It is one thing to theorize about multiple voices or understand it intellectually… but it is quite another to be living with and listening to the real voices around us that come from so many different continents and cultures. Take for example the Israeli-Palestinian conflict… That’s a big one, isn’t it… And sensitive and controversial and complicated… But as you listen to the multiple voices, you realize – and not just intellectually – that each side has a story to tell and that each story can be opposing and yet equally valid. And once you strip away the layers of conditioning or go beyond the distraction of propaganda, you realize acutely that the Israeli and the Palestinian mothers have the same fears and the same dreams… Dreams and fears, that’s no different from mine in India or yours in Indiana, by the way.
And so as you listen closely to the multiple voices, you also realize the double edged sword that history can become… Yes the causes lie in history, but we also need to move beyond that, move forward into a shared “her-story,” where we can come together in a shared compassionate understanding…
And that’s where Fulbright comes in: there were 21 teachers from ten different countries who participated in this year’s Fulbright DAT program. For me, it thus became a metaphorical journey to multiple continents over the last few months! As I tasted the empanadas and was greeted with a warm Kia Ora I started questioning my own presuppositions, my quick assumptions about a person or a place that was a result of my conditioning and education – by that I mean my intellectual understanding. So what Fulbright did for me was twofold (actually manifold but how can I ever capture all of them in words?) – it provided me the opportunity to enhance my intellectual understanding as a teacher of mathematics as well as provided me the freedom to move beyond mere intellectual understanding as a person and to even question those understandings.
As many differences that I can find between myself and the other Fulbright scholars, I find so many more commonalities… Try to list the differences – they are rather obvious and quite superficial, aren’t they? But once you look at what is not visible, then you see the same love for our sons, the same pain and joy of having to raise them as a single parent. You laugh on knowing there’s another clumsy cook out there who needs to know exactly how much salt to put into the pot and can’t estimate, just like me! You share a common love for word games with someone who lives in that part of the world where you wonder how they don’t fall off the Earth! And as they show you a map of the upside down world, you wonder if that is really what the world looks like?
What the world looks like depends on where we are looking from. In other words, on our perspective. Perspective seems to be an underlying theme in many of my reflections. And my peers in the Fulbright cohort provided me a wealth of perspectives: on teaching, learning, loving, sharing, politics, education – in short, on life itself.
Now I am back in Bangalore. CIEDR, IIE, IU, USIEF… so many people and organizations to thank for these magical months. Months where we got to listen to one another, person to person… Sarah from New Zealand concluded her presentation with a Maori proverb: He aha te mea nui o te ao? He tangata, he tangata, he tangata. (What is the most important thing in the world? It is the people, it is the people, it is the people). Thanks to the Fulbright commission, most of all, for making this people to people connection possible. And thanks also to all the American Fulbright teachers, who made this journey all the more special, even extraordinary.
Now this incredible journey of four months has come to an end, but the learnings will stay with me…
Last month I had written about mathematics in ‘unexpected’ places; and it can sometimes be quite as interesting to discover mathematics in expected places, but in unusual or unexpected forms!
Take books for example – you would expect to find a lot of math books and books on math. But to learn about math through the world of an animated sitcom? Yes, indeed and from the few pages that I scanned, Simon Singh’s The Simpsons and Their Mathematical Secrets looks like an interesting read. Two other books that caught my eye recently: Alex Bellos’ Snowflake Seashell Star, and Eric Broug’s Islamic Geometric Patterns. While there are numerous books on mathematics and art, these two books stand out from others. Not only does Broug introduce us to Islamic Geometry and tessellations, he shows us how to create intricate patterns with the help of a ruler and compass with the help of step-by-step instructions. And Bellos takes us on a “Colouring Adventure in Numberland”, through designs you can colour as well as create following simple and complex number patterns. Gems to add to my treasure chest!
You would also expect to find mathematics in schools, particularly in the math classroom of course, but what kind of mathematics would you expect? Here’s what I found:
Geometry in the gym, wise words on a t-shirt, a cartoon on the door…
Fibonacci spiral on a table, and a pentagon yurt floor!
Need I say more?
I’m letting go of all I fear,
Like autumn leaves of earth and air.
For summer came and summer went,
As holy as a day is spent.
I had to let go of so many things I feared, some that I did not even know that I feared. The summer that I was preparing for the Fulbright program was an anxious sleepless summer. Logistics – passport and visa, emotions – for the family I was leaving behind, work – my teaching duties continued right up to one week before leaving, that left me feeling overwhelmed, fears – unnamed, unidentified, of going back to a land where I had loved and lost much…
Fall came. I had a new home away from home. I had the luxury of time and space to explore new possibilities, push boundaries, refresh myself. I made new friends. New relationships, precious friendships. Worked and played with equal abandon as the weeks flew by. And also rediscovered how ‘at home’ I felt in any classroom, with children around me.
