Colouring In

My model of the colouring sequence

My model of the colouring sequence

As you know, all we do in Primary Schools is colouring. No primary school classroom is complete without felt tips or a child whose job it is to sharpen the pencil crayons (The Pencil Crayon Monitor). In fact you can tell how classy a school is by whether it uses pencil crayons or not. And when it comes to extension for the more able, well obviously the first challenge is to draw a picture; the second is to colour it in.

And yes you’ve guessed it, my lesson to avoid embarrassment on the quiet coach was ‘colouring in’. Twenty minutes into the journey, I whipped some felt tips and paper out of my bag (much to the bemusement of the nearby commuters) and not long after that, all the children were colouring in.

But this was no colour by numbers exercise. Oh No. We were heading to a computing workshop at Microsoft and I didn’t want my children going in completely cold. So I told them some rules to follow and asked them to come up with their own four colour sequence. The rules went like this.

  1. Colour a single square in the middle of the paper with the first colour of your sequence.
  2. Colour the squares that adjoin by a single straight line with the next colour of your sequence.
  3. Go back to 2.

I then demonstrated (with the model pictured above) what the sequence would look like after you run it through a couple of times. The children were all of one mind which I would sum up as “Wow! I want to have a go at that.” I’m always amazed at the power of colouring in. This is what happened:

Jules didn’t get it. He suffered from something that I call the ‘Asimov effect’ and produced this:

Jules's attempts to follow the sequence

Jules’s attempts to follow the sequence

I know that in Ofsted terms, Jules made no progress whatsoever. That would be the case if the learning objective was ‘to use rules to describe a sequence.‘ No WALT or WILF achieved here. But as the actual objective was ‘to maintain quiet for the benefit of the other commuters on the coach and therefore minimise my embarrassment’ then I feel vindicated in the effort that Jules put.

Meanwhile, Robert started well, but then faded.

Robert's effort

Robert’s effort

His work demonstrated much of what we do in the English education system: when we make a mistake, we pretend we haven’t noticed and keep on making the same mistake, believing that the end product will still look fine. As you can see. Robert’s colouring looks fine, but he completely failed to follow the sequence after about the fourth iteration.

Sarah's Colouring

Sarah’s Colouring

Sarah’s work, much like Robert’s demonstrated a lack of self reflection. She did get slightly further before the first mistake was made (look at the purple layer on the 9th iteration). But believing that was doing fine, she carried blindly on for a while. I am slightly encouraged that she didn’t go to the edge of the paper like Robert did. This indicates that her enthusiasm was fading somewhat, which is what should happen if you’re doing something wrong. She didn’t however think about checking with me to put her back on the right lines. It’s still a nice picture though, right?

Meanwhile Ebony-Rose’s was much better than those that had gone before. Unfortunately I don’t have the image, because we seemed to have misplaced it somewhere on our travels around London. The main reason she did better was that she kept asking me what the next step was. Remember that Ebony-Rose is the real special needs child in the group, working over 4 years behind where national average is. I need to write a separate blog post to describe the interesting things I observed as Ebs undertook this process.

Melissa did really well

Melissa did really well

Melissa and Luke really got it. Melissa did keep asking me if she was on the right lines, but Luke just flew. He seemed to really grasp the logic of the sequence and if you look carefully at his drawing, you can see he made virtually no mistakes, even when he was on the iterations where he had to colour hundreds of purple squares.

I was especially encouraged by this and I can’t help finding it really interesting that a child who in all practical terms can’t read, can find it so straightforward to follow instructions that produce a sequence as complex as this one.

Luke really flew: this is his finished work.

Luke really flew: this is his finished work.



The Quiet Coach

As it happened, my second day with the Mathemateers was a trip to London. I’m going to tell you the story of that another time.

Today’s story is about the train journey.

No. Today’s story is about the inflexibility of booking systems and the lengths we British will go to to avoid being embarrassed.

There I was, a couple of weeks before Christmas about to click the ‘submit order’ button on the Virgin Trains website. One click and the booking was made. Myself, a teaching assistant and my not-even-nascent group of ‘low-ability’ maths children would go to London, by train, visit Microsoft headquarters, attend a workshop led by Miles Berry, and maybe even see some of the sights.

