Quote of the Week

At the bus stop, some girls were talking about boys and makeup and other such topics. A very short boy gave a loud sigh, turned to the (male) teacher next to me and said

'Can't we talk about something manly? Like...like... Philip Pullman?'

Invention or Discovery?

With snow flurries outside the windows and the prospect of an imminent school closure, you'd think nobody would be feeling particularly focused in year 7 maths, especially given the topic. Order of operations (or BIDMAS/BODMAS) must be one of the dullest topics in the spec, especially on a snow day. However, it was one of the best lessons this week, and I'm trying to work out why.

We always start with a question, such as 5 + 2 x 3 and ask what answers we could give. What would a calculator say? (Interesting, because it varies depending on the calculator.) With such a bright group, we raced through to 'because you do multiplication before addition' and 'because of the rule'. Then, because it's almost reflex by now, I asked 'Why?' It was a particularly bright girl, let's call her Sparky, answering, and she was flummoxed. Why do we have a rule? Why is it THAT rule?

S: 'Because that gets you the right answer'
Me: 'What do you mean, Sparky?'
'Huh?'
'What do you mean, 'the right answer'?
'...'

What makes one answer right? It stopped me in my tracks as well, as the whole class paused to get philosophical.

S; 'The rule says what's right'
Me: 'Why?'
S: 'Well, you've got to have a rule, or you won't know what's right'
Other student: 'Yeah - and people would do it differently'

We'd quickly worked out that the rule gave consistency, so we knew what people meant when they wrote that notation. But we couldn't stop there...

Me: 'So this is just a rule we picked?'
Students: 'I guess...'
Me: 'Is everything in maths just rules?'
Students: 'No, some of it's obvious, it's got to be true'
Me: 'What else is a rule that people decided?'
Students: 'Numbers?'

Then we spent 20 minutes talking about different number systems, and how the way we write numbers is an invention, like BIDMAS, but other things are discoveries. They'd done Roman numerals in history, but never made the link. The point that the rules can also be different was nicely made when a student explained that whenever you have a smaller number before a bigger number, you subtract, giving the example of IV. I wrote 15 on the board, and said 'So that means 4, right?'

They really love the ideas of having some rules, that varied between cultures (we got onto Egyptian, Chinese, Babylonian and Arabic numerals, all through them), and also having discoveries that didn't vary. It is so strange to me that this is the first time these students have thought about this - the idea of discovery and invention in maths. I think it might help a lot for those students who think maths is just 'a load of random rules'. It wasn't on the lesson plan, but I think they enjoyed themselves nearly as much as I did, and I think it was far more valuable than a worksheet.

Update on Trouser Boy

Standing at the bus stop this evening, I spotted Trouser Boy and his brother (who was expelled last year) on the other side of the road.

Trouser Boy: Hey there Miss!
Me: Hi, Trouser Boy!
Brother: Obscenities/inappropriate comments
TB: It wasn't me! Miss! He said that, not me!
Me: 'Yes, TB, I saw who said that. I know it wasn't you.'

They move on down the road, past me, then TB stops and looks back.

TB: '...sorry, Miss' *kicks brother*
Brother: 'Sorry!'

Given the obscenities TB used to greet me with, his history of inappropriate behaviour and his general disdain for all teachers ever, I was gobsmacked by his apology - for something he didn't do! Is this respect?

Misspelling of the week

Obchoos

Smile

Today, Lovely didn't smile at me. She's so sweet and cheerful, I have trouble even thinking of a name for her, so let's just call her Lovely. Lovely didn't smile, so something was up. I asked if she was ok, and she shrugged. She didn't put her hand up all lesson, so I asked again and she shook her head, and muttered 'Home problems'. I commented that that sounded tough, and she just nodded, so I left it.

At the end, she hung around a little, so I asked if she wanted to chat. She said yes, and when the others had gone, she pulled up a chair. I handed her an emergency chocolate biscuit and she burst into tears. Disclosures came thick and fast. Suffice it to say, she's a young carer for the only other two members of her household, and has been managing this for years. When  I asked why she chose to tell someone today, after so long, she said she was 'just feeling tired'. I think that speaks to the responsibility she bears, and it seems impossibly sad.

I passed on all the messages that sort of thing requires, and lots of different systems are jumping into place now she's told someone. There were violence issues, so Child Protection are involved, and so is the school counsellor and young carers worker. I'm not - all I'm supposed to do is pass it on.

