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Posted on February 21, 2016 by Naveen Rizvi

Efficiency in Simplifying Surds

Today, I had a random flashback to a formal observation I had at my placement school. I remember having a discussion with the observer, a maths teacher, where we were debating over one particular point. I was teaching my second lesson on simplifying surds: from √a  to the form k√b  where k is an integer. Given that this was the first time my 9X2 set were learning surds, I went for a very explicit selection of worked examples, structuring one type of method to simplify a surd to k√b form. In my lesson I was structuring the teaching as below, where I wanted pupils to identify the highest common square number, which is also a factor of the ‘a’ in surd √a.

In the lesson preceding this lesson, and in the weeks throughout the year, I would have pupils complete a recall activity frequently in which they had to identify the square number of the first 15 integers, and also square root the first 15 square numbers. The point was to ensure that pupils could recall these facts from memory, and develop automaticity in doing so, to the extent that there wasn’t an act of mental processing.

Picture1aPicture1b

Figure 1 – Worked Examples for simplifying surds effciently

I would ask pupils to select a factor which can divide 72 or 160 and which is also the biggest square number that can divide 72 or 60. They would then identify the square number and then write the root number of the square number below and continue on with the multiplication to simplify the surd to  k√b form. This was done because it is the most efficient and accurate method to simplify surds. If children are taught one accurate method to simplify surds at the start then they will get the correct solution and feel successful. If children are taught one method to get the solution and then you explore the different routes to get the same solution afterwards then you are building on their existing understanding of how to simplify surds.

The observer was suggesting that it would have been more beneficial for pupils to not have been taught one technique but to have explored instead a myriad of techniques. However, I think that what he was suggesting is only beneficial after they have first understood how to simplify surds in one accurate and efficient method. His suggested method could potentially cause several misconceptions insofar as you will have 30 pupils listing 6 possible attempts consisting of 12 different factors of 72. The lack of guidance and structure can lead to misinterpretations which leads to misconceptions.

In the early stages of learning such an abstract concept it is best to provide one accurate, structured and efficient worked example for students to replicate with different problems and in order for them to consolidate their understanding of how to simplify surds. This is, effectively, pattern spotting. Only then you can start to explore the different routes to the same solution without risking many misconceptions developing, as opposed to the converse.

Picture1c

Picture1d

Figure 2 + 3 – Comparing simplifying the square root of 72 using one algorithm, where we always select the highest common factor to be the highest square number that can divide 72, to the other multiplication sums when simplifying the square root of 72.

As a maths teacher, and even when I was as pupil myself, I knew the most efficient way to simplify a surd such as √60 was to have a multiplication sum with a factor, which was also the highest square number, because this would result in an integer multiplied by a surd. I knew this because my teacher explicitly told me. Later on we explored different routes to get to the same solution. Since I knew the answer for simplifying  √60 then when I got the same answer through different routes I felt successful and reassured. Why? Simply because I knew one concrete and accurate method to get the simplified solution for the problem. Teaching pupils one accurate method to solve a problem allows pupils to feel successful, and it further empowers them when exploring how to solve the same problem through different routes.

At Michaela, we spend a significant amount of time discussing our worked examples; whether DaniBodil or I have made the section of the textbook which is being taught that half-term, we discuss what is the best strategy to solve problems where pupils are adding and subtracting algebraic fractions and where the denominators are integers. What is the best worked example to solve problems where pupils are to substitute a positive integer into an algebraic term or expression? We outline it very clearly in our textbook, and we organise three or more worked examples where we interleave fractions, GEMS, decimals etc., but the cognitive process which pupils go through is similar in all three worked examples. This is because we want pupils to look at a problem and be able to identify each step between the problem and solution. How do we do this? We explicitly state it: step 1, identify the lowest common denominator; step 2, form the equivalent fraction by multiplying the numerators by the common factor; step 3, add the fractions with like denominators etc.

Picture1e

Figure 4 – Example of worked example made by Dani Quinn.

Our pupils are taught explicitly and we demonstrate clearly using our visualisers one concrete, accurate and efficient algorithm for the problem in order to get the solution. The different routes to the same solution of the same problem are explored later on once we know that all kids in the room are proficient at solving a selection of well-sequenced and crafted problem types with the one method we taught them initially. Our pupils are mathematically proficient; they love to learn and they feel this way because they feel successful knowing one accurate method between the problem and solution as to how to add and subtract fractions with integers as the denominator, or variables as the denominator, or expressions as the denominator. They then feel empowered when they can get the same answer through different methods.

And so, I respect that our opinions differed but I am sticking with the way I delivered the initial teaching of simplifying surds. It was the second lesson of this topic and despite not 100% of pupils were getting the right answer on their mini-whiteboards – where they were at the fourth lesson.

Posted on February 19, 2016 by Jo Facer

The Means and the Ends

In the past, I have confused the means and the ends.

In my first year of teaching, I thought back to my most recent experience of school: A-level English. Looking at the oldest class I taught, year 10 set 5, I thought there could be no better path than the one teachers older and wiser than I had taken me on. At ages 17 and 18, I had written an essay a week.

So, I decided to set my year 10 set 5 an essay a week.

Obviously, this was doomed to failure. My poor struggling year 10s, so far behind in literacy, failed so utterly in this first homework I lost their trust entirely. It took a very long time to build it back up.

I had confused the means and the ends. Of course I wanted year 10 to write beautifully crafted, intelligent essays. But I hadn’t considered that the way to get someone to write a great essay is not to just write a lot of essays.

