Math and Writing

Here is a short account of how my children started to do divisions and how it led to an unexpected learning outcome.

We had found that basic numeracy was easy for our children to acquire, so much so that we hardly remember how it came about. We never really sat down to do math with them. As she went about her daily chores, Hema had always liked to involve the children, and little by little, in the course of talking about things, both the kids acquired a sound number sense along with a good handle on how to add and subtract.

Before we homeschooled, Abhinav went to two different "liberal" schools in California for 3 years, where at the end, he was expected to do some simple addition and subtraction of mostly one or two digit numbers. Abhi was already numerically competent, so none of this interested him. Unsurprisingly, as the other parents and the teacher told us, Abhinav was rather bored in the class and was often creating trouble. However he continued to be fascinated with math and we let him explore his interest on the Khan Academy website.

One day, while playing with an addition/subtraction math practice program on the website, Abhinav, 7 at that time, got curious about a math symbol he hadn't seen before. So he asked me. I said "This is division" and then remembered my own childhood difficulties about learning this, so I added, "This is too advanced for you." He wanted me to tell him anyway, and as I was forced to respond, my sense of responsibility yielded a simple way to present this idea. I said, "6 divided by 2 means we find out how many 2's are in 6." He chewed on this unblinkingly for a couple of seconds and then said, "But you told me this was hard!" He went back online and spent the next hour or so absorbed in playing with the division practice program.

Sometime later, my daughter, Aparna, then 5, wanted to know this division thingy too. By this time I was more willing to question my own assumptions about what was hard, so I gave her the same simple explanation that I had given her brother earlier. And it worked this time as well. She was so thrilled with this new learning that over the next several weeks she would ask either my wife or me for division problems and then proceed to tackle them with relish.

Soon, I was beginning to get bored with this routine and had to think up something new to keep my own interest from flagging. I started making certain formulaic stories that featured a seriously math-challenged dad and his two children, a girl and her little brother (an example will follow). The stories always climaxed with a division challenge that stumped the hapless dad, and then the two kids would easily do the division and present the solution to the astonished dad. In the telling of the story, I would stop it just before the problem was solved. Then I allowed Aparna to have a go at it first, and I remember clearly how her face would be agog, waiting for this moment. She would scrunch up her face in total concentration and then furiously start calculating. And finally when she had the answer, be very tickled by how the dad in the story can find this so difficult. We must have played this game for months and Aparna never got tired of it.

While she had been interested in many things, Aparna had never wanted to write. This situation changed suddenly last year when she picked up a little notebook and wrote a story about the math-challenged dad. The story is reproduced below with Aparna's permission. (Please note that the story has been reproduced exactly, alternate spellings and all.)

So ultimately, what had started as a math activity, ended up becoming an exploration of the writing process.

- Dev

How many autos? (A story by Aparna Jain)

One [day] the father went to a big big parck. With his family. On the way thay had to take 3 buses 2 autos. Instead of sitting he started to count the autos. After they were ther they let the kids go to the playgrond and ther was a session you can make somthing and go sell it so they went ther. The kid's friends had com so the kids played. whith ther friends. This session was about organic food. When it was lunch time ther was organic food so they ate whith everyone. When they went back home the kids asked ther dad what did you count anything today.

Oh! When we wher going ther in the bus I counted the autos weels, 96. How many autos?  Now readers figure out the answer.

Note to non-Indian readers: The "auto" referred to here is a three-wheeled taxi common in India.

My Head On Your Shoulder

Recently, I got on an early morning train at the Chennai Central. Still sleepy, I located my seat and dozed off even before the train had started. But it was not long before my sleep was interrupted by a tap on my shoulder. It was the girl sitting next to me. I heard her ask: “Can I rest my head on your shoulder?”

I was in a second class coach, where the seats accommodate three people comfortably but with no arm-rests in between. She was a young girl, probably half my age, and I could tell she had just got married, bedecked as she was in a silk saree, jasmine flowers, jewelry and mehndi . Her equally young and new husband was sitting on her other side. They seemed like the people of a small town or a village. In such places, it is not unusual for new couples to not interact with each other.

I said yes to the girl’s request. She promptly tilted her head on my shoulder and we both dozed off. After some time I heard a distant voice talking to that girl. Her parents who were sitting nearby must have gotten slightly concerned. They woke her (and me too in the process); she said sleepily, pointing at me “I had asked her”. That was enough explanation, met by accepting head waggles, and everyone went back to sleep again.

