Speaking Truth to Power: The need for political reform in our education system

Since Michael Gove “came to power” in 2010, politics has played a much greater role in my working life than I had ever anticipated. Gove’s name is mentioned on an almost daily basis by colleagues fed up with ill-thought through changes and confused about what we are actually supposed to be doing. Soon, a new curriculum will be in place, but we have only the vaguest notions of what it will contain and no way to begin preparing our students. I have already lost count of the times we have had to sit down and re-write lesson plans and schemes of work because the hyperactive Mr Gove has changed his mind about something, or decided that changes need to be brought in NOW, RIGHT THIS MINUTE, NO DELAY!!!

And yet, much as Gove provokes an unprecedented level of ire and exasperation from teachers, he himself is not really the problem.

Yes that’s right.

Gove isn’t the problem.

The system is.

You see, we have a system in which the secretary of state for education has almost unbridled power over our schools. On the 29^th of September, mere weeks before our year 11 students were due to take their GCSE maths exam in early November, Gove sent out a tweet (no letter, or email, just a tweet) saying that exam re-sit results would no longer count towards league tables. This edict was effective immediately.

“Bravo!” I hear many people cry. “Teenagers have it easy, they shouldn’t be allowed to re-sit their exams and schools shouldn’t encourage it.” 

The awkward thing is, Gove himself has promised legislation that will mean students HAVE TO re-sit GCSE maths and English if they don’t get a C. So when he labels re-sitting “cheating”, he himself is enshrining cheating in legislation, making it mandatory for a significant proportion of teenagers.

Whatever the rights and wrongs of entering students in for November exams, this particular tweet at the end of September encapsulated the crux of the problem with our education system. The education secretary had an idea, he implemented it immediately, he scored political points for himself, and he generated agonising and immediate problems for hundereds of teachers up and down the country, with potentialy disastrous results for students.  

In our school, we waited a few days, hoping for a U turn, thinking surely, surely he can’t jeopardise our students’ results like this. But with no U turn seeming likely, we called an emergency meeting before school to decide whether or not to pull students out of the exam. We had to balance what was best for the individual students with what was best for the whole school (and the thousand or so other students that attend). We decided to keep most of the students in. They have been working hard since the beginning of September and they wanted to do the exam.  For our part, we wanted to shelter them from the political storm raging above their young heads.

Of course, this debacle should never have happened. We cannot function well in a system where the rules constantly change, where we don’t even know what is on the curriculum, where there is no clear and consistent leadership. We cannot function in a system where things can change at the whim of the Education Secretary. It has to stop.

These are the key changes I feel that we need at a political level:

The secretary of state for education should have no role in deciding the national curriculum. This should be discussed and decided by experts, including teachers, academics and representatives from businesses and employers. No single person should be able to stamp their individual preferences all over the curriculum.

The secretary of state should not be able to announce changes that impact on the current academic year. I do not say this because I am opposed to change; indeed I think it is vital. But if new policies could only be implemented in the next academic year it would give teachers more time to plan, it would make politicians think more carefully about what they are doing, and the resulting changes would be more effective and more successful.

Teachers need a professional body, which should be consulted over every major change. Currently we only have unions. Their job is limited to pay, pensions and working conditions, but I believe that the majority of teachers are more bothered about the negative impact that politicians have on the curriculum. We need a professional body to stand up for teachers and students over issues such as exams and the curriculum.

 

So there are my proposals. I’m not attacking Gove as an individual, I’m attacking a system that allows him so much power. His “crusade” mentality has caused teachers more problems than any other education secretary in recent years, but it is his position, rather than the man himself, that poses the greatest threat.

I have titled my blog post “speaking truth to power”. I don’t have a lot of power. But I am an intelligent, thoughtful person who cares passionately about the young people she teaches. I hope somebody listens.

 

 

 

I'm on strike today, here's why....

I’m on strike today because I disagree with the government’s ill thought through reforms to pay, conditions and pensions. The issues are complex, and I fully accept the need for some reforms. The population is aging and I agree that we need to change the pensions system. However, many of the proposed changes will have a damaging impact on our education system. As a conscientious teacher, who cares passionately about state education in this country, I have taken the decision to go on strike and voice my opposition.

1. Pensions

Clearly we need some reforms to our pension system. People are living longer and we need a sensible solution. I am hugely concerned however, by the idea of making teachers work in the classroom until they are 68, or even older. I am not for a minute suggesting that older people have nothing to contribute, but you have to be realistic about the physical demands of the job. Can you imagine someone aged nearly 70 trying to teach a group of 32 challenging teenagers? We’re not talking meek and mild children who will do whatever you say.  But maybe you think the 70 year old person could manage it for an hour. Then make that 5 hours a day, with break duties, detention duties, marking, planning, meetings, phonecalls home..... It is just ridiculous.  It won’t be fair on the teachers and it won’t be fair on the students.

