Friday, July 6, 2012

Teaching Probability to Shubhendu



One fine, cool, breezy morning I just hopelessly got trapped into it. I did not have classes until the new trimester so I did not have too much of work on my desk. That morning in one unique motivated moment, a teacher within me turned ambitious and decided to walk into the Dean’s chamber. The back ground story is like this – We had a student, let’s call him Shubhendu. Shubhendu had managed to fail in four out of six subjects in the first trimester. Consequently, he had held a lot of meetings with the Dean. His problem was diagnosed as follows :
Shubhendu had been suffering from something called as ‘Mathsophobi’ ever since he passed his third grade in school. He had been trying to win the battle with this disease during all his school and college years and had come out to be a gallant warrior, as he could successfully pass all his classes in school and college, inspite of his chronic illness. The problem had aggravated ever since he left familial comforts and familiar surroundings of Kolkata, when he decided to do his MBA. Apart from all the other pressures, that a MBA student has to face in the first trimester, like, adjusting to new surroundings, making new friends, hectic routine etc.,  there were two monsters who had posed a serious threat to Shubhendu’s flailing health – these two monsters were Quantitative Techniques and Economics. Shubhendu’s older ailment got aggravated in such circumstances and created so much of stress for him that he managed to fail in two other subjects (Organisation Behavior and Basics of Computing) as well.
With a grave look on his face and some lines of strain on his forehead, my Dean had declared that this was a serious problem. I do not know whether it was because of the fact that I really did not have much to do during those two-three days or because of the fact that I was a self pronounced young, motivated dynamic academician, (also clichéd as - always willing to take up new challenges) that I found myself saying, “Sir, I will help Shubhendu with Maths. I will give special tutorials to him on the difficult topics. Let him come to my chamber when he is not having classes”.
And thus a boy, all of six feet, who possessed an unkempt look and who spoke in a sweet voice ( like the way most Bengali boys do) came to my chamber one afternoon and introduced himself as Shubhendu. I must say that there was something likeable about the guy and I was really impressed with his honesty when he related a complete story of his failures at a subject called Maths during all his academic years. Bringing a warmest smile on my face, I had told him, “ Believe me, Shubhendu, Maths is a very interesting subject and I promise that all your sessions with me are going to be great fun. Mathematics is not supposed to make things complex for us, in fact it makes life easier”. Shubhendu seemed to be so pleased and unburdened with all his worries, after our initial discussion that it was not difficult to chart out a timetable for the topics to be dealt with in the next fifteen minutes. When he left my chamber we had both seemed to develop a liking for each other. To my satisfaction the first step had been taken for a difficult yet exciting journey of learning mathematics. I had a wonderfully peaceful sleep that night.
It was decided that I would teach him ‘Calculus’, ‘Theory of Probability’, ‘Linear Programming’ and ‘Permutation and Combination’ to begin with. I gave him some simple problems on differential calculus, the first day. He could solve them but I could also discover that after every third question he committed a calculation mistake. First derivative of 2x2 would invariably become 8x, addition of 4 and 17 would be 20. When I pointed out the mistake he gave a sheepish grin, shook his head, making a movement with his hand with the same time, as if he was taking some sort of a pledge to himself about not repeating the same mistake again and said, “Sorry Ma’am, Calculation mistake”. In the same session I tried to give him a understanding of calculus. Change in Y due to some change in X, where Y is a dependent variable and X is an independent variable…… He listened to me with rapt attention and gave nods at all the right places. Finally he said, “ Yes Ma’am I understood, “eet ees basically changing”. I was satisfied with the first class. Shubhendu had solved some problems and had figured out ‘changing’ in Calculus.
Promptly, he came the next day, just at the right time. I also felt that his appearance was smarter than the previous day, or so I imagined. He had smile on his face, when he told me that the previous night he received a call from his grandmother. He was successful in gathering all my sympathies, when he related complete information about his family, to me and the fact that he had lost his mother when he was very young. The first fifteen minutes of the session were over by the time he finished his story. I quickly opened the book to begin the Day’s lesson. By the time the second day was over I had figured out that Shubhendu tried to strike a conversation with me wherever he got a chance and I had learnt to respond to it with an impish smile on my face and an eagerness to get his attention back to the lesson. Bengali loquacity I thought, at the end of the session, where we had made some progress on differentiation.
