Numeracy Hour

First published in Book of Numbers, Imprimata 2009 which can be purchased here

e is the base for the natural log function. Approximately 2.7, it is a transcendental number and cannot be written down precisely in any number format.

Laura Baker, aka ‘Miss’, was beginning to think it had been a mistake to timetable numeracy hour first thing. A mathematician herself, she couldn’t agree more with the principles of the government strategy designed to give children more of an instinctive feel for numbers, but she did wish she didn’t have to implement it on class 6C at nine fifteen every day. This particular morning, as her mouth moved and sent mental maths questions over their heads, it seemed their reactions were dulled by the sticky feel of sleep. She could almost smell it on them.

‘Six times eleven,’ she said, her voice sharp and bright in an attempt to prod them awake. ‘Eight elevens,’ she pleaded. ‘Tell me a rule for timesing by eleven.’ Every time she spoke, the same two hands flew into the air. Zoe Weaver, wiggling and straining as if her fingers were possessed and trying to fly up to the ceiling against her will and Adam Cant, more reserved but consistent. The rest of the class stayed still, or fiddled with something on their desk, picked at a nose. All except Rachel Winters, a strange little girl who had some kind of broad spectrum disorder her parents refused to follow up on.

Rachel never sat still and, while she had a pencil in her hand, she would be drawing. She didn’t draw the things other children drew. No houses or flowers or stick people but, instead, very clear geometrical constructions of shapes with straight sides, ellipses, circles. Her father, a maths professor at the local university, claimed these drawings were the sign of some special ability, but Miss Laura Baker doubted that. Rachel did okay. She had a higher than average reading age, and was skilled at maths, not that she showed any evidence of this in numeracy hour, but there were no signs of any sparkling talent.

‘Square numbers,’ Miss Baker said, now changing her tone and using a smooth, slick voice like chocolate, hoping to sooth the class into participation on a topic that was relatively new to them. She’d drawn diagrams representing the first few on the board and pointed to them as she spoke.

‘One,’ she breathed in, ‘Four,’ breath, ‘Nine...’ The class joined in hesitantly and mostly continued until sixty-four, which left just Zoe and Adam in its wake, chanting all anticipatory and sing song, the way children do in classrooms. Rachel Winters’ mouth was moving too, but no sound came out, and she was going way too fast to be in sync with the others. Her lips were still twitching as the two class stars faded, then stopped, at one hundred and forty-four. Miss Baker sighed, and drew a parallelogram on the board. Her hand moved and made the marks she needed but her mind was on coffee at breaktime. She had been so sure she wanted to work with children. She wondered what she’d be doing now, had she done the Ph.D. Something more complex than drawing a parallelogram on the board, that was for sure. Something more interesting and meaningful. More beautiful.


i is a number such that i² = - 1. It was invented by Euler in his attempts to prove Fermat’s Last Theorem and is considered by mathematicians to be ‘imaginary’ and not a member of the set of ‘real’ numbers.

Mrs Sally Winters threw two tranquilisers into the back of her mouth and washed them down with water from the bathroom tap. Her eyes were ringed red from lack of sleep and a surfeit of gin. ‘Any mother would feel rejected,’ she told the mirror, hoping it would understand better than her husband had the million times she’d said it to him. Professor Martin ‘Rachel is so special’ Winters who was forever promising to cut back his hours at the University to spend more time dealing with her ‘special’ features. Sally breathed and supported herself by clinging to the edge of the sink. ‘Hold it together,’ she told herself over and over, almost chanting, knowing the meds would kick in soon enough, if not quite soon enough for her liking.

Slowly, she returned to the living room. Rachel was exactly where she’d left her; in her own little world. She was drawing again. Even that had to be ‘special’ with Rachel and her constant geometry. ‘I just want to be a normal family,’ she whispered under her breath. This was another of Sally’s mantras to her husband. ‘Who wants to be normal?’ he replied every time until Sally wanted to scream ‘I do, I do, I do!’