2. Working Conditions

The government have said that they want to see longer school days and shorter holidays. A populist and ill thought through policy.

Many teachers will have come across people who are keen to tell us that the school holidays are too long and the school day too short. The reality however, is that time spent actually teaching classes represents perhaps a third of a teacher’s total workload. People outside the profession can easily (and understandably) underestimate the amount of time planning and marking take. So here is a rough example to give everyone some context: I teach over 200 hundred students. If I spent 5 minutes per week marking each book, that would take over 16 hours and if I spent just 20 minutes planning each lesson (I often spend longer) this would take over 6 hours. That’s an extra 22 hours a week, or 4 and a half hours  per working day. I usually finish teaching/attending meetings at 4.30pm. Add the extra 4 and a half hours and my day finishes at 9pm. This is just a rough example, but bear in mind I haven’t factored in all the extras we do – particularly regarding pastoral work and contacting parents.

In general, the threat to teachers’ working conditions is a threat to the quality of students’ education.  Teachers have a demanding job and if the school day becomes longer, this will result in a drop in quality. We won’t be able to plan, mark and feedback in the same way we do now. It’s just not physically possible.

 

 3.Performance related pay

On the surface, performance related pay sounds like a great idea -

 “Pay good teachers more!” 

“Reward those who work hard!”

 – it all sounds ideal. Surely the only people who could disagree would be lazy teachers concerned that they’ll miss out?

The reality is, as ever, more subtle than the soundbites above would suggest. In fact, I am far more concerned about the impact it will have on students than the impact it will have on teachers.

Firstly, performance related pay raises the stakes in terms of test results. Teachers are already judged on their test results, but the new system will place far more emphasis on them. This means that the culture of “teaching to the test” will be strengthened, not weakened.

Secondly, it is clear that some schools are more challenging to work in than others. What incentive will teachers have to go and teach in the emotionally draining and physically demanding environment of a difficult school when they know it is harder to reach performance targets in these schools? The result will be that students from disadvantaged backgrounds will not get the best teachers.

Thirdly, performance related pay may have a big impact on the community of teachers, particularly within schools. Teachers work at their best when they collaborate: when they share ideas and resources, when they learn from each other’s experience and when they feed off each other’s enthusiasm. Performance related pay could erode this by generating an atmosphere of competition between individual teachers. Will every teacher be willing to share their best resources with a colleague if they are in direct competition with them? After all, the total sum of money for teachers' pay has not gone up. Performance related pay means that for every teacher who gets paid more, some will get paid less.

Finally, performance related pay could impact negatively on set changes.  In the system, “performance” will be based on comparisons with target grades, which can be very erratic. My current year 11 class has a student with a target of a D, who is clearly capable of an A.  In a subject like maths where students are usually placed in ability groups, teachers may wish to “hang on” to students who are performing above their target grades and stop them from moving up to a higher set. Similarly, they may send underperforming students down to the set below, without taking responsibility for improving that child’s grade themselves.

I'd like to finish by saying that teachers are, in general, a very reasonable and caring bunch. Patience is a key characteristic of a successful teacher. But we also have integrity, passion and commitment to what we do. If we didn't think it was worth it, we wouldn't have gone on strike.

 

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Back to school

All this week teachers will be preparing, both mentally and logistically, to meet their new classes. It can be quite a scary time. Will your new classes respect you? Will they cooperate or will they be obstructive? You’re not sure. To make matters worse, these nervous thoughts are compounded by several unhelpful myths that surround the beginning of the school year.

A prime example of one of these myths is the old adage “Don’t smile till Christmas”. This one’s not too bad because no one takes it seriously, but it does reinforce the idea of an “us vs. them” culture, where you can’t let the students know the real you. 

A more pernicious myth goes a little like this:

 Students, particularly year 7s, will arrive in your classroom fresh faced and ready to learn. They will follow all your instructions and instinctively know good learning behaviours, like taking in turns to contribute to a class discussion or asking their peers first if they get stuck. When they start demonstrating different behaviours – calling out when you are talking, forgetting their homework, constantly asking for help, this is because the teacher has somehow “un-trained” them. Standards have slipped and they have regressed backwards because the teacher has not been authoritative or consistent enough. And once the boundaries of expected behaviour have been breached, it is very difficult to build back up again to the halcyon days of the beginning of term.

