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Michaela’s Blog

Posted on March 30, 2016 by Katie Ashford

Women: Know Your Limits.

Growing up, I was fortunate enough not to have to worry about gender inequality. As far as I was concerned, I could run just as fast, shout just as loud, and be just as smart as my brother or any of the boys I knew at school. My dad was a Judo coach, so from about the age of 8 I spent weekday evenings throwing boys twice my size around a hall in the local community centre. Of course I had heard about gender inequality, but I saw it as a thing of the past. From my perspective, the women  who fought for women’s rights had given me the chance not to have to do the same for myself. Through their chastisement of the status quo, I was liberated from the limits that had been imposed on them for millennia, and for that I was grateful.

 

Over the last few years, as I creep steadily towards my 30s, a few things have helped me to see that perhaps I was naïve to believe that women were unquestionably equal to men. The usual stuff kept cropping up: woman are ‘emotional’ and ‘bossy’, must be married with kids before 35, should weigh no more than 8 stone, and should spend more money on hair cuts than rent to avoid being considered a slob. Bla bla bla. But I was most shocked when, recently, at an event hosted by an older man, I sat myself between two guys I know well and respect deeply; the host engaged sincerely with them, shifting his eyes from the man on my left to the man on my right, and yet overlooked me completely. I was more than a little annoyed. My inner Judoka wanted to leap up and thrash him to the floor in the names of feminism and good manners. Of course, I didn’t. I sat there politely and nodded along, trying occasionally to squeeze a word in or earn a second of his focus, to little avail. His loss. I’m great.

 

Explaining these lurking concerns to a devout feminist acquaintance, she declared: “Yes, Katie. Welcome to the Patriarchy!” She’s right. The Patriarchy does exist and it is terrible that women aren’t as equal as they ought to be. But I fear that looking at the world through this lens is problematic. I fear that too much acknowledgment of ‘the patriarchy’, and all the evils that go with it, renders women less powerful. In doing so, we place subtle, damaging limits upon ourselves, and I am not about to let that happen to me.

 

Maybe it wasn’t because I’m female that the host was rude. Maybe he was just rude! Maybe he didn’t like me because he disagreed with something I wrote in a blog once. Maybe I’d accidentally said something that annoyed him. Maybe he thought I was an arrogant idiot (a fair assumption). I’ll never know the truth, but by instantly jumping to the conclusion that his rudeness was a response to my gender, I actually did myself a disservice. Gender inequality isn’t the answer to all of life’s woes. I blamed abstract ideas – ‘society’, ‘the patriarchy’, ‘misogyny’. Ideas are easy to blame, but very difficult to change if they come to define us. It’s like we are all standing around pointing to a massive neon sign saying ‘PATRIARCHY’, giving it more credit than it deserves. By viewing the world through this prism, we subtly impose further limits on ourselves.

 

I may be great, but I cannot control the minds of others. I cannot control their thoughts, their prejudices, their attitudes, their ignorance. I cannot change history, either. Yes, men have had the power since time immemorial, but I cannot change that. Focusing on the fact that this is unfair won’t change it either. It’s a huge leviathan composed of an infinite number of moving parts. It’s extremely hard to pin down. Focusing on it too much risks removing women of their agency and ability to overcome the lingering barriers that society will inevitably present.

 

So I urge women not to allow the problems in society to limit them, but instead to move beyond them. So the next time someone says something that triggers your inner feminist, don’t allow that thought to limit you. Overcome it. Realise that you cannot change what is not within your control. Carry on as you would have, had misogyny never existed. Be brilliant, and work to improve the things about you that you can control. There are things that all of us need to work on, but don’t let gender inequality posses you. Know the limits that lie within, and ignore the limits that lie beyond, and perhaps one day the apparent need for ‘Feminism’ will cease to exist.

Posted on March 26, 2016 by Joe Kirby

I’m a teacher, get me out of here

Francis Gilbert describes his experiences of being a new teacher in a tough school with vivid candour. He agreed to let me share some extracts from the book, which is well worth reading.

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In a primary school I visited in my first year of teaching, children were pulling each other’s hair, tipping water on the floor, scribbling on each other’s faces and prodding each other with tongs.

In the secondary school I went to next, a boy was openly smoking in front of his teacher. He offered me a cigarette.

