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From fear to free thought in mathematics

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 The National Year of Mathematics ended on December 22, marking the 125th birth anniversary of Srinivasa Ramanujan. But what is the state of mathematics teaching in India today?

Speaking at the celebration of the Year of Mathematics early this year, Prime Minister 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 past 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 — the 125th birth anniversary of Srinivasa Ramanujan. It had been a year when many maths conferences were held and much was said about the need for mathematics teachers, better maths education, motivating students towards maths and so on. But what is the understanding we have of maths teaching today? Is maths 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, Indian Institute of Technology, 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 the fundamentals. Teachers offer lengthy proofs which they ask their students to learn thereby inculcating a fear of maths 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 Huge books and outdated syllabi add to this fear.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. 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

Mr. Habib talks of one assignment he gave in the “Maths 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 maths. He continues, “They should understand what it means to be correct or wrong.” Because even if one is going to apply maths only to subjects such as economics or finance, pure maths 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 Shiv Nadar University, 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 maths 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.

Some of the damage happens when people cram for the 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 maths. They have some wrong motivations — such as it will help them later in the Civil Services Examination (because maths is a scoring subject) or in the Common Admission Test 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 maths.

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 Mr. 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 maths 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.

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.

‘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.’


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