I don’t agree with this narrative and I think it can be very unhelpful. When people talk about standards slipping, I think in many cases these ideal standards simply weren’t there in the first place. Sure, you might have a honeymoon period with your new classes, particularly if they are in year 7 or if you have quite a commanding presence in the classroom. But until you have built a relationship with your students, until you have taught them to think about what makes a good learner and what you personally expect to see in the classroom, the supposed high standards at the beginning are merely a façade. The students seem to be cooperative little angles, because they are uncertain. They haven’t pushed the boundaries yet, so they don’t really know where the boundaries are. For most classes, it doesn’t take long before one or two students start exploring.

I think it is much healthier to think of all your new classes as starting a journey towards having high standards, where these standards can go both up as well as down. Of course you should have high expectations from the start, but don’t expect students to know what to do automatically. Students need to learn good classroom behaviour just as they need to learn the content on your course.  To create a culture in the classroom where truly outstanding behaviour is the norm, you need to work at it, reflect upon it, and work at it some more. Rather than feeling nervous of putting a foot wrong and letting standards slip, expect students to push the boundaries and to cross them. And don’t worry if you have a few students that do this several times at the beginning of a year: if they’re a tough class they won’t be perfect straight away. It will take time, patience and enthusiasm, but you’ll get them onside in the end.

Spaghetti Trigonometry - instrumental vs relational understanding

I've been really excited about all my y10 lessons this week. I love planning for them and teaching them because they're great students. My lessons with them are never perfect by any means, but although they're a pretty diverse bunch (32 students, FFTs from E to A) they've got a great attitude to learning and they're just lovely to work with. I also generally plan y10 lessons with a colleague of mine who teaches the parallel middle set group and I really enjoy collaborating with her. 

This week and early next week we're doing Trigonometry and we've had 4 lessons to play with. The students had never heard of it before, so we needed to think carefully about what we could actually fit into the 4 lessons without over-doing it and making everyone stressed. I also wanted to think about how we could get students to have a genuine understanding of trig, rather than just viewing it as a topic where they "follow the steps" and get the answer.


I took to the web and looked around for good trig lesson plans. I found this video (https://www.teachingchannel.org/videos/introduction-to-trigonometry) where a very confident American maths teacher gets out a set of bongo drums and chants Soh Cah Toa, Soh Cah Toa, Soh Cah Toa! with her class. It was nice, but this approach only generates instrumental understanding, rather than relational understanding. (If you watch the video, those of you who know me may be thinking that using bongos sounds like just the sort of thing I might do and well ...... yes... I was quite taken by the bongos part, so I may or may not have had a go on my desk......)

Then I found this video and got very excited http://www.youtube.com/watch?v=AUOgD_Hq70A . Spaghetti trig! I recommend watching the video if you want to do it and need a more detailed explanation, but basically it works like this:

You draw out a unit circle and mark off 15 degree intervals on the circumference. The circle I used had a radius of 12cm, so we took that to be 1 unit. You snap off a piece of spaghetti to be the size of the radius and move it around the circle. You then use other pieces of spaghetti to construct right angled triangles like the one in the diagram.

Since sin(x) = opp/hyp, if hyp = 1 then sin(x)= opp, so the length of the piece of spagetti is the value of sin(x). You can then stick each piece of spaghetti that you use onto the appropriate place on the axis (as you can see in the diagram).

I was really excited about using this idea, but I wasn't sure how it would work out. Usually I don't teach trig graphs to middle ability groups until near the end of their course. It's classed as A/A* grade, so I leave it till the end "if we have time", but it got me thinking that, stuff the supposed "grade" of the topic, it's actually not that difficult, and it could really help students to understand what they were doing. 

So this is how we approached the lessons

Lesson 1: Discovering trig ratios by measuring triangles of 30, 45 and 60 degrees.
I also included a quick intro showing students real life situations where trig is used so that they have an idea of the big picture. I always like to give them an idea of where we're going at the start of each new topic.

Lesson 2: Find missing sides using the Soh Cah Toa formula triangles
They got the hang of the method pretty easily, but then, the method is pretty straightforward if you use the "cover up method" in the formula triangles. They could then answer questions, but genuine understanding was still not there. (Despite the use of desks as bongo drums)

Lesson 3: The graph of Sin(x)

Spaghetti trig! The one I was really looking forward to!

So, how did it go? Was it a useful approach?

