Chromebooks are how much?

Samsung Chromebook

My Original Samsung Chromebook 500

When I first bought a Chromebook back in 2011, I bought an experiment. It was quite an expensive experiment too. Now Chromebooks are so cheap that I can’t imagine buying anything else for use in my school.

So there’s lots of things to say here. I could tell the story of how Chromebooks have come down in price. Or I could explain my belief that children do best with technology when they have a range of different types of device to use. But the main thing is this: it’s teachers that make a difference to children in schools. And that’s why it is important that Chromebooks are cheap – because schools that can minimize their technology spend can maximize their spend on teachers.

Think about it this way – what you prefer: a school with the best devices or a school with the best teachers? I know the answer – it’s both! But we live in austerity times – maintaining and developing the quality and number of adults we have teaching children has to be our priority.

I bought my school’s first set of Chromebooks back in 2011. They were the same kind as the one I had experimented with as a personal device. They were great because they were easy to maintain and perfect for running our Google Apps on. But there were expensive. For twice the price of a Chromebook back then I could buy a device that could do a lot more than twice the stuff – Chromebooks were not superb value for money.

So, 3 years later, when our next device purchasing round came round, I was thinking I would dip my toes into the waters of device-agnosticism and buy something different. But by then Chromebooks were cheaper. At only £165 each I could increase the number of devices the school had to a point where it would make classroom management a lot easier (I’ve always thought children sharing computers is a bad idea). And now I can no longer buy an alternative device that costs twice as much and can a lot more than twice the stuff.

This year it got even harder. Chromebooks at £120 each. “Chromebooks are how much?” I said to myself. Wow! Now I can kit a classroom out with basic devices for less than £4000. I find that my technology budget can go loads further than it did before. And I can still focusing the majority of the school spend on staffing, which (as I said above) is the most important thing.

Why am I saying this now? Time to declare an interest: I’m presenting at the free, online Google Education on Air Conference this Saturday with the title “Chromebooks, the easy classroom companion.” I’ll be telling some of my school’s story with using Chromebooks over the last 4 years and explaining more of why Chromebooks are the ideal device for the classroom. Come along, join in and share your view…

 

Mathemateers and their Chromebooks

Something I’ve not mentioned too often in my posts about my remedial group: the Mathemateers, is that each of them have a Chromebook.

A Chromebook is a complete non-event as a device. All it does is provide seamless access to the online materials you need to use to educate your children.

So I’ve previously written about using Khan Academy and Google Classroom to give my children meaningful homework and challenging practice. Seamless. Khan Academy and Google Classroom just work.

And here’s the thing: my school owns the devices, yet I let the children take them home. How can that be? Where is the safety in that? The management console in Google Apps allows me to enforce safe search in both Google and Youtube. I’m pretty confident that the Chromebooks are the safest device the children have at home.

But it must be an effort managing that sort of thing? No. Not really. It’s less time than marking a set of books and moreover my technician in school spends no time managing Chromebooks. He spends some time distributing apps to iPads and considerable time managing our Windows network, but no time managing Chromebooks.

I’m going to be speaking in more detail about how ace I think Chromebooks are at the Google Education on Air conference at the start of May. Here’s the details of my session. Even better, the Mathemateers will be there in person, through the power of the Google Doc. Might see you then.

Showing Progress in Fractions

One of the great things about teaching fractions to my Mathemateers group is that they knew pretty much nothing about them. This meant that whatever they learned would show oodles of progress – always good for impressing line managers.

(Not that it matters in this circumstance. I am the booster (remedial) teacher for the Year 6 group, therefore reporting to the Year 6 teacher who in turn reports to the Key Stage 2 Phase Leader. However I line manage both these people, so it’s less of a line and more of a circle…)

The assessment system we use showed that all the children in the group struggled with fractions. For example, Sarah‘s profile in ‘number’ looked like this:

Sarah's lowest 'ticks' were in Fractions

Sarah’s lowest ‘ticks’ were in Fractions. My school used the Incerts assessment system.

Of course when I asked Sarah some questions, it transpired that her prior assessment in fractions was, shall we say, over-ambitious, in that the assessment system said “she is developing the ability to use simple fractions that are several parts of a whole”, when actually she couldn’t do this question from ‘Recognizing Fractions 1‘ in the Khan Academy (which I have written about previously).