This is my third major disclosure so far this year, and someone commented that I 'get them all', and asked why. I don't think I do anything special, but what I do do is notice, and ask. I like the fact that I'm there at the coalface with teenagers, when they're going through those awful ages, and that I can notice the differences and patterns that signal a problem, and get involved. I like it because it's real and raw and it makes a difference to them, and I didn't cry on Lovely, or when I reported it, but I cried all the way home.

I don't get it!

In one of my very able groups, there is a girl who thinks she is not so able. Short and Sweet declared to the class at the start of the year that she 'shouldn't be here', and had thought she was going to move down a set. She's small and sparky and cheerful, and nuts about badminton. After a few lessons I found that she does have some difficulties, but her background knowledge is pretty good and she is perfectly capable of the work we are doing - given enough time and encouragement. And that's a lot of encouragement.

 

Every lesson, I'd get 'This is way too hard for me!', 'Miss, I don't get it' and 'I give up!' loudly and repeatedly. Sat at the front of the class, she's throw her hands in the air at the slightest difficulty and start complaining. If I replied that I'd be with her as soon as I'd finished writing on the board/explaining/talking to someone else, she'd start telling the class about how stupid she was, and she was the worst at maths in the whole world. I got so sick of it.

 

One week, she didn't do her homework and forgot to turn up to a lunchtime detention for that, so I had her in an after school detention. As she sat there doing some work, I thought about why she was annoying me so much. I'd just been teaching a bottom set who are older than her, who had been struggling with basic concepts but persevering and building their confidence slowly, despite real difficulties. Short and Sweet, in contrast, had higher than average maths ability, even though she was near the bottom of her set. She didn't know how lucky she was.

 

I found the last test I had given the bottom set and took it over to her. We talked about why she thought she was bad at maths, and where she was in her year group. I asked her what she thought 'bad at maths' really looked like, and showed her the test paper - pointing her to where the student (whom I'd made anonymous) had tried to write the numbers from 1 to 20, but had gone wrong.

 

Short and Sweet was gobsmacked, especially when I told her that this kid hadn't given up, but was still positive and hard working. If this kid hadn't given up, I said, Short and Sweet had no right to give up. How could she throw in the towel and declare herself stupid if kids like this were still trying? How much would they give to have her maths ability? She looked like she was going to cry, so I toned it down a bit and explained how frustrated I felt seeing her give up when I knew she had the ability, and hearing her comments which to me were completely unacceptable - when she said she was stupid, what was she saying about the kids in the sets below her? I told her we were done and she ran out of the room.

 

She hasn't been perfect since, but I think there's been a basic change in attitude. She doesn't panic so much, or shout so loundly that she doesn't understand. Perhaps its the realisation that it's normal to make mistakes and find things hard, even if most people in her set don't. It raises a major and continuing problem, though: how can I push the very brightest, who have been bored by too easy work, and challenge them to push themselves, without making students like Short and Sweet, sat in the same classroom, feel inadequate? I know the answer involves more differentiation, where the ablest are given no method or the bare bones of one, and Short and Sweet gets a scaffolded method, but in a competitive atmosphere even that can dampen self esteem. I'm worried that her positivity is only temporary, and I want to make it last.

Finding Compromises

With bottom sets in years 10 and 11 (leading up to GCSEs), there's a big conflict surrounding what we actually teach them. Thanks to 'No Child Left Behind', we are mandated to teach them the GCSE syllabus, or at least all the content up to C grade level, so that every child has a chance to reach that magic threshold. It's a laudable idea, but in practice, this means that our schemes of work are full to bursting with topics like percentage increase and decrease, area of compound shapes and finding nth terms of sequences - all for students who cannot reliably count to 20.

If I was to try to cover all that content, I would have to go at a pace which means that almost none of it, not even the more basic areas (such as what percentages represent), would be comprehensible to the students. It would also totally prevent me from addressing issues such as: they don't know their 3 times table, they don't have any understanding of decimals, and they cannot subtract any number larger than 5. Don't get me started on division.

As most teachers do, I cobble together the best I can, trying to keep myself accountable but also addressing what I feel there children need to understand to allow them to function well as adults. It's a tricky compromise, and even more so when mock exams and tests are thrown at them ('We haven't done this, Miss!'). Even when I settle the time allocations, it's tricky to find ways of helping them with their basic concepts that are effective, not too boring, and don't feel babyish. Enter the 99 club.

