Category: February 2016

Leading their own learning

Aditi Mathur and Ratnesh Mathur

How can schools create an environment where children lead their own learning? Here are eight steps that teachers can adapt in their own spaces to create learning leaders.

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The backstory of balancing equations

Yasmin Jayathirtha

Teachers find that they struggle to teach balancing equations to children with the result that students find chemistry classes very difficult to follow. So, how can the concepts be made clear first before the equations are understood?

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The Parikrma magic

Arun Elassery

Parikrma is a successful experiment in school education. The Parikrma group of schools are located in poor neighbourhoods and serve children from the slums of Bangalore. The facilities available to the children make them good at sports and academics.

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Colour me red

Richa Gupta
How can colour be harnessed to improve learning? Here are a few tips on adding colour to your classroom environment to up the learning quotient.

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Taking the challenge

Vijay A. Singh
Competitive events related to academics such as the Olympiads in math and science celebrate the best young minds in high school. They are an excellent educational resource and need to be used wisely. School managements and teachers must realise that they offer a glorious opportunity for students to be exposed to the beauty that lies in the subjects especially mathematics. Our Cover theme gives an overview of the Olympiads and how teachers can nurture their students to participate in these events.

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A platform for problem-solving

Shailesh Shirali Mathematical Olympiads have been taking place in the country for some decades now, and it is relevant to examine the significance they hold for the country in a wider sense. Mathematical Olympiads originated in the east European countries. In 1894, a competition known as the Eötvös began in Hungary; it quickly became prestigious; many famous mathematicians have in one way or the other been associated with it. Russia, Romania, and Bulgaria soon started similar events of their own. A particularly notable event is the town-based Tournament of the Towns; it originated in Russia and continues to be held in parts of the world, in modified forms. The event known as the International Mathematical Olympiad (IMO) started in 1959 in Romania. For two decades, participation was limited to the Eastern Bloc countries, but from the mid-1970s, increasingly many countries started to take part, and the latest count stands at over 100. The distinguishing feature of these events is the quality of the problems posed in the examination. They are original, in the sense that they are not simply known results expressed in a different way. To solve them, one typically requires original and critical thinking of a high order. The time given to solve the paper is indicative of this: in the IMO, six questions are given for solution over two sessions: one session per day, 4.5 hours per session! Some IMO questions have gone on to become classics in the field, offering starting points for collaborative research and intense creative inquiry. I can testify to this from my own personal experience. In India, the mathematical Olympiads are organized by the National Board for Higher Mathematics. The national level event is the Indian National Mathematics Olympiad (INMO); it has been held every year since 1989. It is preceded by various local Olympiads (the Regional Mathematical Olympiads, held in individual states) in a pyramidal structure. Students who qualify for the INMO are invited for an IMO training camp held every year in May-June at the Homi Bhabha Centre for Science Education in Mumbai, and at the end of this camp, a six-member team is selected to represent India in the IMO, which is held in July in different countries. The event was last hosted by India in 1996. In 2015, the event was hosted by Thailand. Among the many charming traditions of the IMO is the procedure for the selection of the contest problems: problems are invited from the participating countries themselves, and from the

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A fateful day and an odd proof

Swati Sircar It all began on a historic day for India – Dec 6, 1992. For the country it was the demolition of Babri Masjid; for me, it was the first time that I set foot into the Indian Statistical Institute campus. It was the Regional Mathematics Olympiad (RMO). I made it to the INMO training camps twice – in 1993 and in 1994 – but didn’t make it to the team. But it paved the way for me to be immersed in math henceforth in life. More on that later. The credit goes to my mom, who spotted a tiny announcement, inconspicuous in an inside page of a Bengali daily. She wanted me to appear for the Olympiad; we managed to overcome various odds including a missed deadline and I finally appeared for the RMO on that fateful day. There were nine questions and three to four hours of time. I think I solved three or four of them. These questions were quite different from what I have seen elsewhere – textbooks, board exam or even other talent exams and quizzes. After a few months I got selected for the Indian National Mathematics Olympiad (INMO). Around 30 students were selected from West Bengal for this second round. Each state had its own quota. INMO had nine questions again and the time was about four hours. I don’t remember how many I answered but definitely not more than four or five. The last question was particularly interesting: Show that there exists a convex hexagon in the plane such that (a) all its interior angles are equal, (b) all its sides are 1, 2, 3, 4, 5, 6 are in some order. Growing up with Chinese checkers, I had the triangular grid in front of me. Intuitively I knew that 2, 6, 1, 5 will be the order for four sides. But I was not sure of 3 and 4. So, I essentially used a few pages to draw regular hexagons of side 6 and then slice them off. After a few trials, I had the desired polygon right there! But then I was utterly confused. I had not written a single word. Does this constitute an answer? Being a student of West Bengal State board, I couldn’t risk leaving it so wordless. So I made some observations and jotted them down. After a few months, I got selected for the Training Camp (IMOTC) at the Bhabha Atomic Research Center (BARC). Incidentally, this was just after

