Sowing the Seeds of Mathematics

The seeds were sown early.

I was sitting in Somerville's SCR, reading Steve Strogatz's "The Calculus of Friendship", when I suddenly recalled an old incident from 1st grade that I hadn't thought about in years.

I'm sure I'll get some of the details wrong, but here is what I remember (which unfortunately doesn't include many specifics): We were doing subtraction of numbers, and on occasion we were asked to subtract a larger number from a smaller one; e.g., writing down the answer to "3 - 5" would be a typical problem we had to solve. In such cases, the "correct" answer that we were expected to write down was "not defined" or "doesn't make sense" or whatever. That is, of course, bullshit---and unfortunately for my 1st grade teacher, I had encountered negative numbers somewhere and already knew it to be bullshit. (I wish I could remember the source. My best guess based on what I was reading at the time would be that I saw it in some magazine article about baseball. I certainly learned several other pieces of mathematics, such as decimals versus fractions, from baseball calculations before I ever saw anything like them in classrooms.) So on my assignment, I included negative answers at appropriate points. When these were marked with an 'X' to indicate that they were "wrong", I openly challenged my teacher (which all educators appreciate! :P ) and attempted to explain why it was correct. She made some comment along the lines of not being able to have -2 apples (I don't remember if it was apples or some other object, but my memory is suggesting "apples" as the likely example), and my counter-argument was the standard one of the concept of owing 2 apples. She would have none of that, and I have a vague memory of things escalating to the point that she had to call my parents (which, of course, they appreciated greatly). I also have vague memories of the other 1st grade teacher taking her side and my having to argue my point against both of them, but I'm not sure about that part either.

Anyway, I am confident about my memory that the argument was lengthy and public, and also about the fact that I was stubbornly insistent that I was right and my teacher was wrong (and, in particular, that I refused to concede the point---except that I did subsequently and grudgingly write their version of the "correct" answer on things just so I wouldn't lose points). I know that the argument escalated, but I'm not confident about the '2 on 1' bit with my arguing against both teachers and I'm also not confident that the argument reached the point that my parents had to be called about my bad behavior.

OK, so what seeds were sown here? I don't actually think it's horribly uncommon for somebody to encounter and then understand negative numbers on their own---it is an obvious concept, after all---and that's especially true when one considers the subset of people who choose subjects like mathematics (and other quantitative or scientific areas) as a career. The early signs that we really see here are my extreme stubbornness---and I can recount tons of other incidents that demonstrated when I was essentially (but not literally) arbitrarily young and the fact that I learned very early on that I could be right and my teachers could be wrong. (One could argue that I learned how to disrespect authority early on, but it was really more of a lesson to not assume that the authority was right by virtue of the fact that they were supposed to be the relative "expert" on the topic---or at least that they were supposed to know more than me.)

This was actually the second of four incidents I recalled in immediate succession---the difference is that the first, third, and fourth ones are ones that I have never forgotten, whereas I think the last time that I thought about this second one might well have been before I started college (or certainly not long after that). The first one involves my figuring out multiplication on my own in kindergarden, the third involves my father's $100.00 math challenge (when I was a very young age, but I can't precisely remember how old I was) from a problem he saw in the Los Angeles Times that he only gave me because he seriously underestimated me and didn't think I had a chance to get it right. (He was a bit shocked when he then had to keep his word and fork over the cash. I guess he could have gone back on what he said, but that wouldn't have looked good.) The fourth incident also occurred in 1st grade, and that was my refusal to say the pledge of allegiance because of the presence of the words 'under God'. That one also led to a public argument with my teacher, but I ultimately resolved that one by just opening and my mouth without saying anything at the relevant point (and lip-syncing during the rest of it) and hoping that the teacher just wouldn't notice. I didn't find out until I got to high school that it was actually illegal for the teacher to force me to say the pledge. (There were also a couple of incidents in high school about my refusal to say the pledge, but those were with fellow students rather than teachers.)

I guess the title of this post is a bit misleading (because this type of thing can be construed as mostly independent of mathematics), but this type of stubbornness and nature can be seen all the time these with my career choice---and this type of stubbornness is rather useful for scientific endeavors, behavior during seminars, etc.

Alright, I better get back to work. This post was a lot longer than I intended.

(And, yes, I already was that much of a pain in the ass when I was in 1st grade. I suppose that that will surprise very few of the people who know me.)