Computing is maths

I could say: maths is no longer completely maths.

If you compare the statements in the Maths National curriculum (2014) with the questions in the 2016 sample questions (which is when the first children will be assessed on the 204 National Curriculum you find a curious thing: if you only taught children how to do the things in the National Curriculum, they would do badly on the final test.

For example in the old National Curriculum, children were expected to be taught to make decisions about which operations and problem-solving strategies to use. A comparable statement in the new curriculum is that children should be taught to solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. There is currently no statutory guidance in maths for how problem solving should be taught, only that problems should be solved.

But don’t worry, because computing is maths. In fact in the statutory computing curriculum there are statements that describe how to teach problem solving. For example:

  • solve problems by decomposing them into smaller parts
  • use logical reasoning to explain how some simple algorithms work and to detect and correct errors in algorithms and programs.

In those statements for computing there are clear expectations for how problems can be solved, and I think they apply to maths problems as much as any other subject.

Let’s be clear here. I’m not trying to argue which is the better curriculum; what I am trying to argue is that you can no longer see your children make progress in maths by only teaching maths. You have to teach computing too. Computing is maths.

At the end of the last academic year, like most primary maths subjects leaders I did a maths SATs analysis. What I found was that if our children had solved problems as well as they answered questions about number and calculation, then our school would have been well above average, with the majority of our pupils getting level 5s. As it was, the vast majority of the children scored well into a level 4, but I was left wondering, what if we had taught problem solving just that little bit better…

What the analysis of maths SATs 2014 showed me
What the analysis of maths SATs 2014 showed me

And now the text of the maths national curriculum is even less focused on problem solving and more on arithmetic competence. Yet the tests in 2016 will be unforgiving to those children who have only learned to crunch numbers.

That is why believe me when I say maths is computing and teach computing with all your heart.

We should proud of our computing curriculum in England. Inspired by the Next Gen report by Ian Livingstone and Andy Howe back in 2011, the computing curriculum could become the envy of the world. If only 5% more of our students become competent at computing, imagine the world powerhouse it would make us. Ian Livingstone describes the ideal ‘A’ level combination for a student going into hi-tech industries as maths, physics and art. Computing is not only produced by both the sciences and the arts but it supports learning in the sciences and the arts.

And that is why, when Melissa shone at the computing workshop with Miles Berry at Microsoft headquarters back in January (as I posted last time), I was delighted. It was not just because of the great confidence she had gained, nor the insight into being able to write a ‘repetition’ in code.

It was not just the big tick in the box marked ‘self esteem’.

It was because by doing good computing she had also done good maths. She had solved a problem that I knew would stand her in good stead in the next few months and beyond. As a remedial teacher it was a win for me, because when Melissa gets better at computing, she also gets better at maths.

Because computing is maths.


Why Computing?

As I continue to write about the journey of the Mathemateers in their maths learning, I’m going to divert for a post or two into the thorny subject of Computing – a new subject on the National Curriculum. I’m about to argue that computing is just the thing that schools like mine need to raise standards in maths.

As you’ll remember from her pen portrait, Melissa had very low ability in maths a couple of years ago and has made considerable progress to get to where she is, needing only a small boost now to get to national average. Imagine my delight then, when at Microsoft on 7th January for the Quickstart Computing Workshop with Miles Berry, Melissa stood up to explain to the whole room how she had used the ‘For’ function to reduce the lines of code her turtle needed to draw a square from 7 lines of code to 2 lines.

My delight was twofold:

  • Melissa has very low confidence – part of her problem in maths as an inability to try new things out because she doesn’t want to get things wrong.
  • Melissa isn’t very good at maths – using a ‘for’ function shows a level of logic I didn’t know she had.

The challenge went like this:

  1. Miles Berry asked the children to define a square.
  2. The children struggled to define a square. Apparently this knowledge has been removed from the national consciousness sometime in the last few years.
  3. Mile Berry showed the children how to make the turtle draw a line and turn using Microsoft’s online programming teaching tool: Touch Develop.
  4. The children used Miles Berry’s start to program the turtle to draw a square. Most of the code looked like this:
    Code for how to draw a square on TouchDevelop
    Code for how to draw a square on TouchDevelop


  5. At this point the children near me started noticing that the code repeated itself rather a lot. I wondered out loud whether there was a of making the code repeat and eyed the screen meaningfully.
  6. Melissa immediately started looking beyond the ‘right turn’ and the ‘forward’ button and noticed that there was another button called ‘For’ with the words ‘repeat code’ under it.
  7. She started dragging clicking and dragging things around and soon came up with this:
    Better code for drawing a square.
    Better code for drawing a square.

    We were all delighted and Miles got Melissa up the front to explain what she had done. Since then she has become a bit of a celebrity back in year 6 – her class teacher has been pleased to get her to do the same demonstration to the rest of the class when he introduced Touch Develop. Then Melissa had to go to Year 5 where she again demonstrated her computing prowess.

So. Here I have Melissa, self esteem going through the roof and she has associated this computing success with maths. Over the last couple of weeks, she has solved problem after problem, met target after target – she is truly flying. Maths is going great because of a positive experience in a computing workshop in London.