Most of the children couldn't do this question when we started.

Most of the children couldn’t do this question when we started.

 

Of course there’s the whole issue about performance and learning here. Sometimes children really do know something, but for whatever reason they don’t show it. This is performance. Performance variation is one of the main reasons for the difficulty in carrying out accurate assessment in education.

But for me as a teacher, this is great. I can now teach some stuff to the children and show great progress. And that’s what I did. Pretty soon the children had motored on to ‘Recognizing Fractions 2′ and even managed to do questions like this by the end of the first week.

By end of week 1 children could do this

By end of week 1 children could do this

No I’m not saying this is world-record teaching, but it does show progress. And what’s great is there’s an image, you can talk about it with the child and then the child has to write down the answer in fraction notation. It’s the perfect move from the Pictorial to the abstract. The downside, if you only use the Khan Academy is that children don’t write down what they did in their books and so their progress isn’t there for external visitors. And that’s not good if you’re a very book-scrutiny focused kind of school.

What would be great would be if we had already moved on to the New National Curriculum. However, as you well know, Year 6 are still working to the old curriculum. You see Incerts have just released their tracking system for the new curriculum and it looks fantastic. Here’s a picture of the ticks I could make about Sarah’s fraction learning:

What the new assessment for fractions looks like in Incerts.

What the new assessment for fractions looks like in Incerts.

However I can’t use that for my current group because they’re in Year 6. Nope. I’m going to have to cope with the learning that’s actually happened in the children’s brains and their SATs results in a few weeks time. Speaking of that, the final tool I’ve used to show progress is the Testbase tool that is a store of all the previous SATs questions. Sounds boring, but it’s really, really handy at the stage of the school year when teaching in Year 6.

 

Here comes the Dominator

So of course, it was Melissa who came up with the classic line. It’s a line that I’m sure is heard in many Key Stage 2 classrooms whenever fractions are being taught.

To the question “and what do you call the number at the bottom of the fraction?”

The child responds: “Is it the D-d-d-dominator?”

Fractions are counter-intuitive to many people. They get smaller as they get bigger. When you multiply them they get smaller, sometimes. And when you divide them you make them go upside-down. They are just weird. And then you add new words like the dominator* and the nominator** and the children get even more confused…

I spent quite a bit of time teaching my Mathemateers about fractions in the last term and I’m hoping that my next few posts will detail some of my failures and successes as I attempted to teach them something they had previously known very little about.

I have written some time ago about the importance of accurate vocabulary when teaching mathematics, particularly with fractions.

* by this I mean ‘denominator’

** by this I mean ‘numerator’

If only there was a tool like Khan Academy

So I was speaking to an inspector a few months ago who was trying to look a bit more deeply into my schools maths data. She asked out loud, “couldn’t you make a system that finds out how well children are doing in each individual area of maths, rather than these overall numbers?

Broadly speaking, that is the problem with data in schools. There’s always the danger of there being so many interpretations and approximations between the numbers that come out of the system and what’s actually in a child’s brain that the data becomes meaningless. Here’s how assessment works:

  • we decide what children should be able to do by particularly ages or stages and write it down in sentences.
  • we assess how well children can do the things we wrote down.
  • we turn those assessments into numbers.

Sometimes those assessments are called tests, at other times they are called observations. Either way it’s more or less the same process. However, quite often as teachers we get distracted and over-focused on the last stage of the process – on the numbers and less on the ‘what the children can actually do’ part of it.

This is where Khan Academy is brilliant. I’ve been using it this term with my Mathemateers group, and even though it doesn’t entirely match with the UK National Curriculum, it does help spot the gaps that children can’t do and provide the children with ways to practice skills that they are still shaky on. I also like the way I can focus the children on a particular skills at a time so that I’m not having to teach each child individually. For example for a few weeks I was focusing on fractions, so I directed children to activities that helped them visualise and practice fractions. I used Google Classroom quite often this – I would post a link in the Google Classroom assignments that would take the children directly to the Khan Academy challenge I wanted them to do.

Why Khan Academy fits in to the inspector’s question is that it gives a brilliant assessment of how children are doing in each area. For example, when setting my fractions challenge I mentioned earlier, I could see that one child had already mastered it, another was struggling at it and the rest had never tried it – it meant I could focus the challenge precisely on what I wanted the children to learn, support the child who was struggling and set a harder challenge for the child who had already mastered it. Ace.