Sally watched for a while as her special little girl covered sheet after sheet with circles and ellipses. She could see that these were remarkable constructions and granted that Professor Martin could be right that there was some talent there, hidden inside the puzzle of her daughter.

The drugs began to take effect at last and, together with the buzz left from the gin, they made the world hazy. The sofa felt deep and soft and Sally let it eat her. Rachel could create all the perfect circles in the world but even Sally’s maths was good enough to know that no matter how many, they could never equate to a single hug. Not to an ‘I love you’ or a moment of eye contact and connection, or a smile at the right time.

Any mother would feel rejected.


π (pronounced pi) is a mathematical constant defined as the ratio of the circumference of any circle to its diameter. Its approximate value is 3.14 but it is transcendental and cannot be written down precisely as a decimal, fraction or product of surds.

Rachel’s mother had fallen asleep again. Rachel had noticed this was becoming a habit and had calculated that the average time she slept for was two hours thirteen minutes, after which she would get up, drink tea, and see to bedtime. Rachel didn’t mind at all. She could never work out what her mother wanted from her anyway, never had been able to. Sally would tell her something and wait for a reaction. Rachel knew something needed to change on her face to satisfy her mother but she didn’t have a clue what. She tried experimenting with curling her lips in various ways. Sometimes this worked but, more usually, her mother would shout, or run from the room in tears. Second guessing was exhausting so this new thing, where she fell asleep, it was a relief, really. A relief and an opportunity.

An opportunity to access The Room. This was a place Rachel knew well, somewhere her father took her where she had to be a good girl, draw quietly by his feet and not touch anything. This is why her father was easier. He gave clear instructions and she didn’t need to guess what he meant. It was always hard, though, in that room, to look and not touch. It was the bookcases that were the problem, and the books that looked down on her from the shelves. Sometimes, she would stop drawing and stare at them. They were different from the reading books at school and she didn’t understand the titles at all: Topology of Metric Spaces; Elementary Number Theory, Group Theory and Ramunjan Graphs; Fermat’s Last Theorem. It seemed there was a whole world living on those shelves, one she knew nothing about. The only clue was in a few pictures, similar to the ones she drew so often: circles (inscribed), angles (dissected), regular polygons with lines of symmetry marked in dashes. Rachel was hopeful that this meant the books had her answers.

When she heard her mother snoring, Rachel got up from her drawings and headed towards the hall. Quietly, she pushed the living room door to, pausing as it creaked and peeking through the gap to check that her mother was still dead to the world. There was more snoring from the lounge so Rachel turned and walked down the hall. She opened the door to her father’s study and went inside.


= is a mathematical symbol indicating the equivalence of two values or mathematical expressions.

When Professor Martin Winters arrived home, the house was quiet and the windows blacked out, as if there was a war on. He had left work early, the way his wife had been nagging him to do for several months. It hadn’t been easy. He was working on an extended proof with a senior colleague and they were at a vital stage but, tonight, he had insisted his way out of there. And now it looked like she had gone out somewhere.

He sighed and pulled out his keys, but as he leaned against the front door, it fell open. Now he was worried. He would never forgive himself if something had happened to Rachel or Sally while he’d been wrestling with lemmas and conjectures, and he had a sudden sharp feeling in his chest. Something his wife had said in a row came straight to mind, about priorities, and how his ‘equations and formulas’ wouldn’t thank him when they were older. He hated the way she summed up his work this way, how small she made it sound. But since Rachel had been born he had moments too when he wondered how important it was. He pushed in through the door.

‘Sally?’ Trying not to panic, but louder, ‘Sally, love?’

Martin braced himself as he walked into the living room. ‘Sally?’ Quieter now. And there she was, lying on the sofa. He came a little closer. Just close enough to check she was still breathing. Was she drunk? There was a hint of alcohol on her breath but it wasn’t offensive. How long had she been asleep and who had been taking care of Rachel?