So what’s the lesson here – give children a chance to shine and they will?

No, there’s more than that. Computing is maths. And I’ll explain that statement in my next post.


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.



Key Stage 2 Maths SATs Analysis

Admittedly, not the most exciting post title you’ve ever seen, but let me draw you in with what I found out:

  1. The greatest proportion of maths expectations we need to improve on at my school come from the Year 1 programme of study.
  2. Two of the key questions that we need to get better at are taught through the KS2 computing curriculum, and not the maths curriculum.
  3. At my school we are really good at teaching calculating and number, but we need to improve at teaching problem solving.
  4. Neat, well presented work does not equate to success in maths SATs.

So, I used a useful spreadsheet I found on the TES website to analyse the maths SATs results from 2014 (you’ll need a TES login to access that link). I was particularly concerned about the 6 children who didn’t make 2 levels of progress during Key Stage 2. Six out of thirty is a large percentage for us: it moved us down from well into the top of the half the country (in terms of progress measures) to well into the bottom half. While there was a back story (read: justification) behind each child, I wanted to look more carefully at the results each child had achieved and find out why they hadn’t quite made the grade.

Having analysed the data, I made a presentation for my staff so we could talk through the issues involved. Why not just talk it through with the Key Stage 2 department? Well as I’ve indicated above, many of the statements where we need to get better at are actually taught from Year 1 or 2. I’ve put this presentation into a Movenote here. Please feel free to watch, but don’t expect quality – I was using Movenote to practice my presentation for the staff meeting on Wednesday – it’s a first take, and I’ll be expanding on many of the points during the actual staff meeting.

My two big considerations are the following:

  1. My children need to get better at logical reasoning to achieve well in maths. Logical reasoning is most explicitly described in the computing curriculum – how can I use the computing curriculum to raise standards in maths?
  2. With the foundation for success clearly coming from the teaching in Year 1 and 2, how can I make sure that this teaching is as good as it can be?

It will be interesting to see if my staff agree with me on Wednesday.

Teaching Computing to Year 5

So, as I said in my previous post, I’ve been teaching computing today. It was a year 5 class with no experience of computer science. Of course the expectations in the National Curriculum are that children know words like ‘algorithm’ and ‘debug’ from Year 1. My intention is to speed the children quickly through the expectations in my planning framework, so that they grasp the Key Stage 1 expectations quickly and make good progress into the Key Stage 2 expectations.

Here’s what I chose to do.

  1. Connect with a programmable toy. The children have been using these for years, but it’s great to give a bit of context. We have some Big Trax in school and I used these to remind the children how you can give instructions to a robot.
  2. Start with Logo. I used the handy browser-based Logo Interpreter by one of those friendly Github types, Joshua Bell. I showed the children how to make the first letter of my surname ‘P’ (the program was: fd 40; rt 90; fd 20; rt 90; fd 20; rt 90; fd 20)
    Kasra used logo to make his 'K'
    Kasra used Logo to make his ‘K’

    and then asked the children to make the first letter of their name. This is actually in the planning for a Key Stage 1 class, but the children have to start somewhere!

  3. Encourage the children to hack. Of course, I really should be moving the children on to drawing different polygons, but there are some amazing program on the Logo Interpreter page, and I wanted children to experiment with changing some of the variables and seeing what would happen. I showed them how to do this and then let them play for a few minutes. I was impressed with the screenshots that Evie took, where she not only demonstrated that she could make a letter ‘E’ but also that she had made the ‘tree’ in the logo interpreter into a much smaller version by changing the variable.
  4. Play with a programming game. Some great games already exist out there, but I chose to use Lightbot. It was interesting to see the children wrestling with the precision needed to use just a few commands to get the robot on the screen to do exactly the right thing.
  5. Program the Sandwich Bot. I told the children that I would become the ‘Jam Sandwich Robot‘ and they had to program me to make a Jam Sandwich. I shared Google Slides with them and, in small groups, they each took a slide to write their ‘algorithm’ (instructions) for the Jam Sandwich Bot. After five minutes, I ratcheted up the intensity by showing the video I had made when doing the same lesson with some Year 4 children. They worked with renewed fervour as they were desperate to be the first to successfully program the Sandwich Bot to make a jam sandwich. This is the video of what happened.
  6. Reinforce the vocab. I finished by spelling out ‘algorithm’ and ‘debug’ and talking about where you would see these occur in real life.

The ‘where next?’ includes an introduction to Scratch and using Logo to experiment with repeated sequences. I would be interested to know whether computer scientists out there are thinking ‘No don’t do that!’ to any I have written above, or if anyone has any better suggestions for how to start this kind of work with children who’ve never done it before.

Teaching computing to a blank page

At my school, I’m on a journey of learning how to both lead and teach computing. I wrote about a planning framework previously. These next 2 posts are about lessons.

In some ways it’s easy teaching computing to children who have had no prior experience. Children at my school, whilst they are strong in IT and digital literacy, have had minimal experience of what used to be called the ‘control’ strand of the ICT curriculum, and is now called ‘computer science’. They are very much a blank page.