One teacher I observed, Jesse, seemed exhausted. He encouraged pupils to make their own films, discuss controversial topics and do anything but sit down and read and write. It was hard work, made even harder because the pupils knew he was a soft touch: they ate sweets in his lesson, swore regularly, had fights and verbal slanging matches.

My first ever lesson was with Jesse’s GCSE English class, and there was a play to read. ‘Now then,’ I said, ‘Could we have quiet, please? Could you put your hand up if you want to read?’ Everyone started shouting that they wanted a role, and then when I said they had a part they refused to take it. After ten minutes of trying to allocate roles, no one had a part. The kids were laughing and jeering at me. Sweat was beginning to seep through my shirt. I eventually got the play started, but the faltering voices were drowned out by the other kids who were still chatting very loudly. Daryl Jones was pushing and shoving the boy next to him. He shoved him so hard that his friend fell off his seat. He grinned as I approached and put his head on the desk with his eyes closed. ‘You have to follow’ I said in an angry voice. ‘Oh, f*ck off sir,’ said Jones, ‘I’m just trying to have a kip here.’ The class exploded in laughter. He had humiliated me, and there was nothing I could do.

 

In September, my life as a teacher in inner-city London began. After one appalling lesson with 9A, I was confused and anxious. I had 9A again that day and was none the wiser about how to teach them. I felt I only had myself to blame. I should know how to teach, I should know how to get them to behave…

‘Yer mum is a c**k-sucking whore who takes it up the bum’

‘Yer mum is a c**k-sucking bandit whore who takes it up the bum and more

‘Yer mum is a wh*re’

‘Sir, sir, Bulus just cussed my mum!’

‘He started it!’

Apart from this, my worksheet seemed to have done the trick: 9A was very noisy but nearly everyone was attempting to write the fill-in-the-gaps exercise.

 

A typical afternoon teaching 9A, who I’d been teaching for months now, looks like this. They are jostling against the corridor wall, prodding each other, guffawing and shouting as they wait to come into the room. One of the girls winks at me: ‘anyone tell you you’ve got a nice arse sir?’ She winks at me again. I pretend I haven’t heard. Wahid notes, ‘You got red eyes sir. Very red eyes! Anything the matter with you? You sick? You’re not infected are you?’ Others join in, ‘Red eyes! Red eyes!’ For some reason, since I started at Truss, I have suffered from red eyes. This isn’t from drinking, or form conjunctivitis; it is a Truss-related condition that neither I nor my doctor can get to the bottom of.

‘Now, 9A, I need you to listen. Could you listen please? Sharif, please could you stop hitting Bilal with your book. Your book is for reading. Jafar, don’t flick! I said no elastic bands! And stop tapping Fotik! Stop it! NOW!’ They start laughing at my explosion. Charlene snarls when I tell her to get on with the work, that it’s boring and she isn’t going to do anything. There is a tussle developing between Bulus and Mohibur. Bulus is having fun ripping off the cover of his book, rolling it into a cone and whacking Mohibur over the head with it. ‘You’re going to have to pay for that book,’ I say, realising that I wont being able to carry out this threat. Bulus shrugs and keeps hitting Mohibur. When the bell goes, the pupils suddenly disappear before I can set them imaginary homework. Homework does not happen at this school except in policy documents.

My observation feedback is this: ‘You need to do more groupwork. Their learning is far too passive at the moment.’

Another lesson began. ‘Right, now, quiet, and let’s get on with some work!’ I shouted. There were laughs. Hakim snorted and produced a pack of cigarettes. ‘If you light that I’ll have to send you out on call,’ I said. Despair and panic shot through every limb of my body. On call at Truss was a hassle and a shambles: the teacher had to log the incident in a book, and the senior team were never in attendance. Hakim lit the cigarette. The whole class jumped up and started running around the room. Then they began to move the furniture out of the room. I shouted at the top of my voice for them to stop, but it was useless. Desks, chairs and textbooks ricocheted into the corridor. ‘Want a drag?’ Hakim grinned at me.

I felt humiliated, angry and guilty. The guilt was the worst because I felt as though the whole incident was my fault. I felt so ashamed, I felt like I would never teach again.