It was not until later, when I got off the train, did this event strike me as unusual. This girl’s simple human request illustrated for me a profound difference between the cultures of big cities and villages. She had a straightforward need that I could satisfy, and so she asked. Simply, just like that. No mental clutter of judgments and inhibitions of “appropriate” behavior of “cultured” city folks. Because of this encounter, will I be a little less inhibited when I am presented with similar opportunities of human interaction? I hope so.

-- Hema

This Afternoon On Climate Change

Today was an especially hot summer day (42 deg C/108 deg F) here in Chennai. I stepped out when the Sun was at its peak to buy Nongu (palm’s fruit) from the vendor in the street corner. The soft, squishy pulp of this fruit comes with just a spoonful of sweet water that makes it absolutely delicious on such hot days.  I parked my bicycle next to the vendor and admired how oblivious he was of the heat that was engulfing him. He had no walls, no awning, no chair. Nothing seemed to deter the speed at which he was chiseling the fruit from its shell.

I saw a car pull in and a guy, in his late 20’s, stepped out to buy from the same vendor. I noticed that I was bothered by the fact that this guy didn’t turn off the engine. I knew that the wait could be several minutes long, both for him and me. I considered many options of how to respond to this situation and before long I blurted out to the stranger, thankfully politely, “Hi! Can you please turn off your car?” In utter disbelief the guy peered into his car and replied, “But there are people inside the car!” I wanted to say that they won’t melt in the next few minutes, but held my cynicism back and tried my best matter-of-fact tone to say, “That is okay just for a few minutes, right? Your car is constantly spewing heat and heating an already-very-hot afternoon.”  I realized that I won’t be able to continue the conversation without emotions playing in, and so decided to stay quiet. The vendor was unaware of the drama unfolding in front of him, since we were talking in English. I deliberately chose English over Tamil since, unfortunately, the former commands more attention and respect in the Tamil-speaking land.

Did I cross the social limits? My heart was racing. I wanted to rush back home, Nongu or not. A minute later, I saw the guy on the other side walk toward his car, open the door and turn off the ignition! What did he just do? I felt relieved, surprised and grateful. I started the conversation again – “Thank you! You are unique in the way you responded. I am really sorry if I had hurt your feelings earlier.” He smiled. I went on, after raking my brain a little – “You probably have heard about global warming. I work on climate change and so things like this bother me. I am deeply concerned about the state of the Planet that our next generations will inhabit.” 

Now, do I really “work on” climate change? Maybe so, maybe no! I live every wakeful hour thinking about global warming and planning my every step carefully to mitigate the effects of my actions on this Planet. So, I do work on climate change. But I don’t get paid to do any of this. So, maybe I don’t work on climate change!

He introduced himself as Karthik and got interested in the topic since I am a researcher, according to him. He said that he normally rides his bicycle to work and that he has heard about carpool being implemented in other metropolitan cities in India. I guess he was trying to tell me that he is a conscious consumer.

Now, how inconsequential is my action? There are approximately 5000 new cars hitting the roads of India, every single day. So, if I were to think that I have made a little difference by talking about idling to one Karthik, I would simply be flattering myself. But yet, inaction is not my choice; I will continue to act but not hope. Humility is born from the awareness that one is insignificant in front of the colossal dimension of global warming.

-- Hema

Is “CAT” not “DUCK”?

Abhi being my first child, I was quite ambitious about teaching him. I liked the idea of how English was being taught using Phonics. Since I didn’t learn English that way, I was quite interested in this new method. I watched a children’s video of LeapFrog on Phonics and liked it immediately. Abhi and I watched the video together a few times and before long he had all the sounds right. Armed with this new skill, I was all set to teach Abhi to read/write English. He was less than three then. This is how our conversation went:

Me: “hey Abhi! Do you want to learn to spell words in English?”

He: (probably didn’t understand what I was talking about) “okay!”

Me: “Now, what sound does the letter C make?”

He: “\k\”

Me: “And the letter A?”

He: “\a\”

Me: “And the letter T?”

He: “\t\”

Me: “Now we have three sounds – \k\, \a\, \t\. Can you put them together?”

He: (draws a blank)

Me: “Can you repeat the three sounds in quick succession – \k\, \a\, \t\and again \k\, \a\, \t\?”

He: (faithfully follows my instruction)

Me: “okay, do you recognize the word that you are trying to say?”

He: (no answer)

Me: “I can join you in repeating these sounds and this time we will say these three sounds, one after the other, a little bit faster than before”.

He: (is lost. In my eagerness to teach him, I fail to read his cues)

Me: “Now do you know the word that we are trying to say? I will give you a hint. It is a small animal that we see around often.”