I am aware of the damage that can be done to blank pages. When teachers-who-know-a-little misteach, it makes teachers-who-know-a-lot despair. A criticism of much primary science by secondary science teachers is that children often do the fun stuff without really understanding it at primary, so that by the time they’re ready to do the fun stuff and really understand it at secondary, the students dismiss it because they’ve ‘done that lesson before’. Obviously without Bunsen burners. We don’t have Bunsen burners in primary schools.

Another example is algebra. @oldandrewuk was telling me recently how he would prefer it if no algebra teaching was done at primary, because it would make his job teaching algebra in secondary maths so much easier. Non-specialist maths teachers can’t help but teach misconceptions with a complex area such as algebra and thus it would be better to leave it to the specialists.

I’m aware that computing may be similar and I would be interested to know what secondary colleagues think about the computing teaching going in primary schools – do they expect to have to correct children’s misconceptions? Would it be easier to start from a secondary school blank page? Or is some knowledge a good thing?

Either way, I’ve taught three hours of computing today to a class in my school who were very much ‘a blank page’ and I’d be interested for people to pick apart my teaching and consider what is helpful and unhelpful to their long term progression as computer scientists. I’ll write about my lesson in my next post.

Image source:

Computing isn’t just Computing

I know many of you will have got this sorted in your schools already, but for me, in my school, we’ve taken some time to get our heads around the Computing National Curriculum. Part of the reason for this is that English and maths are our top priority – everything else comes second to those two subjects. Children in my school enter the school way below national average and we have our work cut out accelerating progress so that they leave school with the correct standards for English and maths.

But excuses aside, despite being ‘the Computing Co-ordinator’, I am not a natural computer scientist. Yes, I have taught children how to make patterns using logo. Yes we children program roamers in my school. But aside from that, my expertise, and therefore the expertise of the children and teachers in my school is around digital literacy and creating content using different media and technology.

So I was delighted, when I acquired the ‘Switched on Computing‘ scheme (by Rising Stars, written by primary education technology legend and broccoli fanatic, Miles Berry) to see that they have allocated the statements in the 2014 Computing Curriculum into 3 broad sections: Computer Science, Information Technology and Digital Literacy. It meant my school was already quite good at two of the sections – we just had to learn how to do the first.

For me, one way I like to learn things is through re-categorising them. So I took the stuff I knew about and tried to match it up. I know there are lots of great bits of planning out there done by assorted Computing Subject Leaders across the country, with possibly the best being the Google Site produced by the 30 computing experts who first advised the UK government on what should be in the curriculum. However, I found myself going to three main sources:

  1. The Rising Stars ‘Switched on Computing’ scheme of work. This provides six topics per year with suggestions on how to teach them. In Year 6 it becomes quite complex, with a large degree of prior knowledge expected and the implication being that it will become increasingly cross-curricular to find time within the normal school day.
  2. The Computing at School website, which is constantly being updated with handy courses and advice, but also has some simple expectation statements that can be used to define what children should know by the end of each key stage.
  3. Phil Bagge’s website. If you haven’t seen his Jam Sandwich Robot lesson, you really should, especially as it inspired me to make my own version.

I then re-categorised them as follows to make a kind of curriculum planning tool. Paganel Computing Planning (click the link to see the PDF – or you go straight to the Google Drive folder and download it as a docx).

I think it was important to do this, because I have to be realistic about where the children are at – I can’t impose the Switched on Computing lessons immediately on Year 6 as they require a considerable amount of prior knowledge. But if we have those to aim for, with a document that helps teachers identify the prior knowledge required, it should help us get our children to a good standard as soon as we can. After that, what I am excited about is using computing to make our maths standards go through the roof, which is something Conrad Wolfram talks about here.

Developing Digital Literacies. #3: have a specialist

Having been challenged by Steve Wheeler that maybe primary schools do have a role to play in digital literacy, I’m now thinking about what we actually do at my school to encourage, or even teach digital literacy.

3. Have a specialist.

During my first module on the Mathematics Specialist Teacher programme (MAST) at Edge Hill university I learned some of the things that drove the need to have some maths specialists in primary schools. Firstly there is a prevailing attitude in the UK that it is OK to be be bad at maths. Secondly many primary teachers do not have more than a GCSE grade C in maths. What they were saying was that each school needs to have someone on the team to be both an advocate for maths and a developer of teachers, so that maths teaching is improved.

Surely it is the same for IT (sorry – computing) specialists?

Does every school expect all its staff to be experts in digital literacy? What about just being interested in digital literacy? Or as I posted previously, do all teachers yearn to be digitally literate? Maybe a starting point is for every school to have one person interested in this area.

Certainly it helps to have a digitally literate member of the leadership team. I have spoken to many headteachers who are fearful of Facebook and other social media because of the potential damage it can cause. They hear scare stories about professionals who have brought their organisation into disrepute by misusing Facebook, like this one, and their first response is to lock it down – have nothing to do with it – if it doesn’t come into school, it can’t get us.

This is where the specialist comes in. A specialist can convince the rest of the team that digital stuff can be used positively. They can make the team more productive and more effective. That person can quell the fears and quash the myths that build up around social media. They can be advocate and developer.