Many years ago, I had occasion to invite a distinguished American mathematician to India. He was a highly accomplished researcher and a gifted teacher. However, unsurprisingly, he had had no occasion to deal with any kind of school mathematics or with school children in the context of mathematics learning. During the course of his visit, I sprang a surprise on him by arranging a visit to a school in Delhi to interact with sixth grade students. For him this was a bit of a surprise and since he had never ever done this earlier, he was more than a bit flustered. As we entered the room where he found himself facing 40-odd students, he became tongue tied; even a bit sullen. I had no choice but to take over. Even though his area of research—mathematical biology—was not my area of specialisation, I was aware of the applications of his work on using mathematics to explain how four-legged mammals walk.
Incidentally, his research was being funded by the National Science Foundation and his work had real-world applications of a myriad kind. I began by provoking the minds of the school children with simple questions of symmetry in nature and how to perceive symmetry in the human gait. The students began to answer my questions and began to ask and speculate in a lively manner on the geometry involved. At this point, my mathematician friend suddenly became animated and jumped into the discussion. From then on, he and the school students bonded naturally as he drew diagrams and connected his geometrical diagrams with the walks of various mammals and how robotics could be affected by those ideas.
In a similar vein, I once decided to interact with fifth grade school children. I had thought of exposing them to some very intuitive and basic ideas of probability. To my surprise, these children were quick on the uptake and would answer my queries in ingenious ways. I made them discover and experiment with their own hands by letting them play around with dozens of coins and several dice. This allowed them after some time to make inferences on their own. At that very time I was teaching an advanced course on probability theory to university students, and I found myself talking through examples and illustrations on some of the basic ideas of that advanced course to those school children. I realised that the school children were far quicker on the uptake than my university students.
Similarly, once I conducted an experiment with sixth grade school girls residing at Bengaluru and Delhi. They had just been taught in their respective institutions some basic concepts on parallel lines. I enlisted the help of a mathematician colleague at Bengaluru. Together, we got these girls to measure shadows cast by vertically embedded sticks on the ground at both cities and at the same time. These girls used a little bit of the parallel lines that they had knowledge of and eventually figured out a good approximation to the circumference of the Earth. The one major learning that I derived from my experiences and experiments like the above was that students start their school lives by being creative, curious and spontaneous. However, over time, our schools and parental pressure end up killing their creativity. School teachers tend to lament that they are under pressure to complete the syllabus. I do not buy these arguments. In fact we teach too much from the very beginning of schooling. The National Education Policy has repeatedly emphasised that we must teach less and make the students experiment more.