the sense, they were just reading out from the PPT and some ones not even looking at the audience. The teachers could have given them rehearsals earlier so that they could feel more confident on the stage. But otherwise, the kids did a superb job which was beyond our expectations.

During the valedictory function, Prof. Mahadevan, one of the core Committee members of AMTI, expressed his sincere thanks to the Sri Prakash Synergy school for extending their support and appraisable hospitality. In fact, the teachers and students of the school were having holidays during this time of the year but all of them were volunteering for the event, with a BIG smile and lovingly they were doing their assigned jobs. Usually, employees of any organization start cribbing when they are called to work even for a weekend. Whereas these guys had taken atleast 5 days off their vacation to volunteer for the Conference. The children of the school were really sweet. They would greet every delegate with a Namaste and folded hands. That showed the culture they get from their school. The vision of the school was – Indian roots, International standards. Truly they were living upto that with respect to the values inculcated and infrastructure provided to the students.

After the valedictory, everybody started moving to their rooms or leaving to catch their trains. I had enough time since my train was at midnight. I was back in my room where I sat to pen down my thoughts while it was fresh in my mind.

This National conference of Association of Mathematics Teachers of India was overall a great experience for me. It gave me opportunities to meet a lot of teachers, retired teachers, mathematicians, talented students from different parts of the country and few researchers. It gave a forum to discuss various mathematical ideas with scholars on the subject. The exhibits and paper presentations by the students gave me more ideas of how the same thing can be organized in my town atleast in a small level. The students who came could also learn a lot of things from the Conference. There were a lot of books on Mathematics kept for sale. The reason I thought of penning down this experience is that atleast the people who read it might know some student, teacher or parent who could possibly expose their child to such events which are really great opportunities for them to learn. Let us be instruments in facilitating growth of children in whichever possible way.

# Experiences at National Conference of AMTI 2013 | Day 2

Day 2: 7th Jan 2013

I was all excited since morning because in the morning we were going to have a test based on numerical and logical questions. It was after a long time that I would be appearing for a mathematical contest. The ones who would clear it would go into a final round of multimedia quiz. The quiz started at 9 am. There were 25 questions and 1 hour to solve it. 15 of the questions had negative marking. I was solving such type of questions after a long time and I could see how slow my processor was becoming. I could solve only 14 questions in an hour. My room-mate Shrivatsav and Varada, both solved 21 questions. I got only 9 questions correct and 5 wrong out of which one had a negative marking. So, my score should have been somewhere around 34.

Shrivatsav and Varada both went for Olympiad-coaching in Mathematics and we could see the difference in their speed of problem-solving. It was fun watching them crack any given problem. The same was the case in the students from Kota (in Rajasthan) which happens to have the maximum number of IIT-entrance coaching centres. There the students would be admitted right from 6th or 7th standard onwards and they don’t attend schools at all. I was told that their institutes had tie-ups with schools which permitted the students to do away with regular schooling. The institutes would give them extra-coaching in the place of schools. Their normal coaching hours were around 8 hours a day. But these children are usually extremely bright and even a 6th standard child would know concepts of 8th or 9th standards. The students from Kota had come from Allen Career Institute. There were exhibits displayed by students in few classrooms. Most of these exhibits were charts. But these students from Kota had powerpoint presentations on various topics. One of those was on ‘Paradoxes’ which was explained by Ms. Astha Agarwal, a girl of 9th standard. Her presentation was very lively. She explained what a paradox is (which is usually very new and interesting for school children). She also respond well to my questions. Another was of Paavan Gaur of 10th standard from the same institute. He presented on geometrical representation on Arithmetic Progression, Geometric Progression and Harmonic Progression. He said that he is very much interested in physics and astro-physics. In my mind I was thinking, when I was on his age, I never knew that a subject by the name ‘Astro-physics’ even existed!

I asked both Astha and Paavan how it feels by not going to school. I felt that somewhere inside they missed the school. Paavan said that these institutes, even though they charge a good fee, are able to give them the best of teachers and best of teaching methodology, which should be ideally be undertaken by the Govt. But since our Govt is not able to provide such extensive training in schools for the really talented children, they have to rely on such coaching centres which give them training in depth in their subjects of interest. Some children learn the talk for paper presentations by-heart and fumble if something is asked to them. But these kids were really good with their concepts as well as their presentations. I had a nice time with them before I went for the afternoon tea break.

