A personal mathematical history – Part 1

[Note: This four-part series is a blogged version of a talk I gave in 2011 at a conference which celebrated the 50th anniversary of the Mathematical Association of Tasmania. Some of the anecdotes shared here were not included in the original talk … and, given that I’m writing this up over three years later, I’m quite sure there were bits included in the talk that are missing from this version of things.]

In 2011 I was invited to give the pre-dinner address at the annual conference of the Mathematical Association of Tasmania (MAT), which coincided with their 50th anniversary. (As will be revealed later, there were some other auspicious occasions occurring at the same time.) In preparing the talk I wanted to do honour to mathematics and mathematics teaching, acknowledge the history of the association, and include a little humour (your mileage may vary), and so I decided to use my own personal mathematical history and experiences as an organiser for some of my thoughts.

I decided to get rid of most of history — though not my own — in one slide.

This brought us to the 1960s, the decade in which I was born, some three years after the formation of the MAT, meaning that the association and I are a similar age. The geometric shape that has been a focus of the association’s logo depicts the basis for a geometric theorem made famous by M L (Mac) Urquhart, one of the founding members of the association. I actually designed the middle logo in the 1980s/1990s. Although the current logo, shown on the right, is perhaps more accurate in its depiction of Möbius strip behaviour, it has had to compromise on the readability of the name, has lost the smooth twistedness of the strip (instead just showing sharp folds), and no longer has as natural a representation of the shape of Tasmania.

I have little record of my own personal mathematical beginnings; the best I could find for the purposes of an illustration was this painting done as a 5- or 6-year-old, but I can recall — vaguely — starting to fill a notebook with a list of the counting numbers from 1 onwards. I think I had vague plans to get to 1,000,000 (although clearly with no clue about how long this might take!); I may have made it up to 1000 or so.

The early 1970s, when I was at Primary school, were an interesting time mathematically. Cuisenaire rods were present in schools, although they pre-date the 1970s in terms of their invention and advocated use in teaching. I don’t know that I was taught maths effectively with them, but I had my own set at home, and I certainly learned the order of the colours. They were great for making towers, but must have been the bane of teachers in terms of the clean-up nightmare; however, I quite enjoyed packing my set into its box in an efficient and beautiful pattern.

The other thing to note about the 1970s and mathematics is that “new maths” was evident in Australia, with a surprising amount of set theory evident in my Grade 4 textbook. The second slide below is a closeup of one of the pages on the first slide, where — in fitting irony — the answer to one of the problems turns out to be the initials of the maths association.

I don’t recall that maths was especially “a thing” for me at Primary school. I was a highly able student in a variety of areas, and even in retrospect it does not seem obvious that, based on primary school experiences alone, I should have had maths playing such a central role in my later life. I liked patterns and I think I was good at identifying them, and I was good at learning how to do algorithms, but I don’t think I necessarily understood all that was going on. In fact, it was only as an adult that I came to learn why my method of doing subtraction actually works (this method is no longer taught in schools), and, instead of figuring it out for myself, I had to be told that if you want to make the addition of strings of numbers easier, look for things that add to 10.