 

I went to observe another English teacher. Sean Carson’s class was an oasis of calm and quiet. Sean was a disciplinarian. The riotous behaviour of the same students didn’t happen in his class. He never did any groupwork. In his view, the kids would just muck around. Pupils were either reading or writing. Amid the turbulence of inner-city London, he had built a world of peace. How did he do it? He had clocked up twenty years of teaching experience.

The thought of 9A last thing on a Friday filled me with dread. Yumin was forever jumping up and down and found it impossible to sit in his seat. Bilal asked me awkward questions about my private life: ‘have you ever had sex, sir? When did you last do it?’ Shadi told tales about gang fights and drug-running. I never got a grip on the class during that first year.

Slowly, there were days when I was able to talk without being interrupted at the beginning of lessons. Sometimes I could even get the children to work in silence. Little notes, though, were still being passed around the room.

In a nearby classroom, there were scenes of malign pandemonium, the behaviour malicious and angry. The kids were throwing things at the boards, turning over tables, sweeping Bunsen burners off tables, smashing test tubes and fighting each other.

I wanted to move on.

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Posted on March 26, 2016 by Bodil Isaksen

Going postal about posters

Posters lessons. We’ve all done them. Maybe we were naive NQTs, who believed it really would be a great way for 7 set 4 to synthesise their understanding of the formation of ox-bow lakes. Maybe we were exhausted, the week before Christmas, sleep-deprived to the point of torture, and thought it would tide us over. Maybe it was coming up to the summer holidays, and all the key stage co-ordinator had written on the departmental Schemes of Work was “group work on fireworks”. Maybe Open Evening was coming up, and the yellowing displays needed replacing. Maybe we were taking our tricky year 9 form for PSHE, on a topic we knew little about and felt uncomfortable with; when we’d raised it with the Head of Year, all she’d said was that the other forms were availing themselves of the sugar paper.

Fine. I’ve been there. You’ve been there. But let’s be honest: a poster lesson is a desperate measure, not a rigorous first-class education.

There’s been quite the kerfuffle over Tom Bennett’s reasoned, measured comments about the value of certain lesson activities. Tom was very diplomatic, caveating his assertions carefully with the word “some”. I think he doesn’t go far enough. I don’t think posters are ever an effective use of lesson time. The exception, perhaps, would be graphic design, where the poster can be the point. As IndieP tweeted, “If you want to teach ‘making a poster’, teach it. If you want to teach ‘history’, teach that instead.”

The additional fripperies of poster making merely distract from a learning objective to acquire, practice or memorise knowledge. Thinking about layout and visual appeal takes up precious mental space that should be wholly focused on the subject matter.

A poster on the causes of World War I cannot possibly induce more learning than the same content written in an exercise book. The difference is that the poster will inevitably take much longer; it is much less time efficient. Wasting our pupils’ time is an insult to their futures, their intellect and their dreams.

And that’s assuming the poster is taken as seriously by pupil and by teacher – which, let’s be honest – it rarely is. Often, the less conscientious pupils won’t take the task seriously; the more conscientious will take it seriously, but entirely the wrong things. The bubble writing of the title will be immaculate; the speech bubbles coming from the cartoon Napolean’s mouth perfectly formed; Homebase could turn the border design into a wallpaper pattern. Work is rarely assessed beyond a tick and “2 house points” for the neatest girls’ work. After all, if it’s for display, you can’t sully it with ugly red pen. And if it’s the end of term, marking is as likely as eating your 12 boxes of Ferrero Roche in moderation.

Teaching is a noble, honourable profession… when we’re actually teaching. We are so much better than sugar paper and felt tips.

Posted on March 25, 2016 by Jo Facer

Term 1 at Michaela: what have I learned?

Teaching

For the first two weeks at least, the feedback in my (very frequent) observations was ‘you are going much too slowly. You need to speed up!’ Having worked for over five years in other schools, I’d become adept in the ‘explain it slowly three times and check everyone understands before doing anything,’ and at Michaela that is completely unnecessary – with the expectation for 100% sitting up straight and looking at the teacher, they get it first time, every time.

I was also spending far too much time eliciting information the pupils didn’t know – at Michaela, instead we tell them and then check they have learned it. So, if there is a word they haven’t learned I used to say ‘who knows what this word means?’ And if someone got close, try to elicit them to the right answer. Now, I say ‘woe means “intense sadness.” Annotate it on your booklet.’ And then, at the end of the lesson, I ask the class: ‘what does “woe” mean?’, along with the other new words we have encountered.

