Mathematics – Page 3 – frogphilp.com

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.

The Mathemateers

We had to have a name for the class and I wasn’t so fond of the name ‘Year 6 booster group’.

I’d thought I might go with ‘PhilpClass’ but then it’s a trifle arrogant naming the class after myself.

And I needed a name too. I was planning to use both Khan Academy and Google Classroom as delivery tools for some of the content – more on that at a later date – and both tools require a class name to be set up.

There’s also an argument about identity. If children have something to identify with it can help them engage more. It can channel, even increase their motivation. All of them seemed motivated. As I said last time they had fearlessly told me what they didn’t like about maths and agreed they all wanted to improve. Now if only we had a name…

I’m always wary about opening up such things to children – after all I’m supposed to be teaching them maths – I don’t want to be wasting their time choosing names. But mercifully one of the children came to the rescue. Within seconds of suggesting we needed a name, she said “The Mathemateers.” And it stuck.

I’m now going to introduce you to the Mathemateers. A short pen portrait that may offer a bit of an insight into the children. Obviously I have changed their names.

They are:

Click the links to find out about each child.

Remedial

It’s been a while since I had a regular classroom commitment. I’ve always thought that senior leaders suffer from an authenticity failure when they are divorced from teaching. But that’s another story, to be told another time. And to cut that long story short, this term I am teaching a group of seven year 6 children. Maths. For just one hour a day.

I am ‘boosting’.

Here’s what it says in the dictionary about boosting.
But this is more than a SATs game. Putting my cynicism aside, each of the seven children in my group have a unique perspective on maths. And it’s a perspective skewed by failure.

Now I know that these days it’s cool to fail. Fail: first attempt in learning, chant the students to me. But not when you’ve failed week after week. Not when you’ve been the last to ‘get it’ lesson after lesson. Not when you’re at the bottom of the achievement rocket year after year.

The children's maths weakness: concentration, telling the time, embarrassment — What the children told me gets them down about maths

My seven Year 6 students are old enough to be embarrassed by their inability to do maths that children four years younger than them can do. They can’t tell the time. They don’t know their times tables. They can’t reliably count on or back. And what’s worse, they can all tell me stories of embarrassment, when their failure to do what their peers find simple has been exposed to the rest of their class.

Embarrassment and repeated failure make a powerful poison that taints the waters of learning. And the antidote to that poison is more than mere boosting. If all I do over the next four months is ‘get these children through their SATs’, I will have failed them. They don’t need my tricks and tips to score the best they can on some 45 minute exam papers in May. They need me to teach them well. They need some core knowledge and some confidence.

So as it turns out, I am not going to be boosting after all.

I’m going to be a ‘remedial teacher.’

I know that sounds awfully old-fashioned, but there are some reasons why I prefer that term. I see their lack of knowledge akin to a sickness and the remedy is good teaching. Each of these children has unique reasons for why they are ‘below national average’ in maths. Whilst I can’t remedy all of the reasons, for some I can do the following:

diagnose the ailment;
identify a treat;
present a cure;
give time for that cure to take hold.

I suppose I could label the same 4 point sequence like this:

identify misconceptions
plan some good lessons
teach well
allow children time to practice so that their confidence grows.

The majority of my posting this term is going to be about the journey with these children.

The coming mathematics apocalypse

I am tremendously excited by the current maths curriculum in English primary schools. The expectations are higher by at least a year. It is a no-nonsense raising of standards.

I’m excited because if we can find a way of teaching the curriculum successfully, then our students will have levels of maths previously unheard of in this country. They will be on top of the mathematical world. The average will be above average. They will have the skills and knowledge to found an empire of learning.

Not only is the curriculum at a standard that is a year higher than the previous curriculum, but there is talk of the floor standards, already raised from 60% to 65%, to be raised further to 80%. This means that schools will have to find a way of getting more of their students to a far higher standard. What a fantastic aspiration.