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An evolving culture

Pooja Sudhir The diplomatic sail of Model United Nations (MUN) conferences in schools began in the 1920s and reached India in 1996 when The Cathedral and John Connon School organized their very own MUN in Mumbai. Since then this stimulating debating adventure has flagged prestigious platforms. With a participation strength of 3000 students, Indian International Model United Nations (IIMUN) is Asia’s largest MUN conference and will host its 2016 chapter at New York, the location for the United Nations headquarters. Harvard Model United Nations – India (HMUN) that organized its first Model League of Nations in 1927 and its first Model United Nations in 1953 showcased its Indian dais in 2011. Besides the forerunners, many schools of repute in the country are also converting their enterprising young leaders into in-house MUN chairs and organizers. Trends and statistics beckon compelling questions – What is this maze called MUN? What are the rewards for its myriad mazerunners? Part of the UN educational initiative called Global Classrooms aimed at bridging the gap between classroom learning and real life global-political issues, Model United Nations is an authentic simulation of various UN committees wherein students role play as delegates from different countries and debate over specific and current political conflict or humanitarian issues, to eventually arrive at and pass concrete draft resolutions. For example, one of the committees at CMUN 2015 was the Social, Cultural and Humanitarian Committee (SOCHUM), which debated on the selected agenda of Corporate Human Rights Agendas in order to uphold the UN Guiding Principles on Business and Human Rights approved in 2011. To accelerate the dynamism of the committees, the Chairs plan specific crisis – breaking news about the death of migrant Sri Lankan workers in a factory explosion in Belgium would be an example – and thereby compel the participating delegates to think on their feet for news analysis and configure possible solutions. From research about country’s demographics and foreign currencies to MUN procedures, from strategies for alliance formation to structuring position papers and draft resolutions… one can never be too prepared for a MUN. Schools have not only recognized this need but are also creating a sub-culture of debating and MUNing through on-campus MUN Clubs and exclusive training sessions. Ms. Michelle Rego, Facilitator, History and Global Perspectives, Aditya Birla World Academy (ABWA), Mumbai informs, “When we first started, it was the teachers who would provide the training. Now I am proud to say that every year, I have my Senior MUN club students who

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MUNning and other dress-up games

Achala Upendran A friend of mine was in town recently, and among the topics that came up in our profound discussions was that of the Model United Nations conventions. This wasn’t strange, given that much of our early interaction came about as a result of various (make that two) MUNs. He has a lot more experience in this field than I do, and hence was able to contribute more worthy points to the discussion. All I did was to start the ball rolling with a casual ‘So how helpful do you think MUNning has been/will be for your career?’ (In the course of this article I will refer to the act of participating in a Model UN convention, at a college or school level, as MUNning. Also, I should probably mention that the friend in question is currently doing a degree in Global Affairs, and recently did a three-month internship at the UN in New York.) He thought for a bit, and said that there was no ‘direct’ and easily ascertainable benefit to his professional life. However, the practice of research he’d developed, the ability to read and retain information from newspapers and online archives – that was beyond priceless for a budding wannabe diplomat. What MUNning had cultivated in him, he said, was the ability to care about people in other countries, to feel responsible for one’s own decisions and the impact his interaction with his fellow ‘delegates’ had on countless lives. ‘I loved the feeling of representing someone’ he said, ‘and feeling responsible for so many people’. That experience, as staged as it might have been, has definitely had some kind of weight on his decision to work not just ‘in’ his country, but ‘for’ it. After that, the conversation veered off this earnest course, chiefly because I couldn’t keep a straight face at what I thought was a pompous declaration. He was already, I thought, beginning to sound the part of a high-profile UN employee, a la Shashi Tharoor. Wording quibbles aside, I do not doubt the sincerity of my friend’s statement. I haven’t been a part of many MUNs myself (as a delegate), but I have seen plenty of MUNners. For most, the four-day convention seems a fun excuse to dress up in their corporate, campus-placement best, spend a few hours speaking about themselves in third person and then, of course, have the fun backslapping and catching-up session after committees and councils disperse for the day. Many of those who do

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A preparation toolkit

Ramya Ramalingam The mathematical Olympiads aim to test the problem solving ability and ingenuity of students at the high school level (9th to 12th standard). The topics relevant to Olympiads include geometry (including some trigonometry), algebra (including inequalities), combinatorics, and number theory but knowledge of calculus or other higher mathematics is not required. The relevant topics are generally taught in high school. However, most of these topics require a more in-depth understanding than the one fostered at school (in my experience, combinatorics is touched very briefly and number theory is not part of the syllabus at all in India). So a secure, grounded, well-founded knowledge of these topics is an essential pre-requisite for anyone who wants to do well in the Olympiads. I have found that solving problems of the appropriate level is the best way to prepare for any math competition, and this is more so for the Olympiads than for anything else. Solving previous year question papers and problems of similar nature and difficulty is essential and allows you to get a sense of the type of questions asked and how to approach them. However, it is sometimes difficult to find problems of the right level of difficulty (for a given student) and even harder to find their solutions. The following is a list of books that I found useful in my endeavour to prepare for the Olympiads: Level 0 (Elementary) These books can be used by middle school students (4th to 8th grade) to get a jump start on the topics that are building blocks to problem solving techniques. They are, however, not sufficient for high school Olympiads. E-Z Algebra and EZ – Trigonometry by Douglas Downing published by Barrons (The E-Z series) is a set of self-study books that follow an interesting story-line to pique interest in children. Each book starts off with a few trivial chapters but goes on to discuss higher topics that may not even be covered in high school. Each chapter is followed by a problem set, for which the answers (without solutions) are presented at the back. Pre-algebra by Richard Rusczyk, David Patrick, Ravi Boppana (published by Art of Problem Solving) covers all major topics preceding algebra. Competition Math for Middle School by Jason Batterson (published by Art of Problem Solving) has a multitude of extremely well explained examples and challenging problems at the middle school level. Level 1 (Beginners) These books delve into topics that are essential for Olympiads. All of the Art of Problem

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