I'm going to stick my neck out and say it definitely was a useful approach. Of course it took longer than the standard "use your calculator and plot points on the graph approach", but the pieces of spaghetti snap pretty easily so it didn't take too long. More importantly, it generated LOTS of really useful discussions. Students quickly realised that there were pairs and indeed quads (is that the right word?!) of lengths that came in 90 degree intervals. They had really useful discussions with each other about what might happen at 90, 180 and 270 degrees (is it infinity? is it 0? is it1?) and they appreciated that it would turn into a wave.

We ran out of time at the end of the lesson to go any deeper into the discussion, but I intend to use the graphs at the start of next lesson and stick at least one on the wall. When I teach it again, I reckon I can speed it all up by being more organised with the resources.  Questions I'm thinking about for next lesson are: how could we do cos(x)? What happens when we go over 360? What is the amplitude of the graph? If you know the value of sin(10) what other angles can you tell me?

Hmmm. I'm getting carried away! This is getting into A level terriorty rather than GCSE, and I'm still not convinced that they all understood the point of what we were doing. I'm going to have a good long think about next lesson and figure out a way to draw everything together. Can we find missing lengths without using calculators, just using the graphs? Maybe if we used non scientific calculators then they would have to refer back to the values on the graphs. We have got sets of non scientific calcs in the department........... (voice trails off as Miss King stares into middle distance and gets lost in mathsland.........)

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

MATHS + CAKE = FUN

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.

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.

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 http://www.acme-uk.org/media/10520/20121217acme_post_16_strategy.pdf 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.

 

Practical Volume Activities

Here's a quick post this evening about a sequence of lessons that I've done with y10 on volume.

I often find that y10 and y11 lessons fall foul of time pressure. There is so much content to cover, in such a limited amount of time, that there doesn't seem to be much room for creativity. In y7, y8 and y9 I'm always keen to make lessons as creative as possible but with the older year groups the prospect of exams always seems to loom large and we don't get to have as much fun.


I usually plan y10 lessons with a colleague of mine who teaches a similar, middle ability group and I always find it really useful to talk to her. Two brains are definitely better than one! When we saw volume on the scheme of work, we both agreed that we'd like to get some practical activities involved, and this is what we came up with.

In the first lesson we gave the students some nets and asked them to work out the surface area. We took the opportunity to recap how to work out the area of simple shapes (rectangles, triangles, circles) and some of them took on the challenge of working out more complex shapes (trapeziums, pentagons, hexagons).

In the next lesson they cut out and made the nets into 3D shapes. We then talked about classifying the 3D shapes and they got into the idea of prisms. Not content with the shapes they had made, the girls wanted to look for prisms in the rest of the room. Surprise surprise, there were quite a few dotted around the place (it's not like I was collecting examples or anything) including a lovely octagonal quality street tin that just happened to be sitting at the front.

It was a really worthwhile lesson, although I'm pretty sure the pace would have been considered too slow by Ofsted. It took a while to cut and stick all the shapes, but once they had made them, the girls clearly understood how all the faces fitted together and they had no problems appreicating that the volume of a prism was cross-sectional area x length.

We had another lesson on calculating the volume of more complex prisms including problems where they were given the volume and hade to work out a missing length or area. Then in today's lesson we looked at the cuboid challenge where you give students a single piece of paper and ask them to make an open-topped box with the greatest possible volume. I think this task is usually done as a nice introduction to calculus, or at least plotting the graph of a cubic equation (nrich, as always, have explanations of how it works if you're not sure http://nrich.maths.org/6399/solution ). But, much as I feel a bit pained to say it, I wasn't bothered about the algebra this time. I wanted students to get a feel for dimensions and to have a go at a practical version of trial and improvement. I also wanted to make a big deal of the second part of the challenge, where I gave them 4 multi-link cubes each and asked them to work out how many whole cubes they could fit in their boxes.

The picture above shows the efforts of the winning team of 4 students, and the photo on the right shows a section of working out in another student's book. I asked the girls to work out the volume of every box made by their team and only once they had finished that were they allowed some cubes so they could work out how many cubes would fit inside. At first they were unimpressed with the quota of 4 cubes each, but they quickly figured out what to do and even the weakest students in the class seemed pretty motivated.

There is much more you could explore with volume, but I feel pleased that even in a limited time we managed to cover a lot of content in a way that didn't feel pressured and allowed the students time to become really familiar with 3D shapes. I'm sure that making the shapes, physically measuring them and turning them round in their hands helped the girls to understand what they were doing far more than simply working from a textbook would have done.

Reader, I married him: Going with the flow on ratios

I overheard some year 11s today talking about one of their earlier lessons and getting quite agitated about it. “It’s just structure, structure, structure in those lessons” said one of them. “I think she plans for every second” said another.

