I’ve always enjoyed mathematics, but I haven’t always enjoyed maths class. Back in the 80s, when I was in primary school, maths was largely about practicing algorithms. The teacher would show us how to perform a particular operation—long multiplication, say, or adding a list of numbers—then we would spend the next few lessons doing exercise after repetitive exercise in the hope that the procedure would stick. That approach just didn’t work for me. I was considered to be good at the subject (I was always in the ‘advanced’ group) but it was a very rare occasion when I would actually complete the assigned work, preferring to talk or swing on my chair or anything, really, rather than do yet another long division problem.
The concepts, though, were another thing. On the rare occasion when the teacher would explain a concept rather than simply demonstrate it, I was transfixed. Mathematics could be beautiful, and intriguing, and it had what I would now call a mystical quality about it which helped explain the structure and order of the Universe. That’s a heavy thing for a seven-year-old, but I wasn’t scared of heavy.
As the years went on, my ability to learn grew and maths pedagogy grew up. When I got to high school I found that teachers were far more interested in teaching concepts, preferring to guide us to discovering how to manipulate numbers and shapes for ourselves. Graphs and functions became pictorial ways to describe the world, and the joy I found in divining the meanings of the roots of a function was similar to Sméagol’s quest to discover the roots of the mountains:
‘The most inquisitive and curious-minded… was called Sméagol. He was interested in roots and beginnings; he dived into deep pools; he burrowed under trees and growing plants; he tunnelled into green mounds…
‘But as he lowered his eyes, he saw far above the tops of the Misty Mountains… And he thought suddenly: “It would be cool and shady under those mountains. The Sun could not watch me there. The roots of those mountains must be roots indeed; there must be great secrets buried there which have not been discovered since the beginning.”Tolkien (1997, pp.51–53)
It’s no coincidence that I discovered The Lord of the Rings at about the same time I properly discovered mathematics. I was surrounded by people who loved beauty and found it in both art and the temporal world. My teachers would exult in a delicately wrought passage of literature, or in a sublimely performed symphony, or in the elegant proof of some conjecture. Unsurprisingly, I too, like Sméagol, found myself curious about the beginnings of things. My favourite piece of Tolkien’s writing (or literature in general) is the exquisitely written Ainulindalë, which describes the song that created his universe.
All of this is to say that my love of mathematics and my interest in beginnings inevitably led to a serious fascination with the history of mathematics. I am convinced that if more of my teachers had spent time showing how mathematics had developed over the millennia, and why we do maths the way we do, I might have been much more studious as a younger learner and I might have found myself in a profession requiring mathematical understanding.
This series of reflections will look at some writing about mathematical history and consider some of the key things that have transpired to give us the system we have today. Specifically, I have done some research on how we got the Hindu-Arabic number system we usually use today. That lead to some reading on the evolution of the number zero as a concept in modern mathematics. Finally, I will do some investigating on how arithmetic might be done in Roman numerals, a number system that doesn’t contain zero as a number. This will all be done with an eye to how these ideas might be used pedagogically, as well as a means of engaging students with the subject. There will also be an interview with a professional statistician which will complement the research I have conducted.
Tolkien, J. R. (1997). The lord of the rings. London: HarperCollins.