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Michaela’s Blog

Posted on March 19, 2016 by Joe Kirby

Experiences of a new teacher

This is one new teacher’s account of her first year as a newly qualified teacher in a tough school.

I teach at an inner-city secondary school, where sixty percent of students receive free school meals. Eight million was spent doing up the building, and the new rules said: no chewing gum. Soon, the brand new tables had layers of Wrigley’s and Juicy Fruit stuck to their undersides.

In my first lesson of my first year, a fight broke out between two students. They went for each other’s hair and throats. The whole class were out of their seats, crowding around the two girls. Senior management arrived to remove them from the lesson. In my first year of teaching I did not have a life during term time: I sat up til ten marking students’ work and planning the following day’s lessons.

The first morning back in my NQT year, eighty or so teachers gathered in the echoing dining hall, where Cecelia, the principal, welcomed us, announced the GCSE results, and congratulated us on the rise in attainment: 58% of students had got five or more GCSEs at grades between C and A*. The national average that year was 64%. Only 32%– about 60 students out of 200 or so achieved a C or above in English and Maths.

I knew the Year 10s were going to be a difficult group. They had been at this school longer than I had, which made me think that they know things I don’t. They were intimidating teenagers, predicted Es and Ds in their GCSEs.

One minute into the lesson, and the seating plan has fallen apart. ‘Miss, I don’t want to sit there. I can’t sit with her.’ They’re adamant, forceful: ‘No, I don’t care, I’m not sitting there!’ The students eye me up, arms folded, with a look of outright disdain. I distribute a poem, a stanza to each table. Chaos descends. All the five groups I am not with raise their voices in pandemonium. A few quieter students are attempting the task, but the loud majority make it difficult to hear anything. Every few minutes I strain to raise my voice above theirs and tell them to settle and quieten down, which they do, for a few seconds. Several separate conversations are going on while groups are trying to share their observations. I turn to the girls talking to each other and ask them to stop, explaining that it is rude to speak over other people. They turn back to each other and finish their conversation. Jamie is eating crisps. Group work was an unmitigated disaster. As the door closes behind them, they burst into loud laughter.

No gum is one rule: all lessons must have a learning objective is another, to tell students what skill to be developing. The other rule about lessons is they must be divided into three parts: a fun starter, main activity, and a plenary where students reflect.

‘Adalia, gum in the bin. Chantelle, why haven’t you started?’

‘Miss, can I borrow a pen?’

My box of biros, full at the beginning of term, had already evaporated. Half the Year 10 class needed a pen each lesson. I always forgot to collect them in, so would have to scrabble around on the floor to gather any that the students had been kind enough to leave with me. Scrambling around on the floor also gave me a chance to collect the wrappers and crisp packets they’d dropped once they’d finished surreptitiously eating the contents. I root around on my desk and find a pen for Chantelle.

Chantelle raises her hand.

‘Miss,’ she giggles, ‘have you seen what someone’s written here?’ She points at the desk. I look and see that someone has etched into the desk with a compass: ‘Your mum is a c**t.’ Shocked and annoyed, I instruct her: ‘Don’t tell the others.’

My energy was waning – there was a pile of unmarked homework in the tray on my desk, and I already felt ready for another week off. The Year 10 class didn’t go in for waiting quietly with their arms folded for me to give them an instruction. I had to bamboozle them with Powerpoint presentations and clips of film and music, instructions and tasks and performances. In terms of the pecking order within my class, there were several positions above mine. By being so purely unpredictable and unbothered by the rules, they made me dread each lesson, not knowing what their mood would be.

At the end of a lesson, I looked at the bin. It was overflowing with crisp packets. Drained of energy, I got on to the floor and started picking up the litter that hadn’t made it to the bin.

At home, I settled down for some marking. I noted it was taking me five minutes to mark each student’s work and therefore I would be finishing at ten. But then at 8.30 something strange happened: every muscle in my body hurt, and I suddenly had to crawl to bed, unable to do anything more.

At six o’clock on Wednesday morning I called in sick. I sat down morosely at my laptop to email in cover work, thinking how the poor cover teacher would be so abused by my classes. The students would trash the room. A supply teacher is a school providing students with a human sacrifice…

On my return, I braced myself. Lots of sheets of A4 lined paper were strewn about the place. Some students had obviously managed to write their names at the tops of their piece of paper, but not got any further. I removed the crisp packets stuffed into the cupboard at the back of the room. A pile of incident reports were on my desk:

“Folashade was drinking flavoured fizzy water in class. I asked her to put it away. She refused. I asked her again and she refused again, angrily. She charged at me, and had to be restrained by her classmates.”

“Erez came into class and immediately would not follow instructions or do anything co-operatively. She was given two warnings for refusing to take off her coat and take her bag off the desk. ‘What? What’s my bag doing to you? Is my bag hurting you?’ I tried to send her out of the classroom but she refused to go.”

I heard a piercing scream next door. I ran to the classroom, imagining a fight had broken out, but it was just a drama lesson. ‘It’s ok, they’re just doing drama next door.’ Everyone looked miserable. ‘Why are they always having fun?’ Princess stamped her foot. ‘Please could you take out a pen,’ I said. Rude, aggressive, and undermining, one pupil snarled: ‘Don’t start on me – I’m not in the mood.’ The same confrontation day in, day out.

The glory days with my Year 7s seemed to be drawing to a close. They were in their second term at the school and, after carefully observing the years above them, had started adopting some of their bad habits. They had grown loud. And the louder they grew, the less I enjoyed being in the classroom with them. They’d completely lost interest in hearing anything the rest of the class might have to say.

Day to day I could feel I was falling down a never-ending spiral of tiredness. So much of the time teaching the Year 11s I wanted to shake them and say, ‘Stop wasting time. You don’t know what you’re missing out on. Why won’t you do something about it?’ When your students fail to see something, it naturally feels like a failing on your part. Why wasn’t I a good enough teacher to make them work harder? How did Julia do it? Her students were orderly: she narrowed her eyes at them and they fell into silence. Why would they follow other people’s instructions but not mine?

The Year 7s were always at their worst on a Wednesday afternoon. They had history in the previous lesson, which was taught across the hallway by a long-term supply teacher. His door was closed, and so was mine, and the hallway lay between, and yet I could still hear them rioting in his room. As they surged from his class to mine, I braced myself. The class spent the hour not listening to me or each other. My voice was hoarse. I had no energy. I cannot keep them quiet, I thought: I have lost the will. I can’t do it. I can’t make them listen. Controlling disruptive behaviour was sapping my energy, and I felt, once again, I was having to fight my students in order to teach them. By half-term I was lying in bed with a temperature.

One lesson I asked my class to stay behind for a few minutes during break time – they’d easily wasted more time than that in the lesson. I had to ask: ‘Can you sit down, please, Becky – you’re wasting everyone’s break time.’ ‘That’s f**king extra,’ she shouted. ‘F**king shit. F**k you.’ She left, kicking her chair out of the way.