But it’s the ‘if’ I see as being a problem. Let’s face it: we don’t currently have the maths specialists we need in Years 5 and 6 – the upper years of primary school. Secondary school maths departments complain of misteaching, cramming for the end-of-primary-school SATs and students without the knowledge they need. What will it be like with even higher standards, both on the level that children must attain, and also the number of children that must attain it?

I see three options:

Success – we achieve the ambition. We find a way of teaching more of our children to a higher standards than previously attained. A golden age of knowledge is ushered in.
Cheating – we pretend to achieve the ambition by blurring further the grey line between supporting students and telling them what to do in tests. The nation lurches towards a moral crisis.
The Maths Apocalypse – We ramp up the stress. School leaders put the pressure on their teachers with the higher expectations. The teachers crack under the pressure and shout things at their students like: “why don’t you just get it!” A generation is turned off everything to do with mathematics. It’s a maths apocalypse.

The problem with raising standards for students is that we also need to raise standards of teaching. Many primary teachers have a ‘C’ grade GCSE in maths, yet the maths expectations now required would go a long way towards achieving one of those ‘C’ grades.

The clock is ticking. In 2016, the first cohort of students will be tested on the new curriculum. Only eighteen months away and staff rooms across the country should be buzzing with conversations around how we teach maths and the subject knowledge we need. Networks of maths co-ordinators will right now be exemplifying the standards – turning the words into maths that can be taught and practised. Experts from teacher training will be working closely with schools, finding ways of bringing their new trainee teachers up to the required standard and sharing some of their training expertise with teachers who are struggling with their own maths. Teaching schools will be focusing on developing their Specialist Leaders for Education in mathematics so that schools within their networks without maths specialists have a means of accessing their expertise.

We have time to prepare and to succeed. Doing nothing will only prepare us for the mathematics apocalypse.

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:

The greatest proportion of maths expectations we need to improve on at my school come from the Year 1 programme of study.
Two of the key questions that we need to get better at are taught through the KS2 computing curriculum, and not the maths curriculum.
At my school we are really good at teaching calculating and number, but we need to improve at teaching problem solving.
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:

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?
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.

What is Number Ninja?

The ultimate 'Number Ninja' badge. Nobody has achieved this level yet. — The ultimate ‘Number Ninja’ badge. Nobody has achieved this level yet.

Number Ninja is essentially an assessment system for maths that uses badges to reward children for making progress. It’s for children in the Primary age range from 5-11 years of age.

I had become frustrated with some of the maths assessment we were using at my school. I felt they were either too slow or too lenient and they didn’t reflect what I consider to be the golden triangle of maths achievement – understanding, pace and accuracy. For example we were using a ‘99 club’ – several iterations of this exist. It was a good system, demanding recall of multiplication facts and division facts. Each class would do the test once a term and the children would be rewarded with a certificate in an end-of-term assembly, with a class prize going to the class that had obtained the most certificates. However the one we were using allowed 10 minutes for each test, which was just too long for my liking.

We also use a system called Incerts which calculates a national curriculum level for each child based on the number of statements ticked. I find this system both convenient and accurate, but in my opinion the current National Curriculum under-rewards children for mental mathematics skills.

A second problem was inconsistency across the school. While we had two main whole school systems, teachers were using a range of assessment systems within their own classes that didn’t continue beyond that year group. For example some people were using the excellent mental maths assessment developed by Wigan LEA some years ago (get it while you can – this website is no longer supported). Other people used their own times table systems that they had borrowed from other places or created themselves.

What I wanted to do was create a wider system that demanded more from the children in terms of pace but still maintained a whole school rewards system in a big termly assembly – this is useful to keep a high profile for mathematics.

So I did 4 things:

I kept Incerts and 99 Club – there’s no point throwing away good stuff if it’s already working.
I developed a new mental maths assessment system called ‘Grid Club’. This is much more pacey than 99 Club.
I introduced Khan Academy. While I’m not overly impressed with the instructional videos on Khan Academy, I do really like the assessment system that goes alongside it.
I created a spreadsheet to collect all the scores from the different systems and calculate an overall Number Ninja score – this is what I use to award the badges.

