### Archive

Archive for June, 2013

## Probability and Sex Ed

This week we had our third CT day of the year. (CT Days, or citizenship themed days, are collapsed timetable days where pupils do a range of topics linked to a theme.) I was with my coaching group and we had a great day on the topic of “personal wellbeing”.

The new year 11 (we move up year groups at spring bank) had a day on sexual education. Currently in maths they are learning about probability and one of my colleagues and I decided this was a perfect opportunity to merge the two.

We gathered some data on the probabilities if contracting STIs from an unprotected sexual encounter and they looked at the probabilities involved in contracting things after multiple encounters (here).

We also looked at expected values, and given the effectiveness of different types of contraception, (from here) how many pregnancies a year would you expect if a couple who were always safe made love twice a week. The answer shocked the whole class. They were also amazed by the difference when I asked them to complete tree diagrams and work out the expected value if the couple used condoms and the pill.

This was a much easier concept for them to relate to than picking sweets out of a bag as they could see that this was something that would affect everyone at some point in their lives. It also got across some messages that are important, especially as our school is located in an area with quite a lot if young parents.

## A great classroom explanation

This months #blogsync topic is a strange one, and I didn’t really know where to start. I’ve taught many many lessons now, and in each of them I will have explained many things. I’ve also observed many lessons, and likewise, in each I have heard many explanations. I’ve even heard pupils come up with some brilliant explanations, both during lessons when they were using prior knowledge to estimate what was next and in revision where pupils who remembered how to do something would explain it to their peers.

I’ve been thinking a lot this month about the explanations I give, as I knew this was the topic of the #blogsync, and I’ve had a plethora of explanations to choose from.

This week, off the cuff, I used a simile to contextualise simultaneous equation to a pupil who was really struggling, “is instead of 2x + 3y = 11 is said “2 cups of coffee and 3 cups of tea cost £11″” etc. This real world application, however convoluted it was, help him realise what was going on and he can now solve them.

Also this month I sat in awe as a yr11 pupil (who has yet to hit the c) explained to his girlfriend, perfectly and concisely, how to create a cumulative frequency diagram then use it to draw a box plot.

These were just two of an abundance of brilliant explanations I can think of to mention, but I want to dig deeper and share with you an explanation that has stuck with me for a long time. An explanation I remember from my own school days!

The lesson in question was a chemistry lesson, and the teacher was quite mad! He had some non-verbal behaviour management techniques which would surely be frowned on now. I.e. He would flick chalk at the head of anyone chatting and was a great shot! If chalk didn’t do the trick, the board rubber followed. He also had a giant pestle and mortar and used to walk around with it slung over his shoulder. He would periodically bring it down with a crack on the desk in front if those who were off task. He stopped that the time he smashed one if the desks in half! Anyway, I digress, time for the explanation.

The lesson in question was on bonding, ionic and covalent. He explained it all through simile regarding human relationships with devastating hilarity. He likened covalent bonds to elements who gave found their life partners, fallen in live, gotten married and spent the rest of their lives in wedded bliss “holding hands”. He then moved onto “dirty” ionic bond and likened them to one night stands, a quick switch of electrons and off they go, never to meet again. He also spoke about catalysts, likening them to nightclubs where people go, have a drink and meet people. Showing that the catalyst doesn’t cause the reaction, just gives it somewhere to happen and thus speeds the while process up.

The reason I wanted to share this is that this classroom explanation is the one I remember most vividly. It occurred at least 15 years ago, but I remember it as clearly as yesterday. So what made this explanation stay with me all these years? (As that is the key to a great classroom explanation, one which the pupil will remember.)

Well, the humour was a big part, and so was the clarity. The clarity of the explanation put the topic in terms that I understood, and as such could make sense of. If it hadn’t, then I’m pretty sure it wouldn’t have stuck. But also the humour, it added am element of fun and kept my attention throughout the explanation. I think more goes in, if you are having fun, and I think that these two elements combined in this case to make a great classroom explanation, and for this reason they are two elements I try to include in my explanations.

Categories: Maths, Pedagogy, Teaching

## Maths exams and how we prepare

Recently I’ve been thinking a lot about the way maths is examined and the way we need to prepare for exams, and I’m not the only one. @bigkid4 has written a series of posts on it here: http://mylifeasacynicalteacher.wordpress.com/2013/06/03/how-would-i-change-the-exam-system-ks1-5/ Dave Gale (@reflectivemaths) has written about it here and has also discussed it with Colin Beveridge (@icecolbeveridge) on their podcast here. I’ve read and heard other things too, and had many conversations about this.

The main thing that got me thinking was “that” C3 exam last week. It was really hard and seems to have thrown the vast majority of A level students across the country who sat it. When I first read it I thought it was ridiculously hard. But then I worked through it and realised the the main reason it looked so hard was that some of the questions were phrased differently to previous years. I actually enjoyed working through it, and realised that the students had all the tools to complete it, but if they had relied too heavily on past papers for revision they may have been thrown. Last year I tried to include more open ended maths questions in my lessons, and found some real beauties on some old A level and O level papers dating back to the sixties (when calculus still held it’s rightful place on the O level curriculum!). My year 13’s (among others) loved those questions that I threw in, (one said enthusiastically one lesson: “sir, these questions where you have to work out what maths to use are my favourite!”) and I’m going to build many more.

