Coming out

February 11, 2018 by

I have been thinking for a little while about whether to write this post, and what to write in it. This post is about Autism, Asperger Syndrome, and a personal journey. There are risks to writing this down publicly, but I think the benefits outweigh the risks, so here goes.

Towards the end of 2017, after a year on a waiting list, I had an assessment and received a diagnosis of Asperger Syndrome. In some senses this marks the end of one journey and the beginning of another. So let’s start with the journey that ended with diagnosis.

I don’t know where to start the story. Birth? Childhood? We discussed my schooling in the assessment, and my dad accompanied me to tell the psychologist about my early life. (I also took all my school reports to the assessment, but that’s a whole other blog post!) Long story short, any peculiarities in my childhood were probably masked by the fact that I was very highly achieving at school, so I was seen as being unusual. Studying maths at Cambridge, I really wasn’t that much of an outlier – even though I did not suspect I was on the autism spectrum, I was aware that I fitted in very well with fellow mathmos and their geek culture, pedantry and precision.

I then started my teaching career. How I became a teacher is another good story, but again, one for another day. The structure and routine of teaching fitted me very well, and my Asperger Syndrome continued unnoticed and undetected. I was me, quirky, mad about maths, a bit eccentric, but no-one ever suggested autism. I taught kids with AS diagnosis, and I was patient and kind and understanding of their needs, and angry when they didn’t get the support they needed. My little brother was making his way through secondary school with his Asperger diagnosis, occasionally struggling, but excelling at all things mathematical and logical. (He followed me to Cambridge, did maths, and is now a software developer.) I read books about autism, I attended training to better help the children I taught who were on the spectrum, and I never applied any of it to myself.

After five and a half years in the classroom, the opportunity to work for NRICH presented itself. I was terrified about leaving the safety of the classroom and stepping into the unknown, but I did it, and started to carve a niche for myself. I have been at NRICH for 9 years now, and I think I’ve been pretty successful.

Throughout my adult life though, there was a bit of a black cloud looming. In 2010, my GP diagnosed depression, and prescribed me antidepressants. I also sought counselling, and had various types of talking therapy on and off for the next half dozen years. One of those counsellors, when I was talking about Aspergers Syndrome in my extended family, asked as a throwaway question in the way counsellors do, whether I thought I was on the spectrum. At the time, I dismissed it, but then in recent years I kept coming back to it.

I read the experiences of late-diagnosed women, and it resonated. I read about mathematicians with autism, and their experiences sounded familiar. I started writing things down. I did the “Autism Quotient” quiz, and consistently scored in the 40s (People on the autism spectrum usually score in the 30s or higher). After following autism advocates on Twitter and reading about the diagnostic process, I went to my GP, and said I thought the depression and anxiety were symptoms of undiagnosed autism. He agreed it was a possibility worth investigating, and referred me.

When I told people I thought I might be autistic, there were a few common responses: “of course you’re not, autistic people can’t communicate and you communicate very well!” Or “even if you were, why does it matter? You’re doing fine!” Or “my cousin’s son is autistic and you’re not like him.” But other people, particularly autistic people, were supportive and encouraging. Check it out, they said. Yes, that sounds familiar, they said. You are not alone in feeling like that, they said. I am grateful for friends both autistic and not, who supported me and encouraged me to search for an answer.

Then in December I spent three exhausting hours talking through every aspect of my life, looking at all the ways in which I am different, odd, peculiar, dysfunctional, a misfit. And at the end, the psychologist said yes, I have Asperger Syndrome. I hide it very well; I have excellent coping strategies, but ultimately I have spent 36 years trying to make sense of a world designed for neurotypical people without ever realising I wasn’t one of them.

Diagnosis was a huge relief. Many things suddenly came into focus, I have begun looking back over things that have happened and been able to make sense of them through this new lens. My depression was a result of exhaustion at masking my natural ways of being and responding in order to try to fit in. My anxiety was a fear of the disruption of routine and the security of the known. My low self esteem was from a sense of not being very good at being neurotypical. Just those simple words, “you have Asperger Syndrome” made me feel amazing, because I don’t have to look at my failings as a “normal person” but rather celebrate my successes as an autistic one!

