December 22nd is National Mathematics Day in India. It is celebrated to honour the birth anniversary of legendary Indian mathematician Srinivasa Ramanujan. Ramanujan was born on December 22nd, 1887, in Erode, Tamil Nadu. Despite having very little formal education in mathematics, he was able to make ground-breaking discoveries and find solutions to complex problems. Ramanujan’s work has had a lasting impact on the field of mathematics and is still studied and admired by mathematicians today.
While I was a maths teacher, my students and I drew inspiration from the remarkable stories of mathematicians. Ramanujan’s story carries many important principles for students. Many of these important ideas about mathematics seem to be misplaced today in classrooms that prioritise high exam scores.
Let’s look at a few important ideas that we might learn from these mathematical experts!
Maths experts are motivated by the beauty of mathematics and the challenge of problem solving, not a score on a test.
Ramanujan was an ‘experimental mathematician’. He was curious and used both – his intuition and amazing mathematical abilities to figure out formulae way before the age of computers.
There is a famous story that captures his lifelong fascination with numbers. When G.H. Hardy, the Cambridge mathematician who worked closely with Ramanujan visited him in the nursing home (Ramanujan’s health deteriorated early and sadly he passed at only 32 years old). He told him that came in a taxi with a dull number, 1729. To this Ramanujan replied ‘No! It is a very interesting number! it is the smallest number expressible as the sum of two cubes in two different ways.
However, in schools today, few students have opportunities to explore the beauty of mathematics. Or to experiment or create with numbers. All focus is on scoring highest marks in the exams.
Maths experts take time and persevere, it is rarely about speed.
Ramanujan spent years tinkering with numbers. He spent time reading and learning, and persevered so he could get to the formulae that his intuition told him was possible. He also wrote many letters to mathematicians in Cambridge in the hope that he could pursue his mathematics at a higher level in collaboration with them. Difficult problems in mathematics (just like most difficult problems) take time to solve… often years, not just hours. It is very unlikely that he made his discoveries in a single eureka moment like they show us in movies!
Yet, as a result of high stakes exams in Schools today, children have come to believe that speed – arriving at the answer quickly, is one of the most important things. Maths teachers expect students to solve problems in a few minutes in the classroom because we want students to ace the test. Deep thinking is not encouraged because the ‘wastes time’ in the classroom where the exam syllabus is vast. But speed and mathematical problem solving are not synonymous in the real world.
Maths experts try many different ways to solve a problem. They aren’t just using memorised facts and procedures.
Ramanujan had a phenomenal memory and calculation ability, and very little formal mathematical training. But at the centre of his work was purposefulness – he was on a path of discovery. He created patterns and connections. He made predictions and tested them. He discovered many new number approximations and formulae that were way ahead of its time. And while mathematicians’ study existing knowledge to build on the work of others, they will never rely on the purposeless use of facts and procedures.
In schools today however, students are memorising facts and procedures with the sole purpose of reproducing on an exam. They are often given a ‘solution’ (procedure) to a problem that they are asked to memorise and practise over and over again on the same ‘type’ of problem. We rarely encourage different ways of trying things, even though trial and experimentation is a core part of problem-solving. Because for simple exam problems it is not as efficient as plugging in the one that the teacher has already shown you.
Maths experts make many mistakes, they don’t get everything right on the first go.
Ramanujan was an ‘experimental mathematician’ who manipulated numbers and found ways to represent complex number patterns. Because he used a lot of intuitive thinking and trial and error, he got many things wrong before he got them right. When he did, they were remarkable. Mistakes are often signs that we are pushing the boundaries beyond what is known. It is very much a part of growth. It is also inevitable when we are in pursuit of challenging problems.
But students are rarely exposed to the open-ended more complex problems that mathematicians encounter. And because our maths questions fit into nice simple boxes, we expect students to just pick the right method and always get it ‘right.’ There is little room for mistakes and little reward for perseverance and iteration.
As we – educators, parents, school leaders – celebrate Mathematics Day in India, let us create maths classrooms where:
Students have opportunities to explore the creative, beautiful subject that mathematics is.
Students understand the value of deep, deliberate thinking and are not solely focused on solving simple problems fast.
Students experiment with different ways of solving problems.
Students are encouraged to persevere and iterate and view mistakes as an opportunity to learn.
(Radhika Zahedi, School Director, The Green Acres Academy)