Once upon a time, I wasn’t passionate about mathematics. Up to grade 6, I even disliked it quite a bit – it consisted of only mechanical plugging away of numbers, and training of multiplication tables that I had the feeling I already mastered.
Then something changed. Subtly at first – in grade 7, it started to gain texture, it got beyond the rote calculations ever so slightly. And so I started devouring the old popular mathematics texts my father kept in his bookcases. Soon, I stumbled across a new word – “integral calculus” – and of course asked my father to explain it. And thus it was that I, at the age of 13, got introduced to limits, derivatives and integrals.
I started accelerating. My teacher soon gave up on the sisyphian task of keeping me occupied, and halfway through grade 8 told me to go on at my own speed. So I did. By the end of grade 8, I had finished the mathematical curriculum of grade 9. I started on grade 10-stuff – from the first year of Swedish secondary education. And by the way I switched schools and started with grade 10, I was in the situation that I could go up to my new teacher on the first day and ask for the next book.
This still hadn’t ignited the passion. Merely prepared a glow of fascination.
Then I went to Germany for a year. During my time there, I encountered a more formalistic lecture style; more interesting lecture content; and a mathematics teacher who quickly recognized my interest in the subject and thus brought me along to a series of workshops, held at the University of Erlangen by their (now late) didactics professor Frau Prof. Juditha Cofman.
Cofman has been very engaged in the question of harnessing budding interest in mathematics. She has written several books on her methods. You should go find them.
At the core of Cofmans methods lies the exposure to the potentially passionate students to the possibility of doing guided original work. She ran two parallell workshops. One for students in general – where she ran through things like Mathematical Induction and Combinatorial Geometry at a very high speed, radiating her own interest and giving all of us the feeling that there is MORE out there if we only look in the right direction. The other workshop was containing students she had handpicked from various directions – but mainly from these first workshops. This workshop kept on longer than the general one, and delt with preparing the participants for the next Junior Mathematical Congress.
As preparation, she spent most of each meeting running through some new, charming, challenging subject – such as “Interpretations of the Fibonacci numbers”, “Interpretations of the Catalan numbers”, “Pascals triangle modulo some small number”, “Dragon curves” et.c. As soon as she detected interest from a student, she immediately gave suggestions as to new directions to investigate. New things to do. Variations on known results, but in directions where no work had been done so far. Two guys were doing one 3d-generalization each of the dragon curve. Two girls were dealing with Catalan and Fibonacci numbers. I started writing the reduced Pascal triangle in my notepad, colouring it by the numbers, and showed her in the break. Result? I ended up submitting a poster (though, alas, not participating myself) to the Junior Mathematical Congress 1998.
I owe my passion to Frau Professorin Cofman. It is as simple as that. It was more or less impossible to stay uninterested in the charge of her enthusiasm – it permeated everything.
I have seen quiet a few students grow interested – and grow disinterested – in mathematics by now. Friends. Fellow students. Kids I encounter through the Young Scientists Association. And one of the absolutely dominant themes is the influence of teacher rôles. If a student encounters a teacher bored with the subject, the student loses his interest swiftly – unless the interest is already enough of a passion for it to survive the encounter. My physics teacher after Germany killed my physics interest. He couldn’t touch my mathematics passion, though, since he was so obviously incompetent at it that I stopped listening. If the student, on the other hand, encounters someone who is passionate enough to radiate it – to light up the classroom with their own love for the subject – there is no other boost like it. Almost. You could always go send the student to a Junior Mathematical Congress – or a mathcamp for that matter – and by meeting other kids with just as much, if not more, love for the subject as the student has, the fascination skyrockets.
I realize, and recognize, that A-students are left to fend for themselves so that the teachers resources can be allocated where it’s needed – where the bulk of the students actually gain something. But still, I feel that the step from glow to flaming passion can be so short, if only taken with the right kind of boots, that I can not refrain from pushing more people to take my step with the means I know have been effective.
And this is why the foundation of Junior Mathematical Societies, the organization of Junior Mathematical Congresses and getting the initiatives that are underway to communicate with each other is so damn important.