First few days passed and we had merely done some basics of differentiation and integration. By this time I had gathered complete information about Shubhendu’s family, neighbourhood, cousins, football and durgapuja in Kolkata, and why Shubhendu had developed a deep dislike for a classmate of his in the institute.  Shubhendu looked very confident after having learnt differentiation, a topic of what he called as ‘Advanced Maths’. He had made a call back home, to his father and shared the news of his newly acquired skill-set at ‘Advanced Maths’. I should have let him enjoy his moment of glory but I don’t know why I was getting nervous. We decided to take up Probability as the next topic. Both I and Shubhendu were put to test. The question to be solved was – What was the probability of learning Probability by Shubhendu? I tried to motivate him by telling him that Probability was perhaps one of the easiest topics in Maths if one tried to understand the concepts. Thus began an adventure of a self-motivated, young and dynamic academician, the one of teaching ‘Probability’ to Shubhendu. Our classes began something like this -
Me – “See Shubhendu, Probability is a term we are familiar with. Probability refers to the likelihood of something to happen…………..”
Shubhendu – nod with a deep breath, attentive eyes looking keenly at the book….
Me – “For example, When you toss a coin in a cricket match what is the probability that you will get Head?”
Shubhendu – another nod…
Me – What is the chance Shubhendu, that you will get Head?
Shubhendu – “Ma’am there is a chance”.
Me – “Give me a number in percentage terms”.
Shubhendu – “Hmmm……”
Me – “Is there a hundred percent chance that you will get a Head?”
Shubhendu – “No Ma’am,  Ma’am do you think there could be some fixing done with the toss also, like it is decided by the umpire which captain will win?”
Me – “Do you think this can be done in a toss?”
Shubhendu – “Ma’am like it’s only the Captains and Umpire there. Whatever you get Head or Tail, you can declare its Head.”
Me – “Shubhendu, Don’t you think fixing would rather be done on who should bat first, than a toss.”
Shubhendu – “ (with a wide grin on his face) Yes Ma’am you are right.”
Me – “Yeah so tell me, what is the chance that your Captain will win the toss?”
Shubhendu – “Ma’am, hmmm… the chance is between 40% and 60%.”
Me – “Goood! (Smile on my face and definitely encouraged by his response) Yeah so can you give me an exact number between 40% and 60%?”
Shubhendu – “ Maa’am, err… its 45% to 55%.”
Me – Shubhendu Don’t you think your captain has a 50% chance always to win the toss?
Shubhendu – “(with a wider grin on his face) Yes Ma’am you are right.”
Me –“ Yeah, so that’s how you calculate probability………”
Shubhendu – (playing with his ear) “only if there was no fixing done…….”
Me – “See there is a 50% chance of getting a tail and 50% chance of getting a head, so how many possible outcomes do we have here?”
Shubhendu – nod sideways and backward, grave look on the face…
Me – “Shubhendu, how many possible outcomes do we have here?”
Shubhendu – “Possible Outcomes Ma’am?”
Me – “When you toss a coin you can either get a head or a tail, so how many possible outcomes you can have?”
Shubhendu – “Ma’am don’t know Ma’am, Ma’am ...mmm... One.”
Me – “ One? Youuu either get a Heaad or a Taaiil.”
Shubhendu – “that’s what I said Ma’am, one ….”
Me – “Yeah….”
Shubhendu – “Two” , (by this time may be he figured out one was the wrong answer)
Me – “Yeah! (wide smile on my face) that’s it. Don’t you think it was easy?”
Shubhendu – “(smiling) Yeah Ma’am!”
Me – “So total possible outcomes are two, and you either get a Head or a Tail, so number of outcomes you get is one, that makes it one by two, and thus probability of getting a head or a tail is 50%.”
Shubhendu – “YES Ma’am.”
Me – “Now read the book, the formula is written there.”
Shubhendu –“ (After having looked at the book for some minutes) Yee’es Ma’am.”
By this time I felt Shubhendu was a little bored, there was some sweat on his forehead, which he was trying to wipe out with his handkerchief, while still looking at the book. For the first time, I realized may be learning probability was a laborious task for poor Shubhendu. I heard my self saying -
Me – “So Shubhendu you go home and read the book and I will pick up tomorrow’s session from here.”

*     *             *             *             *             *             *             *             *             *             *             *            

Next Day I asked Shubhendu to write the first formula for probability and gave him some problems to solve. He was quieter than his usual self and looked more attentive.  He could not solve most of the problems,  and attributed the reason to calculation mistakes.
Me- “Shubhendu, five out of these six problems are incorrect.”
Shubhendu – “Ma’am, hmm, Oh! Errr… Ma’am Calculation?”
Me, while looking at his exercise book - “No, not just calculation mistakes!  But why do you commit so many calculation mistakes?”
Shubhendu – “Ma’am I don’t know Ma’am, Ma’am I lose marks because of calculation mistakes only.”
Me, looking up from the exercise book- “Shubhendu, I have realized that your span of attention is very short; you tend to lose your concentration…..”
Shubhendu – “Ma’am I try, I try to……….”