I see this a lot in unit planning, especially at KS4. We’ve become awfully good at drilling to the exam. But two years is a very long time to drill to the exam. We have two years toteach, with perhaps two weeks (or, if desperate, months) to drill exam practice. Too many KS4 units on English language, for example, teach using unlinked, decontextualised texts, like random novel openings or random excerpts from unlinked news articles. Although this is the format students will encounter in their eventual exam, it is surely a wasted opportunity to only teach disparate content in the ‘teaching’ stage. Of course in the end, we want students to be able to write about decontextualised pieces of writing, but in the run-up it is surely much more effective to lead students through a well-designed scheme, for example short stories, or articles linked by a common theme like feminism, or social justice – schemes that will allow students to practice key exam skills, but also learn something.

The means don’t have to look like the ends. In fact, they rarely do.

When successful adults turn around and say: ‘I didn’t enjoy school. I want our children to have a more fun experience than I had,’ they are confusing the means and the ends. Weall want children to have fun; or rather, fulfilling, happy lives. But you don’t get to those ends by making school all about having fun. Many adults have succeeded because of schooldays filled with hard, hard work, not fun and games. We can have fun and gamesnow, because of that hard work.

In Education is Upside Down, Eric Kalenze writes about ‘engagement first’ teaching. This is the paradigm in which I was taught to teach. It was only after too many years of seeing my poorest students make insufficient leaps in their education that I realised my error. We can’t put fun first; we can’t even put exams first.

We have to put learning first, and the means do not often look like the ends.

Posted on February 20, 2016 by Joe Kirby

Supply Teaching in England

Charlie Carroll is a supply teacher whose book is called ‘On The Edge’. I asked him if I could share some extracts. Charlie kindly agreed, so here is the second of two blogposts (the first is here) sharing a supply teacher’s experience of tough schools in England, from Manchester, Sheffield, Birmingham, Yorkshire, Liverpool and London.

MANCHESTER

I was covering at Burns Technology College. During period 1, an ICT lesson, I had to send out Max Darby for playing a game which involved gunning down women. Two boys were playing online pool with each other; three girls were looking at tattoos; one lad playing Pac-Man and another playing The Sims. There was one boy – Elijah – who had done no work all lesson, barely even making the pretence to try whenever I strolled past. At the end of the lesson, he approached me and handed over the report card which had to be filled in by each of his teachers to document how well he had done that day. I wrote the truth in my allotted space: that he had done nothing. ‘Why did you give me a shit report, sir?’ he protested when he saw what I had written, and stormed out.

SHEFFIELD

Hocking was a brand new school. It had state-of-the-art equipment and resources, clean classrooms and corridors, and the students’ uniforms were impeccable. Yet the behaviour was spiteful. The students were vile and cruel to each other.

One day, a 16-year-old came up to me at the end of a lesson to sign the daily report which monitored his behaviour. He had done no work throughout the lesson, and I had written as such. He looked at my comment, said, ‘You’re a f*cking prick, you are,’ and strode out. A teaching assistant laughed as the door slammed shut. ‘We get that a lot here,’ he said. ‘You’ll get used to it.’ Another day I was asked to cover a Drama lesson. It was disastrous. There was fighting, there was screaming. It was chaos.

BIRMINGHAM

‘Mr Carroll, would it be too implausible to suggest that the use of religious imagery within Romeo and Juliet’s shared sonnet is Shakespeare’s way of implying to the audience that they are a match made in heaven?’ It took me a moment to answer. ‘No,’ I said. ‘No. I don’t think that would be too implausible at all.’ Each class beavered away just as voraciously, the only interruption being the odd question. One boy asked if he could take his blazer off. The exemplary behaviour, it seemed, came from the hard work of a team of happy teachers who were plainly supported by their headteacher.

The next school was Boscombe Heights. Period 3 was a nightmare. With the class in unbounded chaos, a boy called Liam did his best to incite a riot. After 20 minutes, I had to send him out, only to find that the classroom I had sent him to – manned by the Head of English – was also so chaotic that he was sent back to me again 10 minutes later.

Year 11 were next. ‘Tough lesson, sir?’ one of the girls asked me as she took her books out. She laughed knowingly, and two of her friends joined in. ‘Don’t worry, sir,’ said someone else. ‘We know how hard it is for supply teachers in this school.’ ‘Let’s make a start on the play.’ ‘Are you a real English teacher, sir?’ ‘I am, yes.’ ‘Could you talk us through it a bit? We’ve had supply teachers for the last month. We don’t really get it.’ At the end of the lesson, a boy piped up: ‘To be honest, sir, it was just good to actually be taught today. It’s not often it happens.’

Taylor College was next. Outside the entrance, three teenagers surrounded by eight younger students. I noticed something change hands. One of them spotted me approaching: all hands quickly shoved into pockets, and each of the teenagers walked off in a different direction. It was not hard to see what was happening: a drug deal had taken place, virtually on the school’s premises. That same afternoon, I overheard one Year 10 boy snarling at another in the corridor, ‘You tell that f**king Adam to stop spreading lies about my stuff – he hasn’t even tasted it.’

My lessons were not lessons at all. Assaults were common. One boy strode out of the classroom to return a minute later with a long plank of wood with which he intended to ‘batter’ a girl –another girl physically restrained him. During a Food Technology lesson, one 14-year-old boy waved a sharp knife menacingly in front of another’s face. It was a frightening place to go to school.

YORKSHIRE

‘You’ll be teaching maths. The school’s called Varka,’ the supply agency told me.

In period 4, at 1pm – 20 minutes before the lunch break – two girls ran out of one classroom and tore down through the block, smacking loudly on doors and barging into the classrooms. Within five minutes all of the students were out in the corridors.

Pupils were play-fighting, though with full-blown punches and kicks; a group of girls were smoking; one lad was being beaten up by six others. Nothing at all happened to any of those students by way of consequence.