In the late afternoon, the host school, Sri Prakash Synergy School, had arranged buses for the delegates to visit a very old temple of Peddapuram. But I wasn’t in a mood to travel. I chose the time to sit alone and pen down something. During this time, I got some students who came from another school that belonged to Sri Prakash group of schools. These boys were really bright. They picked up whatever topics I explained to them. We discussed on different base systems and how numbers could be converted from one base to another base. I also gave them questions to think upon and give me the answers tomorrow. They did come up with the answers and ran towards me, when they saw me, to share their answers. One of them said, “Sir, we did not know these things. When you asked us such questions, we thought upon it and found out answers on our own. Thank you for asking such questions.” I smiled back.

Dinner that night was a buffet with a lot of varieties of cuisines. It was arranged in the school garden. Everyone could be seen enjoying the food and having casual conversations with others. I too took the opportunity to discuss few things with the people I came across.

Post dinner, we came to our room and Varada, Shrivatsav and I started discussing on logical solving of geometric problems. All of us posted questions for which we had to think of easier ways of solving other than the routine ways to solve the problems. Around midnight, we retired to bed.

…to be continued in the following post https://vinayrnair.wordpress.com/2013/01/09/experiences-at-national-conference-of-amti-2013-day-3

# Experiences at National Conference of AMTI 2013 | Day 1

Day 1: 6th Jan 2013

Everyone in our room woke up around 6 am. Srivatsav, the boy of 11th standard, asked me to give him a hand in folding his bedsheet. I was taken aback when I saw him struggling to fold the bedsheet which was a bit bigger than the normal size. I showed him how he could fold it. However he still seemed to find it difficult.

After the shower, I got into a small conversation with Mr. Karmarkar and told him about Mr. Nair’s poem that I penned down the earlier day. He immediately recited a small poetry on fraction-addition in Marathi. I quickly penned down the beautiful composition which I was sure would come handy for a Maharashtrian kid. It was a surprise for me to have met the second mathematician-poet in such a short while.

Soon we headed for the canteen to have breakfast, following which; we proceeded to the lecture hall. The hall was full with around 200 delegates comprising equally of teachers and students. After the inaugural ceremony, the first session was Prof. Bhatnagar Memorial Lecture on ‘Applied Mathematics in solving problems in Aerodynamics’. Honestly speaking, I could follow only what was explained in the first ten minutes. After that was beyond my learning capacity. Yet it was a revelation for me to see so much of applied Mathematics in engineering.
What I understood was that aerodynamics dealt with the study of motion of air (or fluid) past bodies. For example, kite, boomerang, bird, aero plane, missile, etc. The speaker, Mr. Venkateshan Bhaskaran, said that basically the study of motion of flying objects involves four parts:

• The structure of the flying object
• The propulsion of the object
Avionics – the mechanics involved in the flying object
Aerodynamics – again divided into two sections:
o Given the shape of the body, what are the forces that will be faced by it, or
o What should be the structure of the body which has to be constructed to be carried in the given force?

He explained how different kinds of wings of aero planes were invented and that we have thousands of designs of such wings. One just has to choose the right body to achieve his purpose of getting the optimum utilization of resources. He said that airlines have tough competition and research going on in their field so that they can choose the most effective design on the aircraft to suit their needs which will incur minimum costs as compared to their competitors. He explained various differential equations and other topics from calculus. The only few symbols that looked somewhat friendly to me in those equations were 0, +, = and π. But I thought, had we been taught the applications of calculus in college while we were learning to solve the equations, it would have given altogether a different meaning and approach for Mathematics. In college, we just solved equations without knowing the least where and how it’s going to be useful. But there was so much of use of calculus in applied Mathematics of engineering, aero dynamics, etc.