And then the ‘e-ticket’ came back through to me and it said ‘quiet coach’.

QUIET COACH? Why would an automated booking system put a group of 5-15 year old children on a quiet coach? I could feel the embarrassment of the situation and it was still a whole month away. Mid-December and I was worried about saving face in January. Immediately I rang up the Virgin Trains helpline. A very nice man from India answered the phone and told me he could do nothing about it, but he did give me the phone number of the customer care team. I rang them up and a very nice lady from India told me that as it was an ‘e-ticket’ nothing could be done.

I was stuck with a quiet coach. My mathemateers (as I now know them are lovely), but not guaranteed to be quiet. Sarah, in particular, has a hearing impairment and an enthusiasm that knows no bounds. By herself I knew she would ruin the ambiance of any so-called quiet coach.

So I fretted quietly to myself, wondering what I would do in that first week back. On the first day back in January, it was teacher training – I had some time in the afternoon to plan a solution, but I did nothing about it. Then the next day, I met the maths group for the first time and we came up with that name and I decided to blog about what happens as I teach them. I still had nothing. All I could do was plan a lesson. So that’s what I did. Yes, the fear of embarrassment in a public place led me to plan a lesson for a train journey. I know.

And when the day came. After the taxi and wait at Birmingham New Street and the inevitable finding of seats (I always find asking adults to leave their seats due a reservation awkward) I pulled my lesson sheets out…

The lesson didn’t start immediately. I had to let the awe and wonder die down first. You see three of the seven children had never been on a train before. 2 of them had never been out of Birmingham. Only one had been to London.

So after about twenty minutes during which the classic question “Do they have different money in London?” was asked, I was getting increasingly conscious of the looks from various commuters on the quiet coach. So I started the lesson.

Do you know what? – it went really well. But that’s yet another story for another time.


Starting at zero

In my very first session with the Mathemateers last week I spotted a significant thing that Jules was doing wrong.

When he counted he did not start at zero.

It seems bizarre doesn’t it, that someone can get to ten and still be unsure how to count.

However I remember a friend I was at school with, who after finishing his degree in politics, confessed to me that whenever he subtracted in his head he was always one out. When I listened to him subtract I could hear that he counted the first number as ‘one’. So if he was doing, say 25- 9 he would count back 25 as one, 24 as two, 23 as three and so on, rather than starting at zero. He didn’t make this error adding and strangely had got all the way through GCSEs, ‘A’ levels and a university degree with this slight impediment to his maths.

My friend never looked back from the revelation I presented to him. A couple of years later he did a masters in Computer Science and now project manages big software design projects in Australia.

I’m not sure, but Jules seems to have had a similar epiphany. He has stood still in maths for a year or so – he should be working at level four, but is struggling to maintain level 3. On Tuesday last week I noticed that when trying to read the time, he counted round in chunks of 5 to what should have been 30, but read out 35. The minute hand you see was on the ‘half-hour’, Jules knew that each digit on the clock face meant 5 minutes, but somehow managed to construe half past 5 as 5:35. He started by counting the ’12’ as 5, the ‘1’ as 10 and so on, rather than starting at zero minutes.

In my pen-portrait of Jules I mentioned this misconception, thinking that I would be spending the next couple of weeks teaching him how to get out of it. But not so. It seems he is out of it…

From then, he hasn’t  looked back. At the weekend he practised 33 different Khan Academy activities and almost doubled his points (he’s been using Khan Academy for nearly 2 years). When he came in this morning he was bursting with confidence and pride and whizzed through the activities I had for him – I’m going to have to pitch things harder tomorrow!

Was this going to happen anyway? Did he just need a small group to express himself in and a trigger for his confidence? Was it just that he was at the end of an achievement plateau and ready to climb another hill? Or was it just a quick pointer that he should start counting at zero?

And I wonder how many children across the country are struggling right now in maths just because they don’t have this basic skill?

Melissa the Mathemateer

Melissa is amazing. Two years ago, she could barely count to ten, but now she knows written methods for the 4 operations and can carry them out reasonably well. Her progress has been exceptional. Unfortunately she is one of those children who scraped a 2C in Year 2 (more of this later), so while I know her progress is exceptional, it doesn’t look very exceptional to external visitors.