At first I wanted to laugh. I have no idea who they were talking about (and have no desire to know either), but whoever it was sounded like an excellent teacher and I thought the students just didn’t know what was good for them. “Every second planned” they’d said. Crikey. It sounds like the work of a very organised person. Hats off to them.

But then I wondered; why were the girls so agitated about it? They are highly motivated students, the sort that have been turning up for after school revision every week since they were in year 9. They’re not afraid of working hard.

The answer seemed to come in the final comments I heard:

“She never lets us just go with the flow” said a different student. “Yeah,” said the first, “she should just let us get on with it”.

This little conversation links in to an issue that I come back to time and again in my teaching practice. How much independence should we allow/encourage? How much is too much? Do students do better in lessons where “every second is planned” or in lessons when teachers “let us get on with it” a bit more.  An interesting seam, but I think I’ll save mining that one for another day.

Following another thread, it made me think about the lesson I’d just taught. It was year 9 and we were doing ratios. I knew that I’d put together quite a boring lesson. Originally I’d wanted to do something really creative involving the ratio of the string lengths of musical notes, but I hadn’t sorted things out in time and I was stuck with a boring stack of textbook questions. So I started the lesson feeling a bit uninspired, and explained how to simplify ratios into the form 1:n.

The girls were not impressed. What was the point? You can’t get 0.64 of a person. Why not just simplify them in the normal way?

So I said the first thing that came into my head and it went a bit like this:

Well, when I was at university there was a bit of an issue about the ratio of boys compared to girls. My university was split into colleges and some colleges had very different ratios. One college might have had a ratio of 11:10, but another might have been more like 7:3.

They looked interested, so I ploughed on….

So in some colleges, the number of boys and girls was fairly equal, in others there were lots more boys compared to the girls. If you were choosing a college, you might want to know the ratio of boys compared to girls and pick somewhere based on that. It might be difficult to compare the ratios, because you can't tell straight away if 3:7 is better than 16: 21, but if you had them in the ratio 1:n you would always be comparing like with like. Ideally the ratio would be 1:1 or pretty close (I was rambling at this point) although to be honest….. my college wasn’t that equal (really should have stopped to think at this stage)…but I suppose it did have its advantages … I mean I’m marrying one of them so it worked out quite well for me

Cue raucous laughter and bright red face from me.

This definitely wasn’t a case of every second planned, but it certainly livened things up. It took a while for them to calm down and stop pointing out how red I’d gone, but they were clearly interested in the idea. So I ditched the textbook and made up some ratios on the board saying that they were the male/female ratios of different colleges. The students had to simplify them into the form 1: n, then explain which one they would like to go to.

Nearly all of them said the one with the ratio closest to 1:1, so we then ranked the answers in order from most fair to least fair ratio and had a useful discussion about ordering and comparing decimal numbers (is 1:1.6 equally as unfair as 1:0.6? Some of them thought it was at first).

I wish I’d thought of this idea before the lesson. I’ve since been online and looked at the male/female ratios on different courses at Oxford and the results are sadly unsurprising, but they are interesting and hugely relevant to a group of bright young things at an all girls school. The male/female ratio in history is 1:1.02 and in English it’s 1:1.7, but in maths it’s 1:0.44, in engineering it’s 1:0.3 and in physics its 1:0.2.

So definitely an idea worth using again, and despite the momentary embarrassment – I think it shows that it doesn't hurt to “go with the flow" occaisionally.

Egg Box Update!

Note - it is best to have this link playing in the background while reading this post. Open it in another tab and enjoy. http://www.youtube.com/watch?v=2wdWGtTQ7hA


The first set of egg boxes are complete and I have photos!

I'm going to reflect on the project as a whole in another post, but for the time being I thought I'd assume the role of artistic director of the gallery and give you a guided tour. I've put in a selection of designs from top and middle sets. I haven't got a picture of any work from the lower set groups, but I have seen a couple of really nicely decorated cubes and cuboids from them.

(N.B. My tongue is now firmly in my cheek)




1. Untitled
On the left here we have what is considered to be the pre-eminent piece in the collection from two of our gifted and talented artists. The talented duo who created it declined to name the work, but at the gallery we have chosen to refer to it as "Possibly the head of a panda princess?"  A great deal of skill went into the production of this piece and the artists should be commended for their ingenuity in creating the spherical shape. They were also highly commended for their excellent research skills which enabled them to look up the formulas for the surface area of each section.