Another lesson began. With a shrill cry of ‘F*ck yooooo!’, Will jumped up from his seat and began pounding Joe. That was the signal for chaos to erupt. Sam immediately joined in, picking up anything he could get his hands on and throwing it at everyone in sight (including me); Ryan jumped up and down on the centre of a table; Ralph leapt up and started to swing from the thin, bending pipes which flowed around the back wall; Sophie stole a board-pen from my desk and wrote ‘You motherf*cking c**t’ on the wall.

LIVERPOOL

Landstrom College, lunchbreak. A ball hit me in the head. Voices cheered, ‘Ten points!’ ‘Oi, throw it back!’ ‘You can have it back at the end of the day,’ I called back to them. I entered the hut I had for period 5 and locked myself in. The door began to shake and rattle in its lock as it was pulled heftily from outside. The shouts began with a frightening immediacy. ‘Give us back the ball!’ ‘That’s my ball!’ ‘F**king c*nt!’ a loud and resounding thump interrupted me. It was followed by another just as loud, and then another after it. The thumps increased, and the intervals between them decreased, until I found myself in a cage of loud and violent noise. ‘Give me my f**king ball!’ a boy screamed. I counted 11 boys, all revolving around the hut in a weirdly tribal Lord of the Flies dance, smacking the walls of the hut with long and knobbly sticks, screaming for the return of their football. ‘Come out here! I’m going to f**king smash you!’ My heartbeat rose and my adrenaline surged. Then the jeering stopped. The Assistant Head had arrived at the crucial moment.

LONDON

Edgham, an all boys’ school in Hackney, period 2: after 10 minutes the throwing began. First it was a rubber, then a paper aeroplane, then a pencil case, and finally a chair. I should have stopped them when it was just a rubber, but I had left it too late: now there was no chance. Tables were upended and, before I could get out of my seat, one boy had grabbed another and was beginning to punch him gleefully in the thigh. My shouts to stop were so loud that the Head of Department came running in from next door. She removed the violent student, barked a few imperatives at the rest, and seats were returned to.

London has seen the most, and worst, knife attacks in the country. In 2008, 28 teenagers were stabbed to death in the city, and over 6,000 arrests for carrying a knife were made. Many of these incidents happened on school grounds. Metal detectors – ‘knife arches’ – have now been installed at the entrances to hundreds of schools throughout London, Manchester, Birmingham and Liverpool. At Boreham, the Senior Management Team had security wands with them at all times, and never hesitated to scan over and around a student if they felt it necessary. Random knife checks took place often.

Pascoe is a clear example of how first-rate our state educational system can be, despite challenging behaviour. During my third day, a pupil threw his bag across the room and screamed, ‘You f**king twat!’ at the teacher. He was immediately excluded for a week. The outburst was dealt with swiftly and correctly. And this is why Pascoe is so successful. The key is the leadership team. Teachers could teach and pupils could learn.

OnTheEdge

 

Posted on February 17, 2016 by Jessica Lund

Dear Trainee MFL Teachers,

First of all, make no mistake: in a good school, with good systems and a strong leadership, you will find you have chosen the best job in the world.

Now, in your early years of teaching (and if you haven’t already) you will be exposed to a huge amount of collective wisdom and orthodoxy about how languages are best taught. You will be given handbooks, articles and blog posts. You will have many training sessions. You will be given, or directed toward, a vast universe of resources and teaching ideas.  You will probably not have time to read, let alone digest and use, 95% of these things.

You will, in all likelihood, be told to use pictures, all manner of games, Power Points. You will observe topic-based lessons: colours, pets, the environment, ‘what I did during my holiday’. You will see teachers speaking in the target language and miming actions. You will see pupils chanting individual words like ‘fromage’ and ‘ciencias’ and ‘Bahnhof’. Some of your colleagues may, generously, point you in the direction of the department’s set of flashcards and card sorts that you can borrow, but please be aware that some of the sets are missing the picture of the ‘piscine’ or the symbol for ‘Kunst’.

You’ll spend lots of time making resources.  Sensible people will tell you not to reinvent the wheel, but you’ll find some things on TES that you want to ‘make your own’, and so you’ll spend an hour or so each evening in front of the television resizing pictures of fish, or making a super snazzy Battleship slide that you’ll definitely use again with the next module. (You won’t use it again.)

You’ll spend some time marking books.  These will just be short passages of writing, constructed using sentence frames and vocabulary lists and dictionaries and based on examples – no more than 50-100 words at a time.  The sensible, focused kids will make minimal mistakes. Others will make huge numbers of the same mistakes, or write almost nothing. You’ll get frustrated and wonder how they can have failed to understand the task at hand.

In lessons, kids just won’t speak the target language as much as you think they should. The keen ones will enjoy reading out their sample sentences, but most won’t. Accents will be pretty shoddy. Spellings will be even worse. You will be disappointed in the pupils’ levels. You’ll look for the next thing to engage/inspire/motivate/challenge/support. There will be a million suggestions.

Stop.

I have done this – all of this – and I’m here to tell you it’s not necessary. You don’t have to know the theory. You don’t have to read the handbooks. You don’t have to download and tweak the resources. You don’t have to speak 80% in the target language and 20% in English (but only when you’re teaching grammar). You don’t have to work evenings, or weekends. You don’t have to make card sorts, plan games, get out the sugar paper.

MFL teachers are trained to do things that take a lot of time and effort, and can actually damage learning.  Take the use of pictures.

Rationale: Pictures bridge the gap between mother tongue (L1) and second language (L2). Pictures support lower ability or EAL learners. Pictures are engaging.

Reality: Pictures are hugely time-consuming. Pictures distract from the written and spoken language. Pictures distract lower ability learners, and encourage them to focus on pictorial rather than written designations. Pictures have a high opportunity cost: focusing on pictures means less time spent looking at and using the words.

Another example: the use of games.