I’ve written at length about how we give feedback to help pupils improve their writing, but for me this was a totally new way of approaching looking at kids’ work. I’ve learned lots about the best way to explain how to improve, and when it is important to show exemplars to clarify trickier concepts.

I’ve worked on my ‘warm-strict’ balance. In a school with such strict discipline, it is especially important to explain why you are issuing a demerit or a detention – because you love them, because you want them to learn and succeed, and that issuing such a sanction doesn’t diminish your love for them as a human. I can’t emphasise enough how important it is at Michaela to show your love.

I’ve never taught from the front so much in my life, so I’ve had to improve my explanations. Luckily, I work with wonderful colleagues, and our weekly huddle where we annotate the lessons for the week has really helped me become clear on exactly what I will be explicitly teaching the pupils and how. This has been especially important for me with grammar, as I’ve never taught a single grammar lesson in my life. I am eternally indebted to Katie Ashford for spending countless hours going through the resources with me, and in particular for her eternal patience in always quickly answering my occasional panicked text message, which invariably reads: ‘is this an adverb or a preposition?’

Ego

Previously, I’ve been a bit of a praise junkie. I like to be told I’m great. There is no room for ego at Michaela – I’m bringing my A-game to every single day, and still have a such a long way to go to match up to the brilliant people I am surrounded by. It can be hard to see daily the distance between where you are and where you need to be, but being hung up on yourself just makes it harder. I’ve also had moments of panic, where I’ve thought: ‘I need to progress up the career ladder! Why did I quit an Assistant Head position? I need to have an impressive title and feel important NOW!’

Luckily, I’m able to find peace in the realisation that it isn’t about me – it’s about the school. The point isn’t me being brilliant and important, the point is all of us working together in the best way to serve our children. The ego gets in the way – kill it dead.

Purpose

I’ve written before about the intensity of the Michaela school day: no doubt, working at Michaela is hard! The difference is purpose: I’m not doing last-minute marking or planning, I’m not having stressful altercations with recalcitrant children or chasing up a thousand missed detentions: I’m preparing our year 9 units and improving our year 7 and 8 ones.

Reading my year 8s essays on Macbeth, who I’d only taught for a month at that point, was an emotional experience. Every single one contained more genuine engagement, impressive analysis, and originality of thought than any other essay on Macbeth I had ever read – including my previous year 13 class. I can’t take a single shred of credit for that, having only just arrived, but again it affirms my purpose: the sky is the limit for what these children can do, and it makes me want to do everything I can to see what is truly possible.

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Posted on March 23, 2016 by Lucy Newman

Starting at Michaela

I love working at Michaela. Unlike at other schools which do not have tight behaviour systems, Michaela brings out the best in the children and they are lovely and polite. At my old school I had some good classes. At Michaela there are only good classes! Every lesson is one I look forward to. At my old school there was a huge element of unpredictability to each day. I would have pupils fighting in lessons, or a pupil would have to be removed and would start arguing with me. Now I just teach and they listen. It is really quite remarkable, the children are actually listening!

At Michaela we like knowledge. For a humanities teacher the learning load is intense. I love it, I am learning so much. The truth is that if you don’t want to test yourself and learn dates and facts, then this is probably not for you. If you want to grow and change and you love ideas then it is just the most exciting place. If you do not really want to learn and do not like being made to be uncomfortable, probed and questioned, then you will find it hard here. In this postmodern, often nihilistic, morally relative society,you do not often hear the phrase “you are wrong”! You will hear that here, and it is shocking at first. If you want your views to go unchallenged, if you don’t like people telling you when they think that you are wrong, then Michaela is not for you. Michaela is not an army of clones, but there are core values. At Michaela we believe in tradition, respect, and in the authority of the adult. We do not all vote for the same political party. We are not all followers of the same religion; but there is a way of thinking and a set of values that bind us.