It’s clear to me that exams are moving this way, and I think it’s right that they are doing, especially at A level. Dave Gale mentions on the podcast above that S1 questions start “using a binomial distribution”, and I know S2 ones do the same with poisson etc, and this seems too easy. But as I say, I reckon the c3 exam is the first step in a move away from that.

This is a trend we are also seeing in GCSE papers. When my HoD and I went through last Friday’s calculator paper is seemed every other question we were saying things like: “that’s unusually phrased so may have thrown some of them”. I hope (and think) that I already am teaching the maths, and not just the methods to pass exams. But I intend to work on this even more to ensure in future that my pupils are ready for anything that gets thrown at them come next May/June time.

While listening to the podcast above I thought the real life use of solids of revolution to derive the volume of a frustum shaped plantpot was superb, and I’m going to use this when c4 comes around. I also liked the challenge question they asked and enthusiastically answered it afterwards (see below). I think questions like this will be key to fully developing future mathematicians.

Question: an equilateral triangle and a regular hexagon have equal perimeter. The area of the triangle is 2 square units, what is the area of the hexagon. The picture was my initial solution, but I did then realise I could have done it quicker and more simply using similar shapes…

Categories: A Level, Exams, Maths, Pedagogy, Teaching

## Vocabulary and maths are not mutually exclusive

My favourite area of maths is the pure maths side. Following it down to KS3 and 4 that means I like number and algebra best (and bits of shape). Leaving data handling as my least favourite. (Although teaching some S2 this half term has kindle a desire to teach more A level stats, and I do love some probability and the associated game theories, and other areas of data, but that’s for another day.)

The reason I mention this here is by way of explaining why I have taught only a small amount of the data topics over the last year. (I don’t mean I skip over them, just that when a class is split and the other teacher asks “do you wanna do data or algebra?” I always choose algebra, which normally pleases them too.)

Next week, however, I am embarking on a module in probability with my new year 11 class (they are “new year 11”, as in we move up at spring bank, not a new class to me.) They are a high set of intelligent pupils, and as such I will be teaching topics such as tree diagrams. Today I was planning the lesson and I noticed something strange: there is no mention of the terms “mutually exclusive” or “independent events” anywhere, not on the examboard spec, the SoW nor the resources I was looking through. It struck me as strange.

I then had a look at the DoEs draft spec for 2014, the term independent IS there (hurrah!), but the term “mutually exclusive” is missing. I feel vocabulary is important in general, but subject specific vocabulary is imperative if we are to ensure the next generation of mathematicians and game theorists are to make any ground!

Another thing happened today too, one of my sixth formers referred to brackets as “Parentheses”, this is a term I am familiar with, and one the girl in question grew up with, but the rest of the class had never heard. Again, it was an example of vocabulary disappearing in Britain, and I think this is something we should be aware of. This coupled with the fact a student teacher we had needed to explain the words “tedious” and “petulant” to a top set year ten a few months ago makes me think this vocabulary gap needs to be addressed. (Mark Miller has written a series of posts on vocabulary here )

We all go out of our way to include literacy in our lessons, which is great. Words like “linear”, “quadratic”, “expression” etc are revisited again and again, even the lowest ability classed I teach can use these well, and correctly, in the context of mathematical discussions. However, I think we need to go further, we need to use vocabulary such as “mutually exclusive”, and “iteration”, and other such things that don’t specifically appear on our syllabus (“iteration” is on the new draft!). We also need to go further, we need to use a wider vocabulary in our discussions with pupils to increase their own vocabulary.

Addition: I’ve been thinking, this could be an issue specific to the type of pupils we get at our inner city school, I’d be interested to hear how wide vocabularies of teenagers are at other schools with different pupil compositions.

## Michael Rosen and the Revolution!

Last week I was driving home and listening to Simon Mayo on radio two, he had former children’s laureate Michael Rosen on discussing a new book, which was all very interesting. The discussion then moved towards education. He spoke about children needing to be inspired, and wanting to pass on his love of reading to his children. This struck a chord, I want children to be inspired, I want to pass on my love of maths to the next generation (and I also hope to pass on my love of reading to my children). I feel I have started to pass on this love of maths, as I received a card from one of my y13 pupils with this inscription:

It was quite possibly the nicest thing I have ever read, and it made me feel great. It is moments like this that I came into the profession for. And I don’t just mean for the nice ego boost (which was great), but the line: “You have restored my faith in maths”. I feel that my job is not just to teach pupils maths. I need to inspire the next generation of mathematicians.  And I need to help pupils prepare for the real life post school.