Rationale: Games are engaging and fun.  (This is, in truth, the only reason I can now remember for using games.  I wasn’t always this joyless – I passed my QTS on the basis of a lesson that involved the rolling of dice.)

Reality: Games are hugely time-consuming. Games distract learners from the deliberate and thoughtful use of language. Games have an even higher opportunity cost: time spent instructing pupils on the ins and outs of the game, and game-appropriate behaviours, is time lost for language teaching.

I’ve taught this way, and even controlling for my inevitable inexperience and ineptitude, the results strongly indicate that it doesn’t work.

I want to be able to go through all of the things I’ve listed above, deconstruct them, point out their flaws, and suggest alternatives. I will, I’m sure, and I’m very happy to be challenged on a point-by-point basis. But that’s not the best use of my time when it comes to writing to you.

Think about the following:

  • Am I spending longer making this resource than the kids will spend using it? If so, don’t. Do something else. Spend that time reading a [insert target language here] website
  • Am I getting pupils to play games? If so, stop. They’re focused more on the game play than on the language.
  • Am I speaking the target language but miming my instructions? If so, stop. The kids aren’t listening to you, they’re watching your hands.
  • Am I working harder than the kids? If so, stop. Make something that will require them to sit and think and read and write and work, in silence, for a significant part of your lesson.
  • Am I reading lots about MFL pedagogy but not putting much into practice? If so, stop. Spend that time creating rich input, like long parallel-translated texts.
  • Am I getting my pupils to guess things? If so, stop. If you do that, some kids will get it and move forward; others will be left behind and feel stupid. Tell them, explicitly, what they need to know, then get them to use it. Repeat the good stuff all the time.
  • Am I marking work that has lots of mistakes? If so, stop. Teach it again, differently. Get them to look at the words they’re using in detail. They can make mistakes – they cannot repeat them.

There are so many more things you shouldn’t do, like limiting the scope of language based on  the level pupils are aiming for, or doing group or pair work.  But the most important things at the moment are saving yourself time and energy. In five – or three, or in my case one – years time you’ll look back and think yourself mad for the amount of effort you’re putting into unsustainable nonsense.  So don’t do it. Don’t allow them to be ‘creative’ with things they don’t understand. Figure out what you want the kids to know and teach it unashamedly and explicitly and to kids who have bums on seats and eyes on you.

Spend the time you gain mastering the language.  Understand the things that pupils will get wrong and deliberately prevent those mistakes. There is no better use of your precious time and sanity.

And please, please stop using pictures.

Yours, with all my best wishes,

Jessica

Posted on February 13, 2016 by Joe Kirby

Experiences of a Supply Teacher

Charlie Caroll was a successful 28-year old teacher in a great school, who loved his job. In 2008, he decided to become a supply teacher in different cities in England. His encounters bewildered him so much that he wrote a book about them. After reading ‘On The Edge’, I wrote to Charlie and asked if I could share extracts from his book on this blog. Charlie kindly agreed, so here is the first of two blogposts sharing a supply teacher’s experience of tough schools in England, starting in Nottingham.

NOTTINGHAM

Tompkins Technology College. Children were running around, yelling and tussling wherever I looked. ‘Morning, Year 10,’ I hollered over the din. ‘Time to sit down, please.’ Chairs were being flung over, snatches of insults occasionally broke free of the general hubbub, and it appeared that no-one had heard me.

‘Year 10!’ I shouted again, this time louder. ‘Seats, please!’

I looked at my watch; by the time I had everyone seated and looking in my general direction, seven minutes of the lesson had been wasted.

I started to introduce myself. ‘All right,’ I said. ‘My name is Mr Carroll, and I’m here for the next week or so. Today, we’re going to be working on…’-

‘For f*ck’s sake!’ one girl exploded. ‘Give it back, you bitch!’ More yelling, more chairs falling over as they fought over a stolen object. I tried to make them return to their seats, but three minutes passed before they tired of fighting and sat back down. Other pupils ignored me completely and talked amongst themselves. The noise grew. ‘Look,’ I said. ‘We need to …’ ‘No-one’s listening to you,’ one lad told me. I wrote the task on the board: Write a letter to your Headteacher, persuading him to get rid of school uniform.

‘Right, girls,’ I said. ‘What I need you to do is…’ ‘I’m doing it!’ erupted one of them, Tracey. ‘God! Just f*ck off, will you?’

‘I can’t have you talking to me like that,’ I said, calmly. ‘Please go and stand outside.’

She clapped her hands, hoorayed and rushed out of the door. When I checked a moment or two later, she had vanished, taking the opportunity to go for a 20-minute walk around the school.

Suddenly a boy burst into the room. Ignoring me, he reached into his bag and produced a large box of fizzy sweets.

‘Who wants some?’ he shouted. ‘No!’ I protested, but I was ignored by all as they swamped the newcomer.

I had just about got them seated again, when a fight between two 16-year-olds erupted outside my room, and the entire class rushed out to chant and holler. Another five minutes wasted.

Once they were all back inside again, a dark-haired lad suddenly leapt across his table and began stabbing another boy in the back of the hand with a straightened paperclip, drawing blood. Tracey came back, and her return sparked a loud argument among her front-row friends. ‘F*ck off, ya white bitch!’ ‘That’s racist!’

Five minutes before the end of the lesson, the class unanimously decided to pack up and walk out, despite my protestations.

 

As the bell for break-time went, I tried to set up the classroom for the Year 8s and ready myself. The second bell sounded, and they arrived. There followed two hours of noise – of frantic, urgent, unstoppable noise – which echoed about the room with deafening resonance.