The second session was about π. As soon as I heard it, I was very happy because π happened to be one of my favourite topics. But my heart was saddened because the speaker didn’t talk about π in the way I understood it. He explained π using calculus. Yet, I wasn’t totally disheartened because he showed a series by ancient Indian Mathematician Madhavacharya, known as the Madhava-series which said:

1 – 1/3 + 11/5 – 1/7 + … + ((-1)^n)/2n+1 = π/4

As we learn in school that π comes in calculations related to circular shapes, here is a series given by a Mathematician who lived somewhere in the 13th or 14th Cent. CE, where he expresses the value of π/4 in the form of a series and without a circle!! So, π can exist even outside a circle!!

The presenter, Prof. Pandurangan, said that the above formula could be proved using Gregory-Leibnitz series (~1670 CE) which says:

π/4 = z – (z^3)/3 + (z^5)/5 – (z^7)/7 + ….

We just have to take the value of z as 1 in the above series.

It gave me immense joy when I learnt that this was proved by Madhava, an Indian mathematician three or four centuries before the mathematicians in the West discovered it.

The session was followed by lunch break. I took a short nap in my room after the lunch and went back to the lecture hall to attend the remaining sessions. On my way I saw a display of books for sale. And all of them were on Mathematics. Books have always been my weakness. I chose 6 books which dealt with magic squares, a book on Pi, e & i, and few other topics.

A teacher was presenting on a software called Geogebra which could be used to give more visual clarity in clearing concepts mainly in geometry. Constructions could be made very quickly using this software. Everyone enjoyed the presentation because the teacher made it really precise and clear. The next teacher presented upon ‘Exploring & Visualising Mathematics through Graphic Calculators’. She too did a great job in explaining. There is something called as a Graphic Calculator available in the market. In it we can draw graphs and plot the points, draw curves, and do almost anything with graphs. This gives the student an immediate picture of what an equation 4x + 3y = 24 would mean. A graphic calculator can also be downloaded from the internet. Her point was that if we are able to show the children the graphs of functions visually, then they would be able to understand the functions better than what they seem to understand merely in terms of x and y.

I didn’t quite enjoy the next two presentations by two teachers who almost emphasized that everything should be electronic and using technology. In their explanations they almost left no space for a teacher to think and set a question paper. Even that was suggested to be prepared from using a software. However, certain points were good and acceptable to me.

The following session was presentations by students. The students were divided into two classrooms and the audience could choose whichever classroom they wanted. I chose Classroom 1. The presentation skills of children in the classroom where I went into, were average even though they spoke of very nice concepts. It seems they were trained on the concepts more and less on presentation skills. Nevertheless, the kids did a great job on the stage. I was told that the students in Classroom 2 had done excellent presentations. My roommate, Shrivatsav, had his presentation in Classroom 2 of which I wasn’t aware and I missed it. His presentation was on methods to solve complex problems in simple ways using logic and observation.

I came to my room after the students’ session and didn’t go for the cultural programme that was arranged. I chose to take a quick nap for 20 minutes and started going through the notes I prepared and working on something. Soon it was time for dinner and I came back to the room immediately after dinner. I asked Shrivatsav how his presentation was and he said that it was good. I asked him what he feels about Calculus (which most of the students are scared of.) He said, “It’s easy. I like it.” I was surprised. This was the same boy who found Calculus a lot easier than folding his bedsheet. I had never imagined that easy and difficult things could be so relative!

We retired to bed by 11:30 pm.

…to be continued in the following post https://vinayrnair.wordpress.com/2013/01/09/experiences-at-national-conference-of-amti-2013-day-2

# Experiences at National Conference of AMTI 2013 | Day 0

Day 0: 5th Jan 2013

I was all set to attend the National Seminar of Association of Mathematics Teachers of India (AMTI) going to be held at Sri Prakash Synergy School, Peddapuram near Samalkot Junction which is some 3 hours train journey from Vishakapattanam (Vizag, Andhra Pradesh, South India). I boarded the train from Mumbai on 4th afternoon. My wife had packed my favourite curd rice for dinner and the following day’s lunch. Luckily, my co-passengers were busy talking amongst themselves and (luckily) I didn’t seem to be an interesting person to them. That gave me enough time and room for me to do my work.