 

2. Bright Yellow Rabbit with Oversized Teeth and Cavernous Eyes

This is the work of another one of our most distinguished artistic duos. The work encourages us to reflect on the contrast between the jaunty yellow colour that dominates the head of the rabbit and the deep black colour used for the creature's eyes. Again, this pair of artists were highly successful in calculating the surface area of each section of the work, not forgetting the ears.

3. Chateau de l'Oeuf (unfinished) 

This ambitious work was sadly unfinished as the artists had to run to their next lesson, but one can get a sense for the scope of their design by this partially completed exhibit. This exemplifies a trend in some of the middle set groups towards creating "buildings" for their eggs. Judges were particularly impressed by their use of the formula 3/4 x pi x radius squared, for the cone shaped turrets, which were made using 3/4 of a circle.

4. The Eggcitement of Easter
This egg-box design, showing a rabbit in open-mouthed delight as it is about to consume a chocolate egg, encapsulates the joy of the Easter season. Although they had never been taught how to calculate the correct dimensions when designing the net of the cylinder, this group should be particularly appluaded for their "can-do" attitude and problem solving approach. When discussing how to work out the length of the rectangular part of the net, the group realised that it had to be the same as the circumference of the circle, but they had not been taught a formula to work this out. Instead, they took a piece of string and used that to measure the circumference of the circle. Ingenious!

5. The Nodding Rabbit

 This design demonstrates that sometimes simpler is better. The group used 2 cubes, attached with a piece of card at the back. Viewers in the gallery are encouraged to interact with this exhibit by tapping the head of the rabbit, which bobs up and down. Although not particularly ambitious from a mathematical point of view, this is a much valued contribution to the gallery and will be used as a model to inspire future generations of artists, especially those who are less confident.

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6. Sheep
As artistic director, this is my personal favourite in the gallery. Again, the acutal net is not particularly mathematically adventurous (it is a cuboid) but who could fail to love an egg box covered in cotton wool and made to look like a sheep? 



7. Egg-Barn

Our guided tour concludes with a very accomplished piece of work from two artists who have made fantastic progress this year. Not content with a simple cuboid shape, the pair decided to construct a triangular prism for the roof of their Egg Barn. They realised that the length of the triangle had to be the same as the length of the corresponding side of the rectangles in the net. With some assistance from their artistic director, they were guided to experiement with using compasses to construct inter-secting arcs to find the third vertex of each triangle.Once they had mastered the technique, the artists became experts in their field and showed another group how to do it.

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Musings on the pedagogical uses of laughter....

One of the most important things in teaching is building a relationship with your students. I always think things are going well with a class if they can laugh at/with me in a good natured way AND I can laugh at them (just a little bit of course).

Both of my current year 11 classes are pretty good at this.One class recently described me as "like a really funny Mum", which I took as a compliment, even though I'm only 10 years older than them and couldn't possibly be their mother. A student in the other class recently said "Miss, you should do that thing where teachers go on TV and teach difficult kids. I'd definitely watch you." I thought this was quite a big compliment, so I made the mistake of asking why. "Oh because you're really funny when you're cross".  Ah. That swiftly deflated my ego!*

Laughing at someone else is easy, but laughing at yourself takes real character. Even as adults, not everyone can do it. I have recently realised that some of the friends and family I admire most are people who can laugh at themselves and don't take themselves too seriously.


I'm pleased to say that most of my y11s seem to have this character trait. One of the most able students that I teach (and one of the most confident) stared at a distance time graph recently and shouted across the room "Miss this scale is all wrong. It makes no sense. It goes one thousand, one thousand and thirty, one thousand one hundred, one thousand one hundred and thirty. What is it doing?" Rather than give her the answer, I just burst out laughing. "You'll find it funny when you realised what you've done" I said. "Read the question again" (It was a distance time graph, so the scale actually read 10.00, 10.30, 11.00, 11.30). Similarly, in the other y11 class I asked the girls what the letter D stood for in 2D and 3D. "I know!" shouted one student "Dime... Dim..... Dementia?" To which I burst out laughing as well (along with the rest of the class). Again, in a great show of character, she took it on the chin and laughed along with the others.

We ask our students to cope with criticism every day. They are constantly being told how to improve their work, or being asked to correct their mistakes and think about which topics they need to revise. It can't be easy. In my first term doing a history degree at Oxford I felt completely out of my depth and I knew I was handing in rubbish work. I was so embarrassed that I couldn't bear to read the pages of comments my tutor wrote on every essay. If I had done, I would probably have improved much more quickly. As it was, it took about 3 months before a different tutor took me to task and verbally went through how I could make my writing better. She described the next week's essay as "a transformation".