Omar had a penchant for sneaking up to the board whenever I had my back turned to draw large and often spurting penises. Zoe had to be moved five or six times after starting loud arguments with anybody she happened to be close to. Raymond made his best friend cry when he graffitied the words ‘Mr Carroll swallows’ on to the cover of his book, held it up for me and the rest of the class to see, and then exclaimed ‘Sir! Look what Dimitri wrote!’ Sharn, after ceaseless taunting from Zoe, unloaded her tormentor’s bag all over the floor, kicked aside her chair, and then stormed out, never to return. And just when I thought it could get no worse, Luke calmly walked over to Habib, and spat on his head.

‘Luke!’ I shouted, my temper close to ripping. ‘Go and stand outside of the room now!’ The boy’s face filled with anger. ‘You can’t send me out,’ he spat. ‘I didn’t do anything! If you send me out, I’ll break your nose.’

‘It’s a very serious thing,’ I began, ‘to threaten a teacher, Luke –‘

‘I don’t care!’ he yelled. ‘I didn’t do anything!’ With that, he ran from the classroom. I followed, but by the time I reached the door he had disappeared. I came back in. A paper aeroplane sailed over and bounced lightly off the top of my head. ‘Oi, sir!’ Terry called out, ‘Chuck it back!’

I spent five days in Nottingham, enduring insults and continuous disobedience, having to make any request at least six times before it was even acknowledged.

I vividly remember a Year 7 lad obnoxiously shouting at his classmate, an orphaned Somali refugee, ‘At least I’ve got a family to go home to! At least I’ve got a family to go home to!’

On entering my lesson, a year 10 girl sang (to the tune of ‘If You’re Happy And You Know It, Clap Your Hands’):

‘If you think Sir’s a waste,

Clap your hands.

If you think Sir’s a waste,

Slap him round the face

If you think Sir’s a waste,

Clap your hands’.

I stopped her at the door. ‘Tracey,’ I said, ‘there is no way I can let you into this classroom now.’

‘What the f**k are you talking about?’ she hollered, spinning in circles and addressing the gang of youths surrounding her. ‘I ain’t done nothing!’

‘Tracey, I heard full well what you were singing,’ I said. ‘I cannot let you into this classroom after that.’

She shouted back: ‘Are you f**king mad? I wasn’t even singing! What the f**k is wrong with you?’ I tried to start the lesson. But it was difficult. Tracy was outside screaming so loudly that she drowned out my instructions. Abdul threw a chair at Peter. Vicky began playing loud dance music on her phone. Alan stole Tyrone’s left shoe, and ran about the room with it ululating. Charmaine produced a lighter, and tried to set fire to Tyrone’s exposed sock. And, all the while, Tracey stood outside, shouting that I was a twat, a prick, a wanker. Kris, a quiet lad, came up to me and, with a wry smile, said: ‘You know, the Head would probably have come and got her by now if you was a normal teacher. But you’re just a supply teacher.’

Then, out of the corner of my eye, I saw Will advance ominously towards Ashley. ‘What did you just say?’ Will hissed, squaring up to Ashley. Will pushed Ashley hard. Ashley fell back a few steps and then flung a wild swing at Will’s head. It was all Will, the larger of the two, needed. Grabbing Ashley by the jumper, he struck him twice in the face. ‘Stop that!’ I shouted, but Will ignored me. As Ashley careered backwards, he advanced, smashing him in the face with another resounding punch which spun the smaller boy around. Will kicked him hard in the back, sending Ashley flying out over a chair and on to the floor. As he lay there, Will stamped on his stomach.

As Will stood backwards, I stepped into the gap. Heady with adrenalin myself, both arms splayed outwards to prevent him moving any closer to the floored Ashley, I said, ‘Get out!’ He looked at me, and then at Ashley. ‘Get out now!’ I said. Will turned and left. The class, for the first time that day, were completely silent.

Violence in many tough schools is a reality pupils and teachers have to deal with. In one year alone, 740 children were permanently excluded for assaulting teachers; 8,240 were temporarily excluded. In many cases, nothing is done about it.

 

Next week, I’ll share extracts from Charlie’s experiences in Manchester, Sheffield, Birmingham, Yorkshire, Liverpool and London. His book is called On The Edge.

OnTheEdge

 

Posted on January 28, 2016 by Dani Quinn

Long-Term Solutions (Or: Why Make a Textbook)

This is my sixth year of teaching and I think it’s the first time I have taught equations properly to a KS3 class. I was almost there last year, and thought I was doing it well, but I now know there are several topics where I completely let the pupils down. This post is about how I could have been better-prepared earlier in my career, and avoided leaving later teachers with a mess to clean up.

———

Naveen Rizvi’s piece yesterday in the TES caused a stir that surprised me. Many people had a negative reaction beyond what I would have expected (I won’t link to them) and was followed by some negativity – or at least concern and alarmed questions – when Bodil subsequently shared an example of two pages from the booklets we give to pupils.

As I see it, these are some of the main barriers preventing pupils from achieving their potential in maths that CAN’T be dealt with by better resourcing:

  1. Limited working memory (i.e. there is a limit to how many new concepts the pupil can form and connect in a single lesson
  2. Fear of maths; strong and paralysing anxiety around maths

 

 

  1. Poor mathematical foundations from primary age
  2. Poor literacy (insofar as it limits their access to everything in education, and their ability to practise independently)

 

 

  1. Unsupportive home environment that leaves the pupil unprepared for school in a practical or emotional sense
  2. Low attendance
  3. Fixed mindset around maths, often meeting its first major challenge at secondary
  4. Passive behaviour. This could charitably be called low motivation, or disengagement. It could less charitably be called laziness.
  5. Disruptive behaviour and avoidance techniques
  6. Their peers’ disruptive behaviour
  7. A class culture that doesn’t value effort and hard work
  8. A class culture that penalises mistakes and revealing or discussing errors
  9. A class culture that makes it uncool to want to see the links between ideas in maths
  1. A weak teacher who isn’t trying to improve (either wilfully, or due to disenchantment borne of circumstances)
  2. A weak teacher who is trying to improve but isn’t there fast enough (typically an NQT, a teacher transferred from another dept (usually PE or geography), or a teacher who has been neglected in terms of development)

 

Possible solutions:Improved teacher pedagogy and understanding of how memories and connections are formed.