I spent my time in the train on some official emails initially and then I watched a few videos on Mathematical Thinking that I had downloaded from www.courera.org where one can register for online courses offered by Professors from various Universities across the world at absolutely zero cost. I had found this course really interesting because it said that it was not on solving mathematical problems but developing that ability to solve mathematical problems; in other words, to develop the mathematical thinking. Professor Keith Delvin from Stanford University was the Course Instructor and was taking the course very interestingly. So, I spent time on the side-upper berth to watch the videos and came down occasionally to recharge my laptop. The quiet journey and simple food made the journey very comfortable.

As I reached Samalkot Junction, couple of teachers from the host school (Sri Prakash Synergy School) along with two students of the school had come to receive delegates who were arriving at the railway station. There were other delegates and Members of AMTI who had arrived at the station during that time. We were escorted by the students to the school in auto rickshaws. In my autorickshaw was a Mathematics trainer, Mr. Bharat Karmarkar (in his fifties), from Nigri (in Pune) who took classes to improve conceptual clarity in Mathematics both online and through home visits. Since we had the subject of common interest and since I had all the patience in the world to listen to such people, we began the discussion even before we exchanged our names. He said that his objective was to make the concepts clear rather than scoring marks or getting homework done from children. I was happy to see such a teacher after a long time. He also conducted annual excursions for children where they get to learn a lot of things practically through their visits. I was totally impressed by his ways of educating.

In no time we reached the school and were again greeted by the student-volunteers and their teachers. The school campus was big and their hospitality was really appreciable. Few students greeted us at the reception with a smile and Namaste. They applied kumkum (turmeric powder mixed with lime which gives it a red colour, often used in Hindu occasions) on our foreheads and sandalwood at the back of our palms. It was so nice to see the humility with which they greeted us. One of them asked me to keep our luggage at a place and proceed for the registration counter where we were to fill up a form and proceed to our rooms. Another student-volunteer took us to our room. Everything was so well organized that we didn’t face any hurdles at all in getting the initial procedures done.

In my room, there were four beds. One of my roommates was none other than Mr. Karmarkar and two others were Varada and Srivatsav, boys of class 9th (from P.S. Senior Secondary School, Chennai) and 12th (from Padma Seshadri Bala Bhavan School (popularly known as PSBB), Chennai) who had come to give presentations in the Seminar. The boys were really smart and energetic.

As we had reached the entrance of the school, Mr. Karmarkar met a friend of his – Mr. Prabhakaran Nair, a retired school teacher from Calicut, Kerala. They were delighted to see each other after a couple of years. Mr. Karmarkar told him that there’s another Nair with him (which was me) and then we greeted each other.

Me & Mr. Karmarkar were in room no. 104 and Mr. Nair was in 102. First thing I look for when I enter a new room is the charging point. And I was surprised to see that there wasn’t any! At last I found a point in the small dressing area before the rest rooms. But the plug had some loose contact and hence it wasn’t working properly. Finally we found two plug points outside our rooms (in the verandah of the floor) for the whole floor which had ten four-bedded rooms. Luckily Mr. Karmarkar had carried an extension cord (a tip for those who travel to such places where you never know how many plug points you might get.) I got my mobile charged for some time and we all went to the canteen for dinner.
After dinner I got an opportunity to talk to Mr. Nair and we both walked into his room continuing the conversation. His teaching experiences fascinated me a lot. Mr. Nair, to my utter surprise, was 70 years old. He didn’t look more than 60 to me. He was full of glee and energy while he was talking. He was a school teacher and also a mathematician-poet (a very rare combination we find these days.) He said that while he used to go to take classes for the differently-abled children, he found these poems handy to teach them concepts of Mathematics. One poem was such that a boy saw a flock of parrots flying in the sky and he asks one of those parrots how many you are in number. The parrot replies that ‘us + us + half of us + one-fourth of us + me, will make 100. Now you calculate how many we are in number.’ Saying this, the parrots fly away. The boy isn’t able to calculate and asks his grandmother. The old lady immediately gives the answer as 36. The answer forms a simple equation as x + x + ½ x + ¼ x + 1 = 100. Solving it further we get 2 ¾ x = 99, i.e. 11/4 x = 99. Thus x = 36. The boy gets a question that if the number of parrots were different, what would be the answer in the place of 100? He goes exploring and discovers an Arithmetic Progression 12, 23, 34, 45, and so on. Thus, in one poem, Mr. Nair explained simple equations and arithmetic progression. I’m sure if a student gets something like this, then undoubtedly he would find a flavor to Mathematics. It reminded me of all the great Indian Mathematicians like Bhaskaracharya who wrote down Mathematical questions in poetry and gave it some spice thus encouraging the students to get to the answers.