Winter is coming. It is almost time to go home. Attended the ‘cultural re-entry workshop’ where I realized that the home I thought I was going back to might not be there waiting for me. I have changed. The people I left back at home have also changed. And so it might be a new ‘home’ I will be going back to, that will become my home over time.
Wondering what made me carry this particular frame with Rumi’s words from my home in India?
Many a holy day was spent in this beautiful land, now it is almost time to take me home…
It is a sunlit winter morning outside, so unlike the overcast grays of yesterday. Yet I find no joy as the world seems to have been plunged into a darkness of our own making… after Brexit, there’s Trump. I sit here numbed and sad…
Last week I had been in Philly, laughing and joking about the elections. Yet overnight, the jokes have turned into a nightmarish reality. I can’t help but remember the faces of the little children in Philly’s schools who asked me if they could move to India should Trump win. I remember the faces of the teachers in Indy who shared how much their students feared the ugly electoral rhetoric and its possible future consequences for them.
Them being all others – the multiplicity of Others to the traditional American Identity of a privileged white heterosexual male – the women, the Blacks, the Hispanics, the Native Americans, the immigrants…. I wonder how many are left at the end of it?
My previous visit to the US had taken me to the deep South during Bush’s terms and the Iraq War; that was also when I learnt in depth about the racial history of America. Given all that, I had not been particularly keen to revisit the country. Yet this time, being in Washington and Bloomington and Philadelphia, meeting so many educators and visiting several schools showed me an entirely different perspective and gave me hope. I saw such thoughtful focus on equity and diversity in the schools, I saw children who were so much more aware of the world and schools that focused on relationships. And I thought that this is what makes America great. That underneath it all, is a real desire to understand one another, to question our assumptions, to work together to make the world a better place.
And now Trump. I can feel the sadness of my American teacher friends through their posts on Facebook. I find shock and disbelief from my fellow international Fulbrighters. I read article after article where people are being rudely woken up to a world that they didn’t think existed but that is now so real. Is it the end of sanity?
And teachers are asking, “What do we Tell the Children?” (http://www.huffingtonpost.com/entry/what-should-we-tell-the-children_us_5822aa90e4b0334571e0a30b ) Reading it, I feel a glimmer of hope… or am I clutching at straws? Will the sane compassionate voices be heard in the coming days, or will hatred and bigotry overcome all the good work? How do we meet hatred? Do we wait for a Gandhi or a Malcolm X? Or do we wake up and realize that the world is not quite what we want it to be, but that we can all stand up and work hard, much harder than we have ever done, to keep the world sane?
There is a cardinal outside my window. Trees in the background matching its colours. The sun is still shining. A beautiful day.
We usually meet people and places with certain expectations in mind – for example, when visiting an art fair, one expects to find creative expressions captured on different media, and does not usually expect to find science or math in such places.
So there I was, exploring the different stalls put up by various artists at the 4th Street Art Festival, each one a feast for the eyes, when a dazzling display of pure geometry caught my eye:
Lines, shapes, angles, and light – what beauty! And here was another stall, which had kaleidoscopes in fantastic forms. Look through one, and you would be transported to the wonderland of shifting patterns, and could lose yourself forever in that maze:
Next stop: The Lilly Library, which houses several rare and ancient manuscripts and special collections. The description of the place did not prepare me to find some math related gems inside, including mathematical puzzles and a page of Abraham Lincoln’s math homework!
Third stop: Ceramics studio of a professor of chemistry, Dr. Trevor Douglas. You would expect art and science, but math beyond kiln temperatures? I was pleasantly surprised to discover some fascinating mathematics, and learnt about viruses along the way…how there’s a ‘defect’ in the molecular structure of the HIV virus that comes from irregular asymmetrical tessellating structure, how a flat or two-dimensional tessellation can become a closed solid or a three-dimensional object when a kink is introduced into the regular tessellations.
Of course, “the first thing to understand is that mathematics is an art.” Having read these words of Paul Lockhart (A Mathematician’s Lament) several years back, and having a passionate love for mathematics, I do know that there are no ‘unexpected’ places when it comes to mathematics. It is there all around us, from the quotidian tessellations of kitchen tiles to the sublime beauty of a Fibonacci spiral or the fractal of a fern. Mathematics, as Lockhart says, is dreamy and poetic, radical and subversive, psychedelic even. As math teachers, can we move beyond the recognizable procedural arithmetic of Lincoln’s time to such subversive, psychedelic math?
