I’m really sorry, Maths. People try to get me back into you. They talk me patiently through cashflows, urge me to take the right mindset to our relationship. We rub along okay together, don’t we? But you and me, if we’re honest, it’s like wading through mud. I have no real answer to where we went wrong, Maths, but I can take an educated guess. Do you remember when we were young? Pouring water from jug to jug, squelching in puddles on the floor. Sunlight spilling through the classroom windows and dust motes spinning in the air. We went with a few friends, do you remember that? Into the secret place that was our head teacher’s office, to talk through some puzzles. We were happy then. We had no fear.
But later, do you remember, things started to go wrong? You put me on the spot, insisted on answers I just didn’t have. Told me you were numbers on a grid, that I must remember (or else). Then later on, someone said you weren’t really for girls, anyway. And that was me done. We began to lose touch. We drifted apart. But do you know what swung it? It was when I met Miss Ladd, and Valerie and Hilary. They showed me how words could open up my world. That I could use language to make sense of my thoughts. And that was me, gone. Yes, I honestly believe you are beautiful, and magical, and full of wonder, Maths. But I’m really sorry to have to tell you this. I’m just not that into you.
Freeing the Angel 
You teach in a primary school still, right?
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No.
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You’re not? What are you doing now?
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My biography is on my website. Did you have a comment on the blog post?
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I do… I’ve been mulling it over since a previous post. One was on mindset, the other, I could’ve swore was also on mathematics, mentioned cash flows, and talked about how you seemed to struggled to comprehend any of it, and not for want of trying!
Frustratingly, I can’t find that last one for some reason, so can’t find the exact words again. But anyway, at the time I remember thinking it retained that air of the ‘myth of ability,’ that some people have a ‘maths brain’ and some people don’t.
While there are some people who we might categorise as having some form of significant cognitive impediment, they are the tiny minority. While there are some people who appear to exhibit some form or extremely rare talent or gift for mathematical thinking, it is just that, rare. Nearly all of us fit into the ‘average’ category for the most part, and then all that differentiates us is experience.
So it sounded like you were getting frustrated to the point of having given up; a sense of ‘I’ve never been able to ‘do’ maths, and I guess I never will;’ but I would maintain that it’s still down to insufficiently effective teaching, not anything lacking in you.
This relates to the mindset post, which reminded me of this cartoon (of which there are a few variants):
One of the life-lessons I probably learnt a bit too late in life, but one which some people never learn, is the power of an objective-oriented mindset, and the rejection of excuses. In entering teaching, I was delighted to find that teachers seemed to have become so accountable, and that in Teach First especially the whole ethos is geared around what are *you* going to do to ensure the kids succeed? Eschewing utterly the alternative mindset of ‘good kids’ and ‘bad kids,’ wherein there’s only so much a teacher can do with a ‘thick’ kid, or a ‘poor’ kid one from a ‘bad background.’ etc.
But, unfortunately, I also quickly saw the damage that taking this to its extreme conclusion had done to children in schools. The attitude of a great many failing children, and that of their parents, was exactly as expressed in the cartoon. It was the teacher’s fault, the teacher wasn’t good enough, if they get a C grade, they’re doing it *for* the school, we should be grateful if they do any work at all.
A travesty of education.
Institutionally, we had allowed the children growing up to abdicate all responsibility for their own learning and development, in the name of increasing teacher accountability. They expected the school or the teacher to somehow guarantee them a certain grade, without having to do much themselves, or without having to take any responsibility for their own success – if they fail, it’s the school’s fault anyway.
Bringing this back to mindset, and your concerns around those who try hard and still seem to succeed little – I’ve shared those concerns on occasion. Here’s how I’ve ended up concluding on it:
It is the child’s responsibility to work hard, and to do as we ask. If they are working as hard as they can, and doing all that we ask of them, then and only then can their accountability for failure be passed to the teacher. If working with a motivated, determined child, that child fails to learn anything, then of course the teacher must take responsibility at this point, and be prepared to do all that they can in turn to help that child succeed; because they can, and they will, in all but the tinniest minority of cases.
Linking this back again to your experience of mathematics, there is, I am certain, nothing wrong with your brain. You have as much a maths brain as any of us, you just haven’t been taught in the way that’s needed to help you realise that; and by now, sadly, perhaps you never will.
There’s a substantial difference between prepared to rationally acknowledge that there might be beauty and awe and wonder in mathematics, and actually experiencing it for oneself. The first is really more a recognition that so many others say it’s true, so it must be true, while also acknowledging that you don’t see why (I understand that feeling, since until two years ago it was exactly how I felt about poetry, and before that, philosophy, and history, and so many more of the arts and humanities.)