I rang her mum. I filled in the forms: the incident report and the record of the phone conversation with her mother. I passed the report to senior management, so that they could record what action they’d taken. The forms were returned to me. I stapled five copies of the phone record to five copies of the incident report and then spent five minutes in the staffroom finding the pigeonholes to post the copies to everyone involved in Becky’s care. Students rarely attended detentions, and then what? More phone calls home; more paperwork. I remembered that in my first year I’d tried to hold Becky back on a Friday for a detention. I’d gone down to the school gate to make sure she didn’t slip away. She saw me and ran for it. I called home, and then sat down and wrote another report on what had happened. My frustrations were increased tenfold by the feeling that there were no real consequences at my disposal for misbehaviour. Nothing ever seemed to really come of all this paperwork. There was no feeling that, as a teacher, I was being supported. It made me angry, but there was nothing I could do about it.

The Year 7s in particular seemed to be growing more and more challenging by the day. The students who had come up from primary school so well trained and able to listen to each other politely, had all turned into mini-volcanoes, spewing out noise. I tried to cut down on all evening activities, to preserve energy. God, I thought, I can’t imagine working where I am and also having children.

When I asked students about their lives at school, I heard experiences of being bullied on buses, bullied in the playground, mayhem, fights and disruption. Several students had attacked another outside of school.

With only two weeks to go before the holidays, I plodded through the lessons. The Year 7s were completely exhausting. Becky just sat graffitiing her exercise book. Mahima shredded her worksheet into small squares, which then fluttered down on to the floor. If I stuck to the three-strikes-and-you’re-out rule, most of them would be out within the first few minutes of the lesson, if indeed they managed to make it into the classroom. ‘Good, I didn’t want to be in this stupid classroom anyway,’ many an evicted student uttered.

Teaching groups of thirty rowdy, disaffected teenagers with my lack of experience meant I couldn’t get enough control. But I also felt it was because the students were not schooled in the work ethic that they needed to make real progress. And every evening, hordes of cleaners tried to scrape gum out from between the grooves of the carpets in the classroom.

One lesson, I tried dazzling them with activities: freeze-frames, drama, improvisation, matching exercises, picking up the pace of the lessons in groups of four so that there was no time for the girls to start discussing their latest plans for hair extensions. Lessons had never been this fun!

Afterwards, out in the corridor, I heard shouting. I ran out and saw two of my students – a new girl and another – trying to rip hair from each other’s heads. I bellowed ‘What on earth do you two think you are doing? Rose, go and get on-call please . . . Everyone else to break.’ Adrenalin flew through my veins, and I deposited the two by this time hysterically crying girls in different classrooms. I felt a bit responsible. Had the chaotic lesson added to their agitation?

The next lesson, ‘Miss . . . why are the lessons back like this again?’ Folashade asked. ‘Like what?’ I asked. ‘Boring,’ she said. ‘I’m sorry you feel that way, Folashade, but we have to do some writing at some point.’

I returned home from school crying three evenings in a row. I was feeling trampled. The end of a lesson didn’t feel as though a stampede of elephants had run me down in the way it had in my first year, but the effort was still draining: the full timetable, an after-school club, the planning, the marking, the meetings and department responsibilities. Encounters with unfamiliar students still left me feeling battered and bruised. In a school of one thousand, there are a lot of students you don’t know and who don’t know you. It irritated me that, even if I did take the time to write up confrontations, nothing would come of it. I felt the school did not demand that students showed respect to the staff, and teachers had to pick and choose their battles. I worried that a large handful of my students would be fired if they ever managed to secure a job, because they wouldn’t see any problem in speaking to their employers in the way they addressed their teachers. I felt exasperation at the endless disruptive behaviour. I just couldn’t summon up the energy to be on top of my classes.

I still felt like I’d been run over at the end of each day. It was time to move on.

HandsUp

 

Posted on March 19, 2016 by Jo Facer

Reading all the Books

I’ve written before about marking, but just to summarise: it has always been something I’ve loved doing. There was something in that Boxer-like satisfaction of ploughing through an unending pile of books, leaving lovingly crafted comments in an array of coloured pens and stickers that just looked like it would work so well. How could pupils fail to make progress when I’d spent so many hours on them?

So something I was nervous about when starting at Michaela was their approach to marking; that is, don’t do it. I’d read Joe Kirby’s blog and spoken to him at length, but remained steadfastly concerned that marking worked – if you ensured pupils

acted on feedback. I then moved to the idea that marking worked, but at what cost – a teacher with six or ten classes cannot be expected to give the detailed feedback the lightly-timetabled members of SLT seem to manage on a weekly basis.

In my second week at Michaela, we had a department meeting where Joe brought up the excellent question: it’s great for workload that we don’t mark, but how do we make sure we’re giving feedback to make pupils’ writing better?

One of the main reasons I think I find marking helpful is because it holds me accountable – I am actually reading if I am putting a pen to paper to say something about it. (I annotate the books I read in the same way – it helps me to remain focused.) But while this is an essential strategy when it is 7am on a Saturday, pre-intervention, and you want to clear the last 20 books to enjoy a semblance of a weekend when you return home that afternoon, or 9pm on a Wednesday when you just want to sleep, actually, I had underestimated my ability to focus.

To begin with at Michaela, I couldn’t get out of the habit of marking. I would spend two hours with about 60 books, circling and underlining when I couldn’t resist; writing limitless notes to share with the class, photocopying paragraphs to get pupils to annotate their peers’ examples. Joe’s comments on this kind of feedback were: ‘would you want all teachers to be photocopying twice or three times a week? Is it worth the time getting the pupils to annotate a piece of paper they are then just throwing away? What else could you be doing with that time?’ Moreover, I was reminded of why marking is not always the best method – if I’d put the merest hint of a mark on a child’s book, their hands shot in the air: ‘why is this circled?’ ‘I can’t read your writing on this spelling correction.’ ‘Why is there a question mark here?’ Marking breeds over-reliance on the teacher.

Now, I’m getting into the swing of the Michaela way. I read my pupils’ books once or twice a week. I teach four classes, each with between 28 and 32 pupils, so it is about 120 books in all. I read 60 books in 30 minutes. As I read, I make notes: spellings lots are getting wrong, things they’re all doing well at, and the main issues they need to improve. I note down anyone whose paragraph is amazing to reward with merits or show the class; I note down anyone whose work is messy to give a demerit to. It looks something like this:

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In the following lesson, I teach the spellings from the front, and then test pupils. They will write their corrections out in green pen, interleaving the ones they got wrong, or the ‘toughest three’ if they managed, on this occasion, to score 100%. I’ll test them again the following day. I’ll share the positive things I found and celebrate the star paragraphs, and then explain carefully, perhaps modelling on the board (as Katie Ashford has described brilliantly here or occasionally putting a great paragraph from the class under the visualiser, how they can all improve their own paragraphs. And then they improve them, in green pen. It looks like this:

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The second powerful tool is in-class feedback. With an excellent behaviour system, silent writing for 25 minutes means I can see every child’s paragraph twice while circulating, giving them suggestions and tweaks while they write. On my colleague Lucy Newman’ssuggestion, I’ve also started using my visualiser more. This way, we can take a pupil’s book, display it to the class, and show pupils how to edit their mistakes in that very lesson, just by giving oral feedback on the common errors they are making, or the aspects they really need to focus on improving. 