Melissa is cared for by her Nan, after her natural mother was deemed incapable of caring for her. Nan is pretty close to illiterate, Mum was educated in special school, so I always think it’s a vindication of our education system when generations of families achieve progressively higher academic standards. I have high hopes for Melissa.

Luke the Mathemateer

Luke is amazing. He is probably the sharpest in the group with mental maths skills, knowing some of his times tables and being reasonably fast with his number bonds. His inability to read is his biggest barrier, and whilst that shouldn’t affect his maths, it does.

He is the member of the group who is newest to the school, coming from his previous place with a dreadful attendance record of less than 30% and his dad facing a huge fine. After a shaky start, where he spent his first week running out of school he has settled really well and now is a quiet, hard-working member of the class. He just needs to learn to read.

Sarah the Mathemateer

Sarah is amazing. Despite a hearing impairment that has kept her off school for significant chunks of time, she has an unflappably upbeat attitude to life. She is constantly cheerful and positively engaged with all aspects of school life. She is really best friends with Robert, but occasionally they fall out badly and behave like an old married couple on a cantankerous row. These arguments tend to blow over within thirty minutes or so.

Sarah was especially pleased that she learned to tell the time so quickly in our few sessions in the first week and kept telling me how she was helping the other children in the group. I’m not entirely sure how the other children viewed this.

Jules the Mathemateer

Jules is amazing. His parents recently broke up acrimoniously, yet he has stayed calm and serene (on the outside) during the hard times. He was one of very few Year 6 boys who volunteered for a part in the Christmas production and gamely learned his lines in a short period of time. Jules is a great artist with a talent for accurately reproducing images his has seen in line drawings that goes beyond his years.

Jules appears one of the more confident ones in the group mathematically, yet when I asked him to read a clock he counted round in 5s for a time that should have said 6:30 and read out 6:35. I saw straight away that he had counted the starting number – now I know where to start teaching him!

Ebony-Rose the Mathemateer

Ebony Rose (or Ebs, as she likes to be called) is amazing. She is a great communicator with her friends and knows everything that is going on in the class – who is friends with whom and who has fallen out with each other. She is great at locating things, seeming to have a natural gift for knowing where things are. Her Nan runs a small pony yard and it means Ebs gets to ride ‘her horse’ every weekend. She would love to work with animals when she’s older.

While Ebony-Rose is the most socially gifted in the group, she is the least gifted mathematically. The others, all working below national average as they are, will still sit the SATs in May, but Ebs won’t, as for her achieving a level 2 would be brilliant (SATs at Year 6 currently test levels 3 to 5). She seems to find it really difficult to retain anything to do with numbers. She tells me she can count to a hundred, but a distinct fear appears in her eyes when I mention an number greater than two.

Robert the Mathemateer

Robert is amazing. The other children look up to him as a kind of mini-professor. He is quiet, well spoken and has a great vocabulary. He is both a big Minecraft and a Lego fan. Suprisingly, his favourite Lego is Minecraft Lego.

Robert has had a statement of special educational needs since he was very young and was previously educated in a Resource Base for speech and language. (A resource base is a kind of half-way house between mainstream and special school, providing a special school type education within a mainstream school). Robert is also a looked after child: he has been brought up by his uncle, after his mother rejected him when he was a baby. You see Robert has a disfigurement that affects his eyesight and the shape of his head. Still, Robert is lovely. He calls his uncle, “Dad.”

Elsa the Mathemateer

Elsa is amazing. It was her idea to call the group ‘The Mathemateers’.

She is creative and wacky and fab. Her drawing is accurate, expressive and her creative spark knows no limits. She has a brilliant flair for drawing and is particular good at drawing unicorns, griffins and other fantastic creatures. She loves the Harry Potter stories and is particularly fond of wolves (the animal, not the football club) – in the past she has been known to play wolves, howling for long periods of time on the playground. She has a stunningly beautiful singing voice and got to play the lead role in our play before Christmas.

She claims she finds it hard to concentrate in maths. “My eyes get distracted by colours” she tells me. She lives with her mum a long way from school and has to catch two buses to get here every morning, even though her dad lives close enough for her to walk to school.