Worthy of note, you mentioned cash flow analysis (and I’m sure you mentioned it once before…) – this is *not* mathematics per se. Cash flow analysis is mostly number crunching, and at its best, arithmetic modelling – the grown up equivalent of ‘A bus has 20 people on it, 3 get off, 7 get on, how many are now on the bus?’ Very, very few people are ever inspired by this super-narrow sub set of mathematics. Yes there can be elements to it from which some individuals can find satisfaction or derive a certain forensic puzzle-hunt enjoyment, but really to call it mathematics would be equivalent to reading the following and declaring that you just can’t find a passion for literature:
http://www.printingforless.com/paperdescriptions.html
Arithmetic is also the most mentally frustrating and, often, dull part of mathematics. It’s almost sad that we call maths in primary school ‘maths,’ because it leads to everyone growing up thinking that mathematics is arithmetic. It is not. Arithmetic is, again, a narrow component of mathematics, and one which divides people the most in terms of their ability to process it.
I feel like you must have heard of this story before, but if you want any glimmer of real awe and wonder you need to look at things like the story of the rice and chess board. Sometimes set in China, other times in India, it features a king who loves chess, and frequently challenges visitors to a game. Upon losing to (insert character depending on story variant) he offers any prize the challenger would claim. The challenger requests that a single grain of rice placed on the first square of the board, and then double that on the second square, and double that on the third, and so on.
Mathematically that’s 1 x 2 x 2 x 2 x 2… and you keep doing that 64 times in total. Grab a calculator (your computer has one) and try it and you’ll quickly see why some stories have the challenger being executed by the king! While others have him in eternal debt to a god:
http://www.singularitysymposium.com/exponential-growth.html
If you take a sheet of A4 paper and fold it in half a few times, obviously it becomes a bit thicker. How many times would you reckon you’d need to fold it before it reached the moon? Ball park estimate… ?
Forty-two, is the surprising result. Perhaps even more surprising, if you could fold it 102 times then it would be as thick as the universe! (Though I worked it out to be 99 folds – maybe they started with thinner paper?)
http://www.singularitysymposium.com/exponential-growth.html
All the more remarkable is the the mathematical thinking that underpins both these stories, of chess playing kings and paper on its way to the moon, is the same! It just looks different on the surface.
For awe and wonder you need to understand why the Pythagoreans would be prepared to murder one of their own for fear that he revealed the dark secret they had uncovered about the nature of the square root of 2
Or to recognise that perhaps the Egyptian Pharaoh Cheops, whose pyramid was the tallest building in the world for nearly 4000 years, did not build his great pyramid solely as an eternal resting place, or some act of devotion to the gods, but to be responsible for building something on so enormous a scale as to be entirely observable, but also completely immeasurable; to have subjects look upon a wonder they cannot understand for now and forever, and know their small, proper place in this world.
How exciting, then, to learn the story of an unlikely hero, the underdog Thales of Miletus, one of the first of a new breed of thinkers, from Greece, who around a thousand years after the pyramid was completed took a trip to Egypt, and while there opted to prove the immeasurable measurable with his newly discovered understanding of triangles, bringing the hitherto mystical knowledge and understanding of this ancient Pharaoh back into the public domain.
Any of these stories can spark imagination, and hopefully with them, a thirst to better understand exactly how and why these ideas work. Knowing it takes 102 folds of a sheet of paper to reach the edge of the universe is astounding! Having the power to challenge that and argue maybe it’s 99 is all the more thrilling.
But, that comes with years, and years of study and deliberate thought. Not everyone who’s already post-school years is likely to make it any more. They don’t have access to the teachers they need, and don’t have the time even if they did; maybe we can do better for the next generation.
I guess my points, in sum, were that if you feel like you could never get there, it’s not because of anything you did wrong necessarily, the mathematics teaching you’ve received just hasn’t been good *enough,* no matter how patient, kindly and well-meaning those who’ve since tried have been. And cash flow analysis is not ‘mathematics,’ it’s just some number crunching. It’s alright, but nothing that inspiring.
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Sorry, paper universe link here:
http://www.iflscience.com/space/fold-piece-paper-half-103-times-and-it-will-be-thick-universe
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Thanks for your detailed comment. I’m perfectly aware that my inability to ‘do’ maths now is probably as result of some of the teaching I had as a child, because this is the point I was trying to make in the blog. I’m not so sure you can abdicate all responsibility for motivation to the student, to my mind that in part comes from the passion of the teacher (which is where the English teachers I mentioned came in – they showed me its value, and purpose, and consequently motivated me to learn about it). I mention cash flow only because this is the only meaningful interaction I have with numbers these days, when ensuring that our preschoool does not become financially unsustainable.
Just in passing, Kris, and I hope you won’t take offence, but sometimes the way you comment on my blogs feels more than a little patronising. I’m aware of many of the mathematical examples you give above, and I sense your passion for your subject, but I am uncomfortable with the way you seem to assume you know how I should think or feel better than I do myself.
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Nothing of the sort was intended. Apologies if anything came across that way; though obviously can’t promise it shan’t again as it was never intended in the first place! It’s just stream of thought, often – not necessarily well-considered, on my part.
You’re probably right about motivation. That’s a tricky one. I’m not sure we’ll ever nail that one completely for everyone. Could you imagine a country filled with tens of millions of children all universally motivated to learn everything…?? I’m not sure I can ever picture that becoming a reality, which is a shame.
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