People weren’t sure how to respond when I shared the news. Those I love most dearly were quick to remind me that nothing has really changed, I am still unique, quirky, wonderful, expressive Alison, I just have a new label that better explains me to others. I think “congratulations” is a nice response, although those who took the time to ask “how do you feel about it?” are my favourites. Those who say things like “are you sure? You don’t seem very autistic to me…” can… well, I think maybe those are words that are inappropriate for this blog.

And why have I chosen to post this rather personal narrative on what is usually a maths/pedagogy blog? Well from now on, my journey through life includes the knowledge that I see the world differently from most. When I work with students and there are aspiring young mathematicians who are autistic, I am a role model for them in a slightly different way than before. I am fascinated at how many people on the spectrum seem to find a niche in mathematics and I would love to explore that further. But most of all, I am not ashamed of my diagnosis, and I want people to know, this is what an Actually Autistic person looks like. I am still me, but now you know a little bit more about who I really am.


A STEP too far…

June 2, 2017 by

This morning I performed an experiment. Around a quarter of my time at work this year has been spent working on materials for the STEP Support Programme, and I thought it would be useful to put myself through the experience of doing a timed test. I chose last year’s STEP II paper, printed out a copy of the formula book, got a fresh pad of paper, some pens and a pencil, and set the timer on my phone for three hours.

Wow, what an experience. I have learned some valuable lessons that will certainly inform the responses I write on the STEP Support forum, and the messages I share with students when talking about STEP at events. And the messages I share with teachers, for that matter.

Having spent lots of time this year working through questions, I was pretty confident that even under time pressure I’d be able to produce some pretty good mathematics. And in places, I did! I came up with sensible ideas, did sketches, wrote stuff down. But I also did some disastrous mathematics, and exhibited some of the worst exam technique you could imagine. (I also took a fifteen minute break in the middle to check email, get a glass of water and go for a wee. I promise I didn’t cheat or think about the questions during that break though.)

Having looked at the mark scheme afterwards I think I probably scraped enough marks for a comfortable Grade 3… disappointing.


A decent sketch makes all the difference. This wasn’t.

Here’s where I think I went wrong, and what I have learned:

  1. I’ve been doing a lot of STEP III questions lately, so I think I overcomplicated things in a lot of places because I had forgotten that STEP II is on a narrower and simpler syllabus. I expected it to be harder than it actually was, thought to myself “It can’t be that easy…” so I did lots of unnecessary algebra. And once I was in that mindset, I couldn’t see the wood for the trees.
  2. Having got myself into lots of messy algebra, I found that I made lots of mistakes. This is the difference between me at 18 and me at 36 – at 18 my full time job was preparing for A Levels and STEP, and as I was doing Maths, Further Maths and Physics, I was spending a significant proportion of every day performing integration, differentiation, curve sketching, algebraic manipulation, trigonometry… Let’s face it, I’m rusty! I only spend a few hours a week working on STEP level maths these days, so it’s unsurprising that these skills are no longer fresh.
  3. Question choice. The bit that I did right was in reading through the whole paper before I started – I checked the timer and I think I took about 8 minutes circling things, annotating the paper, and thinking about what I might do. Then I did something daft and picked a Mechanics question, to prove that I can do mechanics now. And got stuck. And panicked. And spent too long. When I looked through with the mark scheme, I reckon I would only have got around 10 or 11 marks for what I did, but I spent more than a quarter of my time on it. As it was, I only attempted 4 questions, and two of those were little more than fragments.

But hang on – isn’t this exactly WHY we tell students to do a timed test before their exams? (Or preferably more than one!)


Further up the page, I failed to integrate correctly. Then I criticised myself.