The thing is, what makes the difference in their writing is the quality of the feedback and how timely it is. They don’t need feedback on a paragraph they wrote two weeks ago. At Michaela, they can improve the paragraph they wrote yesterday, while it is fresh in their minds. I miss marking, I do. But I’m realising I did it for me, not for the pupils.

Posted on March 18, 2016 by Jessica Lund

Something we do – Speaking

The teachers at Michaela speak a lot.  They are founts of knowledge.  They might spend the majority of lesson time talking.  Much of that is instructional; a lot of it is questioning.  Rapid-fire, constant questioning is a feature of many Michaela lessons.  Critics of traditional teaching methods might imagine a silent classroom in which the teacher talks at length and then the pupils write down their answers to questions or do practice drills.  If you were to visit Michaela, you would see a huge amount of interactivity, hands shooting up to demonstrate recall and to ask and answer questions.  The kids are proud of their contributions, and they have plenty of opportunities to make them.

With respect to speaking, the Michaela French department is no exception.  You can’t shut us up.  We love the sound of our own voices.  We’re actors and actresses with audiences of 30 children four or five times a day.  What you may not be able to glean from the way in which we describe our teaching is how much the kids talk too.  (And shout and chant and sing and try to outdo the opposite classroom with the volume of our alphabet and number recitations – it gets pretty loud).

Last week, I wrote about how we read.  Nearly all of our reading is done out loud, which allows pupils to practise and perfect their pronunciation (if you listen to the examples in that post, you’ll see that it’s working!).  We also read out loud individually.  How does that work in a classroom of 30-odd pupils?  Each pupil puts their hands over their ears, and then reads and re-reads a passage of text so that they can hear themselves but not anybody else.  It works.  We can then walk around and catch any errors or encourage better pronunciation of particular words and phrases.  We can also nudge those who are not putting in enough effort into their projection, articulation and expression.  At the end I also give merits to pupils who have put real thought and effort into those things.  Pupils can then read out loud one at a time to the whole class with a greater sense of confidence.  This opportunity to practice beforehand is perfect for less confident pupils to go over the text a few times before reading to others; it’s perfect for all the others to develop a sense of the meaning of the text and read with expression, in addition to understanding.

The teachers read out loud a lot as well.  We do this in a very theatrical fashion, with a hammed up French accent and putting deliberate emphasis on accents and the sounds of particular vowel combinations – we’re overemphasising the pronunciation because pupils so easily under-emphasise it.  We intercut our reading with notes on what we’re reading – either to do with the meaning or the morphology of the word.  Remember, this is all done as a parallel text, so the meaning of the words is already clear.

“J’adore fAIre mes devOIrs – my homeworkS, in French, c’est au pluriel, mais évidemment les lettres ‘s’ sont [they all chime in ‘MUETTES!’] – en Écoutant, É-cOU-tan, la lettre ‘t’ est muette, il y a un accent, quel genre d’accent, oui un accent aigu – de la musique – of the music. Mais franchement – franchement, onze lettres, fran-che-ment, the -ment means ‘ly’ in French, like normally, normalement – je prÉfÈre lire – I prefer to read, regardez le mot ‘préfère’, il y a deux accents, quels accents? Oui, un accent aigu et puis un accent grave, it makes a mountain towards the f…”

In this way, reading a short (10-15 lines) passage of text, and repeating the bits they know less well, can take up to ten minutes.  We ask questions while we’re doing it, and get pupils to commentate on the words as well.  They really enjoy putting their hands up to interrupt with observations we might ‘forget’, saying things like “alors, Mademoiselle, évidemment il faut souligner les voyelles AI dans le mot ‘faire’.”

Much of the rest of the speaking in class is done as rapid-fire translation:

Yesterday – Hier – I went – je suis allé – to the stadium – au stade – with my brother – avec mon frère – but unfortunately – mais malheureusement – one must say that – il faut dire que – it was – c’était – rather boring – plutôt ennuyeux – because – parce que – I don’t like – je n’aime pas – to play at foot – jouer au foot. So – Donc – it is rare that I go – il est rare que j’aille – to the stadium – au stade – because I prefer – parce que je préfère – to stay at home – rester chez moi – where I watch the telly – où je regarde la télé – having done my homeworks – ayant fait mes devoirs. Tomorrow – Demain – I’m going to go – je vais aller – to the swimming pool – à la piscine – with my mates – avec mes potes – and it will be great – et ce sera genial – because I love to swim – parce que j’adore nager.

There are hundreds of similar phrases that we construct using regularly recycled, wonderfully rich and varied vocabulary.  Our Year 8 pupils can translate at length on a range of subjects, including language learning itself:

Pour moi, et évidemment c’est un avis personnel, si on veut maîtriser une autre langue, la chose la plus importante, c’est la lecture.  Ça va sans dire.  Mais ça ne vaut pas la peine de lire si on ne réfléchit pas en lisant…

This can go on for several minutes!

As a result, our classrooms are full of pupils speaking French.  Reading out loud, translating beautifully, and giving answers about spellings.  This is a typical exchange with my year 7s:

“Le mot ‘introverti’, comment ça s’écrit (how that itself writes)?  Ikram.”

“I-N-T-R-O-V-E-R-T-I [note: this is spelled using the French alphabet].  Mais Mademoiselle, il faut ajouter la lettre ‘e’ à la fin si c’est féminin.”

“Oui, tu as raison (you have reason, you’re right).  Et comment dit-on ‘me interests’, Alex?”

“Moi, je dirais ‘m’intéresse’”

“Oui, c’est ça. Mais est-ce qu’il y a un accent?  Oui?  Quel genre (what type) d’accent?”

“Bah, Mademoiselle, ça crève les yeux, il y a un accent aigu sur le premier ‘e’.”

We don’t use pictures for anything.  We will have to at some point, in order to enable pupils to respond to the image stimuli in the new writing and speaking exams, but for the moment they use the written and spoken word as their cue.  We don’t play games.  And – this is the bit that might ruffle practitioners elsewhere – the pupils hardly ever speak to one another.

