'Kolam' is Not Just Aesthetics But Also a Mathematical Marvel: Prof R Ramanujam
The 'kolam', the traditional
designs drawn by women especially in
Tamilnadu, Karnataka and Kerala in front of the houses or courtyards should be
admired for its aesthetics as well as the mathematics behind it. For
mathematicians it lends itself to a deep analysis of the several mathematical
shapes and patterns, according to Prof R Ramanujam, Professor of Theoretical
Computer Science at Institute of Mathematical Sceinces, Chennai.
Delivering the keynote address titled 'Guidemaps for Mathematical Exploration' at 9th National Conference on Mathematics Education organised by Regional Institute of Education, Bhopal and being held from December 20 to 22 via virtual platform, Prof Ramanujam said that it is amazing to analyse the squares, triangles, fibonnaci and pascal patterns or curves and dots used by women to draw such 'kolams.' They are drawn using white rice powder, chalk powder or rock powder and is believed to attract goddess of wealth 'Lakshmi' and it also welcomes birds and insects thus bringing nature to home surroundings.
Prof Ramanujam said that analysing and classifying 'kolam' is an integral part of the curriculum at Institute of Mathematical Sciences. You can give fifty sheets with 'kolams' drawn in different shapes and ask students to analyse. There are various types of symmetry such as diagonal symmetry, mirror symmetry seen in 'kolams'.
The analysis is a four-step process involving classification, analysis, finding the symmetry and transformation and finding the curvature of the 'kolams'. The problem of orbits in 'kolams' take you straight to algebraic goemetry and he said that his student in Princeton University has done research on 'Geometry of Kolams.'
Learning mathematics should be an exploratory journey for the student. It involves visualisation, representation, argument (not proof) He said conventional style of mathematics teaching was to have problems and solutions but every solution should end only by raising a new problem. For exploratory learning knowledge, skills, aptitude and disposition is needed.
He also touched upon the three types of exploration- question driven, concept driven and goal driven. Mathematics has to be taught in a manner that children raises more and more questions that aids learning, he added.
To a question from Sreekumar Raghavan, Editor of Pallikkutam as to why exploratory learning methodology is not taught to mathematics teachers he expressed the hope that it becomes common practice in teaching. Mathematical pedagogy was not at all developed in India unlike other countries and just as the heart of science is experimentation while that of art is creation, mathematics is about questioning and creating throwing up new problems from the solutions that emerge rather than have a set of questions and having its solutions at the end of the book. This has to be understood and implemented in our learning process. What is the space given for experimentation in science for students? Same is the same problem faced in mathematics when it comes to generating problems from solutions in an exploratory manner as well.