“Concepts are caught, skills are taught”

Vaishali Lakhlani

This quote by P K Srnivasan sir has played a vital role in my journey as a math teacher and mentor. I was formally introduced to Srinivasan sir as one of the greatest mathematics teachers by my then school principal, Shri S. Sundaram. Srinivasan sir and Sundaram sir motivated and inspired me to start a math club for students, where we could explore various concepts and go beyond the regular school syllabus. Here, I share some of my experiences with the club.

While planning activities on angle bisection and trisection using Origami for the club, I came across an article by Arvind Gupta, titled Maths missionary – P. K. Srinivasan. In the article, Arvind Gupta writes about his first meeting with P K Srinivasan in 1986 at a workshop organized by the NCERT at Sri Aurobindo Ashram in Pondicherry.

“PKS gave each teacher one sheet of paper and asked them to fold an angle of sixty degrees. The teachers were at sea! Schooled into drawing angles only with a protractor they didn’t know any other way of doing it. After 15-minutes of struggle the teachers gave up. Then PKS folded one straight edge (180-degrees) into 3 equal parts and produced an exact 60-degree angle! The teachers were amazed. It was almost like a revelation – all so elegant and beautiful. He showed them half a dozen different ways of folding 60-degrees. For instance, fold a strip into three equal parts and then into a triangle. All angles of this equilateral triangle would certainly be 60-degrees.”

The related discussions on creating 2D and 3D shapes using Origami opened a Pandora’s box and I found students thinking about geometry and Origami from a different perspective.

From P K Srinivasan’s book Resource Material for Mathematics Club Activities, I learnt about the traditional method – Sriramachakram (Discovery of Patterns) – used in ancient India to construct and alter magic squares, including Ramanujan’s Magic Square. When this activity was conducted in the classroom, all students thoroughly enjoyed it and created their own birthday magic squares. While reading this book, I realized the role of recreational mathematics in conceptual learning. We then started playing some of the mathematical games mentioned in this book in our lab periods.

Once, while teaching square numbers, I discussed the properties of pairs of consecutive square numbers as written by Srinivasan sir in his book Romping in Numberland. I drew a visualization chart on the board as mentioned in the book.

When we take the sum of consecutive square numbers we get, 5, 13, 25, 41,…. The students did not know about arithmetic progressions, so I initiated the idea of taking the difference of two numbers leaving out the number in the middle. We subtracted 1 from 9, 4 from 16, 9 from 25 to get 8, 12, 16,… which was the same as the difference between 5, 13, 25, 41,…. Now the students were able to see a pattern in these successive terms. Our small exploration led to the learning of linear and quadratic sequences. The students were eager to find more properties through visualization charts. I realized that they could learn some of the difficult concepts easily through patterns. All we need to do is to help them become curious learners.

The author is the Head of Curriculum for Math at GIG International Schools (Vijayawada, Bengaluru, and Singapore). She can be reached at vaishali.n.lakhlani@gmail.com.