There are a few reasons for this:

  • It’s unnecessary. There is plenty of opportunity to speak in lessons, to practise pronunciation and use all sorts of language, transactional and otherwise.  We also quiz pupils in the yard or at lunchtime – many is the breaktime I’ve sat with a few pupils and listened to them reading and quizzed them on their French.
  • It prevents misapprehension and the reinforcement of mistakes. Two pupils speaking French to each other increases the likelihood of speaking poorly and going uncorrected, or developing bad habits with regard to accents and phonics.  If we can listen to what they’re saying the vast majority of the time, we can reinforce good habits.  This is helped by the fact that 59 minutes of every hour is active teaching time – our slick routines and transitions mean that we have far more time to listen to each pupil read and give answers.
  • If we allow pupils to speak to one another, even for brief periods, the outcomes they get are completely dependent on the individual motivation of the pupils. The vast majority of our pupils would dive into the task with real focus and willingness; the small minority would use the chance to just talk and not engage with the task.  If we give them the chance to do that, we allow them not to make any improvement, or do any practice, in that time. This is unacceptable.  We’re thinking about carefully designed tasks that involve pupils quizzing one another on specific key bits of language, but that’s further down the line.

The results: our pupils speak great French with competence, confidence and superb accents.  They love reading out loud, answering questions, pointing out things about the words and pronunciation throughout the lesson.  They also – of course – love shouting the alphabet as loudly as possible to beat the kids in the opposite classroom.  And they love it when you get to ‘seventy’ in the number chant and they can go ‘soixante-dix’ and adopt a ‘duh!’ face when they’re doing it, remembering the time they thought it might be ‘septante’.  And, importantly, they understand everything they say, which only adds to their sense of mastery.

If you’re reading this with incredulity, I don’t blame you.  What the pupils at Michaela can do is unlike anything I’ve ever seen in a classroom.  I’m going to try and sort out some videos to post on the school’s Youtube channel so you can see all this in action.  Of course, the best way to see it in action is to come and visit the school – we love visitors, and the kids love showing off what they can do.  Email me at jlund@mcsbrent.co.uk – we’d be happy to welcome you any time, give you a tour and you can stay for lunch and speak to our lovely pupils.

Posted on March 13, 2016 by Naveen Rizvi

Sequence of Instruction

School visited: Uncommon Collegiate Charter High School

Class observed: AP Grade 11 Statistics (UK equivalent Year 13)

Theme of post: Pedagogy and Curriculum

This is the second blog of a series to complement a workshop I delivered at #Mathsconf6  on Mathematics Pedagogy at USA Charter Schools, following my visiting a selection of Uncommon and North Star academy schools in New York and New Jersey. During the workshop, I discussed how the common denominator in each maths lesson I observed was the level of academic rigour. I am still trying to find a way to define this term, because it is overused and poorly defined.

Nevertheless, I believe I can state that the teaching and learning delivered by such extraordinary teachers in the classrooms I observed displayed features of academic rigour. These features of academic rigour are evident in the structure of a teacher’s pedagogy and instruction:

Academic rigour featurse

In my workshop, I discussed the four main elements that all teachers up and down the country can implement into their teaching practice with minimal effort and maximum impact. I will discuss each of these four elements in turn, by way of one per blog post; today I will discuss the sequence of instruction.

I was observing a lesson, Grade 11 Statistics, and the teacher had organised the lesson so that he was trying to have pupils factorise cubic expressions where one of the expressions in the factorised form could be further factorised into two expressions because one group  was a difference of two squares. (Figure 1) The sequence of instruction to explain to pupils how they can factorise such cubic expressions is what made his lesson so powerful.

Fig1SIFigure 1 – Sequence of Instruction in terms of expressions used in teaching

Here, I entered the classroom, and the teacher had displayed the following algebraic expressions that he wanted pupils to factorise. (Figure 2) Before the pupils had even started to factorise he spent some time identifying the common features which determined this expression to be a difference of two squares. It is known as the difference of two squares because we have even powers, square numbers as coefficients and one positive term and one negative term.

Fig2SIFigure 2 – Difference of two squares expressions + common features of this type of expression

What I found really fascinating was the examples that he had initially chosen in order to begin teaching pupils how to factorise such expressions. Previously, whilst teaching, I would begin teaching the topic by using the following examples and non-examples to state what the common features of an expression known as a difference of two squares actually looked like, and therefore what it would not look like. Therefore, I utilised simply examples and non-examples. (Figure 3)

Fig3SI

Figure 3 – Examples and Non examples used in the initial stages of teaching how to identify an expression known as a difference of two squares

The way the teacher started was better, because the expressions he had used made the common features more obvious to pupils. So the initial examples of a difference of two squares that I would have started to teach from are actually more nuanced and special; the coefficient of x2 being 1 is hidden, and instead of having two terms where the variables both have even powers we have a constant which is a square number.

Second, he then introduced the consistent algorithm he wanted pupils to use to go from the expanded form to the factorised form of the expression. He was very systematic (Figure 4 – consistent algorithm):

Step 1: square root both terms;

Step 2: divide both exponents by 2 and

Step 3: Write your answer as such.

He did this with a selection of examples, as you can see below:

Fig4SIFig4aSI

Figure 4 – Consistent algorithm to factorise an expression known as a difference of two squares

Following this, he then introduced the notion that the pupils would now learn how to factorise a cubic expression. At this point in the lesson, I wasn’t fully sure with where he was going (until we reached the end of the lesson). He stated that when we factorise a cubic expression as such we need to factorise the first two terms and the last two terms. He structured it for his pupils because he pre-empted a common mistake that pupils would have made unless he structured it for them. We are factorising the first two terms by dividing both terms by 1, whereas with the last two terms we are going to factorise by -1, because -1 is the greatest common factor of -8p and -24. (Figure 5)  Therefore, the first step of the algorithm is not line 2: it is line 3. This was so powerful because by pre-empting this misconception, and by being very explicit with this instruction and guidance, it made the lesson run more smoothly because pupils were more independent to get on with the practice set of questions – because they weren’t making this mistake.

Fig5SI

Figure 5 – Structuring the first step of the algorithm

He then carried on to lay out the consistent algorithm between the expanded form and the factorised form.

Step 1: factorise the first two terms, and the last two terms. (be careful when factorising the last two terms)

Step 2: Now factorise the greatest common factor for both terms (ensure that you are factorising the GCF of the coefficients as well as the variables) However, he posed the question one more time: “What is the greatest common factor  of 16p^3 and 48p^2?” Students then noticed that we are no longer factorising by identifying the greatest common factor of the coefficients but also of the variables of each term. (Figure 6)

Fig6SI

Figure 6 – Step 2 – Step 4 demonstrated

Step 3: factorise the greatest common binomial of the expression:

Again, the algorithm was consistent. Furthermore, he said factorise “the greatest common binomial”. This level of technical language being used in the classroom is fantastic, and is something I certainly intend to implement in my teaching practice.