Me, with an assertive voice- “No Shubhendu,  I think this is the basic problem with you, you need to do something to increase you span of attention, otherwise it would be so difficult for you to study, you get distracted very quickly.”
Shubhendu, serious and intently looking at me – “Ma’am isss there a way to increase span of attention?”
Me- “Yes, if you do meditation you can increase it.”
Shubhendu – “Ma’am but I don’t know meditation, I will have to do a course… I will have to find …..”
Me – “Meditation should help you, and it’s not a big deal you can start practicing some meditation from today itself.”
Shubhendu – “Ma’am when I was a kid my meditation was good……it was only after my mother passed away that………………”
Me, smiling – “Shubhendu, your concentration was good perhaps……….”
Shubhendu – (smile) “yes Ma’am, Ma’am till fourth standard I used to top…………”
Me, earnestly - “See there are simple techniques of meditation, I can teach you.)
Shubhendu – “Ma’am.. err… ok”  (nod)
Me- “You might have seen your Grandmother chanting some mantra on a mala that is one simple form of meditation that you can begin with.”
Shubhendu – “(With earnestness) Yes Ma’am yes,  my grandmother chants a mala twice a day, My Grand Father, in fact my Great Grand Father used to go to Ramkrishna Mission. Everybody is very religious in my house.”
Me- “She chants mantras! Do you know anyone of those mantras?”
Shubhendu – “Yes Ma’am a few of them.”
Me- “Then you can start off today itself, you can pick up any of those mantras and chant it on a mala. If you do it twice a day it will help you.”
Shubhendu – “Ma’am, bhen my mother passed away, I was deesturbed for some days, so I lost my meditation, before that I was very good, I was…..”
Me- “Shubhendu, Twenty minutes of this exercise morning and evening will help you gain a better concentration.”
Shubhendu – “Ma’am but I don’t have a Mala here”.
Me- “Ok. I will get one for you tomorrow. Now let’s get back to Probability….”
Shubhendu – “Ma’am do I have to remember some God also…”
Me- “You can remember any God you have faith on, Now let’s get back……….”
Shubhendu –“ Ma’am I am bothering you so much, Thank you, so much Ma’am for helping me”
Me – “That’s Ok Shubhendu, Now let’s get back………”
Shubhendu – “Ma’am I get up late in the morning……….”
Me- “Shubhendu, let’s get back to Probability…………………”
It was clear that my attention was shifting from Maths to Meditation and I realized that too. But a young dynamic, motivated professor had to solve all her student’s problems. Next day I got a mala of rudraksh beads for Shubhendu. He thanked me many times for that and really looked obliged when he left my chamber. If I say that a thought of Shubhendu having fun with a bunch of students, showing them the Mala I gave her, did not cross my mind, I would be dishonest. Because, it did. But a positively motivated Prof. drove away all the negative thoughts off her mind. ‘Nishkaam Karma’…. Do your duty selflessly!!!
Our progress on probability was much slower than what I had expected. It was clear that Shubhendu was finding it very difficult to retain concepts with him, what were taught the previous day. Meditation did not seem to work, although Shubhendu tried to convince me that he had visualized a lot of change in himself, since he started meditation (only in the evenings- for mornings, he took an excuse. There was no one in the hostel who could wake him up. The alarm clock failed to do so because it was only a clock, Shubhendu could easily shut him off.) I was getting a little impatient. I expected Shubhendu to get a little frustrated too but surprisingly he was cool. My knowledge about his likes and dislikes about things in general – like food, people, music, clothes, girls etc. had increased. I had come to know about a lot of his family history. Shubhendu managed to maintain his somber expression when I showed signs of irritation. It was not a good idea perhaps to take up probability as a second topic to teach, I thought, and this is how I consoled myself.
When I was contemplating about changing my teaching style and to be innovative in order to evolve some new teaching pedagogy for making probability simple and easy to understand for students, Shubhendu met with an accident. He had an injury in his leg and because of that he had to return back to Kolkata. This also meant that he would take his make-up examination for Quantitative Techniques at the Kolkata center. This is how; some amount of rash motor bike driving by Shubhendu, ended his sessions with me. The next trimester was about to begin and I got busied in preparations for the same. Did I miss Shubhendu, and my probability sessions with him? I think I am not yet clear on that, as in a way a sudden end of afternoon sessions with Shubhendu had brought a sense of relief to me too. But I was certainly concerned about him,  his exam and wished that probably if I had more sessions with him, I could save him from failing in the exam a second time.
In retrospect, I think Shubhendu’s accident did a great service to the Young Academician’s Self esteem. She was saved of facing the first failure in her journey as an academician. Shubhendu’s accident saved her from all the distress and dishonor that such failures bring.
It was almost ten days that Shubhendu had gone. Suddenly one afternoon I received a call from him.