The next thing Michael Rosen was asked by Simon Mayo was (and I paraphrase): “If you were the education secretary, what changes would you make?” and his answer really got me thinking. It was: (and again, I am paraphrasing): “The first think I would do would be to hand back my powers to the professionals.” He spoke eloquently and at some length about how education secretary after education secretary have come in and used the position as a political football. How various people in the role have come in to attack teachers, rather than to work with and help them. He spoke about the department of health and how they have major links with doctors when it comes to policy making and how education needs to be more like this. All these points hit home for me, and were very similar to a lot of the things mentioned in the May #blogsync (http://blogsync.edutronic.net/).

There was one final thing though, that got me thinking. He said that the way the culture was becoming, with league tables and performance related pay, that it seemed that the current regime were moving to pit teachers against each other, rather than working together. I think that if you look at education policy, it certainly does seem to be that way. The year before last I went to another school for a few days to complete training they were offering, during the time there I was speaking to the lady who ran the training and she told me she was becoming disillusioned with it all because her school were moving towards being a “teaching school” and that the D of E (that’s the Department of Education, not the Duke of Edinburgh!) has told her that she needed to start charging around 4 times as much as she did now to other schools to take up the training. We spoke about our ideals and both agreed that we should all be out to help each other wherever we can, because we all have a common goal, to improve the outcomes for young people. Rosen’s comments reminded me of this conversation, but also made me think of this picture I saw recently (which i can’t now find!), I had the words “The revolution will not be televised, it will be on the internet” on it.

The reason it made me think of this is because it seems that we are living in a time where there is an online revolution going on. If you click on TES resources you can find tons of resources for your lessons, shared for free, by tons of teachers across the world. The internet is alive with blogs about great lesson ideas and how to improve your teaching. If you tweet “help, I can’t think what to do for a lesson on {insert topic here}” you instantly get loads of ideas tweeted back at you. On top of this is the teachmeet movement. Teachers, from NQTs to SLT members, are giving up their time, for free, to share their ideas and experiences with others. The common goal has been rediscovered online, against a backdrop of PRP and league tables the teachers are rebelling. We are sharing good practice freely and trying to help our colleague become the best they can be, while we strive to become the best we can be.

## New timetable, PE, Rugby and a Teachmeet!

Last week was a brilliant week. There were parts of it that were knackering, and tough, but all in all it was a great week.

At our school may half term signals a timetable/year change. The old y11 and y13 stand down on study leave and everyone else moves up a year. We all get a new timetable and we get a half term to work with our new classes before the summer, leaving only new y7s names to learn in september. This year it’s an even bigger change as we’re moving from 6 periods a day to 5!

On the face of it, I’m pretty happy with my new timetable, it’s got an excellent mix of key stages and abilities, although I really loved my old one and my new classes have a lot to live up to! I’ve kept my GCSE group, who I am really enjoying teaching.

Obviously, with no Y7s or y12s, we have lighter timetables and all important “gained time”. I intend to use mine to write a KS5 SoW (part of my new role), and to observe as many teachers as possible to improve my own practice. Last week though, and this week, there is little time for that because we have Old Y11s and 13s in at every opportunity to cram in as much revision as possible!

Teaching wise, I’ve loved the revision and I’ve got off on a good foot with the majority of my classes, which has been good. I’ve also learned most of the new names!

On weds, a colleague from PE asked if I would go and check out his starter, and I stayed to see a very enjoyable lesson on Ultimate Frisbee! He has been trying to add literacy and other cross curricular links into his starters/lessons, and as such had asked me to head down and watch. The starter involved the pupils coming up with things they expected to learn about UF using the letters of the name to be the first letter if each idea, in a similar fashion to an acrostic poem. This worked really well and we got some great answers. He asked if I had any other ideas for him, and I’m working on some but haven’t finished them yet. (Do comment if you have any other ideas!) I loved the starter and the rest of the lesson was superb, showing great examples of chunking, group work, competition and higher order questioning. There were a few ideas I have taken away to integrate into my own lessons!

On Friday I was lucky enough to be able to watch three of our pupils turn out in an U13s match which pitted the best of North Leeds Schools against the best of South Leeds Schools. The match was superb, thoroughly enjoyable. And I watched with immense pride as our three superstars hit tackle after tackle and took drive after drive. It was a close game, and unfortunately we were pipped on the final hooter. But it didn’t matter, the lads did us proud. I was especially pleased to see one lad playing as he hadn’t even considered playing rugby 9 months ago, but after some persuasion from me he joined the school team and now he plays for school, a club and the schools representative team!

If all that excitement wasn’t enough, I attended my very first “Teachmeet” on Saturday, and saw some superb presenters speak on an array of topics. The Teachmeet was English themed, but I managed to keep my mathysness under wraps and got out without taking a beating! There were some great ideas to take away that I could apply to maths, and the ones that were purely English focused were still very enjoyable as I love the subject (but shhhhh, don’t tell the English department! [nb that said, maths is still much better!])

The week was topped off with a Bon Jovi concert(which was awesome). Throw in some cricket, a trip to a Leeds Rhinos match and the lions tour, it’s no wonder I’ve not found time to listen to the exciting new episode of “Wrong,but useful” yet!

Categories: Pedagogy, Starters, Teaching