The poem in Malayalam was really beautiful; not as dry as I explained it above. He shared a couple of more poems. One of the other poems he shared was that of a boy who asks his father, ‘why are there only two types – even and odd numbers?’ (This ‘why’ is not a usual question from a school student.) His father somehow gives some explanation and tries to cover up his own ignorance. Then the boy corrects his father and tells him that in ‘even number’ of circles, each circle can be paired with another circle. But that’s not the case with ‘odd number’ of circles. In case of odd numbers, one circle will stay unpaired. When you combine two odd numbers, say 5 and 7, then the circles which were left out alone in 5 and 7, will be paired with each other. That is why when we add two odds we get an even number.

Mr. Nair also shared some ideas on how we can induce some thinking ability in children and ask them questions in general to make them think on ideas and encourage them to explore more. It was wonderful discussing with him till 9:45pm. I wished him good night and came out of his room to pen down this experience. In a few minutes another gentleman, Prof. Govinda Reddy from Nandyal (a place in Andhra Pradesh) came to me. I had met him last year at a National Mathematics Seminar at Rashtriya Samskrita Vidyapeetham, Tirupathy (Tirupathy is a place known for the famous Balaji temple in Andhra Pradesh.) In our earlier visit I couldn’t interact with him much. But this time, it was compensated. We sat till 12:45 am and finally I had to send him to his room to take rest.

Prof. Govinda Reddy was an old retired Mathematics teacher from Nandyal. He seemed to me to be in his 70’s (I was astonished to hear from Mr. Karmarkar that Prof. Reddy was 81!) He was tall, lean, dark and soft-spoken. He has his personal library which comprises of around 1000 books on Mathematics. He collects books on Mathematics from different sources. He subscribes some foreign magazines like Crux (a Canadian publication) and Putnam (a USA publication for Mathematics Olympiads.) Sometimes his students gift him some books but most of the times he purchases from his pension. He started the Nandyal Association of Mathematics Teachers 10 years back where he organizes Teachers’ Training Programmes, Contests on Mathematics for students and various other programmes. He showed me one of the question papers for the 10th standard in one of such contests. It had 6 questions and the students were given three hours to solve the paper. The levels of questions were very high but it would definitely bring out the best of upcoming mathematicians into light. He said that the cash prizes of some contests went as high as Rs.10,000/-. I was astounded to hear this and asked him from where does he get funded for such activities in a small town like Nandyal? He smiled and said, “I get a pension of Rs.27,000. My monthly expenditure comes to 7,000. My house rent is Rs. 6,000. The books that I buy amount to Rs.1,000 per month. After some miscellaneous expenses whatever is remaining, I save it for such purposes. At the end of a year, whatever amount is saved is spent for such events.” And he kept smiling.

I was speechless! What kind of dedication he was showing towards his subject. How different are people. Some places we even find teachers who hesitate even to give a prize of a small toffee to their students and here is a teacher who spends his entire pension to bring up the upcoming talents in Mathematics. Here was a man, sitting before me in a plain white shirt and a white dhoti, whose hand shivers while he holds something, and is in his early 80’s, at such a stage in life what he is doing such remarkable things which the Govt. or other institutes should be taking up.

He showed me a book which was going to be released the next day. It was about brief life sketches of many mathematicians across the globe along with their photographs so that children can remember their faces when they hear the mathematicians’ names. He had also brought along with him some 132 flexes on the life of Srinivasa Ramanujan which explained the life of Srinivasa Ramanujan with photographs at various stages of his life. I couldn’t help myself wondering as to how much effort Prof. Reddy was putting in the field of Mathematics even at this age!

Finally, we retired to bed at almost 1 am.

… continued in the following post https://vinayrnair.wordpress.com/2013/01/09/experiences-at-national-conference-of-amti-2013-day-1/