Shubhendu – “Good Afternoon Ma’am! How are you?”
Me-“I am good Shubhendu. How are you? Have you recovered?”
Shubhendu – “Ma’am not yet. Ma’am in Nagpur the doctor said, I had no fractures, but then I showed my leg to a doctor here in Kolkata and he said that I had broken my ligaments. This was a shock for me as I had not expected it to happen. How could a Nagpur Doctor not diagnose it properly…………………Ma’am I am still not well………”
Me –“ (After having heard all about his injury, medication, diagnosis etc. for ten minutes) you will get well soon Shubhendu, Now tell me why did you call me up?”
Shubhendu – “Ma’am if I got medical aid in time, I would have been fine by now. Because of my sickness I was not getting much time to study also but somehow I tried to keep myself busy in studies as much as I could ………….”
Me – “Shubhendu, you are on a long distance call. Come to the point.”
Shubhendu – “Ma’am tomorrow I have my exam.”
Me – “Yeah…….so are you prepared?”
Shubhendu – “Ma’am I will write the exam at Kolkata center. Here I met a lot of students who have a back in QT and Economics………..”
Me – “Shubhendu, tell me why did you call me up?”
Shubhendu – “Ma’am I called you up so that you can tell me some important questions, if you can Ma’am.”
Me – “ Important Question??? In QT ???”
Shubhendu – “Yes Ma’am and in Economics. Although I plan to do the entire course but still I will focus more on these important questions.”
Me – “But Shubhendu I am not in a position to tell you the important questions……”
Shubhendu – “Ma’am my Grandmother was also not keeping well since I came here………”
Me – “With a subject like QT, it does not help when you ask for Important topics…….”
Shubhendu – “I had to take care of my Grandmother also Ma’am. I will prepare some questions…..”
Me – “Look Shubhendu you cannot do a selective study, it can be fatal…….”
Shubhendu – “Ma’am I will study all, but some parts I will do well…”
Me – “You should practice all the problems…………”
Shubhendu – “Ma’am if you have any idea what would be asked in the paper……..”
Me – “How would I have any idea? I think you should ……..”
Shubhendu, interrupting me  - “Ma’am faculties have an idea about question papers, Ma’am Please help me………”
Me – “Shubhendu, I wish to help you and that is the reason I am telling you………”
Shubhendu, interrupting me  again– “Ma’am please tell me some questions………. I will pass……..”
Me, firmly – “I think I cannot help you regarding that…………..”
Shubhendu – “Ma’am you helped me so much, please help me one last time……….I am trying for a center transfer to Kolkata, May be I will get it because my Grandmother is also not keeping well.”
Me – “Shubhendu, instead of wasting time on phone I think you should sit and study. I Wish…”
Shubhendu – “Ok Ma’am, I will do the complete course……….. Ma’am I heard that faculties can have an access to question papers…..”
Me – “Shubhendu, Is this all that you called me for?”
Shubhendu –“ Ma’am ok Please tell me which topics should I study…….”
Me – “You have to study all the topics……..
Shubhendu - Ma’am how much of theory are we going to get?”
Me – “Shubhendu, Is this all that you called me for?”
Shubhendu – “Yess …..Ma’am……mmmm…… Ok Ma’am….. Thank you so much Ma’am. “
Me – “All the best! Shubhendu,  for you exam. Bye.”
Shubhendu – “Thank you so much Ma’am. Bye”


Shubhendu got a center transfer to Kolkata center. I could never know whether he passed his QT and Economics papers or not. I was not very hopeful though. I do not know whether he could ever complete his MBA. But I guess if Shubhendu managed to complete his MBA, he must have got some marketing or PR job in a FMCG, IT or Insurance company in  a booming economy. He must be good at selling insurance or savings Bank Account, hopefully. He talked well and could easily divert the conversation to a topic he wanted to discuss. He would perhaps do well in life. I do hope that Shubhendu did learn something about ‘Advanced Maths’ from my sessions with him.
However, there were some important lessons that had been left for me to learn -
  1. Not everyone is meant to learn Probability in life. There are some who are not. Still they do well in life, perhaps.
  2. My time is a resource and I should consider it as a resource.
  3. There is an opportunity cost attached to everything in life, and that includes time and energy too.
  4. Academicians can also be hopeless romantics.
The young, dynamic, motivated academician promised shubhendu that she would make learning Mathematics fun for him. An old Sanskrit saying says, knowledge should be given to the person who is worthy of it. In Shubhendu’s case his worthiness was adjudged by a management entrance examination, which works on a cutoff system. Shubhendu and many others like him managed to be above the cutoff and thus qualified as someone worthy of knowledge.  In retrospect, I am bound to think, Shubhendu did have fun during those sessions. Only, at the dynamic, young academician’s cost.