Improved teacher understanding of what fixed and growth mind-set actually is (not just a gimmick to console pupils when they underperform… my heart bleeds for Dweck).

Possible solutions:Effective intervention and catch-up programmes in school (ideally supported at home).

 

Possible solutions:School leadership foments a culture that challenges this (supported by classroom culture created by individual teachers), either through super-high expectations/tough love or alternative approach that challenges and changes issues that hold pupils back in school. Possible solutions:Head of Department leads maths-focused CPD
Caveats:This is not easy. ITT doesn’t seem to cover this adequately, and it appears to be a relatively new part of most teachers’ pedagogy*, relatively complex to understand and highly complex to begin to incorporate into practice (particularly for the weakest pupils).

* This is, of course, excluding some very experienced and successful practitioners. In their case, it appears to be something they’ve come to understand intuitively and isn’t easily shared as it isn’t codified.

Caveats:There are many programmes that appear to have high impact in closing the gap between pupils’ reading and chronological ages, or the gaps in their mathematical foundations. In particular, direct instruction programmes such as Connecting Maths Concepts (McGraw-Hill scripted direct instruction programme) and Lexia appear to be effective ‘off-the-shelf’ interventions (based on my own experience!). Caveats:Really brave leadership on school culture, especially in challenging circumstances, is too rare (in my limited experience). Many bloggers have written about the gap between their school’s behaviour policy and the ‘real behaviour policy’ (teachers are left to defend their own classrooms, with little or no back up). In the best cases I’ve seen, there is total clarity about the positive, learning-focused culture the headmaster/mistress seeks to embed, and the behaviour policy serves this and is always upheld. Caveats:This is incredibly time-consuming. Most HoDs simply don’t have the capacity to do this well. The number of conflicting interests they have makes this difficult: teaching as many of the critical/tricky classes as possible (as they are, hopefully, one of the strongest teachers), writing SOWs, managing staff shortage (it is maths, after all), retaining staff and keeping them happy, improving teaching quality. And, ideally, reading widely to prepare for new exam specs and maths education research…!

However, there are more issues than this that are – I think – relatively neglected outside of the rarefied atmosphere of online edu-chat and conferences.

Barriers created in lessons:

  1. An capable but exhausted teacher who can’t prepare adequately for lessons (their department is under-resourced and teach a full and varied timetable)
  2. Confusion about what they should be covering to prepare for the end of Y11 (it is unclear what the pupils covered in Y7-9, or in how much detail; there is uncertainty about what should *actually* be taught when they see ‘averages, 1 week’ on the SOW… Does it mean calculating the mean, median, mode and range only, or complex questions where some values are missing and then one value is changed?).
  3. Painfully optimistic allocations of timing to teach topics (expressions – 1 week; fractions – 2 weeks), due to insufficient clarity about what should actually be taught.
  4. A gap between what they cover in lessons (superficial) and the rigour of the exam (increasingly higher, hopefully). A recent example of this was the GCSE question: Solve for a: 2a + a + a = 18. This question is beyond trivial, but many teachers had not prepared their class for the possibility that simplifying and solving could be used in the same problem.
  5. Unclear explanations, or rule-based explanations, that makes it difficult for pupils to use their knowledge flexibly or to ask useful questions (e.g. “change side, change sign” to solve linear equations because it seems quicker and easier, or convoluted steps to solve simultaneous equations).
  6. Inadequately scaffolded and varied practice in lessons that doesn’t prepare them for the variety of forms maths can take in the real world (or in exams…) (We all suffer from textbooks that escalate the difficulty of questions too quickly, so that your weakest pupils get only 2-3 questions practising questions in the form a+3=10 before they’re moved onto the other three operations).
  7. The practice gap (i.e. getting much less practice than pupils in other schools). Most textbooks DON’T HAVE ENOUGH QUESTIONS. At all. Most of the newest books boast how many more questions they have. It is not enough. If a pupil has only just begun to grasp a procedure, they need to do it many times to build their confidence and then begin very careful and gradual variations.
  8. Pupils forgetting that they have learned something (“I swear down they never taught us that”). This comes from haphazard, or no, continuous revision or interleaving (weaving old topics into current topics).
  9. Pupils doing what seems obvious to solve a problem, rather than what is mathematically correct (e.g. writing that 3/4 + 1/2 = 4/6). As above, an absence of revision and interleaving.
  10. Pupils knowing they’ve learned something, but muddle it (e.g. calculating the mean when asked to comment on the median). Also as above…

I am increasingly convinced that a good textbook would begin to address these ten problems. A good textbook:

  1. Offers interesting talks and prompts for pupils to have high-quality discussions in pairs and with the class. These can range from puzzles to problems that provoke cognitive dissonance (e.g. which is closer to 1/2, 1/3 or 1?)
  2. Offers worthwhile questions that allow pupils to use multiple strategies to solve a problem or to calculate (e.g. 4.5 x 24)
  3. Plans for revisiting old topics, particularly those that are high impact (directed numbers, fractions, equations, manipulation, mental maths, calculation) or easily confused (e.g. minimally different topics such as perimeter and area)
  4. Has carefully and thoughtfully sequenced content in the big picture (e.g. equations preceding graphs) and in the fine detail (e.g. breaking down directed numbers into the many strands of understanding and procedure that pupils need to grasp).
  5. Has identified key examples that a teacher might want to use with a class, covering the most important problem-types for a concept or procedure.
  6. Offers clear and highly accurate explanations of WHY something works.
  7. Has distilled clear steps to scaffold pupils’ work as they begin to tackle a new procedure.
  8. Offers memory devices to help pupils retain and recall concepts or steps (Chants for the 7 times tables, or mnemonics such a KFC for dividing fractions (Keep the first, Flip the other, Change to times, it’s no bother).
  9. Offers LOTS of practise at each level of difficulty in a procedure.
  10. Has lots of interleaving available, but sectioned off, so that the teacher can judge the level of complexity students should experience.

