The Link #26 - Mathematics for the Millions: a personal story

Mathematicians are born, they say. In other words, a true mathematician can be identified at an early age. As children they may, for instance, show signs of preoccupation with an ancient unsolved problem, as Andrew Wiles did at the age of ten when he first encountered Fermat’s Last Theorem, which he ultimately proved just after turning forty.

My own journey into the world of mathematics was not a journey through genius. On the contrary, I disliked maths as a child and frequently did very badly at it in school, finding alien Greek symbols and algebraic expressions too abstract and impersonal for my taste. As I grew older, my distaste for the subject grew proportionately, until I had become secure in my segregation from the subject and my alignment to the ‘humanities’ camp. I was not a science person, and that self-definition suited me well. Teachers can have a tremendous impact on the mind of a developing adolescent; good teachers, in particular, leave an indelible mark on the appreciative student. My non-mathematical brain, however, barely registered the efforts of my otherwise excellent teacher ... until the inexplicable happened. I suddenly, for no apparent reason, started developing a relationship with mathematics, with the abstraction, with the interwoven statements that encased secrets – secrets that could be unlocked, that could be ‘tackled’.

I had suddenly detected the simplicity of it all. It was acceptable not to have the answer ready in my mind; it was fine not to know it all in advance; my lack of immediate insight into the problem at hand didn’t matter. As long as a relationship with the problem could be established, I was communicating with it – learning. I began to actually ‘read’ every problem as I encountered it. Where earlier I would be intimidated by the excessive jargon, the x, y, z symbolism that prevented me from fully taking in the problem, I was now attending in complete concentration as I delved into the complexity of trigonometric identities. I began to understand the building blocks of calculus. It was no longer a race to just start scribbling something: I was reading every word, every statement, noting every axiom, every assumption, until the ‘hidden’ solution was no longer hidden. It was now not about procedure but about a deeper understanding.

Ever since my own ‘mathematical awakening’ in the last years of school, I have wanted to teach mathematics, and not in a way that would be didactic or instructional but rather as an interactive process where the demarcation between teacher and taught would be blurred – where the classroom experience would be a shared one. And it would not be about mathematics only.

I began to suspect that pastoral care and a general state of inquiry are not only important but necessary for the blossoming of a student of mathematics. Textbooks and instructional guidebooks have their role to play in the classroom, but it isn’t just about that; it isn’t just about exams and the mastery of the exam technique. It is much more about the dissolution of the mental blocks we construct for ourselves. It is about addressing the selfimage we have of ourselves as non-maths-types.

as long as a relationship with the problem could be established, I was communicating with it – learning

On several occasions I have spoken to university professors, teachers, colleagues and academic advisors about their views on the teaching of maths at the school and early degree level. I could almost hear a unanimous voice proclaiming that learning maths involves, primarily, inherent talent, self-generated interest, survival skills and stamina; only the very able manage to survive the ‘filter’ and go on to higher mathematics or related subjects. I got the clear impression that most educators are comfortable with this sieving process that eliminates students who aren’t capable of surviving the grind. The exams are made tough so that only an expected percentage do well. This deliberate survival of the fittest approach refuses to pencil creativity into the subject; it refuses to develop the truly scientific mind, wherein rational thinking isn’t restricted to the lab or the classroom. What surprised me most was the lack of questioning of the system as it stands, and a general acceptance of competitiveness as the primary driving force in learning.

A recent mathematics conference I attended at the Lighthill Institute in London, on bridging the gap between school and college teaching, was an eye-opener in many ways. School teachers and university lecturers from all over England had come together for talks and discussions – all with the specific aim of making maths both more accessible at the school level and less daunting at the initial ‘degree’ stage. There was a gap, it was felt, and maths was somehow losing its appeal among young students who are easily put off by a heavy syllabus and the drab routine of classes.

University students from Imperial College had organised a programme that involved their active participation in classes, through talks and seminars and informal lectures, at several schools and sixth-form colleges. It was felt that their non-textbook approach and enlivened discussions were much more inspirational and drew students towards the subject. Examples of how nature embodies mathematics – the fractal structure of cauliflowers, the way leaves arrange themselves on a stem – whetted the appetite of curious sixth formers.

However, there seemed to be a dominating concern about the dropping standards of Alevel students who are serious about pursuing degree-level maths. So, how to bridge that gap? How can a student be best prepared to face an impersonal lecture hall, to be interested in a sustained manner, to take notes and to continue working diligently despite the sudden increase in work load and the pressure to perform well in difficult exams? How can students learn to face the reality of competition and survive the system and ultimately do well?

After this long day of ‘maths talk’, I made my way back to Brockwood, my mind chock-ablock with questions. Filling in the gaps and bringing students ‘up to speed’ only partially addresses the difficulties facing young students of the subject. Somehow, I felt that a major point had been skirted. The real reason for learning mathematics and enjoying mathematics seemed to have been bypassed.

The classroom experience does not begin and end at the blackboard; it also involves a relationship between teacher and student, a relationship with the symbols and the language of mathematics, a relationship with the evolving history of the subject like the passing of a baton, a revelation of the fundamentals on which mathematical complexity rests; and nowhere had we faced the importance of the overall emotional and psychological development of the students. A holistic approach to education itself is required. Surely if we foster a general spirit of inquiry, one that uncovers and emphasises a deeper understanding of the essential principles of the subject rather than mere training to recognise patterns in solving problems, there would be not only a much gentler transition to college science and maths, but also a kind of learning developing within students that could allow them access to much more than that.

I continue to experiment with these notions as I teach, encouraging my students to help me to be a better teacher and communicator, and to help in creating a spirit of inquiry so that the subject comes alive. Although I stand on the other side of the classroom, as a teacher facing students, I am also very much engaged in a process of learning.

Ashna Sen, May 2006