 

Trialling Google Classroom

Google Classroom: a streamlined easy experience

Google Classroom: a streamlined, easy experience

I mentioned early on in my Mathemateers posts that I would be using Google Classroom to help me ‘deliver content’. So a few words about Google Classroom.

It’s easy. Really easy.

As the teacher, I choose my students from the Google Apps for Education users (we have Years 2-6 set up as individual users). The children receive an email to ‘accept’ the invite, or they can enter a code to join the new class that has set up. From there I can do one of two things:

  1. Make an announcement.
  2. Set an assignment.

The only difference in functionality between the two is that the children don’t have to respond to announcements. With assignments I write a title, write a sentence or two of description, set a due date and then I can attach ‘content’ in various ways:

  • as an uploaded attachment,
  • as a Google Drive file (docs, slides, sheets or drawings),
  • as a Youtube video,
  • as a URL.
The assignment screen on Google Classroom

The assignment screen on Google Classroom

It’s over to the students then. Each of my students has a touchscreen Chromebook – this may seem extravagant, but at less than £170 per device I think it is well worth the investment.

I’ve added Google Classroom to the screen of their Chromebooks via the Google Apps admin console, so it’s right there whenever they log on to their device. They can open it and quickly see which assignments they have done, or are yet to do, or (occasionally) are late at handing in.

Like the teacher, they can attach work to their ‘turn in’ comment. So far this has range from Google Drawings to screenshots of other work they have done online. This takes a bit of training, but once they’ve been through the routine a couple of times they soon have the hang of what to do when they have finished their assignment.

So far I’ve mainly used it for homework – it’s so satisfying to know that students are doing meaningful work without sending them home with polypockets full of photocopied worksheets.

It’s early days so far – I’ve only been using it with children for four weeks, but I can’t wait to get it going with the whole school. It may just revolutionise the way we do homework…

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.

 

The trouble with three

I noticed a really interesting thing when I was working with Ebony Rose in the Colouring In lesson.

She has a real problem with ‘three’.

As you’ll have worked out if you’ve read the post and considered the problem I set, the children have to colour in different amounts of squares. There are only two choices – when you come to a new colour you’ll either colour one of each square next to the old squares, or you’ll colour three squares. That’s the choice: one square, or three squares.

But Ebs has a real problem with three.

She could cope with all the ones. She could see that each old square would generate one new one, but every time we came to one that would make three squares she froze. If I wasn’t watching here, she would just blithely colour in a single square, even though three were required. And then when I was talking her through it, and getting her to talk it back to me it was like she didn’t want to even say the word three – whenever we came to it, it was like she was trying to out-wait me – to see who would crack first before saying the word three.

It became really hard work. The fact is that during the activity you have to colour in three squares lots of times – she wanted to progress and do well, but she didn’t want anything to do with the number three. I begun to believe that she had some kind of ‘three’ phobia – as if she thought it was cursed or out to get her or something.

Over the weeks since then I’ve begun to understand why: Ebony-Rose often confuses the ‘3’ digit with the ‘5’ digit. Show her ’50’ and she may say “thirty”. Show her ’13’ and she may say “fifteen”.

I remember last year when I was working with a child who, at the age of seven, couldn’t reliably count to ten (or for that matter in tens to 100). By ‘reliably’ I mean she could do it, but 4 out of 10 times, she would get it wrong. When I listened to her count I noticed that she didn’t like pronouncing the ‘f’ in five or fifty: she found it awkward to say. So instead of saying it she would just move swiftly on to six or sixty. We worked for  a few weeks on this reliability and (this academic year) her year 4 teacher tells me she is flying in maths.

Imagine being ten and trying to do maths when you can’t reliably differentiate between a ‘3’ and a ‘5’.

Now I know there may be lots of excuses I could throw at Ebony-Rose at this time  – dyslexia, dyscalculia and all of that stuff. But the excuses aren’t going to help me this week or next week. I need to teach her know how to diferentiate between those two digits. I need to get her confident at knowing ‘the threeness of three’ and give her practice at using threes.

Who knows, she may even master the 3 times table by half term…

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.