Maths in the Library

Last week, there was a maths class in the library for the first time ever at my school. It was amazing. I was trying to figure out why that 'data' topic - a quarter of the course - is so damn dull. I found it dull and, as I discovered at uni, I love stats! I figured that it might be partially to do with the fact that you never get to deal with data you care about in school, so of course the results are boring. And frankly, the colours-of-cars / survey pseudo experiments that are often said to be the solution are almost worse than the textbooks in terms of providing data the kids might actually find interesting.

So, the library. Every kid got a data set that they were actually interested in - world records for the 50m front crawl, for the boy who swims for the county. CD sales per month for the girl in love with Bieber. And one kid - that one, and he's top of the class - comparing sales of cheese to GDP.

Now, every lesson they all draw a particular type of graph - Thursday was scatter graphs - using their own data, and to their own level of challenge. Pick the scales for your axes. Find equations of lines of best fit and predict more data, do some research, do other people agree with you?

It's amazing, producing nearly 100% engagement and raising interesting questions about how to present difficult data that doesn't fit neatly into categories. As a side benefit, I chummed up with the librarian. She just emailed me with a question.

The library 'maths books' budget hasn't been spent for the last 8 years. The ordering deadline for this year is a week away. Is there anything you'd like me to buy?

So, everyone, is there anything I should buy - of course there is! What?

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.