Step 4: “Are we done with this problem?” he asked this question with the intent of having students identify that the first expression in parenthesis is not fully factorised – which pupils identified.

Here he paused and said to his pupils “Now you are thinking that we are finished because we have two groups that can then be expanded and simplified to form the expanded form which we start with, but we are not finished. What is the greatest common factor of the first group?” However, he posed the question one more time “What is the greatest common factor of 16p^2 and 8 ?”.Pupils then identified this to be 8. He then proceeded to do a selection of examples to complement the first example, and to also reiterate the consistent algorithm. Figure 7 

Fig7aSI Fig7bSI

Figure 7 – Further examples of factorising cubic expressions presented in class using a consistent algorithm

Now, this was the pinnacle of the lesson. This was the point where the teacher introduced the next expression to factorise but in doing so he was combining the procedural knowledge of factorising a cubic expression where one of the groups could be factorised because it was a difference of two squares. The sequence of instruction was incredible. Let’s have a look.

Again, he used the consistent algorithm he showed in the previous examples:

Step 1: factorise the first two terms, and the last two terms. Pre-empt that we may be factorising the last two terms by 1 or -1.

Step 2: factorise the greatest common factor of both expressions:

Step 3: factorise the greatest common binomial of the expression.

He asked “can you factorise the greatest common factor of the second binomial? Hands up – what is the greatest common factor of the second binomial?” Pupils confidently answered – “1”. The teacher responded “Excellent, you can display it like this (teacher writes it on the board) and can you do the same on your mini-whiteboards please.” Again, he pre-empted another misconception that the pupils could have potentially made. (Figure 8)

Fig8SIFig9SI

Figure 8 – Structuring a key step in the algorithm where pupils are more likely to make avoidable mistakes though explicit instruction.

Figure 9 – Introducing an expression where one group is an expression known as a difference of two squares

Step 4: factorise the greatest common binomial, which he got above (Figure 9):

He asked pupils to pause. He then asked pupils to look at the problem on the board (the one above). “Can you raise your hand when you can identify what type of binomial expression we have for the first binomial .” Ten hands were raised within the 5 seconds. In total there were 22 hands raised 10 seconds later. Now, after 30 seconds in total following the initial posing of the question, the teacher had an overall 28 out of 32 of pupils’ hands raised. The teacher selects a pupil to state the answer: “Sir, the first binomial is an expression which is a difference of two squares.”

The sequence of instruction here is incredibly effective. What I saw in real time, and what I have outlined for you, is not necessarily profound or extraordinary – on the contrary, it is very simple. It can be performed by all teachers.

It was evident from this lesson that the teacher had put a significant amount of thought into the sequence of his instruction to his pupils. It was well-crafted and sequenced so that all pupils could see the re-iterated key points. What are the characteristics of a problem which is a difference of two squares? What are the characteristics of factorising a non-linear expression? What is the greatest common factor of this expression – ensuring the greatest common factor including coefficients and variables?

I am still working on trying to collate a few different examples in my teaching practice of minimally different examples, and how I have interleaved concepts via sequence of instruction. I shall get back to you on this. Watch this space. Any questions then please do not hesitate to contact me or DM on twitter.

Posted on March 12, 2016 by Joe Kirby

Year 8 on Macbeth

Y8 Macbeth Witches.png

Y8 Lady Macbeth.png

Y8 Lady Macbeth 2.png

Y8 Macbeth Conclusion.png

These are some paragraphs of Year 8 pupils writing about ‘Macbeth’, on the witches, Lady Macbeth, and an essay conclusion comparing Macbeth to the play they studied in Year 7,‘Julius Caesar’.

Snapping and sharing pupil paragraphs is a good opportunity for us to reflect on what is working well about our English teaching and what we want to help pupils improve.

Strengths: Vocabulary and Connections

One strength of pupils in English at Michaela is the vocabulary we have developed in them. Pupils are using ambitious words like ‘eponymous’, ‘pejorative’, ‘despotic’, ‘ambivalent’, ‘susceptible’, ‘diabolical’ ‘paradoxical’, ‘contradictory’ ‘asymmetric’, ‘tyrannical’, ‘protagonist’, ‘conspiracy’ and ‘patriarchy’, and largely using them accurately. They are using technical vocabulary, such as ‘soliloquy’, ‘antithesis’, ‘pathetic fallacy’ and ‘chiasmus’, and largely using it accurately. Sometimes, though, they are misspelled, as in ‘purnicious’, and sometimes, they make mistakes, such as seeing an oxymoron where none exists!

Pupils are beginning to make some striking connections between, for instance, the context and the play: for instance, on the regicidal 1605 Gunpowder Plot, or James I’s 1603 accession and his belief that he was descended from Banquo. Contextual connections are a real strength of our knowledge-led approach to the curriculum. They annotate and improve their own paragraphs, as you can see in green and blue pen. 

Improvements: Le Mot Juste, and Perceptive Insight

At this stage, I find pupils struggle to find ‘le mot juste’. One has written: ‘This emphasises the witches’ cloudy, disturbed and tempestuous mindset, bleeding into Macbeth’s mindset.’ I’m not sure ‘cloudy’ is the best adjective this pupil could have chosen! Another has written in a contrast between Macbeth and Caesar: ‘we cannot make these characters equal, however, because Caesar was a victim of conspiracy and assassination, Macbeth was part of conspiracies and murders.’ I find the phrasing of ‘make these characters equal’ a little clumsy, and the sentence is missing a ‘whereas’. Articulate, sophisticated syntax is an area for improvement.

Increasingly, what I’d like to improve about our teaching is this: sharing concrete examples of perceptive insight – moments in their analysis that make the reader of the essay see the play in a different light. I will try to do so in another blogpost.

By the time our pupils finish Year 9, they will have studied five Shakespeare plays. Year 10 begins with a synoptic Shakespeare unit where they compare villains and stagecraft, themes and plots from Julius Caesar, Romeo and Juliet, Macbeth, The Merchant of Venice and Othello, before they start on The Tempest, Shakespeare’s last play, for their GCSE course. By then, their intertextual connections, comparisons and contrasts should be increasingly insightful. It is an exciting prospect!

Posted on March 12, 2016 by Jessica Lund

Something we do – Reading

At Michaela, pupils read a lot – hundreds and thousands of words in every lesson.  The same is true in French. This is a snip of our Year 7 booklet:Capture

As you can see, it’s full to bursting with words.  Long passages of French with parallel translations into English.  And not just normal English – dodgy English that enables pupils to see the precise connections between French and English words.

“Yesterday, I am goned to the pool after having done my homeworks.”

“Hier,           je suis allé   à la piscine  après avoir fait     mes devoirs.”

