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Thursday, 30 May 2013

Maths + Cake = Fun

I had my final official lesson with both of my year 11 classes last week and I wanted to do something really fun with them, so I racked my brain till I came up with some inspiration.....

We could make EDIBLE revision notes by decorating cakes! : ) Yay! (Miss King beams)

The learning objective written up up the board was: To test out the "well known" argument that


and see if it worked when CAKE was substituted for BISCUITS (biscuits being the cheaper option)

Admittedly it was a bit of an expensive lesson - it cost me around £15 for all the biscuits, writing icing, marshmallows, strawberry laces, chocolate drops, silver balls....... (yes I did get a bit carried away), but was it worth it? I reckon so. I've been teaching some of these students for 3 years now and I've had a great time with them so I didn't begrudge a penny.

The big question is though - did the students enjoy it? And did they learn anything?

I was quite surprised by the reaction of the first class actually, I was expecting a bit of silliness and giggles, but instead they all got down to business very seriously and they actually worked really hard, producing 4 or 5 top-quality biscuits each. I thought the atmosphere might get a bit raucous, but instead it was more like an atmosphere of deep concentration as they all tried to keep their hands steady.

The girl who made the exterior angles biscuit (pictured above) spent ages painstakingly drawing footsteps around her hexagon to show that if you walk around the shape you have gone one full turn. Another (usually very vocal) student sat in silent concentration to produce a net and 3D drawing of a cube.

By the end of the lesson there weren't many actual biscuits left, (having mostly been consumed by the hungry workers) but the photographic evidence gave me a wealth of great pictures. Some were simple demonstrations of formulae or theorems (like the circumference formula biscuit on the right) whereas others posed questions to be answered (like the forming an equation with angles biscuit which is below).

Having created all these tasty looking pictures, I thought it was worthwhile doing something with them, so I've put most of them in a powerpoint so that each biscuit is on its own slide with a question, followed by a slide with the answer. I emailed the powerpoint out to the students and wondered if it was worth the bother. Would they care about looking at them again? What I had forgotton of course, is how much students love having their work shown to everyone else. The next day some girls came up to me to say that not only had they tried answering the questions, they'd particularly looked for "their" questions and shown  those pictures to friends in other classes. Result!

Obviously this was not the most efficient method of revision - writing with writing icing takes a lot longer than writing with a normal pen and given the choice of so many decorations, there was always the danger that aesthetic sensibilities would overtake mathematical ones (!) but I had an ulterior motive in mind. I want my students to leave school with positive feelings towards mathematics, and if appealing to their sweet tooth can help that, then I make no apologies for doing so.

At the end of the lesson, when the class pestered me to make a goodbye speech to them, it was this thought that was at the forefront of my mind. So after a bit of reminiscing about the past 3 years, I took a few seconds to say something heartfelt. I told them that no matter what grade you get in the summer, whether it is what you were hoping for, or if you end up just missing out; you need to remember that they are GOOD at maths. Grade boundaries can move around, you can have a bad day, but after you leave school, when people mention maths, I want you to think to yourself, "I'm good at maths" and I want you to have a go at solving any problems that might come your way. A lot of you probably know more maths than your parents do (cue vigorous nodding by about half the class) and you should be really proud of your achievements.

I stopped then, before getting emotional. And I think I better stop writing now, for the same reason.

Thursday, 16 May 2013

Background noise and awkard silences

Have you ever experienced a moment in a lesson where, without warning, the whole class suddenly goes quiet for a while?

I had one of them today. As ever, it was an unplanned moment. The students had been working on task for a while, with the usual level of classroom noise, then suddenly, as though there was some telepathic signal between them, silence descended.

This happens in my lessons every so often and it usually feels a bit wierd. For a moment it's calm, then it feels a bit awkward, then I feel a sense of pressure descend on the class. I always worry that one of the students might want to ask a question, but they don't want everyone else to hear, so they don't ask and end up feeling a bit trapped.

Inevitably, it never lasts more than a few seconds before one of the more vocal students says something inane.  "Why has it gone quiet?" is a popular one, asked in indignant tones, as though it's the responsibility of the rest of the group to keep up an incessant stream of background noise. Or they say something like, "It's really quiet. I don't like it!" as though the brief silence is something to be endured rather than a moment of calm.

To be honest, I'm usually as relieved as the students when the spell is broken. A few nervous giggles and we're back to normality.

Recently however, I've been wondering if silence might actually be a useful pedagogical tool. It's not something that comes naturally to my style of teaching, but I think it's worth pondering.

So what are the benefits? Well, working in silence would give students a chance to become more engrossed in the task at hand rather than getting involved in off topic conversations around them. Teachers should never forget that school is a highly social experience for students and they can often feel pressurised to manage relationships with their peers at the same time as learning anything academic. This sort of social scenario in the classroom is the antithesis of the psychological concept of "flow" when you become completely absorbed in what you are doing and you don't notice anything else that's going on. I think I've experienced "flow" when playing the piano, writing certain essays and even when solving some particularly engaging maths problems. It's a great feeling and a very productive state of being. A normal classroom environment, full of distractions, doesn't seem conducive to inducing a state of "flow" in anyone.