Doing STEP questions with no time pressure, with the ability to look things up, to go away and think about it, to concentrate on one topic at a time, is a million miles away from actually sitting the exam. This exercise of trying a paper under near-exam conditions helped me to reflect on ALL the skills students need for STEP. Because as well as the problem solving mentality, the good ideas, the willingness to try things out, you also need fluency, timekeeping, common sense, self-discipline… I think my work this year has developed the first set of skills with regards to STEP, but it was never intended to address the second set. Perhaps I was too unkind to myself calling me “FOOL” but the sense of frustration that I have lost the ability to integrate accurately under pressure and concentrate on STEP questions for hours without a break overwhelmed me. And perhaps this is the final lesson to take from my experiment – preparing for an examination like STEP is overwhelming. It’s not just about developing the fluency, practising lots of questions, managing time effectively; it’s also about being kind to yourself, remembering that you are only human, and acknowledging that it’s just an exam. Once it’s over with, there will be music, dancing, flowers, love, and other things that really matter.

That’s easy!

May 31, 2017 by

There are various words I would like to ban, or rather, as I am generally quite liberal in my views and don’t tend to go in for banning, words I would caution against using carelessly. I may blog more about such words in the future (Ha! Who am I kidding? When did I last blog?) but for today let’s talk about the word… easy.

“Let’s start with something easy!” “I know it looks hard, but don’t worry, it’s easy!” “If you can do x you’ll be able to do y because it’s much easier!” Familiar? These sort of phrases trip off the tongue, particularly if you are an educator who wants to make your learners feel safe. They are all messages designed to make the listener less anxious, and more capable. They are intended to empower! Unfortunately, I know from personal experience that such messages can be the opposite of empowering.

You see, “easy” is not a property of a task or a concept. It is a relationship between the task or concept and a person. There is no such thing as an easy question, because it depends on whom you are asking. (Don’t even get me started on political interviews in which someone is badgered to answer a “very easy question, yes or no” where actually a more nuanced answer is necessary and neither “yes” nor “no” is a satisfactory answer).

In some cases, it is glaringly obvious that “easy” is not a straightforward absolute concept. For example, if I were to ask an A Level Further Maths student to find the values of x such that x2+5x+6=0, I would hope they would agree with me that it is an easy question. If I asked my 11 year old niece, she would find it very hard. If I asked my friend’s toddler, he would find it impossible to even understand the question.

I can see two problems that may arise when using the word “easy”. Firstly, using the word glibly without knowing your audience. This can happen when teaching or presenting to a group you do not know well, or a group where you make assumptions based on their prior knowledge, achievement and experience. You start off with an icebreaker, something everyone will be able to handle, and you introduce it as such. Then you find out that you’ve massively misjudged the situation, and people are stuck on your easy task! Or, perhaps worse, everyone does find it easy, except some poor soul who is then left behind (or hides the fact they don’t understand and just feels utterly rotten). This can be mitigated against by using “Low threshold, high ceiling” activities where literally everyone can get started and you can assess what “easy” means in the context of the group in front of you. And if you introduce the task with “here’s a thing” rather than “here’s a lovely easy thing”, so using neutral language, you’re not setting people up for failure if they don’t get it straight away. The flip side of this is that if you introduce something that many people might find difficult, but with neutral language, you’re not in danger of setting up a self-fulfilling prophesy. I remember teaching the technique of completing the square to a group who were not expected to tackle such questions because they were in one of the lower sets. I didn’t tell them it was a “hard” topic until we’d finished. Their response? “But that was EASY, miss!” It wasn’t often I heard that class say THAT!

The second problem is more subtle. This can happen when you know someone well, and make assumptions about what they will find easy from what you already know they can do. The problem with this is that there isn’t a nice linear spectrum from easy to hard with everything in the same order for everyone. This one has bitten me in both directions. It has taken me decades to understand that just because I find some things very easy that other people find hard, it doesn’t mean I won’t find hard the things they find easy! For example, I am pretty good at solving STEP maths questions, and I am terrible at recognising faces or noticing when people have changed their appearance. There have been times when people have made me feel awful by saying things like “but you can do x, of course you must be able to do y!” I am pretty sure I have also made other people feel rotten by assuming that they would find something trivial based on my knowledge about other things they could do. (Sorry! I really will try harder in future not to do this! If you catch me doing it, call me out please.)