Teaching at Michaela is completely about teaching and learning. This was very strange at first; you realise that most of the time when you taught before, behaviour was the focus of your mind. Suddenly it is not the same game; if you have been used to lessons where the bad behaviour was very extreme then it is hard to give a child a demerit for persistently daydreaming in the lesson. It feels odd, you think and feel,“what’s the big deal they are all sitting and being quiet”. That is all you ever wanted at your old school! You feel like a fraud, you give a demerit but you do not fully believe in it. Then as time goes on you realise that if someone is consistently looking away from you during the lesson then you know that means they are not listening, and then you actually give a demerit with conviction. At first it feels silly saying 3, 2, 1 before each instruction, and it feels like you are acting out the role which is all a bit strange and foreign. After a while, with enough time, the routines you are told to carry out become like breathing, they are second nature.

The end result is the learning that goes on is just exceptional. I worried before coming to Michaela that I might miss teaching A level classes, but honestly, teaching year 8 here feels like an A level class; not because of the standard, but because of the intellectual focus and the lack of bad behaviour.

As Katharine says, ‘in the Michaela boat everyone is rowing together’ to the same destination. The ethos, the feedback, the teaching routines, the behaviour policy, they are all worth it, at the end of the day these kids are getting the best life chances and they are very happy and as a teacher I am much much happier. The pupils that will leave Michaela will be kinder people and contribute to society and you will be the best teacher you can be.

Posted on March 23, 2016 by Jonathan Porter

Did it work? Year 8 history essays on medieval England

Essay title: What was the most significant challenge to the king’s power in medieval England?

Conditions: Exam conditions. 50 minutes. No notes. From memory. Pupils DO know the title of the essay in advance.

High ability paragraph on the Church.

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Mid ability paragraph on the nobles

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Low ability paragraph on the peasants

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High ability conclusion (typed out verbatim)

‘In conclusion, the most significant challenge to the king’s power in the medieval period was the Church. It’s spiritual and temporal power, and the last grip it had on the population made it a clear rival to the State. The ‘Magna Carta’ was not a major challenge to the king’s power as even thought it restricted the king’s power for a very short amount of time, King John declared it invalid. The peasants were not a significant challenge to the king’s power in the medieval period as the rebellions such as ‘the Peasant’s Revolt’ were crushed by the king. The Church’s hegemonic influence made it a significant challenge to the king’s power’.

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Strengths: knowledge and memory

One of the things I like about the way we assess at Michaela is our emphasis on memory. All our pupils (from top to bottom in ability range) do their assessments from memory. Almost all pupils wrote for the full 50 minutes and almost all wrote three paragraphs on each of the three challengers to the king’s power: the Church, the nobles and the peasants.

What I particularly like about the essays is their clear command of the facts. They have used dates, people and concepts to support their judgement. The high ability pupil has remembered that Thomas Becket was murdered in 1170. Specific people such Thomas Becket, John ‘Softsword’, Richard ‘Lionheart’, William de Braose. And specific places such as Runnymede, Brittany, Normandy and Anjou. Most pleasingly, the pupils seem to be using challenging conceptual vocabulary such as ‘spiritual’, ‘temporal’, ‘independent’, ‘authority’, ‘tyrannical’, ‘clergy’, ‘lenient’, ‘rivalry’ and ‘hegemony’. All of these were taught explicitly and the pupils have used them, with reasonable accuracy, in their assessment.

One of our less able pupils even managed to remember that pesky apostrophe in ‘the Peasants’ Revolt’ – my favourite thing of all!

Improvements: explanation and judgement

However, I want to see more sophisticated explanation in future. The high ability paragraph on the Church is good, but I don’t think it is as well developed as it could be. There is also some speculation in her explanation: ‘This was a significant challenge to the king’s power and authority because the peasants would have judged the king when he was in the streets and, ultimately, threatened his status in the social society.’ How can we support our pupils to make more incisive comments about the significance of this event and what it tells us about the power of the Church in the period? How can we support them also to ‘zoom out’ and see the bigger picture?

I also want pupils at the bottom end starting to see their essay more as a single articulation rather the sum of three discrete paragraphs. You can see that quite clearly in the high ability conclusion in which the pupils weighs up the challengers to form an independent judgement. But it isn’t there in the low ability paragraph: the pupil simply introduced ‘another significant challenge to the king’s power’. 

If you think you have what it takes to help us to improve our pupils’ work and take them to the next level, you should apply to teach with us. Follow this link for more information: http://mcsbrent.co.uk/vacancy-humanities-teacher/

Posted on March 19, 2016 by The Music and Art Departments

Quality Music Education Remains the Preserve of the Privately Educated

http://www.newstatesman.com/culture/music-theatre/2015/09/why-music-education-britain-so-poor

I read this article earlier this week, and two statistics have stuck with me.

