Grace under pressure

 Last week's internet meme and slag-fest?

That would be 15 y.o. Gracie Cunningham fixing her face while musing on the fundamentals of mathematics for her tik-tok pals. She's on about Y = bX + c, the algebra representation for a straight line, where does that come from? she asks. Someone decided that it would be heroic to post this on Twitter as an example of how vapid and shallow the youth of today are. Loadsa other Twitter Knobs piled in to mock Gracie for being a teenage girl asking stupid questions . . . because of course they knew all about the works of محمد بن موسی خوارزمی the Persian polymath who eponymised algorithm for us and laid the foundations of algebra.

I don't tik-tok - I R old - and I only lurk in a teeny-tiny corner of Twitter and Friendface is a closed book to me, so I rely on my pals to filter the memosphere for me and send me the choicest, kindest and most heart-warming bits. For me that would be Metafilter where Gracie's clip and the shallow, cruel and shouty back-lash was cited and explored. Needless to say, in that forum, as in the wider and more thoughtful mathematical community, Gracie came out tops. Thus  muddgirl : "I used to be a middle/high school math tutor and I'd love to have a student as inquisitive as she is. I think history and philosophy of science is so rarely and poorly taught even at the college level". My strong feeling is that if you can't answer the bored, bemused "Why, Sir, are we doing this?, What value does it have for us?" then you should think about changing your teacher duds for a chef's apron or some dungarees and go and do something useful.

But the truth is that someone has to teach math in every high-school and that cohort is far larger than those who really know and care about math. So good Leaving Certificate math teachers know a lot of tricks and carefully read past exam papers and coach their students to answer the likely questions without ever really understanding what it all means. Let alone so structuring the process that the kids find out something anything for themselves. Teaching to the assessment is the hollow heart of education, because the curriculum expands to fill the hours available in two school years and there is no time no time to allow some free-play in math. There's a famous story about sub-teen Euler [blobboprev] looking idle in class and told by his teacher to add the numbers between 1 and 100. It took the chap 10 seconds to fold the sequence in half : 1 2 3 4 . . . 50 vs 51 52 53 54 . . . 100 and add 50 identical pairs of numbers [50+51] [52+49] [53+48] . . . [2+99] [1+100] and "5050, Sir".

A number of competent commentators on Case Gracie suggested that mathematics is all about noticing patterns and thinking about whether they are extendable or whether they can be related to other aspects of the world as we know it. That's how Andrew Wiles cracked Fermat's Last Theorem.  On the Metafilter thread on of the not-math-heads mentioned the thrill of discovering that the square numbers {1 4 9 16 25 . . .} were separated from each other by sequential odd numbers 1 + 3 = 4 + 5 = 9 + 7 = 16 + 9 = 25 . . . Which is indeed pretty neat, especially if you discover it your self. The math-heads got all excitey and showed how this relationship could be derived algebraically in several different and intriguing ways. Good for the math-heads, eye-glaze for everyone else. But that's okay because a different Metathread will bring linguists, historians and railway-buffs out of the woodwork.

Nobody thought to mention that, before the Muslims invented the abstract notation of algebra, the Greeks did all their math as geometry: drawing pictures in the dust of the agora. Each successive square adds an L-shaped block to the previous one. You can see that in a way that algebra is really not good at. Algebra otoh scales up for numbers far too big to scratch in the dust.  I did take the forum-opportunity to cite Gabriela, another 15 year old who was thinking outside the box: which garnered me 6 favorites!

One of the more gracious and respectful commentators cited in the original MarySue piece about Gracie Cunningham was a mathematician called Francis Su "One of the great things about math is that it equips you to see the unseen: things otherwise invisible. There’s structure—patterns—all around us, governing the motion of planets, the spread of a virus, the data that Netflix uses to guess what you want to watch next".  If you're in the business of teaching, especially if like me you're not teaching in Harvard or Heidelberg, you could read with advantage Francis Su's essay on Grace [no no not, in this case our Gracie]: Grace in Teaching. The thing is that, while students in [insert Top Uni here] have their own problems and peculiarities their academic abilities are not in doubt.  What Francis does, and I have tried to do at The Institute, is explicitly recognise students as people, not just as gradable entities. Which has been a hard transition for me because I was really good at schoolwork. There are many posts in The Blob back-catalogs where I've been brought up all standing to realise that something which I accounted as "obvious to all thinking people" was not! See Curse of Knowledge. People may be crap at maths but nevertheless be kind, thoughtful, hard-working, skillful and creative . . . heck, they may be dancers!