In general, I think as educators we should use the word “easy” with caution. There are better and clearer ways to express the meanings we are trying to capture, and if we allow learners to make up their own mind whether something is easy or hard, and listen to what they have to say, perhaps they will become resilient and resourceful, rather than feeling rotten.

Thinking about Dotty Grids

May 1, 2014 by

There’s loads of stuff about dotty grids on NRICH at the moment. I’m trying to get my head round Pinterest, and figure out what content can be shared there, so why not check out my dotty grids pinboard? I’m sure I’ll add more to it once I figure out what can go there!

Meeting maths

May 21, 2013 by

At NRICH meetings, we like to devote a little bit of time to working on some maths together. Today I’d like to share the problem that m’colleague Mike presented.
Mike provided dotty paper and circular objects to draw round, and invited us to investigate the convex hull of the points contained within circles of our choice. (The convex hull is what you get when you join together the points nearest the edge of the circle without being allowed any concave bits – imagine the circle is a rubber band on a pegboard and when you let go of it it springs round the outermost points.)

Mike threw a few possible questions at us, and then let us get on with it. This is my favourite type of maths investigation; very open ended, and no compulsion to work on something that someone else finds interesting, at the expense of exploring my own avenues. I started by centring my circles on a grid point, and exploring possible shapes. After a very short while, I got distracted and wanted to know whether I could create something in GeoGebra to help me. Others were busily discussing symmetry, whether shapes with different numbers of sides were possible, what happened as circles got larger, and much more. We even talked about practical applications of the mathematical ideas, approximating circles on a square grid such as pixels on a computer screen.

Alas, the meeting was over all too soon (not something you’ll hear me say very often!) and I had to get back to other things, but I saved my GeoGebra file to explore a bit more when I have the time. And if this starting point provokes any interesting questions for you, do let me know in the comments!

Charity Shop Maths 2

October 29, 2012 by

My second charity shop find is the marble puzzle that some of us played with at October MathsJam.

I picked this puzzle up in a charity shop somewhere down south while waiting for my brother to have a job interview this summer. I recognised the puzzle because my other little brother had it as a child and I used to spend hours playing with it after he’d gone to bed, when I was babysitting.

The object of the game is to use the Knight’s move from chess to swap all the blue marbles with the… well… I think they’re brownish, or maybe pink? Anyway, the marbles of the other colour. According to the box, 50-55 moves is average and 45 is excellent. I seem to remember I used to be able to solve it reliably, efficiently and quickly, but having played around with it again I have forgotten all the little tricks and skills I had as a teenager.

If I get any spare time in the next twenty years or so, then implementing a computer version of this puzzle would be an interesting programming challenge. It’s probably already been done, but it’s the sort of thing I can imagine rather enjoying having a go at for myself. Meanwhile, when I get bored of using my Tower of Hanoi as a stress-reliever that lets my mind wander, I have the Knights problem to occupy my hands too.

Charity shop maths 1

October 22, 2012 by

I have a good excuse for not blogging for a while – over the summer I was finishing my Masters thesis. Now that it is handed in, I’d like to get back into the habit of blogging, so I thought I’d do a short series of posts on my habit of finding mathematical stuff in charity shops. My other half is a record collector so I spend lots of time waiting for him while he browses record racks, and I use that time looking for geeky stuff in among the bric a brac and the books. It was actually from his record collecting that I got the idea of this series of posts; on his record forum they have a ‘charity shop challenge’ where people post about cool stuff they’ve found.

I found this in one of the charity shops in Ely, near Cambridge, some time ago. It looks hand made, and cost a couple of quid.