None of this replaces planning lessons. You still want to share enthusiasm, build excitement, anticipate common errors and misconceptions, explain clearly, model explicitly and unambiguously, check for understanding, grow their confidence in the face of setbacks, celebrate success, maintain pace and focus in a safe and happy environment and – of course – go back and refine the plan and resource after you’ve taught it. This all takes planning, deep thought about your classes and huge love of maths. I don’t understand how the existence of such a resource would compromise the idea that teachers tailor their teaching to their classes.

Sadly, such a resource doesn’t appear to exist. That’s why we’re making a textbook. Please get in touch, have a look, and help up improve it!

Posted on 12 November, 2015 by Bodil Isaksen

I could care less: detentions for pens

Pen (n) an instrument for writing or drawing with ink, typically consisting of a metal nib or ball, or a nylon tip, fitted into a metal or plastic holder.

Who knew so many tweets could be generated by such an inoffensive item?

It all began with my disagreement with this tweet:

View image on Twitter

140 characters were certainly not enough to explain my stance. So here are 4000 more.

High standards, high support

Have you noticed how no one uses the phrase “false dichotomy” anymore? Edu-twitter debate tropes have moved on since 2013.

Nonetheless, I’ve been breaking out the well-worn phrase a lot over the past couple of days. Retro.

Some common responses were:

“A conversation is better than a detention”

“Supporting the pupil with their organisation is better than a detention”

“Giving the pupil a pen is better than a detention”

“School-wide systems to provide equipment are better than detentions”

You can give detentions and still do all of the above. I know that – because that’s what we do at Michaela.

We have sincere conversations explaining our standards, upfront at the beginning of year 7 and constantly reiterated. Staff devote hours and hours to improving motivation and changing mindsets through one-on-one chats.

Struggling pupils have daily check-ins and check-outs from a City Year mentor to get them into good habits regarding attendance, punctuality, homework and equipment.

If a pupil turns up a lesson without a pen, we give them a damn pen and get on with learning.

Our school shop is open every morning before registration for pupils to restock on equipment they need.

We have high standards, but we also have high support.

Nudging, signalling

Fine, but can’t you just have the support without the detentions?

No.

A detention is a slightly unpleasant half-hour experience. It’s enough to give pupils that nudge to check their equipment the night before. Pupils aren’t especially bad or lazy, but they are human. As a human being, we don’t enjoy unnecessary effort. A detention tips the balance in favour of sorting your pencil case out.

Detentions also signal that we say what we mean, and mean what we say. Our words (that it’s important to be prepared) are backed up with something that shows we really do prioritise it. Unless you have a completely consequence-free discipline system, what you sanction matters. It tells pupils what you really care about. It speaks far more loudly than words could.

The whys and wherefores

Still, why do we care about them bringing pens?

A school has to make a choice about what they provide and what the kids sort out. Calculators in maths are a classic example. In some schools, there are class sets. In others, the pupils bring their own. It would be absurd to sanction a pupil for not bringing a calculator in a system where they are provided. So sure, at Michaela we could all provide pens and avoid the whole detentions-for-equipment thing altogether.

Why don’t we?

Firstly, just doing what’s always done, I suppose. I’ve never known a secondary school where pens are provided for pupils. When we were setting up, it’s not something that was ever questioned.

Secondly, minimising faff. When pupils are moving about from classroom to classroom, making sure pens don’t go walkies, replacing them when they’re broken, and so on is more hassle than it’s worth.

Thirdly, pupils are more likely to look after and value something they own than something that’s a public good. Again, not because they’re bad, but because they’re human: the tragedy of the commons is not the preserve of inner city teens.

Fourthly, it sends a message about personal responsibility. We won’t sort everything out for them all the time.

Fifthly, it’s a gentle introduction to good habits of organisation that will prove most useful in life.

Care is a doing word

We show we care about our pupils through our actions. I’m giving a detention for a pen because I care. Maybe that’s a different choice from yours – but it’s still driven by wanting the very, very best for those I teach.

I give a detention because it doesn’t stop me from providing support. I give a detention because it encourages pupils to make the right choice. I give a detention because I think having a pen is important. I give a detention because I care.

 

Posted on 11 November, 2015 by Bodil Isaksen

What do you want to get out of twitter?

What do you want to get out of twitter?

Do you want to self-promote? Do you want others to congratulate you when things are good and commiserate when things are tough?

Do you want to be intellectually stimulated and challenged? Do you want to debate and pull apart your ideas? Do you want to be forced to defend your stance so you question things more closely?

If you want to do the former, the strategies suggested by Sue Cowley and Teacher Toolkit make perfect sense. Mute, block, ignore. (Everyone does this a little: you tire of engaging with a certain line of debate or individual and stop responding.)

But I believe you are missing out on a massively beneficial side of twitter if you do so as a general policy. You’re missing out on the chance to develop your thinking.

What I’d like to challenge, though, is the perception that people who engage in robust and forthright debate care less. They (we?) are often painted as uncaring and emotionless. That’s simply not true.

You do not have a monopoly on emotion simply because you choose to ignore or react badly to forthright discussion.

I have emotional responses to tone that feels off. I have my fair share of mental health issues. I have received tweets where my instinctual reaction was one of anger, or sadness, or frustration.

