'Mathematics is all about exploration'

'Mathematics is all about exploration'

Since 1987, Dr. Shirali has been closely involved with the Mathematical Olympiad movement in India. He has taken part in the training programmes for the Indian IMO teams each year from 1989 till prese

Dr. Shailesh Shirali has a Ph.D in Operations Research from the University of Texas. He has taught mathematics at Rishi Valley School (Krishnamurti Foundation India) for more than two decades. He served as Principal of the school (1992-2004) and received the National Award for Teachers 2003 from the President of India. Presently he is the Principal of Sahyadri School, Pune.

Since 1987, Dr. Shirali has been closely involved with the Mathematical Olympiad movement in India. He has taken part in the training programmes for the Indian IMO teams each year from 1989 till present.

He is chiefly interested in Euclidean Geometry, Non-Euclidean Geometry, Projective Geometry, Number Theory, Combinatorics, Combinatorial Geometry, History of Mathematics, software for doing exploratory work in mathematics.

Dr. Shirali also serves on the Council of Editors for Resonance, an expository journal for science and mathematics education, published by the Indian Academy of Sciences, and is the Founding Editor of Samasya, a problem-solving journal for school and college students, published by the Leelavati Trust. He is also the founding editor of At Right Angle, a journal published by Azim Premji University. He has also authored many books including A Primer on Number Sequences, First Steps in Number Theory: A Primer on Divisibility, A Primer on Logarithms,Adventures in Problem Solving, A Sourcebook of Mathematics for CBSE XIIth Standard, ISC Mathematics-1 1 and ISC Mathematics-1 2.

In an interview with GK reporter Syed Rizwan Geelani, Dr. Shirali, who was recently in Kashmir, talks about the reasons for dearth of trained mathematicians and various initiatives that can be taken to make students excel in the subject.

Tell us about your visit to Kashmir?

I am here on my personal capacity with my family to tour and look around the places here in Kashmir. I have always been fascinated by  reading about Kashmir and I grabbed the chance to come here.

Given your experience and contribution in teaching mathematics,what steps can be taken to generate interest in mathematcis subject among students here?

I am not very much familiar with the status of mathematics here. I think they would have to start by looking at the whole education system and check where are the difficulties encountered. This is the problem which is there all over the country and Kashmir may be suffering little bit more than many other states. But really, it is an all India problem.

What are the reasons?

The fact is that the supply of trained mathematicians all over India, who know it more than just a subject, is critically low.  When I say trained, it means who have idea about the culture of the subject, an idea about its history and the beauty of the subject. They should be able to communicate the beauty of why do we study mathematics. There should understand the beauty of problem solving.

Where are some these loopholes in the system and what can be done to bring change?

The fault exactly lies here in the kind of exposure as teachers simply reflect the same way they have learnt. They just transfer the same kind of education they have picked up and cycle goes on and on. It doesn’t break up. Students are not given much space to speak and articulate their own thoughts to develop their own thinking. They are simply taught some answers. Something is taught and they are supposed to show that they have mastered that. So that is simply giving material and asking them to digest it. And I think if at all there is a problem in Kashmir this will be the source of that problem.

What are the reasons for dearth of trained mathematicians?

I think it is partly lack of interest and thinking on the part of public. There is very little interest in education itself. If you look deeper, the problem is not just mathematics but there are so many subjects which are taught very poorly. History and languages are also taught poorly. This education sector is under crises in whole country.

How do you see the present education system in Kashmir?

In Kashmir the problem is little bit more or worse than many other places but it is bad in many parts of country. Governments have been talking about teacher training but if you look at the budget allocations, what percentage of budget is allocated to teacher training, which in other words means education of teachers, it is almost nothing. It is so sad that government doesn’t seem to realize the absolute vital necessity of good institutes for traning of teachers and good salary structures.  Like this, so many other factors are involved. Government priorities lie somewhere else than education. The initiative should come from the government. In natural way it should come from the society as well. But government has to play a proactive role and take initiative.

You said teachers simply teach the same way they have learnt. What can be done to train them well so that they can improve and teach in an engaging manner?

There are two aspects of mathematics. First is the subject itself and second is the way you communicate it to the students. They way you communicate it to the students may not be the same or identical to the way the subject is itself structured. They way you communicate must be done in a slightly different way in which the subject is logically structured. This I’m talking of school level particularly. At college level or PG level, the two can be same. The way you develop it logically and teach can be identical as by that time students are matured. But at school level, we can’t talk in every mathematical abstract way. You have to start with what child already knows and draw it out of the child. You have to encourage the child to invent ideas and put the child in a position that he or she comes out with ideas. Problem solving is very important in teaching of mathematics and the art is finding the right level of problem for a child.  This is where teachers need to do research on what is a good teaching method. As teachers we commit mistakes sometimes by putting forward such a difficult problem that nobody knows the answer of, and students look at the problem and say they can’t do anything. By this you are de-motivating the child. And the opposite extreme side of this is that you give such an easy problem that the child gets an answer in a one second and then he becomes overconfident. You should be able to ask the question of which the child doesn’t know the answer and has to struggle to get its answer. That is where the teachers have to think very hard to find the right level of questions. A teacher has to be very sensitive and know what kind of students he is teaching.

Given the dearth of quality mathematicians here at college and university level, what initiatives can be taken to generate interest for the subject?

Make use of more online courses which are available in foreign countries. We can use technology to develop some expertise amongst the students. The other way is making better use of resources available within our own country. Here the government would have to take the initiative. They have to identify the people in different parts of country who are doing good work. Record their lectures and courses and then play the same here for the benefit of students. Some steps have to be taken. The best thing is to have a live teacher but if you don’t have it, at least get an electronic teacher. If this thing can’t be done, then things would remain static. People have to be sufficiently interested in solving this problem. They have to find new types of solutions. May be change in budget allocation would be part of it.

Let me say what government can do. To create interest among students, government should get speakers here on regular basis who will speak to the students. That is how budget allocation needs to be revived. It will create its own effect. Second is to create enough love for reading as reading is very important.

Mathematics is not about speed. It is not about finding quick answers to problems. It’s all about exploration to find the answer of a problem.

What will be your message for teachers and students of mathematics?

Two things. Just solve as many problems as you can. By problems I don’t mean problems written in book but I mean problems of exploration to which no answers are given in books. Second, read more. Lot of material is available. Begin to enjoy your subject the way you enjoy a good novel.