For those unfamiliar with the old problem, this is a Tower of Hanoi puzzle. The object is to transfer all the rings from one peg to another. You can only pick up one ring at a time, and you can never place a ring on top of a smaller one.


This shows the puzzle after a few moves have been made. (How many?) Altogether, there are nine rings. I did move all the rings successfully but not all in one go. This was a great find, because I’d been familiar with the Hanoi problem for many years, but actually having a purpose-built puzzle to play with it ‘hands on’ refamiliarised me with the task. If I was introducing the problem to kids, I’d want them to have something to manipulate. When we were little, we used to do it with the brass weights that went with the kitchen scales, as they were little discs of different sizes that stacked.

Have you met the Tower of Hanoi before? Have you used it in a classroom or masterclass situation? Have you ever found anything cool, mathematical and geeky in a charity shop?

Maths I saw on my holidays – Toronto edition

June 19, 2012 by

Well I guess it must seem like all I ever do is go on holiday! Actually, work and life have been so hectic that the only time my batteries are recharged enough to blog are after I’ve taken time away. Check out the Cambridge MathsJam blog to see what else I’ve been up to in the past few months.

So I had the chance last week to spend a few days in the Canadian city of Toronto and the surrounding area. Here’s some of the maths I spotted.

The very first walk we went on took us past Canada’s Walk of Fame, where I snapped this picture of a ‘star’ who lends his name to a problem that causes arguments among probability enthusiasts the world over:

A little further along the road, I was outraged by this misuse of mathematical symbolism:

No wonder our students misuse the equals sign to be a “the answer is” sign!
Moving on, while stocking up on some important groceries I noticed that in Canada you can buy cereal with magnitude and direction:

The most awe-inspiring parts of the trip were the natural beauty and force of nature that is Niagara Falls, and the towering man-made achievement of the CN Tower. First the falls:

Here are some facts about Niagara falls. I wonder what it’s possible to deduce from the picture.

And here’s a view looking pretty much straight down from the CN Tower. I wonder if it’s possible to estimate the height from this picture. Visit the CN Tower Website for all your CN Tower factoids.

Well after all that I’m pretty hungry. Can you estimate the calories in this picture?

Finally I was drawn in by this basketball court.

I’m sure it’s to put mathematicians off their game by distracting them with intriguing patterns!

I’m already thinking about where to go on holiday next, once my Masters thesis is submitted. Any suggestions of maths-rich holiday locations? Any favourite maths pics from where you are?

Maths I saw on my holidays

February 28, 2012 by

I’ve just come back from a lovely long weekend in the Netherlands. We stayed in Zwolle, capital of the Overijssel province, and also visited Ommen, Giethoorn, Zutphen, and we stopped off in Utrecht on our way home. Of course I kept my eyes open for maths while I was away! Some of the pictures are only mathematical in a very tenuous way but I hope you enjoy them anyway. Click on the photos for bigger versions.

First, the obligatory Dutch windmill shot. The sails look a little like a plus sign – that’s mathematical, right?

Next, a couple of floor patterns, one from a department store and another found on a pavement outside a supermarket.

There’s loads of maths in this photo of a cheese shop! How many cheeses? How many kilograms of cheese? How far would I have to jog to burn off the calories if I ate it all?

I loved these cute little mushroom shaped signs showing the distances to nearby places. Note the European comma where we would put a dot for the decimal point.

Right by the mushroom sign was a hexagonal cycle route sign. The world should have more hexagonal signs.

Next, a couple of clocks. I love clocks, particularly station clocks and clock towers with bells. I learned that the Dutch word for clock is ‘Klok’.

If you look very carefully at the packaging for the mini waffle I got with my cup of coffee, you’ll see a tiny diagram showing that it has a diameter of 4.5cm! Ideal if you want to compare waffle sizes between different cafes.

The waffle diameter cafe also had these brilliant salt and pepper pots. I’m not sure how you tell which is which. Is salt a 5 sort of condiment or more of a 3?

