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.