Themes in Mathematics

Leonhard Euler came to Purulia this Winter!

Cheenta is transforming Mathematics Education in rural Bengal. Learn how a few kids in the remote town of Anara, are experiencing world class mathematics!

Leonard Euler came to Purulia this winter! And he was mildly surprised to find Sukdev from the town of Anara. This is the story of an experiment in mathematics education in rural Bengal; an experiment that hopes to transform mathematics education in India for good.

Forgive me for the bit of theatrics in the opening line. But when you find students of class 4 to 7 from interior of Bengal, enjoying the famous Koenigsberg problem from Graph Theory/ Topology, you do feel a bit ecstatic. 

We started a sequence of ’online Math OIympiad classes’ in mid November 2019. Nanritam Ngo runs Filix school in the remote town of Anara in Purulia. The promoters of the school have an eye for innovation in pedagogy. Cheenta was delighted to find a partner in this organization.

The Cheenta-@Nanritam Ngo collaboration began with a Math Circle in the line of erstwhile Soviet Union. Later on this math circle matured into a Mathematics Olympiad Program with an organized curriculum. This program was designed to provoke imagination and curiosity in the young mind. It is carefully crafted to infuse a love for problem solving with an affinity for detail.

We kick started the 8-week program with a central theme: INVARIANCE PRINCIPLE. The first couple of sessions were utilized to ‘draw’ platonic solids, count the vertices, edges and faces. Drawing platonic solids efficiently is tricky. It requires an eye for the projective image. 

Next, we moved on to 2-dimensional projections of these solids. That quickly led to the first glimpse of Euler Number. It was wonderful to see kids drawing the pictures and identifying the patterns with great interest. After several experiments, we were convinced that no matter how we transform the polyhedron (in a controlled manner), V-E+F seems to remain unchanged. As if this quantity reveals the innermost story of these solids. This was the first invitation to the invariance principle, that is a cornerstone of mathematical sciences.

Next, we wanted to know a bit more about these vertices, edges and faces. Hence, we digressed into Euler’s Koenigsberg problem. We understood the notion of Eulerian circuits and quickly came into terms with that fact that imagining regions as dots is a great idea. Drawing ‘adjacency’ as edges is a fantastic visual tool. 

Since then we have moved on to ‘INVARIANCE’ in two other areas of mathematics. The first one is the famous problem of golden ratio. We explored Fibonacci Numbers and were delighted to find the ratios of terms in that sequence stabilizing to 1.61ish value. We reinterpreted this number as the [value] from which if you subtract 1 or take the reciprocal, you would end up in the same thing. 

As our journey into outstanding mathematics continue, I see a transformation in the spirit of the kids. The audience is now more patient about the unfolding of ideas, they are more curious to experiment with possibilities, and more excited to play with the problems. The ‘journey’ is now more exciting, than the end result. 

We are carefully documenting our progress through this program. We hope this will end up in a new ‘curriculum‘ for kids in school. A curiosity and problem-solving driven curriculum in mathematics has the promise of transforming children’s experience with the subject. We are also adding a teacher’s training program to expand the process. I hope 2020 will be very productive.

By Dr. Ashani Dasgupta

Ph.D. in Mathematics, University of Wisconsin, Milwaukee, United States.

Research Interest: Geometric Group Theory, Relatively Hyperbolic Groups.

Founder, Cheenta

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