Our hotel lift pleasingly used the negative numbering convention for floors below the ground floor:

In the UK we have signs saying ‘No Under 18s’. In the Netherlands, they use a strictly less than < sign instead:

Finally, when I’m not being a mathematician I dabble in music. We saw a wonderful display of harmonicas in a shop window, including this fabulous six-sided harmonica :

Alas, the shop was closed so I couldn’t buy it.

What do you think of the photos? Which ones are the most mathematical? What maths have you spotted on holiday?

You are welcome to use and share these photos for non-commercial purposes, as long as you credit me and link to this post.

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How to start a MathsJam

January 25, 2012 by

Take three pounds of mathematicians. Peel, remove any stones, and place in a pan with a little water and sugar. Bring to a simmer and stir occasionally. Test the jam on a cold saucer until it wrinkles when you push a finger through it.

Actually, that’s not how you start a MathsJam at all. I waited for some time for someone to create a Cambridge MathsJam, having seen the success of the ones in other cities and enviously following events on Twitter wishing I could be there. After attending the first two MathsJam annual conferences and having a jolly good time, I realised that everyone else in the Cambridge area was also waiting for someone else to start a MathsJam, and despite having the organisational skills of a very disorganised thing, I thought I’d give it a go.

I asked a few close friends if they’d be interested in coming along, and got in touch with Katie Steckles who organises the Manchester MathsJam. She provided me with oodles of advice from her own experience, together with some words of wisdom from Matt Parker of London MathsJam. Then I contacted the pub where we tend to go for pub lunches from work on the rare occasions that I’m allowed out of the NRICH office, and asked if they could reserve a couple of tables for us. “Probably between half a dozen and eight people I would guess”, I said when the landlord asked how many to expect.

So we had a venue, and a date. Now came the publicity! I sent a couple of tweets, and they were picked up and retweeted. Now that we had a venue we’d been added to the MathsJam website, so people started getting in touch that way. The close friends who had encouraged me to go through with this then invited everyone they could think of, and those people also mentioned it to their friends. I emailed the landlord: “Actually, it’s going to be more popular than we thought – maybe as many as a dozen or 15 people!”

While I was out shopping, I saw some bits and pieces – some of those wooden puzzles with rings that you have to disentangle, some playing cards, a set of dominoes, and I started building a MathsJam resource bag. I also stocked up on paper and pencils, chucked a couple of calculators in, and dug out one of my spare Rubik’s Cubes. Then yesterday evening I turned up early at the pub with my little brother in tow, got a drink and something to eat, and spread the maths paraphernalia out on the table so that people would know who we are.

“Is this the MathsJam?” “We’re here for the MathsJam.” “Hello, I’ve brought some maths!” The lovely thing was that people just sat down and started talking to each other. I’d prepared a sheet with a few NRICH problems to use to break the ice, and this proved to be a good idea, because once people were talking they started sharing other problems, card tricks, origami. I kept an eye on Twitter and read out some problems that were being worked on elsewhere, although we didn’t get round to sharing much of what we were doing. At one point, I counted 23 people in our corner of the pub, all working on maths and enjoying a drink! As people started to drift off at the end of the evening, I heard a lot of “Cheers, see you next month” and “I’ll bring you that problem I told you about”. I regret that I didn’t get the chance to talk to everyone and I didn’t catch everyone’s names, but I have high hopes that the people I didn’t spend time with will come back next month, and the month after, and the month after that…

A huge thank-you to everyone who made the first Cambridge MathsJam a success. Here’s to many more!

These are the problems I put out on the table at the start of the evening. We are building a collection of similar problems on NRICH and eventually they’ll have their own page. They should require no knowledge beyond A Level, and many can be solved using GCSE level content.

The next Cambridge MathsJam will be Tuesday 21st February at the Castle Inn, Cambridge. Visit the website if you want to join the mailing list. To find a MathsJam near you, see