Pupils read with their rulers under each line (the better to see and track exactly what they’re reading.  They are questioned constantly to see if they are making the connections between the English and the French.  If they struggle to see and retain a link, we make it even easier for them:

“Quelqu’un.  Someone.  Quelque means ‘some’ and ‘un’ means ‘one’.  Obviously you can’t have two vowels fighting it out in the middle so the ‘e’ becomes an apostrophe.  Look at the spelling – QUeen ELizabeth is off visiting another QUeen who has a feather ‘ in her hat.  And look at what she’s riding: a UNicycle.  And if you can’t remember that, it’s 6 letters then 2 letters.  Count them.  If you remember that it’s 6’2, you’ll know how to spell it when you need to.”

As one pupil reads at length, pupils track what they are reading for themselves.  A beautiful thing happens: pupils who aren’t reading out loud are silently mouthing the words so that when their turn comes, they remember the pronunciation.  They listen intently to their peers, and if they make a (very rare) mistake, hands shoot up all over the room to correct it.  Pupils are now in the habit of self-correcting as they read.

So, pupils are always looking at French words, and having their attention drawn both to the syntax of the sentences and the shape and spelling of individual words.  They are always hearing French words: if it’s not the teacher reading out loud, modelling excellent pronunciation (always with a bit of a dramatic flourish to emphasise key vowel sounds and accents) then it’s their peers practising.

Their peers are confident in their reading.  Why?  Because a) we do it so much, b) they are positively encouraged all the time (“PLUS FORT! Lion voices!”), c) we make it easy for them with two key techniques:

  1. We put dots under silent letters.  Pupils don’t pronounce them.  They know they’re there, and that they need to be written, but they don’t say them.  If they, on the rarest of occasions, do, their peers fall about laughing and they quickly correct themselves with a grin.  We don’t dot them forever: by February, year 7 read competently without them.  They become used to the fact that ‘évidemment, les lettres -nt à la fin sont muettes, Mademoiselle’, and they tell me, too.  Yesterday a pupil saw the word ‘jettent’ for the first time – it didn’t even occur to him to say the -nt at the end.
  2.  We underline the common vowel and letter combinations that differ from English. ‘in’, ‘en’ and ‘an’ are common ones that pupils might slip up on – we are constantly reinforcing their pronunciation by drawing parallels to other words. Lapin, sapin, main, maintenant, dingue, zinzin, radin, malin, calin, intéressant, intelligent.  Eu – peu, eux, peux, veut, neuf, malheureusement, chaleureusement.  They become used to sounding these out correctly.  As a result, ‘new’ texts are never really new – they’re simply a reordering of things they’ve seen hundreds of times before.

When I was training, I was told that reading was a presentation/input activity, not a production/output activity.  N’importe quoi!  At Michaela, it’s both – we read out loud, all the time, sometimes for entire lessons.  Because we foster confidence, pupils love it, and they are starting to really act with it.

Having recently started to read ‘Ticked Off’ by Harry Fletcher-Wood, I thought I’d create a ticklist of things that our pupils do when reading.  Here it is:

Do they read lots, at least a few hundred words per lesson? Do they understand, and are they able to recall, what they read? Do they read high quality, interesting, real-world French? Do they regularly read mark-winning structures, including PROFS (past, reasons, opinions, future, subjunctive)?  Do they read out loud with confidence and pizazz?  Do they notice vowel combinations and patterns that aid with pronunciation, recall and accurate spelling? Do they quickly correct themselves, and others, when they make a daft mistake? Do they absolutely love reading?

I would absolutely love to get more people visiting Michaela to see what we do – both in the French department and across the whole school.  If you want to know the answers to these questions, come and visit any time – have a tour, have lunch, watch a lesson, talk to us. It’s brilliant. Email me at jlund@mcsbrent.co.uk. It’d be lovely to see you.

Posted on February 21, 2016 by Bodil Isaksen

What’s the point of knowledge if you don’t use it?

Production. Outcome. A result. Project-based learning seems intently focused on this. Ron Berger’s An Ethic of Excellence has a lot going for it: its attention to disciplined, persistent work is admirable, but it, too, falls into this trap. Learning is only seen as valuable if something is donewith it.

In a similar vein, Debra Kidd said of School 21:

What is the point of learning if no-one hears you? What is the point of academic success if you can’t interview successfully? What is the point of knowledge if you don’t use it to change the world?

This view of learning just doesn’t resonate for me. There is intrinsic value in learning: in making your mind a more interesting place to be; in the wonder and awe that new information can bring. We may be unlikely to use, in a practical sense, much of what we learnt in school, at university and in life, but I certainly feel privileged to know it. Why do David Attenborough documentaries get so many viewers? Why do long reads get millions of clicks? Why do books still sell in an age of Kim Kardashian apps and Candy Crush? Because learning is wonderful, whether or not it is shared or used.

As for interview skills, my mind is immediately drawn to my first week of university, at the matriculation dinner. By the third course, the computer science students had ceased engaging in conversation and broken out their laptops. A lot of them would be the first to concede they would not interview well (how do you know a computer scientist’s an extrovert? They look at YOUR shoes when they’re talking.). But that damned well did not render their academic success pointless.

It’s not just ivory towered academics who benefit from knowledge in the absence of interview skills. A plumber probably won’t need to know much Shakespeare on the job, but knowing which plays he wrote and some of the fabulous lines would mean he feels just as entitled to go and see a play at The Globe as anyone else – and why not? The works of the Bard are worth knowing because of their greatness, regardless of whether you use them for practical purposes.

Corporations will inevitably concentrate on production and utility: I expect the CBI will be grumbling about skills for work on the Today programme every few months until I retire. But we teachers need not fall into that trap. We can recognise and celebrate all knowledge: the useful and the useless, the easily accessed and the esoteric, the applicable and the arcane.

Knowledge is an inherent good. Let’s stop obsessing over what we can produce with it, and simply laud learning in its purest form.

Posted on March 9, 2016 by Dani Quinn

Masses of Maths: what should pupils learn by rote?

Should maths be learned by rote?

Some of the most egregious pedagogy is born when the answer to that question is ‘100% yes’ or ‘100% no’.

“100% yes” conjures up – perhaps rightly – an image of maths as a joyless subject whereby pupils are learning algorithms without meaning. Although it can feel like an easy way to teach, pupils are unlikely to succeed with equations such as  = 17 if the approach to linear equations has simply been ‘change side, change sign’ and practise only the simplest problem types (e.g. 4a + 3 = 23). Automaticity with times tables, simple written calculation and being able to regurgitate the order of operations is of limited help if the pupils aren’t taught how to think flexibly (i.e. if they can’t see the deep structure of a question).

calvin_education

“100% no” is also problematic. Typecast as the progressive approach to maths, it is founded on exploring maths as a way to develop deep understanding (and an assumption that fluency and confidence arise from there). It is championed by academics such as Jo Boaler and many teachers (and maths consultants…), and the heart of much debate. This approach argues that relational facts needn’t – and shouldn’t – be taught as such and certainly don’t need to be explicitly memorised.