Here’s an example of what the Number Ninja spreadsheet looks like. It’s from the Year 3 class. Teachers enter the numbers in the coloured columns and the number on the far right is what the spreadsheet generates. It is colour coded to tell you what ‘Number Ninja’ level the child is on.

Any questions or suggestions about Number Ninja – I would be grateful to hear them!

Welcome to Fraction County in the United States of Maths. Population: ⅗

I’ve often heard it argued that learning maths is like learning another language. There is a whole vocabulary and a way of speaking that is alien to people who don’t live in the land of maths. Abstract concepts are understood by saying things that only maths people understand. The conjunction is the equals sign; verbs are operators; a degree-level literature essay is a second-order differential equation.

If that’s true, then Fraction County is the kind of place where the banjo stops playing when you walk into a bar. The talking stops. The locals all put down their home-made moonshine and all that can be heard is the faint rustle of tumbleweed blowing along the street outside. And you realise that the language they were talking is a completely different dialect from one that you’ve understood before.

It is no wonder that many children panic when they hear the word “fraction”.

Think about this.

The children walk into a room and see ¼ written on the board. The teacher asks “how do you say this?”

A brave child sticks their hand up and says “one line four”. Another child, emboldened by the first contribution, suggests “one point four”. Then someone asks “is it a fourth?”

“That’s not exactly how we say it,” corrects the teacher, obliquely referring to some shadowy group of people the children have never heard of. A group of people that obviously can already speak ‘Fraction’. “We say ‘quarter’” The teacher smiles reassuringly, but inside is concerned. She knows that the children should already be able to read and say a quarter and she utters a silent curse at the children’s previous teacher.

The lesson continues. The children learn that fractions are something to do with pizza (or if you listen to Sal Khan, pie). Then, after seeing that ¼ of a pizza is one piece out of 4, the teacher holds up 4 multilink cubes that are all joined together in a small tower. She asks the children how many cubes are in the tower. The children say “four”. The teacher breaks off a cube. She asks how many cubes she broke off. The children say “one”. “Ah, but what fraction did I break off?” asks the teacher, with an air of mystery. “Half?” asks a child. “A third?” asks another.

Ever patient, the teacher persists. “How many cubes were in the tower?”

“Four.”

“So what is the ‘out of’ number?”

“Four.”

“So this cube is one out of four,” declares the teacher triumphantly, writing ¼ on the board again. “How do we say that?”

“One line four” says a child.

“One four” says another.

“Quarter” says a third.

“Yes,” says the teacher, pouncing on the learning. She vigorously shakes the child in sheer joy that someone has got it. “And we write a quarter, one over four.”

The problem is in the language. The children have already learned that division is one word that means two different things – sharing and grouping. Now there’s the whole same thing going on with fractions. They’re sharing pizzas and calling each piece a fraction. Then they’re grouping sets of objects into equal subsets and calling each subset a fraction. Then despite the fraction being called “a quarter”, the teacher describes it as being “one out of four” whilst explaining that you write it “one over four.” The concepts behind these aren’t impossible to grasp, but the language we use to describe them is just so inefficient.

This is one of the reasons that my favourite thing to come out of the old National Numeracy Strategy was the book on maths vocabulary – describing the kind of words that children should be taught in each subsequent year.

But knowing the words is only part of the problem. I know some French words and some Spanish words but (to my shame) I find it hard to put them in the right order. The language of ‘Fraction’ is similar. It takes practice and good teaching to put them in order. If your teacher is woolly in their teaching and you don’t practice enough, you won’t learn the language. Worse, I know plenty of people whose maths teacher lost patience with them during some maths lesson or the other and shouted at them for not getting it quickly enough. This is often a reflection on that teacher’s subject knowledge, not the maths ability of the student. It is a reason why I recommend Derek Haylock’s excellent book on teaching maths.

So next time you’re on the road to Fraction County, make sure you’ve rehearsed some of your lines – you may just teach your child to know their denominators from their numerators.

A greater stretch in mathematics? If only.

