It is only after leaving school that I got to know that Florence Nightingale was not just the ‘Lady with the Lamp’. She was also the first woman to become a fellow of the Royal Statistical Society. During the Crimean War, she used to prepare and present accurate data of casualties in the form of tables and diagrams. What an inspiring story this could be for schoolgirls, of a woman who was a nurse, a social reformer and a statistician. Alas, most mathematics teachers who teach in high school say that they neither have the time nor the inclination to tell stories in class.
In defence of the maths teachers, it can be said that they are not only required to complete the syllabus but are also expected to show their students how to solve examination papers. Outside of school, tutors help students grapple with the dreaded competitive tests. The students themselves are even more pushed for time. Indeed, they work longer hours than adults these days. Moreover, unlike adults who come home to rest after a hard day’s work, students return home to face more hours of work, attending to homework and other assignments for the next day. How can we expect them to sit and ponder the amazing ancient Indian number system or the efficiency of the decimal point?
Very often, parents complain that their children were unable to solve in class the same mathematical problems that they worked out at home or in front of their tutors. Listening to them, I am reminded of Clever Hans, the horse who had been trained to solve mathematical problems by a German high school teacher. Hans had created waves all over Germany when he exhibited his mathematical proficiency to the public. He indicated the right answer by stamping the ground with his hoof the required number of times. Eventually it was a psychologist who unravelled the mystery. Hans was merely responding to the subtle changes in his master’s facial expression when he reached the right answer. The psychologist demonstrated that Hans was unable to ‘answer’ accurately when his instructor was positioned at a distance. I observe the same phenomenon among schoolchildren who look for the elusive answer in the teacher’s face rather than in the problem itself. I suspect that students who have not grasped the related numerical concepts are unable to tackle problems independently. In addition, there is the overarching fear of not getting the right answers in the stipulated time in tests and exams. It is possible for students who perform reasonably well in other subjects to do disastrously in the mathematics paper.
To illustrate my point that children are quite accustomed to doing maths without understanding, I shall share my own experience. One day, some years ago, I was sent off to a junior class to fill in for the mathematics teacher. While moving around the classroom, I found that the students were reducing fractions to the lowest terms. When I asked one of the girls what she was doing, she replied that she was ‘cancelling’. I asked her further what she meant by ‘cancelling’. The look on her face clearly indicated what she thought of the level of my mathematical knowledge. She proceeded to explain patiently that the class had been taught proper and improper fractions and that some of these fractions needed to be ‘cancelled’. Still not satisfied, I pressed on till the girl sitting next to her decided to come to the rescue. “We’ve been taught how to scratch out numbers above and below the line, so we are scratching,” she declared with an air of finality. Left unsaid was: “No more silly questions please!” It was abundantly clear to me that day that students work out mathematical problems mechanically.
We need to accept that not everyone is comfortable with numbers and symbols, especially when they perceive no connection between them and the realities of everyday life. This is one reason why mathematics loses some of its appeal as a student moves out of junior school. Most senior teachers claim that they cannot remedy the situation because their brief is to complete the syllabus and assure respectable exam scores. Where do they have the time to delve into the niceties of mathematics or its application? They do not even have the time to pause to find out the depth of their students’ understanding. So students end up working at the subject just to be able to reach the ‘right’ answer, which, in turn, will fetch them the marks they want. And I know from first hand experience that it is possible to work out certain sums correctly without understanding the significance of the process — you just have to know the formula. I could solve the numerical problems related to our B.Ed mental measurement course quite effortlessly but did not have a clue as to what these figures had to do with education or teaching. It was only when I looked into the possibility of devising a fairer way of measuring scholastic performance that I began to understand the different kinds of averages and measures of variability.
I remembered this experience when I went to observe a maths demo lesson the other day at Mace, our continuing education centre. The topic was “Teaching Mathematics at the Primary Level.” The instructor began by asking the class how many of them were comfortable with maths. Not a single hand went up. Moreover, they unanimously held their school maths teachers responsible for their plight. It so happened that I had just read a book called Mathematics Minus Fear and I was immediately reminded of the author’s description of the ‘remote and tyrannical mathematics teacher’. This is how it went: “His intense love of numbers has damaged his interpersonal skills. He dismisses hours of labour with a few scratchings of his red pen. And he scrawls incomprehensible explanations on the blackboard and then expects his students to solve the problems on the sheet in front of them by some mystical form of osmosis. The fear of getting an answer wrong means that for most the best chance of survival is silence.” No wonder students define a mathematics teacher as ‘one who talks in someone else’s sleep’. How lucky we were, I have often thought, to have had a gifted mathematics teacher in school. We had a great time with her, learning about Pythagoras and making up stories to explain the ups and downs of our graphs. I still remember that I had to produce a bar graph representing the footfall at the Horticultural Garden annual flower show over a particular week.
We enjoyed our mathematics lessons and probably assimilated concepts because our teacher took the trouble to relate learning to the real world. In fact, when the Mace trainees declared quite unabashedly that they stayed far away from anything that smelt of mathematics, the instructor demonstrated on the spot that all of them without exception were closely involved with calculations of some sort every day of their lives. They were reminded that they did mental calculations when they went shopping, read maps or music, checked their bank statements, prepared a meal, packed their bags or ordered curtains for their rooms. Such examples are found in plenty around us. We are all familiar with the child who performs miserably in mathematics tests but rattles off elaborate cricket statistics to prove a point. And we have also seen how the local grocer tells you almost instantly the exact amount to be paid for the sundry items you have asked for, in varying weights and measures. Having said this, I have also heard of a great mathematician who could not add up his laundry list.
This is because mathematics is not sums, calculations and formulae, just as history is not events and dates. Each subject has its own language and the language of mathematics fascinates only some people. I read with great interest what an author called Joan Brady had to say. Brady was a ballerina who got tired of hearing that ballerinas were cerebrally challenged — or to put it bluntly, plain stupid. So she decided to do something about this. Brady succeeded in getting into Columbia University to study philosophy and maths. Soon she realized that she could “manage the meat of math but remained lousy at numbers”.
All these thoughts and experiences over the years have convinced me that after the elementary level, that is, from Class IX onwards, there should be a separate course of mathematics for those who wish to be engaged with the language of mathematics. They would pursue the discipline in its pure form. Eventually, some of them may be found worthy of joining the band of disdainful purists who complain that these days “even the most pure and abstract mathematics is in danger to be applied.” Such mathematicians are customarily held in great respect by all — including mighty physicists — because ‘mathematics is the language God used to write the universe’.
Today, every country is especially concerned about its numeracy programme for a single reason: mathematics is vital for business and development of the economy. So the third R in school, arithmetic, has developed a special status. It leads to the fourth R — the Rat Race. Hence high school students well appreciate the practical importance of mathematics for their future in higher studies, business schools and ultimately, in the job market. Ironically, it is this urgency to score in mathematics that makes students so anxious. And it is this anxiety that prevents students and teachers from exploring the wonders of the subject and deriving pleasure from it. As mathematics becomes more and more important in the scheme of things, mathphobia resulting from performance anxiety becomes more and more widespread. While every student knows that mathematics must be dealt with as competently as possible, for each of them it is a relentless race against time.
Can students and teachers be made to believe one day that mathematics should also be studied for the same reasons we study literature, music and art?