Relational facts are those that can be derived from a smaller field of arbitrary conventions (such as ‘angles in a straight line sum to 180o is derived from the convention that angles around a point sum to 360o) or easily understood and recalled relationships (e.g. I can calculate 3 x 8 by doubling a relationship I do recall – 3 x 4 = 12 – to get 3 x 8 = 24).

There is clear merit in an approach that builds relational understanding1. It is an important part of building the storage strength of concepts2 (how well a concept or fact connects to other memories and concepts) but, used alone, it ignores what is happening in pupils’ brains as they work.

Simplistically put: as pupils work on a new problem or idea, their working memory is gradually being ‘used up’ until there is little capacity for additional processing. Take this problem:

0.8 + 0.4 x 52 ÷ 0.01

A pupil has to think about all of the following:

  • The order of operations (that they should complete the multiplication and division first AND that, within that, that they should work from left to right)
  • What the notation []means
  • The value of 52
  • A strategy to multiply an integer by 0.4
  • A strategy to divide by 0.01
  • How to add 0.8 to the answer

That is a lot to think about! If trying to think about each idea from scratch, their working memory will soon overload, making the calculation seem more complex than it is.

In comparison, the problem is much simpler for a pupil who confidently knows the following facts by heart:

  • 52= 25
  • ÷0.01 = x100
  • To multiply an integer by a decimal, I can ignore the place value at first and adjust afterwards
  • 4 x 25 = 100
  • 4 x 25 = 4 x 2.5
  • 4 x 2.5 = 10

…will see this instead:

0.8 + 0.4 x 52 ÷ 0.01 = 0.8 + (0.4 x 25 x 100) = 0.8 + (4 x 2.5 x 100)

A much less daunting calculation, and one where much less tricky processing or self-doubting thought has taken place.

 

What does a knowledge grid have to do with it?

In the Michaela maths department, we aim to identify all the facts and relationships that can be codified as a single nugget of knowledge (or set of clear steps) that will reduce pressure on pupils’ working memories. This frees them up to tackle more complex and interesting problems and allows them to feel confident in their reasoning and solutions.

This does NOT mean teaching without understanding. It is the opposite: we aim for pupils to understand why something works, or is the way it is, and then to be so confident of that fact or relationship that they can recall and use it with minimal effort and worry.

The purpose of a knowledge grid – explained in detail by Joe Kirby – is to set out what these facts and relationships are, and to support pupils in learning them by heart.

Take indices, which the Y7 pupils have just learned about:

indices knowledge grid

This sets out what we expect pupils to know by heart if they are going to be able to tackle more complex or interesting problems involving indices (e.g. What is the final digit of 10100+999+598?). Know by heart that ax a= ab+c doesn’t replace knowing why this relationship is true. But, knowing it by heart – and practising explaining why it is true – frees pupils up to tackle problems like ‘evaluate 2x 52x 2x 53′.

Here is the grid for Y8 pupils at the outset of learning to solve linear equations:

masses of maths 3

Here is an example for Y8s learning to substitute and use formulae:

masses of maths 2.PNG

Sometimes it is solely a collection of relationships, such as the grid Y7 are about to work from:

masses of maths 4

(shading in grey typically indicates ‘optional’ knowledge, in that it is possible to be successful in maths without knowing those facts by heart…at least not at their stage!).

A useful rule of thumb is: if we, as maths teachers, know these facts by heart because they help us work more efficiently and confidently, then the pupils should know it by heart too.

How is it used?

In lessons, the knowledge grid lays out the agreed definition and procedures that we want to share with pupils. The constraint of the definition means we teach to a higher technical standard, ensuring that we stick to language like ‘eliminate this operation’ (instead of saying ‘get rid of the 4’ in a bid to make the maths feel more accessible). Knowing that the pupils must understand and use a phrase like ‘isolate the unknown’ forces us to explain it with greater clarity, check they understand it precisely, and then use it constantly.

In most lessons, pupils are quizzed on the terms and facts in the knowledge grids. This can be cold calling (asking questions and picking students), checking everyone’s answer on mini-whiteboards, or giving a 1-minute quiz in books (e.g. “write the formula for the area of each of these shapes” or “rewrite each of these as a multiplication: ÷0.5, ÷0.1, ÷0.25, ÷0.125, ÷0.01, ÷0.2”).

Once a week, pupils ‘self-quiz’ at home on the definitions and facts the teacher has set for that week. Typically, this is 10-15 facts/definitions. Pupils first practise saying the facts to themselves, then cover the right-hand side and write the definitions based on the prompts on the left-hand side, and then correct their errors in green. They continue this until a page is filled. It is possible to game it by mindlessly copying, but it becomes obvious if they’re doing so because…

Once a week, pupils take a formal, but low-stakes, written quiz, of which half will be a knowledge grid test (the other half tests their ability to apply procedures and try unfamiliar problems).

The levels of scaffolding vary; these are the knowledge grid sections Y8 took recently:

masses of maths 5.PNG

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Pitfalls We Fell Into

An easy temptation is to produce a ‘revision mat’ full of facts, examples, diagrams and mnemonics. Although this is close to a knowledge grid, it isn’t as useful. It must be REALLY EASY to test yourself from a knowledge grid without ‘accidentally’ seeing the answer, or having prompts. It must be really clear what they should know by heart (the definitions and terms and facts) and what is just useful for jogging their memories (examples, where appropriate).

Another easy error is to go overboard with how much you try to codify and write down. If you, as teachers, struggle to articulate the definition or steps for something, it probably isn’t useful or suitable. Make steps for a strategy (e.g. solving equations) as generalised as possible so that pupils aren’t learning multiple minimally different steps and becoming muddled and frustrated. The more generalised the steps, the more they can be used to illuminate the common features of varied problems (and thus help pupils see the underlying structure).

Pitfalls We’re Still Trying to Avoid

We are still struggling to decide which aspects of algebraic simplification can be listed as facts: here is the start of a debate I was having in my head this morning for updating the facts in the ‘expressions and simplification’ grid:

masses of maths 7.PNG

Any that are included are there because pupils had become faster by recalling them as facts (as opposed to working them out) or their work was slowed because they weren’t confident when simplifying a fundamentally identical expression.

 

I hope it goes without saying that we would love to know what you think and if you have tried anything similar. Do you have facts and rules, besides those set out in examination specifications, that make a big difference to your pupils when learned by heart?

 

Whether this fascinates or enrages you, get in touch and come see the pupils (and grids…!) in action. You’ll have a great time 🙂

 

1: See Skemp, R.R (1977) Relational Understanding and Instrumental Understanding, Mathematics Teaching, 77: 20-6

2: See https://www.youtube.com/watch?v=1FQoGUCgb5w for Bjork discussing research in this field.