But I know that’s just an emotion. I can control my reaction to it. I can control my thoughts stemming from it. I can certainly control the actions I take – including what tweet I send in response.

I think it’s a real shame if your choice of action is to block, or to respond emotionally rather than engaging in the substance of the argument. I think it’s a shame if your choice of thoughts is the least charitable interpretation (“that person doesn’t care about children” rather than “I wonder what’s led them to think that”). I think you’re likely to learn less and grow less.

But. As I said. Your choice.

Posted on November 8, 2015 by Katie Ashford

Grammar and the Art of Writing: ResearchED Literacy

Here is a write up of the presentation I gave at ResearchED Literacy in Swindon yesterday, in case anyone missed it and is interested in what I have to say about grammar (feel free not to be!).

What makes a good writer?

When I first began teaching English, I thought carefully about what it meant to be a great writer, and how I might be able to help my pupils get better at writing themselves. At the time, I was reading ‘Revolutionary Road’ by Richard Yates. It has since become one of my favourite books, and I re-read it at least once every year. The story is good, but I adore Yates’ writing style. There’s something beautiful about the way it flows. Struck by a couple of wonderfully rich, yet concise, sentences of his, I came to a conclusion. I believe that great writing is characterised by the ability to control and manipulate clauses. So that is what I needed to help my pupils get better at: controlling clauses. By beginning with a clear goal in mind, it is easier to understand the direction and purpose of grammar teaching. From there, I began working out what knowledge pupils needed to know in order to be able to control clauses effectively.

Parts of Speech

Joe Kirby began sequencing a grammar curriculum into three parts: the parts of speech, syntax rules, and punctuation rules. I agreed that these were helpful categories.

One of the main criticisms grammar receives is that parsing sentences is a waste of time. I hear some teachers say that knowing that the word ‘run’ can be both a noun and a verb is unnecessary. I can understand why some may see it this way. On the surface, knowing the parts of speech doesn’t appear to be particularly useful. However, since I’ve been thinking about this, I’ve come across a number of examples that demonstrate why this knowledge is in fact extremely helpful.

Take the following examples:

He married an intelligent, charismatic woman.

 He wore a bright red coat.

 Why is a comma necessary in the first sentence, but not the second? The parts of speech hold the answer: ‘intelligent’ and ‘charismatic’ are two adjectives and therefore should be separated by a comma. ‘Bright’, however, is an adverb modifying the adjective ‘red’, so no comma is necessary. Knowledge of the parts of speech also enables us to understand why we say a ‘bright red coat’ rather than a ‘red bright coat’. Red does not qualify the adjective bright; rather, the adverb ‘bright’ tells us how red the coat is.

Whilst most people will intuit this knowledge, many people will not. As teachers, we should be as systematic as possible to ensure that every pupil knows how to punctuate sentences properly. Even the humble listing comma cannot be applied correctly without an understanding of the parts of speech.

I gave more examples of this during the talk. I’ve attached the presentation to the bottom of this blog post if you’d like to read more on this.

Sequencing

Sequencing a grammar curriculum is key. I argue that it ought to have 20% of curriculum time at KS3. Over three years, pupils ought to study 9 units.

Year 7: The basics of the parts of speechsyntax and punctuation. These units should provide a broad overview. For example, when teaching the parts of speech, you wouldn’t want to go into the detail of types of nouns (proper, common, abstract, etc.) as this will overload pupils. Instead, simply teach them what a noun is. Come back to nouns in year 8 and then teach the different types.

 Year 8: Detailed breakdown of the same three units. Here is your opportunity to teach the more nuanced aspects of what was taught the year before.

Year 9: Deepen pupils’ knowledge of the complexities of grammar. A strong emphasis should be placed on its impact on meaning.

A Grammar Lesson

Grammar lessons should be ‘DEaD’ good: that is, it should contain a clear definition, illuminating examples and unrelenting drills.

For example, when teaching adjectives to year 7, I would begin the lesson with a recap of the parts of speech that I have taught previously. I would do this by giving pupils a few phrases to parse, for example:

Our house

Lucy’s kite

A window

The door! Jamie!

Karen’s doll.

 Next, introduce the concept. At Michaela, we have created a short story about grammar. In each chapter, a new part of speech is introduced in the form of a personified character. The Adjective Ladies are the eponymous heroines of this lesson. They are a group of gossipy old women who sit around and describe people. The story contains several examples of adjectives, all italicised.

The next step is to learn the definition. Pupils learn that adjectives describe nouns and we chant this together as a class. This is quickly followed by a sequence of examples and non-examples.

Once pupils are consistently giving correct responses to the question ‘adjective or not an adjective’, they are ready to practice. Begin by asking them to circle the adjectives from a list of simple words. Increase the challenge in subsequent activities by asking them to circle the adjectives in simple sentences, then more challenging sentences. Increase the challenge further by asking them to tell you which noun the adjective describes in every example.

Finish the lesson by carrying out further parsing activities, this time including adjectives. For example:

Our lovely house

Jane’s delicious meal

The music? Wonderful!

Matilda: a reader

Frightening, that ride.

 To ensure pupils don’t forget this in between grammar lessons, and to increase the chances that they will apply grammar to writing across other lessons, carry out daily drill exercises. For the first five minutes of every lesson, pupils parse a few sentences/ underline all the subjects/ punctuate sentences with non-restrictive clauses, etc. as appropriate. On the whole, these should be aligned to the unit you are currently teaching them, but recap of previously taught content is also helpful.

Thanks to Tom Bennett, David Didau and Ruth Robinson for organising what was a brilliant event. I’d highly recommend looking into the work of James MurphyEric Kalenzeand Dianne Murphy. I attended their talks yesterday and all three were totes amaze!

Here is the PowerPoint I delivered yesterday, which includes the sample lesson I have explained above: ResearchED Literacy Grammar