By encouraging students to laugh at themselves when they have made a mistake, we can help them see that making mistakes is part of learning. But to have that sort of atmosphere in the classroom, we need to let them laugh at us too. Using humour in the classroom is a risky strategy, but I think that when it pays off, it's hugely worthwhile.

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* To re-assure readers that I'm not a complete idiot in the classroom, I am hardly ever genuinely "cross" with this class, because they are really nice. Instead, I tend to say things like "if you haven't brought your calculator I'm going to give you a dirty look" and I pull a face at them. 

Easter Egg Box Project

I don't remember a huge amount about maths lessons when I was at school. I remember enjoying the SMP system in year 7 where you worked through lots of little books and essentially taught yourself. I really liked that. I didn't like the GCSE coursework where you had to count words in sentences and then work out the standard deviation of the sentence lengths. As a lover of literature I despaired to see To Kill A Mockingbird reduced to such soul-destroying analysis.

However, some lessons did capture my imagination and I remember particularly enjoying a series of lessons where we had to design an easter egg box. Luckily for me, I was allowed to work with my hugely talented best friend who was both a mathematical high achiever and ridiculously creative. She came up with the idea of designing a net that looked like a hen's head.

It was pretty impressive. It consisted of an octagonal prism and a cone all in one net, which we decorated to look like a hen's head and beak. I've searched on the internet for something similar and this is the closest image I can get to it, but it doesn't really do it justice.......

So I wonder what our y7s and y8s will come up with when we give them the same project in a week or so's time.

Here are the resources on the TES: http://www.tes.co.uk/teaching-resource/Design-Your-Own-Easter-Egg-Box-Project-6323990/

If you are looking for a project to do before easter, I think it should be a good one. It wasn't difficult to put together and so far I think it's ticking all the boxes (ho, ho! I love a good pun)

Which boxes has it ticked? Well it......

*hasn't taken long to plan
*helps to deliver quite a lot of national curriculum content
*allows students to be creative
*has a cross-curricular element
*gives us the chance to assess objectives without testing students to death
*shows how maths applies to real life situations
*AND is open-ended enough for all students from level 3 to level 8.

The resources on the TES include a powerpoint  and a student assessment sheet. I haven't uploaded the nets that we are going to use because we've taken most of them from www.senteacher.org. We also drew some ourselves on sqaured paper, so that the level 2/3 students can count squares.

If we get any particularly impressive designs, I'll post them up on the blog too.

darts project resources

A quick update! Here are the darts project resources.

http://www.tes.co.uk/teaching-resource/Darts-Project-number-and-geometry-project-6323154/event/22/

Enjoy.

Codebreaking resources

The resources for this lesson

http://www.guardian.co.uk/teacher-network/teacher-blog/2013/mar/04/codebreaking-second-world-war-maths-history

Are available here:

http://www.tes.co.uk/teaching-resource/WW2-cross-curricular-codebreaking-project-6323054/requestAction/add//

twitter account

Hellooo lovely blog readers.

 I've had more people asking about resources. A good way to contact me is via twitter @chk_ing
If you follow me - I follow back, then you can send a direct message.

: )

Where To Find The Teaching Resources

Hi everyone,

I've recently had some requests to send people some of the resources I've been blogging about, especially the darts resources and the codes resources. I'm going to put them up on the TES and put a link to my profile on the TES on here.

Have another look at the blog in the next couple of days and the links should be up by then.

:)

The mathematical magpie

Prime Minister For A Day

I like maths because I enjoy solving problems. I like the feeling of challenge, the sense of intellectual stimulation, the satisfaction of getting the right answer. I particularly love that feeling you get when you're in the flow. Do you know what I mean? The feeling that time no longer matters, where distractions cease to distract, where you find yourself in an almost trance-like state, entirely concentrating on the task in hand.

Perhaps there are maths teachers out there who can induce a similar atmosphere in their classrooms. Maybe. Maybe their students get in "the flow" when faced with solving quadratic equations or using circle theorems. Maybe. Just maybe.

I'm certainly not one of those teachers. Sometimes my students are happy to get stuck in to a puzzle (re-arranging difficult formulae with y10 went down better than I expected) but too much maths without a context usually turns them off.

So I jumped at the chance when a colleague of mine suggested having a "teacher mash-up" where we would team teach my y9 maths class and give them a politics lesson with a bit of maths thrown in. He had a resource called "Prime Minister for A Day" where you are given a list of govenrment run programmes and £500 million to spend of them. As a politics taster lesson it's already got a bit of numeracy in there because the students have to add and subtract large numbers, but we felt there could be more mathematics involved if we scratched the surface.