3: https://pragmaticreform.wordpress.com/2015/03/28/knowledge-organisers/

 

Posted on March 6, 2016 by Jonathan Porter

The Golden Mean Part 2: Sample and Domain

In my last blog I spoke about the ‘Golden Mean’. This is the Aristotelian principle that what is virtuous is always between two states: one of absolute excess, the other of absolute deficiency. I suggested that this could be quite a helpful way of thinking of teaching and curriculum design. I said that over the next few posts I would try and explain how this insight has informed my thinking on teaching and assessment in KS3 history. Here are three questions that came to mind:

  1. How do I strike the right balance between the sample (the end of unit test) and the domain (in this case, the period of history in question)?
  2. How do I help my pupils remember what they need to remember for the assessment, as well as helping them to remember what I think is just important for them to remember?
  3. And how do I guide them towards an answer without answering for them?

Sample and domain

 In my last blog, I explained why I think the sample/domain issue is one that particularly afflicts the teaching of history at KS3. The more our assessment system leverages the assessment, the more tempting it is for the teacher to narrow the domain and teach to the test. This is particularly so in schools like my own where pupils, even in Year 7, do all assessments without notes and from memory. The alternative, however, is arguably just as bad: unpredictable tests sprung on new arrivals to the school, which help us to norm-reference one pupil against another, but potentially crush a child’s confidence in the process.

For this reason, I am in favour of giving younger pupils the question in advance. But only if the question itself avoids the sort of ‘narrowing’ I’ve described. An example of this sort of narrowing might be a very specific question about the significance of the Magna Carta or the ‘greatness’ of Alfred the Great rather than a broader question that aims to assess whether pupils have retained a good knowledge and understanding of the period in question. Alfred the Great is perfectly interesting, but I don’t want my pupils’ appreciation of Anglo-Saxon history totally dictated by what could become both a semantic and substantive discussion of his ‘greatness’.

In part, as was put to me, this is just the age-old question of breadth vs. depth. In the case of history, we often choose to sacrifice breadth over depth. With a limited amount of time, we cannot possibly cover everything that happened in, say, Anglo-Saxon or medieval England. We also want to ‘scale-switch’ and to help our pupils see continuity and change in the short, medium and long-term. I think this is true.

But I think what we’re also seeing is some of the effects of the ‘skills-centred’ attitude to the teaching of history. That is ‘We don’t need to worry about teaching a broad sweep of Anglo-Saxon history because it is learning to think about causality/significance/continuity/change that is most important.’ I think this is a mistake. Why? Because I think KS3 gives us a great opportunity to put in place the broad domain knowledge that we need for long-term expertise. In the long run, enquiry questions that are too narrow have the potential to erode the domain at exactly the point in a child’s development when, in my view, the domain should be most broad. With that in mind…

All enquiry questions are equal, but some are more equal than others.

 I think we can find a Golden Mean between the sample and the domain – between breadth and depth. I think we can have enquiry questions that ask our pupils to consider second-order concepts while also giving them the best possible opportunity to learn – and remember – as much as they can of the period in question.

Here is the question that we settled on for our unit of work on medieval England:

‘What was the most significant challenge to the King’s power in medieval England?’

 I expect a good response to include a paragraph on each of the three challengers (the Church, the nobles and the peasants) and top answers to include a fourth paragraph in conclusion. The pupils have 45-50 minutes and all pupils write from memory without notes or sentence starters. We try and achieve this through regular self-quizzing of both the upcoming ‘sample’ (What was the most significant challenge to the King’s power in medieval England?) and the broader domain (the chronology of medieval England). You can see that I’ve tried to place an equal emphasis on this on the pupils’ knowledge grid, which they use in weekly self-quizzing as well as in class.

Slide1

My hope is that this strikes a ‘golden’ balance between the sample (right-hand side) and the domain (left-hand side). The pupils learn about, and have to remember, important events in medieval English history (The Battle of Hastings, the Anarchy and the Battle of Agincourt), which are not needed to do well in the end-of-unit assessment. At the same time, I hope I’ve also supported all pupils to learn the specific information that they’ll need to do well in the assessment.

Next time, I’ll write a little bit more about how we use these grids, low-stakes testing and songs to try and help pupils automate people, dates and concepts so that their working memory is focussed on the most challenging parts of the assessment.

Posted on March 6, 2016 by Naveen Rizvi

Minimally different examples

School Visited: Uncommon Collegiate Charter High School

Class Observed: Algebra 1 Grade 9 Statistics (UK equivalent Year 10)

Theme of post: Pedagogy and Curriculum

This is the first blog post in a series complementing a workshop I delivered at Mathsconf6 entitled “Mathematics Pedagogy at USA Charter Schools”. Here I spoke of my experiences whilst visiting a selection of Uncommon and North Star academy schools in New York and New Jersey.

I discussed how the common denominator in each maths lesson I observed was the level of academic rigour in the teaching delivered to pupils. I am still trying to find a way to define this term, because it is overused and poorly defined. However, I do believe I may be able identify the evident features of academic rigour in the structure and delivery of each teacher’s pedagogy and instruction:

Academic rigour featurse

In my workshop, I discussed four examples of academic rigour that different teachers up and down the country can implement with minimal effort and maximum impact. Each blog post will discuss one example at a time. Today, this blog will address using minimally different examples during instruction.

Agenda

Minimally different examples are examples to explain different concepts where the difference in the algorithm between one concept and the other can be distinguished as one additional step. This was one example I witnessed in one of the classrooms I was in.

 

Minimally different examples 1

The teacher presented the first expression to factorise, where the coefficient ofa in the quadratic expression is 1. This was a recap exercise where she stated the values for the coefficients, and then she determined the two values of which the product gives us the value of c, and the sum gives us the value of b. She wrote the expression in its factorised form.

She then introduced the next expression to factorise. She stated that it looks visually very different to the first one, but that there is only one difference between the algorithm to factorise the first and second expression. She defined the minimal difference between the two as one additional step – which was at the start of the algorithm. She asked her pupils, “What is the greatest common factor (GCF) of all the terms in the expression?” Pupils spotted the GCF to be 3p, which she then factorised. She said “look, we now have an expression in the parenthesis which looks similar to the first expression we factorised.” The minimal difference between factorising the first and second expression was classified as one additional step. Traditionally, in my training, I would have seen the algorithms to factorise both the expressions as isolated and fragmented. Instead, they are connected; pupils were empowered to factorise more complex expressions from prior knowledge of the algorithm to factorise the first expression. Minimally different examples are a good strategy and example of academic rigour in the classroom because they help pupils to understand knowledge and concepts which are initially complex and ambiguous. Here, the difference between the two examples is classified and determined as one additional step in the algorithm. The possibilities are endless.

I plan to show different examples of how I have used the idea of minimally different examples in my teaching, sometime this week.