Maths evokes only two reactions from everyone — you either love it or hate it. Perhaps it’s the way we are taught in school when even if we get the correct answer, we lose marks for missing a step! The stress is on calculation and the perfect way to calculate than on the practical applications of the subject. So we end up learning maths in the abstract and thus want to get away from the subject ASAP, though the reality is that we are confronted with numbers on a quotidian basis.
India is also “transiting from an agricultural society to an industrial one. Technology is going to play a major role. It is essential to have people who are mathematically literate as it is a useful tool to understand day-to-day issues,” says Ronojoy Adhikari of The Institute of Mathematical Sciences, Chennai.
Maths is not just definitions. It’s a way of thinking. Mathematicians have the uncanny ability to break down complex issues into manageable components and then find a step-by-step conclusion. But the lacuna is that we’re not moulding our students to think that way. “Pattern recognition is what’s followed in many Indian colleges. Students are essentially exposed to someone’s teaching and that’s why there’s a disconnect with practical life,” observes Adhikari.
Unlike the USA and UK, research is divested from pedagogy in India. We have universities that focus on research while undergraduate courses are the domain of institutes. So students are taught by professors who have no idea on what’s relevant for the industry today. “The curriculum is decided by some official committee and colleges are forced to follow it. Teachers are given no incentive to do research,” says Adhikari.
According to A Raghuram (professor and coordinator of mathematics at Indian Institute of Science Education and Research, Pune), “One of the fundamental problems is that the idea of making a career out of mathematics does not seem financially viable, in comparison to the more traditional engineering and medicine routes a student could take. For example, most students who do well in the Mathematics Olympiad also usually do well in IIT-JEE and end up studying in the IITs.”
Scope has widened
Twenty-five years ago, it was assumed maths graduates can only join the academia but that’s not the case now. And it was assumed a maths graduate would/should continue studying, perhaps finish PhD to get a respectable job in the education sector. The scenario has changed. A lot of companies are hiring mathematicians. “India has seen a boom, which is based on information technology. As time goes on, these information technology majors have to accept that they simply can’t be executing someone else’s order. They will have to move up the value chain to analysis,” which would naturally result in more jobs for mathematicians, says Rajeeva L Karandikar, director, Chennai Mathematical Institute.
To start with, the curriculum can be modernised. Applications of maths need to be stressed — finance and biology use a lot of maths these days. “With the growth in information technology, tonnes of data is being generated. We need people who can analyse data intelligently, and also suggest on how best to utilise this data in business. The social networking sites have added a new paradigm,” says Karandikar. We reveal a lot about our personal lives on social media. This data is a minefield for businesses, if analysed properly, and this is where Karandikar believes mathematicians would prove effective and useful.
An interdisciplinary approach would also work, academicians believe. The Indian government set up Indian Institutes of Science Education and Research (IISER) precisely for this purpose. In 2006, the Indian government began the process. IISERs function in Kolkata, Pune, Mohali, Bhopal and Thiruvananthapuram. Teaching and research is integrated in IISER and the aim is to instil in youngsters a basic curiosity in the sciences, which would hopefully lead them in new paths. Every IISER student gets paid `5,000 per month while studying for their BS/MS degrees. “This is a relatively new concept on the Indian science scene and I personally am totally convinced that in some years time IISER graduates will be changing the face of science education in India,” says Raghuram, who shifted to India, though he has a tenured faculty position at Oklahoma State University, USA. “The idea of blending research and teaching at the level of undergraduate education holds the possibility of producing our future scientists and mathematicians. We need more PhDs in the basic sciences who would then be teaching science and mathematics in a more electrifying way. This will have a dramatic impact on higher education in the basic sciences.”
Karandikar argues for a broad spectrum of courses from which students can choose to study what they want — either theory or applied maths. “This is not to say that theory is inferior, it is just different,” says Karandikar. “Students have to be exposed to real-life problems and then convert it to an equation to find solutions.” Attractive graphics and videos could be great way to teach maths. For instance, Khan Academy, which has revolutionised the way maths is taught in US schools. “We perhaps have to package it in five-minute bundles and focus only on one idea per session,” adds Karandikar.
According to Adhikari, “School syllabus has to be modernised. The university system in India must be revived — research and teaching must go hand in hand.”
Raghuram believes that students must understand that mathematics is beautiful. “Every mathematician worth his salt is driven by an inner sense of aesthetics. This must get across in the classroom. The other ideal is the ‘sense of discovery’ that must be conveyed in the classroom. It is not just teaching a theorem and its proof and asking students to regurgitate that in the exams, but it must more be along the lines of why a theorem is there in the first place and get students to walk — partly or mostly by themselves — the line of argument of the proof,” he says.
Conrad Wolfram, managing director of Wolfram Research, UK, believes mathematics can be made attractive by devising it as close to reality as possible. “If we can make people learn by using problems they are interested in, they are much more likely to want to do mathematics. Mathematics will then become a tool to solving problems they care about,” he says.
Wolfram is an advocate of computer-based maths education. He believes that by allowing computers to take over the calculation part, students can spend a large part of their time on solving problems. “It is crazy for us to spend 80 per cent of the time teaching people how to calculate by hand when computers do it much better. For instance, ‘How much can I compress a video, sound or a photo?’ Studying that with a computer is vastly better because you can actually play with the example and see the result,” he says. “Anything to do with data, you could do much better on a computer because you could use real data and find 50,000 data points instead of 5,000 data points. One can also go much further with calculus, it’s faster and can apply calculus in many places in a better way. Similarly networks, graph theory and all of statistics and data science.”
Raghuram does not believe computer-based maths education will make the subject more attractive for students and enable faster absorption of concepts. “In mathematics, real learning happens only when pen meets paper and students learn how to do calculations by hand. Once one knows what is it that one needs to calculate, and also one has an idea of how to go about calculating it, then a computer can come in,” he explains. “For example, we learn in high school how to solve a quadratic equation. A cubic or a quartic equation is solvable, but the formulas are somewhat messy that we do not expect students to memorise them. If the need arises, they could look it up, write a short program and solve it, or there are enough computer packages to that anyway.”
As always history is a good way to elucidate the significance of any issue. Let us for a moment look back on the life of James Clerk Maxwell, who formulated electromagnetic theory. “Maxwell was studying some differential equations and trying to solve them. He wanted the solutions to have a certain symmetry — he was being guided by his own sense of what makes an equation beautiful. It turned out later that the equations he was studying were just right to model the theory of electricity and magnetism,” says Raghuram. “Just look around yourself. All the gadgets and appliances that run on electricity, these came out of a mathematician doing what he does! If one wants to create an atmosphere where such stories were to happen then one must be paying importance to mathematics and its education!”
Our lives have become more quantitative than it used to be 20-30 years ago. The fact of the matter is that technical jobs are raking in the moolah and if you want to be a part of the boom, then begin learning problem-solving skills. Lastly, to survive in today’s society and to logically train your mind, you actually have to be quite mathematical.