As I sit at my desk trying to work on my inquiry project, my eyes stray to the little pine cone and a piece of tree bark I had picked up on a couple of my walks. And I remember the other things not on my desk, but seen, felt, heard, or touched and how happy they all make me feel…
The leaves swirling around in a gentle breeze, some velvety, some glossy, in all possible fall colours….
A tiny little acorn, and with it, the memory of those red brown squirrels who love nibbling on them…
The pine needles brushing against my palm when the day is so glorious you just have to reach out and touch it in some way…
The groundhog who welcomes me back to my home away from home by running into the hedge as soon as he (or is it a she?) feels my footsteps on the path…
The leafless tree, stark against other leaves, whose branches remind me of the deer that had unexpectedly leaped across that very space on another evening…
A swirling mass of clouds set aflame by the setting sun…
And with these images swirling in my mind, some songs start swirling around too…
Philosopher and poet RabindranathTagore’s Akash amay bhorlo aloye, akash ami bhorbo gaane… (the sky has filled me with light, I will fill it up with songs)
Singer, song writer, poet Carrie Newcomer seems to echo the same emotions as I remember her luminous songs in the beautiful not yet… And I believe, borrowing her words,
That what I do not know,
Or might not see coming,
Could leap out in unexpected glory,
At any given moment.
Sometime in the third or fourth grade, in our Geography class, we learnt about tundra and taiga, ‘Eskimos’ and kayaks…and given that I learnt it from a conventional textbook in India several years back, I only had a mental image of what a kayak looks like – based on the description given in the book. That geography lesson was soon forgotten, and kayaks and canoes became interchangeable terms for me to describe something narrow that floats on water!
Far removed from lakes and without a personal context for canoes and kayaks, little did I imagine that sometime in the future I would be paddling in a canoe as well as in a kayak! I now realize the difference between the two; I have also discovered that in the UK, the term canoe refers to a kayak, and having inherited the colonial educational system, that might explain why I would confuse one term for another.
For the uninitiated – like I was until a few days back – here are the major similarities and differences between canoes and kayaks. Both are human propelled narrow lightweight boats. You paddle using a paddle rather than row using an oar. The canoe has an open hull, the person paddling usually sits above the waterline on a raised seat and uses a single bladed paddle while a kayak has a closed hull, the paddler uses a double bladed paddle and sits inside the cockpit with legs stretched out in front, at the level of the water line.
[Two people in a kayak in Alaska, photographed by Curtis in 1930] [Wood and canvas canoe built by Morris company in 1912]
I was invited to a picnic by the lake and also to go canoeing with my friends a few days back. Not being a swimmer, I entered the canoe with much trepidation, bolstered somewhat by a life jacket and two fellow paddlers, one of them quite experienced. Griffy lake also looked promisingly shallow and full of aquatic plants, as if they would hold out a net for me should I topple into the water. Sitting in the middle, my main role was that of a photographer rather than a paddler. After an hour of canoeing, we returned safely to shore.
Having successfully weathered my canoeing experience, I said a confident ‘yes’ to kayaking a few days later, little knowing what was in store for me! Finally, the day arrived – a glorious fall day with no wind. And I came face to face with a kayak – where I had to paddle on my own and sit almost at (what seemed to me standing up) eye level with the water! Somehow, the beauty of Lake Monroe and a trust in my mentor made me sit inside the kayak and float off with the paddle, pushing aside all my various fears.
It turned out to be an incredibly beautiful, peaceful and memorable experience… We saw egrets, a kingfisher, some herons and even bald eagles. We spent hours on the lake – paddling, drifting, lazing, gazing, enjoying the quietude. A dragonfly came and settled on my knee. The water skaters created intricate patterns on the water’s surface. The heron tucked in its long legs and flew off from the shore, the eagle spread its wings and glided from the tree top – both so silently and gracefully…
As I sat down to write all this down, I discovered so many things I had not known an hour back. How there are Greenlanders, Inuits and Native Alaskans, rather than the blanket term ‘Eskimos’. That the word Eskimo might have originated from the French word esquimaux which refers to someone who nets shoes (http://www.npr.org/sections/goatsandsoda/2016/04/24/475129558/why-you-probably-shouldnt-say-eskimo ). That the word canoe has a Caribbean etymology (kenu = dugout) while kayak comes from Native Canadian and Native Alaskan origins (Yup’ik qayaq from qai = surface). That historically, their precise make was determined by local availability of raw materials – trees in one place and whalebone with sealskin in another. That the somewhat similar but slightly larger dinghy that I had been on last October in the mangrove forests of India (Sunderbans – West Bengal) comes from the Bengali word ‘dingi’… That the shape of these boats determine speed and maneuverability, and I found first hand that the angle of the paddle determines direction…
How much my geography lesson (as well as Swami’s, in Malgudi Days) would have come alive if it had been connected to history and language and science and math… Real life is not compartmentalized into different subjects, yet why do we persist in having different subjects in schools?