  • “Despite the fact that music is taught at the majority of schools in the country, admissions at leading universities from state schools are on a par with subjects like classics and theology; both subjects traditionally seen only at independent schools.”
  • “Music at GCSE and particularly A-level are the most under-subscribed of all elective courses by some margin, with only 1 per cent of A-level entries in England in music or music technology.”

Why is it that the academic study of music at GCSE and A-level is undersubscribed, despite being a compulsory subject in every school? Why is it that the academic study of music at university has admission rates comparable to subjects which are only taught to the privileged few, when all children have access to a music education in school? The answer is simple. Because the academic study of music isn’t really what’s taught in schools. Music, the rigorous academic discipline, is taught in private lessons. The children who enjoy studying music, who are successful at studying music and who elect to study music further are the children who learn music outside of the classroom, and unfortunately, they are the privileged few.

 

A typical child who is paying for music lessons will:

  1. learn how to read music.
  2. be exposed to and spend time learning an enormous range of music, particularly music written before the 20th
  3. study music theory.

 

A typical child who is studying KS3 compulsory music in a state school will:

  1. study ‘accessible’ music genres like film music, samba, reggae or calypso
  2. spend time listening to compositions made up in lessons by their peers
  3. create posters about music

 

The child receiving private lessons is learning music. The child whose only music education comes from compulsory music lessons in school is receiving a dumbed down and simplified version of the subject. We need to remember why it is that music education is compulsory in the first place: to make music accessible to all. We think that, by simplifying the content that we teach as part of the compulsory music curriculum, we are making music accessible. The sad truth is that, in doing so, we are ensuring that quality music education remains the preserve of the privately educated.

This fact may not sit well with some readers. But we have face the facts – music as a compulsory curriculum subject is failing. Every child in a UK state school studies music until they are 14. How many of them can read music fluently? How many of them have studied the scores of the great composers? How many of them know and understand the circle of fifths? At Michaela, we believe that being able to read music, being exposed to a broad and detailed history of music, and understanding the theory of music is what makes a music education, and those are the things we teach in our compulsory music lessons. Over the next few blogs we will go into more detail about what this looks like, how it works and why we do it. We drill pupils in reading music. We explicitly teach them music theory – up to grade 4 by the end of year 9. We don’t make music accessible by lowering expectations; instead we make music truly accessible by actually teaching every one of our students a rigorous and academic curriculum.

Posted on March 20, 2016 by Naveen Rizvi

Assessment-driven teaching

This post will be outlining the academic rigour I have seen in the teaching and in the assessments created by the Uncommon Schools Network. I shall explain how we can develop such rigour in our classrooms as individual teachers.

Each grade (year group) has an interim assessment exam which is determined centrally by a subject lead teacher; although collaboratively made, a subject lead teacher will finalise the exam produced. Once it is finalised, all teachers within the network will have access to view the assessment but will not have the access to make any amendments/alterations.

I was very impressed by the interim assessments made, because they are created in a way in which pupils’ mathematical knowledge is tested in a manner where they are forced to manipulate the knowledge they have: it tests and masters the fine balance between procedural fluency and conceptual understanding in each question. It also made me reconsider how I plan my teaching, how I now combine concepts in different problem types and how I try to make rigourous low-stake quizzes including questions like the ones you are about to see.

I am going to look at one question which I thought was brilliant, then explain how I would plan a selection of lessons, in a sequence, inducing pupils to become mathematically proficient and confident in order to attempt such a question.

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Here I am assuming by convention from how I was trained and from what I have seen in my experience, previously I would begin by teaching the concept of square numbers and square roots, by getting children to identify the square numbers by multiplying the root number by itself, and then drawing the link: that once you square root a square number you will obtain the initial root number which, multiplied by itself, then results in that square number.

Then, I would have possibly explored completing calculations with square numbers and square roots. After that, in years to come, I would teach square numbers and square rooting in relation to fractional indices and with surds. When teaching surds, I would bring in the idea of rational and irrational numbers. Here is what I now suggest!