We started by putting a more contemporaneous spin on things by giving the y9s the same list and telling them they had to cut 4.25 billion of spending. This meant cutting approximately 75% of the programmes on the list. We then gave them some pie charts represting opinion poll data from different groups of people. I created the pie charts and had a go at exaggerating the opinions of differnet groups of people such as pensioners, young mothers, guardian readers, business people, daily mail readers and 11-17 year olds.

We talked to the students about sampling and opinion poll data. They recapped what they had recently learned in their data handling project about stratified sampling and how that could give a more accurate picture of the views of the whole country. We talked about what the number 4.25 billion actually looks like (and eventually got it right after I messed it up the first time!). They discussed the huge numbers involved in government spending.

The lesson was great fun and my colleague delivered it brilliantly, but for me the best moments came when I realised how much my sutdents already knew. Eariler in the year we had done a project called "money matters" where they looked at wages, salaries, rent and bills. I'd given them articles from BBC news about average salaries and the difference between high and low earners and the students had clearly taken it on board. Near the beginning of the lesson they discussed the taxation system and whether rich people should pay more. They gave an impressively accurate figure for the average salary (£26,000). They had a discussion about what percentage of the population might be considered rich and made the point that the top 10% of earners are quite spread out. They knew that the super-rich didn't constutite 10% of the population.

At the end of the lesson they hadn't ticked off any new objectives in the national curriculum. But they had furthered their understanding of government finances, sampling techniques and large numbers. AND they had practiced debating, empathy, and rational decision making. All in all, a worthwhile lesson.

Bullseye! The mathematics of the dartboard....

Playing darts is a great way to help kids improve their numeracy skills - its fun, fast paced, and helps them improve their addition, subtraction and multiplication skills.
But the dartboard has a lot more to offer in terms of mathematics. Our department recently used it to both teach and assess a range of different skills.. and have a bit of fun in the process.

The project
At the beginning of this school year we ran a project with all of y7 and y8 about the mathematics of the dartboard. We began by getting all of them (yes EVERY SINGLE ONE - and we have got some very weak students) to construct their own dartboard using a ruler, compass and protractor. It took some of them several attempts, but in the end they produced some great work and improved their construction skills.

Then we asked them to complete a series of levelled challenges. They ranged from level 3 to level 7 and incoporated basic arithmetic skills, problem solving with numbers, reasoning about multiples, and thinking about how to approach a long task systematically.

Here are some example challenge cards

I really enjoyed doing this project with my classes and I'm looking forward to running it again next year with a few improvements. A key development for me came through the input of an English teacher in SLT who teaches some KS3 maths. She put together an assessment grid for us which enabled us to break the project down into a list of very specific skills and assess each student on every skill.

The fun stuff
The project itself was quite enjoyable to do and lots of students really enjoyed creating their own dartboards, but it really came into its own when we set up an inter-house competition linked to the project.
We invited all of y7 and y8 to take part and had about 100 students in total in the sportshall. We lined them up in their house groups infront of 7 different magnetic dartboards (one for each house). At the word GO! they began their team game of 501 down.

Here's how it worked. Each player had 3 darts. They threw their darts and worked out their total, then took away their total from the running total of their team. The next player could only take their shot when the previous player had worked out the correct answer. Maths teachers refereed each team and checked all their calculations.

It was very fast paced and the kids loved it. They were encouraging each other to use different addition and subtraction strategies "break the number down into tens and units", "take away the hundred first!" and generally having a great time doing mental arithmetic. Who would have thought it?

I've since had several y7 students ask me when the next maths related competition will be. Suggestions anyone?

Real Life Maths: Circle Theorems and Ship Navigation

Eureka! I have just found a truly shiny thing. A prized possession in my magpie collection of shiny resources.

A video that explains why CIRCLE THEOREMS are useful.


Hooray! I love circle theorems. I love the way you have to visualise shapes inside a complex diagram, but once you've seen the visual links, the actual calculations are not hard at all. They make for lots of lovely "ohhhh, I get it" moments.

The only problem I have with teaching circle theorems is that I can never think of a practical use for them. But I've just found one: Calculating the distance of the visible horizon.

Here is the link: http://www.youtube.com/watch?v=VRvvtOAHDG0&feature=player_embedded

Its particularly good because the nice young man in the video explains why maths is so important to his job first, then gives you a lovely clear example of how to use the circle theorem that the angle between the tangent and a radius is 90 degrees.

The only problem is that I just taught that topic to y11 today. I wish I'd found it yesterday!

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