Speaking at the celebration of the year of mathematics early this year, Prime Minister Dr Manmohan Singh said, “Since Ramanujan, a number of mathematicians from the country have distinguished themselves by performing at very high levels. However, it is a matter of concern that for a country of our size, the number of competent mathematicians that we have is inadequate. Over more than the last three decades, many of our young men and women with a natural ability in mathematics have not pursued the discipline at advanced levels. This has also resulted in a decline in the quality of our mathematics teachers both at the school and college levels.”
The national year of mathematics ended on December 22, 2012 — the 125 birth anniversary of mathematician Srinivasa Ramanujan. It is a year when many math conferences were held and much was said about the need for mathematics teachers, better math education, motivating students towards math, etc. But what is the understanding we have of math teaching today? Is math inherently such a difficult subject so that only those born with the ability can excel in it or can it be taught well like other subjects?
The heart of the problem
W.B. Vasantha Kandasamy, associate professor, Department of Mathematics, IIT-Madras, says that though many students have the potential to do mathematics, the damage is done at the school level itself, when students are asked to memorise fundamentals. Teachers offer lengthy proofs which they ask their students to learn thereby inculcating a fear of math in them. Huge books and outdated syllabi add to this fear. “Teachers should take the time and effort to teach students the niceties of the subject instead of rushing them through the syllabus,” she says.
How does the teacher recognise this? “This shows up in the way students tackle assignments,” says Amber Habib, Shiv Nadar University, Delhi (SNU). If the question involves simple steps or formulae, students are able to handle it. However, if the assignment involves reading many books, organising what they read and generally deeper study, there is trouble.
Fear of the new
Amber Habib talks of one assignment he gave in the “Math in India” course he is teaching, which is a mix of mathematics and history. Part of the assignment involved reading two or three books and figuring out what trigonometric identities were being used back in time, and if these were different from ours, to understand how they differed. The work involved making tables and manipulating numbers. Most students did not even attempt this part!
How do they tackle this? He says,” We pretend that they have not even gone to class 12. In the first semester, we have a pre-calculus course, where we teach functions, sets, limits etc. In the second semester, students learn calculus of one variable and in the third semester they do calculus of many variables. In addition to this, in the first semester, they have courses such as Linear Algebra and Programming where they learn something new … this is always good.”
However, at least a year should be spent in not necessarily teaching new things but in teaching students to appreciate math. He continues, “They should understand what it means to be correct or wrong.” Because even if one is going to only apply math to subjects such as economics or finance, pure math is needed, such as measure theory and stochastic processes. Also, these subjects develop from axioms in a mathematical way.
Another thing he emphasises is conversation about mathematics. “Apart from exams there needs to be a conversation between the teacher and the student about the philosophy of mathematics and where the student is heading, and so on.”
Though it is done over four years at SNU, it can be done over the regular three-year programme itself, he believes. All it takes is a conscious attempt to provide a bridge between the way math is done in school and the way it is done in university.
It is also important to incorporate this into the curriculum. It is unfair to give students a 30-hour load and then tell them to learn things over and above that.
Offering the right motivation
Some of the damage happens when people cram for IIT-JEE or when they learn from handed-out notes. The whole exercise becomes one of getting perfect marks. It’s studying for a specific exam. The other problem is the reason why people enter math. They have some wrong motivations — such as it will help them later in IAS (because math is a scoring subject) or in CAT to get into IIM (because the question paper is mathematical) or it will help if they sit for the JEE again next year. Obviously, if they get in with any of these motivations, it is unlikely that they will enjoy studying math.
Students have to be given various kinds of choices. For this, the course has to be structured such that it offers them two or three different routes. This is usually done by offering electives and papers. This is not sufficient, “they (the students) do not know where they are heading, so they need to be told — there is one more year, so think about what you want to do,” says Amber Habib, and they need to be offered a package or two which will take them along routes of their choice.
It can be a rewarding experience for the math teacher to see student go from fear to fortitude to flight-like mastery over the subject, but it is a road of trials and it is to be hoped that our system finds within itself the means to reward commitment and achievements in math teaching.