This is how I would map out teaching the topic of square numbers, square roots and holding a root number, to an index number greater than 2, and introducing rooting greater than a square root. Kids must have gotten to a stage where such calculations are memorised:

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Why not bring in the idea of interleaving fractions, decimals etc?

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Then, I would build upon the previous questions systematically, in a way in which students can create a fraction which can be simplified.

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Also, I would introduce from an early stage the proposition that when we square root a square number we get positive and negative of the root number, which can be a really valuable discussion to have with children. Introduce calculations afterwards with square numbers and square rooting. This type of thinking is driven by another question I saw in a North Start Academy assessment:

assessment 4

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The question is touching on key knowledge that when x is equal to a square root then we assume a positive value as an answer, however when x is held to an exponent the values of x will result in a positive and negative value.

Eventually I would introduce a base number to an exponent greater than 2 and interleave it into calculations:

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I could get pupils to then go into the following questions:

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Or, have pupils determine the value of unknowns through trial and error:

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Now, I am going to draw a link between square numbers, square roots and rational numbers without linking it to fractional indices and surds. The purpose behind this is to (for now) restrict what I would teach at Year 8 or 9 but, at the same time, providing that conceptual scope. Simultaneously, it also provides the opportunity for multiple choice questions that have the academic rigour for our pupils.

I would define a rational number and then go into the necessary vocabulary such as ‘a rational number is a number which can be written as a fraction of two integers. A rational number cannot be written as a non-repeating or non-terminating decimal’, for example, in comparison to 0.45454545 which is a rational number. I would then provide a selection of example and non-examples.

I could test children’s understanding through mini whiteboards or hands up: 1 if it is a rational number and 2 if it is an irrational number; selecting the order of questions such as 2, 6, 100, 15, 1/2 , 5/6, 10/100, then bringing in the square numbers and asking pupils to show why it is a rational number or irrational number such as √16, √36 or √144

Pupils could type in the value of √12 or √3  in a calculator to see that you will get a non-repeating or non-terminating decimal that cannot be written as a fraction of two integers therefore categorising such non examples as irrational numbers.

Also then mentioning that square rooting a square number will result in a rational number, and cube rooting a cube number will result in a rational number etc.

You would then be able to explore the idea of rational numbers in which you are square rooting square numbers using your calculator:

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Following this, discussion will be made of the notion that the following are rational numbers in regard to the definition of a rational number being a number that can be written as a fraction made of two integers:

2fig10

Then, the idea of either the numerator or denominator being a whole number should be brought into my teaching:
2fig11After that, I would introduce problem types where you can simplify the fraction:

2fig12

Discuss that the problem below results in an irrational number because the numerator is irrational and overall the solution cannot be written as a fraction of two integers:

2fig13

 

 

Will the following number sentences produce rational numbers?

2fig14

Children need to be comfortable in identifying that  is not a rational number because it cannot be displayed as a fraction of two integers. The definitions need to be consistent so that children are confident in differentiating between a rational and irrational number using square numbers and square roots, and then moving onto powers greater than 2. If we expose children to the following above we are providing the academic rigour which future exam boards are attempting to build upon.

All of this is just an idea which I am trying to explore in order to provide students with the academic rigour, in terms of their classwork and in the assessments, that they will be taking.

assessment 2

Everything that I have written, the problem types I have created and the interconnections between square numbers, square rooting, and rational numbers, is a result of looking at such questions above. These questions guided me to plan a selection of lessons which provide the balance between enabling students to become procedurally fluent in calculations and in developing conceptual understanding of this topic.

Through creating difficult assessments you can guide your teaching to induce that academic rigour. I have never taught maths like this, but I do plan to in the future. This was all inspired through looking at this question at North Star Academy in New Jersey. The academic rigour present in the interim assessment guides to create academic rigour in what is being taught and learnt within the classroom.

Posted on March 19, 2016 by Bodil Isaksen

Don’t mind the gap

How many digits of pi can you remember, Layla?

Only twenty, Miss.

Layla sees nothing extraordinary about the fact she remembers four times more digits of pi than her maths teacher. Not when her classmates can remember 40, 50, 60… hundreds digits of pi*. Not that she’s upset about it, mind. She knows that a fortnight ago, the most anyone in her class knew was three digits. She knows that the reason for the difference now is sheer hard work.