The 99 club is fantastic. It's not my invention at all, and it's used in primary schools across the country, but I can't find any company or organisation claiming credit. This is the way I do it. The students start off trying to do 11 times tables questions in an allotted time (say, 3 minutes). When they can get them all right, they try to do 22. Then 33, 44 and so until they can do 99. To differentiate it further, the '11 club' (where they try to do 11 questions) only involved the 2 and 10 times tables. One times table is added each club.

The students love the routine, and the fact that they're all working at their own level of challenge. Every student in my tiny bottom set can be on a different club. They can mark it themselves, and it ensures that I can start every lesson with 5 minutes of silence, followed by lots and lots of praise. And it motivated them to learn their times tables like nothing else I've found. It could be competitive, but I try to make it about individual progress, giving equal praise for any student who makes progress, whatever club they are on. Students who would argue about doing 5 for a starter will happily do 33 now, because the graded work means they start off being successful. As I collect the sheets in every lesson, looking at the hard work on them, it invariably puts me in a good mood.

Insult of the Day

12-year-old boy to 12-year-old girl: 'Go and sit in a pond!'

Spontaneity

Yesterday, a very able set were reviewing different types of quadrilaterals. This is usually covered pretty well in primary school, so a few years on I expected the review to take about 10 minutes. I always start this topic by giving the students a bunch of little cards with quadrilaterals on them, and asking them to sort them into groups however they want. It makes the categorisation come out of concrete examples, rather than being some names put on the shapes by a teacher. It makes them think about the properties and argue about them, and it's the only way I've ever had kids remember this topic.

However, NOBODY came up with parallelograms, trapezia and rhombi. After discussion (which took a while; there were some great groupings, and it's a good review of shape properties) I asked them to sort them into ones with 2 pairs of parallel lines and ones with one, but they still weren't using any names. So we played hangman! We finally get to trapezium, and they all said 'Ooooooooh, yes, we remember that word! But aren't they really complicated?'

Of course, it isn't, and they'd already sorted the shapes - with the classification coming describing the groups of shapes. They were soon happy with the definitions, but it appeared that they were confused with how the classifications related to each other. We were now totally off the lesson plan, and I knew they needed something else to reinforce the concepts and the relationships between them.


I remembered a fantastic idea I was introduced to last year, but didn't use. I got them to clear their desks apart from the shapes, gave each pair a whiteboard pen and told them to draw as large a circle as possible on their desks - board marker comes right off. They went wild. We drew a huge Venn diagram on their desks and they sorted the shapes into it, then added new ones. They were extending the diagram, talking about the relationships, discussing where the square and rectangle fitted, and generally squealing about drawing on the desks.

After 20 minutes, they sketched it into their books and as they packed away, one girl asked if she could take a photo on her phone. They were soon all snapping pictures, and I told them this was my new criteria for a successful lesson - so good the kids want to take a photo of it!

The Tale of Trouser Boy

Trouser Boy is another member of year 9 bottom set maths. He's not a great fan of this fact, or of me. First lesson, he refused to sit where I asked him and then refused to write. We've improved since then, but very slowly.

His mathematical ability is actually not too bad, but he manages to distract from this quite effectively. You see, Trouser Boy wears his trousers so very low that I can always see the pattern on his boxer shorts (waistbands, I can deal with - this, not so much). Perhaps this is because his trousers are too tight? They certainly look small, and in recent weeks he has taken to complaining about this fact loudly, combined with standing up, wriggling and - no, really - putting his hands down his trousers. Repeatedly.

He can't freak me out, he can't freak our (awesome) TA out, and the rest of the class are frankly bored of him doing this by now. However, the frequency and dramatic nature of these events had been increasing. So why? I'm not buying genuine discomfort, he's taking cues from and studying the audience far too much. He may have initially been trying to make me uncomfortable, but he can see that's not working. He's failing to amuse or distract anyone else- so he's doing it for him.

I got his parents in, eventually, to talk. I planned my strategy beforehand, opening with my perception of Trouser Boy's genuine mathematical ability. I described incidents when he had grasped a concept far better or more quickly than the rest of the class, and he grudging recalled those occasions, soon adding to my accounts as we talked to his parents. There was one problem, I said. Just one. They looked astonished, and that wasn't what I was meaning to say at all - there were multiple problems, culminating in the trouser incidents. They had looked so hopeful. I had to wrap it up in one problem.