We became tourists in the Windy City for the weekend, and I’m back in Bloomington with a bag full of memories and mementos of Chicago. This city offers the unsuspecting tourist quite a few unexpected perspectives as I discovered.
The first unique angle was to look at the city from below the street level, as we passed beneath some of the major ones of downtown Chicago while on the architectural river cruise. I saw the underside of numerous cars, without having to squeeze myself under any chassis! Though I never did get to photograph their silhouettes as they whizzed by overhead, try as I might. Side note: The Museum of Science and Industry also provides a view of the underside of a car while you can remain vertical.
Sitting on top of the hop-on-hop-off bus gives you an entirely different perspective of the city. The languid pace of the ferry is replaced by the familiar bustle of a metropolis, waving couples from the overhead bascule bridges are replaced by blinking traffic signals. Skyscrapers that look like dormant behemoths from the river side transform into busy hives of activity. Side note: The view can get blurry if you get caught in a shower on the roof less top of the bus, and blurrier still if you wear the plastic rain poncho that comes free with the ride.
If you’re in the mood for a giddy perspective, head to the Navy Pier and ride on the giant Ferris wheel there. One can take in the breathtaking expanse of Lake Michigan, the jagged Chicago sky line and the charm of the pier itself in one enormous stomach lurching sweep. Side note: Imagine the view that the seagulls have!
But what really tops the list and flips your stomach is the infamous ‘Tilt’… where you are almost suspended above one of the tallest buildings in the world. You are tilting over and away from the side of the skyscraper and hanging on to the steel bars next to you for dear life! You know there is a layer of glass keeping you from the tug of gravity but it is scary nevertheless. Side note: Would I dare to be a skydiver?
Finally, there is the hidden perspective… the unseen side of this city… These are the invisible but indispensable alleyways behind the buildings that house the not-so-decorous dumpsters that hold the various excesses of city life. I am told that the alleys also have the cables and pipes and other such things that people don’t want to look at. End note: I wonder what else gets pushed to the alleys and corners that we don’t want to look at or be reminded of in every city? I am reminded of Slavoj Zizek’s idea of ‘the obscene underside’ … Is the hidden the obscure or obscene, the invisibilized or the marginalized? The other side of every city, away from the glitz and the glamour of the neon lights, the dark side that we don’t see or don’t want to see…? But enough, let my frame remain the simple spatial perspective…
I have been learning a lot about the American school system lately – reading about them, visiting several schools. And naturally, what I see and hear is based so much on my own reality back home. I am trying to be alert to this and separate my observations from my interpretations. I shall talk about my experiences in the US schools in another post, let me share some glimpses from my own school here…
For the last few years, I have been living and working in a small school on a large forested campus in the south of India. Children learn in mixed age groups without any textbooks or tests in the junior and middle sections, while senior schoolers prepare for the national exams and participate in a wide variety of other activities. Our founding day is celebrated with a ceremonial tree planting event every year. A typical day begins with an assembly where everyone gathers to sing, chant, watch a presentation, or just be silent as we listen to the other inhabitants we share the space with…
Now when I read about constructivism or project based learning or the critical stance, I see reflected in them some of the things we do in our school back in India; and when I visit the different ‘buildings’ here – as school is referred to in the US – with their gleaming corridors and spotless tidy classrooms, I begin to miss my school quite a bit!
So yes, my school is messy, but in so many nice ways. Once, Sports Day got disrupted by heavy showers and everyone remained on the field – students, teachers, parents and even the principal – without any dampening of the spirit! Soon our clothes were equally wet and muddy and all those distinctions disappeared. And sometimes first graders have the privilege of ending their school day with a lot of splashing and playing under the water hoses kept for gardening, without having to wait for the rains!
Some other ways of getting wet and messy in our school:
- falling into the pond trying to spot that particular pebble your friend is showing you
- getting really involved in the pottery or land care class
- making mud cakes during free play
- running from one classroom to the next when it is the rainy season (there are very few corridors in our school)
I am left pondering these … On the one hand, this is what the dictionary says about mess: 1. Cluttered, untidy place 2. Confusing or difficult situation; Synonym: disorder. On the other hand, the American creativity guru Roger von Oech says, “The most beautiful order is a heap of sweepings piled up at random”. Which one do we believe? Or is there a middle way, a harmonious balance of the opposites without embracing the extremes?