How is it possible for a 12-year-old child in an inner-city comprehensive to see knowing 20 digits of pi as unremarkable? By not minding the gap. In fact, we encouraged the gap through competition. Two weeks ago, the gap between the best and worst in the school at reciting pi was three: between those who had no clue, and those who knew 3.14. Now, the gap is in the hundreds.

In absolute terms, the achievement and progress has been excellent. Pupils, including the weakest, reel off scores of digits. In relative terms, it’s a disaster. Layla can say twenty, but Aliyah can recite 160: an eight-fold difference. In relative terms, we were better off a fortnight ago, when the difference was a mere handful of digits.

“Closing the gap”: a well intentioned policy, but one that worries me. I worry about its effect on our Aliyahs; that it encourages us to rein in their potential artificially. But I also worry about our Laylas.

When we focus on closing the gap, our implicit messages are toxic. We imply that there’s only so much we can expect; that there’s a cap on what’s reasonable to achieve. Our monitoring and scrutiny doesn’t leave room for pupils to go off and propel themselves, independently, beyond what our limited imaginations can fathom for them. Round-the-clock interventions for those struggling, while the top end go off and revise on their own, induces a learned helplessness; a sense that work can’t be done without a teacher holding their hand. The intensity of the teachers’ attention implies to the children that their teachers are responsible for their grades, not them. Pupils may even come to recognise that the less they do, the more the teachers worry, and the more the teachers do for them. Pupils are not allowed to fail, and thus gain no experience of the link between laziness and failure; the link between hard work and success.

In fact, I’d posit that if your gap is narrowing, you’re doing something wrong. The Matthew effect states that with the same inputs, the knowledge-rich will get richer more quickly. My experience is that the top end will accumulate knowledge more quickly even if given a fraction of the input of the bottom end.

We should not be concentrating on “closing the gap”. An obsession with relative under-performance doesn’t just harm the top, but also the weakest we are trying to help.

Encourage competition. Encourage every pupil to do their best. It won’t close the gap. It will widen it. In relative terms, it will be a disaster. In absolute terms, it will be a triumph.

 

*A note on pi: this was an optional competition, a bit of fun for pi day; pupils learnt pi of their own accord outside of maths lessons. I don’t think learning pi is maths, but it was great at creating a buzz!

Posted on March 19, 2016 by Barry Smith

Turning Heads

On Thursday we took 120 kids from Wembley to Greenwich. It’s the second year running we’ve taken kids to the Observatory. This trip was like every trip at Michaela. The kids really shone.

They walked in single file and in silence, eyes front, from school to the tube. They stood tall and proud. Ties tight, shirts white, shoes shining bright.

As per normal,  we entered the tube car, we stood in silence, we got our books out, we read. When seats became available we sat. When adults needed a seat we immediately stood and offered our seats.

We changed at Canary Wharf. We formed a perfect line again. We stayed in order. We counted down, each person shouting out their number, in French, until we got to the ‘last man’, number thirty.

On busy, but narrow, pavements we stayed eyes front, silent, single file. Not a second was wasted.

Again and again, and this always happens when we take our kids out, members of the public congratulated the kids, congratulated the teachers, stopped and pointed, took photos as a perfect line of Michaela pupils proudly walked by. Michaela kids turn heads.

As ever, staff at the venue said they’d never seen such polite children. The kids shone in the shop. Their manners were impeccable. They spoke clearly to shop staff, they wished shop staff, ‘Have a nice day!’, they made great eye contact.

As we queued to enter the planetarium the kids showed off, reeling off loads and loads of French, using a broad range of structures, projecting beautifully, their accents stunning members of the public. French tourists were overheard discussing how smart and how polite our kids were. They also went on and on about how good our kids’ French was.

In the planetarium the kids were exemplary. You could hear a pin drop. They asked some superb questions. They demonstrated impressive science knowledge. They did themselves proud – yet again.

This is what ‘being Michaela’ is all about. Our kids turn heads. We’re not ‘normal’. We don’t want to be ‘normal’. We’re Michaela.

If you fancy working in a school  where kids are grateful, kind, hard-working and polite, if you believe in  didactic teaching and holding kids and parents to account, if you believe in ‘tough love’, if you’re willing to jettison everything  you’ve ever been told about ‘good practice’, if you believe the term ‘outstanding’ is a nonsense – you should get in touch.