He: (relieved that he has found the answer that would please me, his face glows) “I know! It is DUCK!”

I was totally flabbergasted. It took me a few seconds to hug him and laugh with him. This was a moment of revelation for me. I realized a lot of things that have helped me and guided me since then:

- learning is not necessarily linear -- just because he learned the individual sounds, it didn’t mean that he could put those sounds together

- learning without an appropriate context is meaningless

- trusting the child’s instinct and enjoying child-initiated learning, whenever it happens

Luckily, for him and also for me, I stopped “teaching” him after this episode. The insight that I gained helped Aparna too (In which I realized that it is not necessary to “teach” reading).

-- Hema

An outlier on the train

I was on a totally packed train from Chennai to Bangalore. I lacked a reserved seat and was forced to travel standing. Tired of standing for a while, I was relieved to find a teeny bit of space that I could squeeze into. The guy next to me very generously gave up his seat and asked me to sit comfortably. I thanked him and pulled out a copy of “The Continuum Concept” from my bag and started reading.

To kill time people usually get chatty on long-distance trains and if they read at all it is either a cheap magazine or the daily but not much else. Since I was reading a book, my co-travelers thought that I was going to college. The woman in front asked me which college I went to. I said I was done with college a long time ago. My slightly-puzzled neighbor asked me where I would be getting off and if I was working in that town. She was surprised to hear that I was not working and that I was a stay-at-home mom with two kids. I was wearing no special marks that would readily identify me as a married woman. Nor do I wear much jewelry. 

I could see that I had much confused my fellow passengers. By this time two men in the same seating area couldn’t contain their curiosity either. Now three, the questioners started firing questions that would be considered personal in any western country: “You don’t look married! Why don’t you wear the marks and accessories that we women do?”, “We thought you were hardly eighteen!”, “Which caste do you belong to?”, “Are you a Christian?”, “Are your folks okay with your ideas?”

After my sojourn in the US, sometimes I have to remind myself that in India there is nothing personal about these questions. In fact I liked that these questions were genuine and that my co-travelers were not hiding what they thought about me. I went on to answer each one of their questions. A few minutes later, I heard them talk among themselves, and not so discreetly either. I am pretty sure that I heard the woman say, “I don’t know what to make of people these days”. Obviously, the whole experience was unsettling for all of them. They started looking at me as if I was an animal in a zoo. To avoid their gaze I started reading my book again.

This conversation had somehow made me a part of this very temporary community. During my trip to the toilet my questioners helped me hold on to my seat and made sure I got ready on time to get off at my destination.

-- Hema

Questions that led to further questioning

Abhinav was seven and was going to a Charter School in Northern California. I loved everything about his school – small-sized class, a lot of parent volunteers, very progressive etc. But he didn’t think so.  He was visibly upset when it was time to go to school.  We tried to keep the transitions from bed to school as smooth as we could, but the effect of going out to school every day was disastrous on him. Once every few days he asked me questions that I didn’t have answers to and questions I didn’t want to think about in my life. I don’t remember all of his questions, but some of them I do and here they are:

Abhi: “amma,  you have told me earlier that one goes to school to learn many things. Is there anything that can be learned only at school?”

Me: “Well, learning is just one aspect. Apart from that, at school you get to see your friends and play with them”

Abhi: “amma, I can’t play with my friends when *I* want to. I can play with them only when the teacher lets us play and she decides how long we can play”

***

Abhi: “amma, Did you know that the bell rings very often at school? Sometimes I can't wait for the bell to ring, because I just don't like what I have been asked to do. At other times, I really wished the bell didn't ring because I was thoroughly enjoying what I was doing. Why should we stop doing what we are doing when the bell rings? ”

***

Abhi: “Do you have any plans for this weekend?”

Me: “Not yet”

Abhi: “Please don’t make any plans. I don’t want to go anywhere – no parties, no outing, no swimming. I want to stay at home”

Me: “okay. But why so?”

Abhi: “amma, I go out to school every day, so I don’t get to spend time at home. I want to spend all my weekends at home.”

Me: “okay, done!”

Abhi: (now he is sad)”amma, our home is the best place on earth. I love being at home, with you and Aparna. Why should I leave my favorite place and go out to school every single day? When I come back home in the afternoons, I am quite tired and I can’t enjoy our home. Why do you send me out, amma?”

Abhi's questions started haunting me and I decided to find genuine answers. Little did I know, when I started my journey, that it will change the course of our lives forever.

-- Hema