I read the letter from Michael Gove to Tim Oates about how the new National Curriculum Review would affect the Programmes of Study within Primary Schools with a great deal of anticipation, and then a growing feeling of disappointment. There are various areas that disappoint me, but the area of maths teaching is perhaps the greatest. I read:

In mathematics there will be additional stretch, with much more challenging content than in the current National Curriculum. We will expect pupils to be more proficient on arithmetic, including knowing number bonds to 20 by Year 2 and times tables up to 12 x 12 by the end of Year 4. The development of written methods – including long multiplication and division – will be given greater emphasis, and pupils will be taught more challenging content using fractions, decimals and negative numbers so that they have a more secure foundation for secondary school.

Minor Disappointments

Let me break this down then. Here are some of the minor points that disappoint me:

“Knowing number bonds to 20 by Year 2“ – this is already the case. How can it be more stretching to maintain an expectation – surely the bar should be raised somehow.
“Times tables up to 12×12 by the end of year“ – this is a slight rise in expectation as children are currently expected to know up to 10×10, but in my experience it is not the knowing of extra times tables facts that hold back children in the latter part of primary schools, it is the lack of knowledge of corresponding division facts (which happens to be part of the current national curriculum).
Greater emphasis on written methods (like long multiplication and division) – this sounds good, but it’s already in the current programme of study. Just saying something more doesn’t make it more rigorous, nor does it necessarily raise expectations. In addition, I’m all for children learning skills in school such as the skill of performing long division, but I had been under the impression that the new curriculum would be more knowledge based.
“Pupils will be taught more challenging content using fractions, decimals and negative numbers.“ Again, these are all in the current programme of study for children from the age of about 7. Whether children are taught these are up to their teachers and their schools.

So when I read the phrase “much more challenging content“, and put it next to the above examples of challenging content, I’m struggling to see the giant leaps in standards that Michael Gove would be hoping for when his new National Curriculum is implemented.

A medium-sized disappointment

A greater disappointment is to see the phrase “more proficient in arithmetic” without any reference to algebra. As I have written before, children start learning about algebra from a very young age when they start investigating concepts such as larger and smaller. It is the concepts involved in algebra, often linked with precise language teaching, that I think are under-taught or mis-taught at primary level. Teachers shy away from this vocabulary-driven area because it doesn’t feel like maths to them – there aren’t numbers and operations written in children’s books – it doesn’t look as good as arithmetic. When children leave primary school I think they are often under-prepared for algebra – it is in this area that I was hoping for higher expectations within our new National Curriculum.

If you’re good at arithmetic you can go to the shops. Or maybe become an accountant. If you’re good at algebra you can become a rocket scientist. Not that education should just be about gaining a decent job – Gove himself says he wants “a love of education for its own sake” – but I have a feeling that for many algebra isn’t the elegant thing of beauty that I perceive it as, but is a rather lumpy, ugly thing, ringed with fire and tears.

A major disappointment

Aside from my algebra foibles, there is a further disappointment that I think will have a wider implication on maths teaching: teacher subject knowledge. No matter how detailed a Programme of Study or a National Curriculum might be, neither address this problem: we have many teachers within the primary sector who do not have sufficient subject knowledge to teach mathematics effectively. Many primary teachers only have a grade C at GCSE and have had to repeat their mathematics test required by teaching training in order to pass their course.

I have no problem with teachers teaching mathematics concepts that they’re not to sure about, so long as they know what to do when they’re stuck. There should be an expert teacher within each primary school – the maths co-ordinator or similar – who can share their knowledge and expertise when others don’t know the next steps. Too often less-skilled maths teachers don’t seek help from their more experienced colleagues, but struggle with the text of the National Curriculum and any scheme books that support it. Not knowing what to do, they either miss the tricky areas or teach it badly – characterised by repeating themselves more loudly and more slowly, a bit like the traditional Englishman abroad.

It is not a new Curriculum that is going to improve standards in mathematics. We will stretch primary mathematics only by increasing subject knowledge within our teachers.