Rachel. Her name shook right through him and stopped everything for a moment. Then he was on the move. ‘Rachel!’ He was not sure if shouting her name might make her freak out but, unable to help himself, he called louder, ‘Rachel!’ He searched her room, under her bed, in her wardrobe. What had Sally been thinking, napping mid-afternoon and leaving his baby to wander god knows where? He scoured the room he shared with his wife, then the kitchen and bathroom, where he saw the pill bottles left carelessly on the sink. He had to make an effort to breathe.

Standing in the hallway trying not to fall to his knees and scream, he noticed a crack of light coming from under the study door. For just a moment his concerns moved from Rachel dead in a ditch to expensive books ripped into pieces or scribbled all over with felt tip pens. To his computer smashed into pieces in the corner. He shook his head. He couldn’t care less about any of this just as long as his little girl was in the room safe and sound. He pushed open the door.

Rachel was sitting in a pile of books with her usual reams of white paper and a worn down pencil. She was crying. He had never seen her cry before. Shout, tear at her hair, bang her head against things, he’d seen all that but never tears. Confused, he swept her up and into his arms. He sat her on the desk and fell into the chair beside her, still faint from his fear. She was clutching a piece of paper and, softly, he pulled it from her.

It was covered in Euler’s identity, eiπ = - 1, written over and over, one of the best known equations in the world but surely something his daughter didn’t understand. And yet, she’d written it in words, e to the i pi is minus one, and copied the definitions of e and i and π from somewhere too. It was this equation that had led him into mathematics in the first place, when he’d learned about it at sixteen and it had melted his brain. An imaginary number pulled from the air as a convenient answer, and two transcendentals, numbers you couldn’t write down with any precision except as symbols, combining to give such a definite answer. He used to think it contained all the beauty in the world. He turned to look at his daughter, who made eye contact and, then, goddamit, she only went and smiled at him. He realised then he had been wrong.


-1, minus or negative one. Defined as the value equivalent to 0 – 1.

Miss Baker was considering cancelling numeracy hour. Of course, she wasn’t allowed to, and given that she agreed in principle with its importance, she didn’t actually intend to. But as she called out simple sums, she fantasised about the activity’s demise. She imagined burning her fill-in-the-blanks pages and dumping the number cubes on the fire they made, watching them melt and the flames turn blue. This was not what she had spent four years at university for. It certainly wasn’t the reason she’d struggled over differential equations, and fought with algebra and various kinds of infinity. There had to be more than this.

‘Tell me the third square number...’ she said, looking around the class for a suitable victim. ‘Rachel?’ She knew this was wrong, putting little Miss Asperger’s on the spot, but she was feeling evil. Rachel didn’t seem to notice she’d been asked a question; she carried on scribbling and whispering whatever it was she whispered to herself. ‘Zoe?’ she said, reverting to the dead cert, but even Zoe was distracted, turning at the last minute and clearly unaware of what the question had been. Laura sighed. This was a disaster; she was even losing her more able and diligent pupils. What was wrong with them this morning? She wasn’t asking them anything they hadn’t done in class, anything they shouldn’t know. She breathed; told herself they’d done nothing wrong. But bad behaviour would have been better than this complete lack of animation. She wanted them to do something, anything. She could suddenly understand the things she remembered from when she was at school and had always found appalling; the teachers who threw boardmarkers across the room, who banged loudly on desks with rulers just to get a reaction. She could see a picture in her head, another version of herself walking around the room poking kids with sticks.

There were murmurs around the room. Children are astute; they know immediately when someone’s losing it. She began to mumble questions then, maths she knew they couldn’t be expected to understand but was tempted to ask them anyway, just to see what they’d do. Then something came out, degree level and louder than she’d expected. ‘For God’s sake year six, I might as well ask you lot about e to the power i pi!’ It was a weak moment, and she looked at her shoes, feeling ashamed. Sarcasm is evil when directed at children under twelve.

A sudden movement made her look up sharp and she saw a hand had shot up into the air.

Rachel?’ Miss Baker’s voice was weak and small.

Little Rachel Winters spoke clearly though, as she looked Laura Baker right in the eye and gave her all the beauty in the world as an answer.