'Sometimes, Trouser Boy, I think you look at the work and think you can't do it. It's scary, and you feel like everyone else is doing better than you, so you don't want to try it. So you look for something else to do.' After a pause, he started nodding enthusiastically. His dad started talking about similar feelings at school. We spent 15 minutes coming up with strategies and solutions, and emphasising Trouser Boy's ability when he pushed through his fear.

When his parents stood up to leave, his dad leant over. He thanked me for being so positive, and said that he'd expected 'doom and gloom', not strategies or even the acknowledgment of his sons ability. He asked to shake my hand, and as he did, he said quietly 'You know, no one has every talked about my son like that.' 

Perceptions of adult life

Small Mop: 'Mrs!'
Me: 'Who's marrying me off? I'm a Miss!'
'Oh, aren't you married?'
'No.'
'Oh........are you divorced, then?'

Other small child: 'That's rude! You can't ask that!'

Argh! Algebra!

Every year, with every class, in every school, it's there on the scheme of work: Into to Algebra. A lesson of review or true introduction, depending on the class, and how much they've forgotten from last year. There's rarely any guidance or ideas provided for this lesson, even though it's crucial to how the students perceive algebra. I haven't taught it the same way twice yet, but this is where I'm at so far.

We talk about how sometimes, either we don't know what a number is (how many pencils in this box), or the number can change (how many siblings someone has, will change depending on the person). This is when we use letters. We go straight from there into simplifying - one jar of sweets, plus another jar of sweets, is 2 jars of sweets. j + j = 2j

I haven't seen other teachers do this, but I think it's important to get straight into manipulating the letters, rather than using numbers straight away (substituting or solving), so the students get used to using the letters. We use the simplifying to explain the hidden multiplication signs in expressions like 2j, and then think about why we write 2n not  n2. I ask the students to tell me a thing that begins with n - the best so far is ninjas. If, I ask, Sophie and Charlie suddenly revealed that they were ninjas, what would we say? We'd say 'Look, there's....' I repeat this short pantomime until the whole class are shouting at me 'Look, there's 2 ninjas!' Would we say 'Look, there's ninjas 2!'? Clearly not!

That's enough abstract algebra for most 11-13 year olds to handle, so back to the numbers. Everyone pick their favourite number. Yes, go on, do it! You can call that number by the first letter of your name. Alex's favourite number is 7, so he's going to use A for 7. Then, using their favourite numbers, the students have to make a list of numbers that I give them, writing the rules using the letter. So if Alex was making 20, he could write A + 13. Students like to feel clever, so soon they start coming up with more complicated ways, as I encourage them to write multiple methods for the same answer. 2A + 6, for example, using their simplifying knowledge. It's a good lesson in equivalence too.

We review this exercise by asking people for what they wrote, and I write one 'answer' next to every target number on the board. For 20, I might write Alex's answer: 2A + 6. Then we try to guess Alex's number.

The great thing about this lesson is that, after some explanation of simplifying, the kids can figure everything else out by themselves. I go slowly on the simplifying, taking maybe half an hour, so that everyone can follow. Then they're off! They can make the problems as complicated as they like. I'd like to make the simplifying half of the lesson less teacher-led, and mind-mapping might work for older students, but when they haven't seen algebra before, there needs to be some instruction. Possibly a card sort could replace some of it?

Ankle-socks

Ankle-socks is 11 years old. She's small, blonde, pretty and popular. She's in middle set maths and doing well, but the rate at which she puts her hand up has dropped over the last term, from 4 or 5 times a lesson to hardly ever. It wasn't a total surprise when I got the email.

Ankle-socks is 'school-phobic'. Her form teacher and parents have noticed that, despite her academic and social success, she does not enjoy school. She seems happy enough in lessons, and I have watcher her at break times chatting with her friends, but when she gets home every night she bursts into tears, and when she gets up in the morning she is desperate not to go to school. She has panic attacks at the bus stop, and has almost completely stopped eating.

The lesson after I got the email, she was smiling and enthusiastic about the work, and chatted to her classmates. I noticed her drifting off sometimes, but that's not altogether unusual. If I hadn't seen her that morning in tears in the front office, with her parents and form teacher trying to persuade her into school, I would hardly have believed the email. What to do?