Working in silence might also give students a chance to be more reflective about what they are doing. Rather than racing through their work, they would have more time to concentrate on the task at hand (because they would spend less time chatting to each other). This may particularly be the case for problem solving questions, where students have to approach something from several different angles and refer to various different facts or techniques in a single quesiton.

Hmmm. I'm definitely not suggesting that I will try to insist on silence for a whole lesson, or even the majority of a lesson. As a general rule, I always encourage students to talk to each other throughout lessons and I have no intention of dramatically changing this modus operandi. My classroom is arranged in groups, not rows, specifically to facilitate discussion, even though I know it means I have to work a bit harder to get them to focus on me when I'm teaching from the front. And I'm not at all averse to background noise. Whenever I work at home I tend to have music on, particularly when I'm writing. Currently, iTunes shuffle is soothing my ear drums with "All the young dudes" by Mott the Hoople, which I consider to be pretty good writing music.  Oooooo. It's just changed to "White Winter Hymnal" by the Fleet Foxes. Even better writing music.

But I think it might be worth trying out shorter periods of silence, maybe 5 minutes at a time, after students have had a chance to talk to each other about what they are doing. I like the idea of giving a class an extended question, asking them to discuss a strategy for answering it, then telling them that it's time to put their plan into practice, but they have to do so in silence so that they can concentrate better. I don't know how well it would work. It might just feel incredibly awkward. They might completely resist it, or they might embrace it. Whichever class I choose to try it with though, I know that I'd have to explain my reasoning first. I wouldn't want them to associate the period of silence with punishment or boredom. I'd have to explain that we were going to use silence as a way to help them concentrate and produce their best work. It would be a planned silence, a friendly silence, and most of all, a productive silence.

Friday, 10 May 2013

Hurry up Gove! Post GCSE Maths Qualifications

A y11 student asked me today if it was a good idea for her to study A level maths. "I like maths" she said, "I don't want to stop learning it after year 11".

I wish I could respond with unhesitating encouragement. I'd love to advise all my students to continue with maths post-16 and I know that many of them would like to. I reckon that about half of my y11s have talked about taking A level maths, or have said that they will miss maths next year and wish they could do it in the sixth form.

So why didn't I just say go for it?  Why don't I encourage all my students to take A level maths?

Well first things first, I firmly believe that everyone can achieve highly in maths, its just that some people need more time to understand things, or need to learn in different, often more visual ways. I also can't stand putting limits on myself or anyone else. I think anyone can do anything if they put their mind to it.

But we have to be realistic. It's not fair, in fact it is irresponsible, to encourage students to do something that they are unlikely to be successful in. Maths is a linear subject where you need to understand basic principals before you can move on. There is a substatial gap between achieving a C or a B in GCSE maths and tackling the subject matter in the A level course.

So when students who are on track to achieve a C or a B at GCSE ask about doing A level maths, I never tell them that it's out of the question, but I am honest with them. I tell them that it is hard work, much harder than GCSE and I tell them that they will need to do a lot of work in the summer between y11 and sixth form, to bridge the gap. I try to strike a balance between encouraging their ambition and being realistic about what can be achieved.

Even as I write this I feel awkward. I didn't become a teacher to put limits on students or to tell them that something is "probably too hard for you". But I have found some cause for hope from an unlikely source: the department for education. The turrential downpour of new initiatives, reforms and policy changes from the DfE has been pretty difficult to keep up with over the past couple of years and I have to admit that I hadn't seen this which is a report from the  ACME (the advisory committe on mathematics education) about options for post-16 mathematics, published in December last year.

I was very encouraged to find this paragraph:

A new [mathematics] qualification should be developed and introduced as
part of wider A level reforms.
This qualification should:
  •  Be distinct from A level Mathematics, with an emphasis on solvingrealistic problems, using a variety of mathematical approaches, and should be for students not currently doing AS or A level Mathematics
  •  Give students the confidence to consolidate their understanding ofmathematics by using and applying mathematics already learned in GCSE and new mathematics beyond GCSE developed during the course.
  •  Have a smaller volume than AS level and be designed to be studied over two years
It sounds good to me. I like the phrase "give students the confidence to consolidate their understanding of mathematics by using and applying mathematics already learned in GCSE". I'm feeling cautiously optimisitc about the idea of a sixth form course that focusses on using and applying GCSE mathematics plus some extra content. I certainly agree that we need a course with "a smaller volume than AS level" for students who aren't ready for the onslaught of AS and A level maths. 
So hurry up Gove, get a move on with this one. After all, its not like you to wait around!
I just have one plea: make sure you introduce it as an optional course, with engaging real-life content, suitable for those C/B grade students who want to keep going with maths. If you try to make it compulsory it will be "one-size-fits-all" and it won't work. Use it as an opportunity to give teachers and students more choice, not less.