The challenges of promoting a growth mindset

 

Carole Dweck’s growth mindset theory is powerful, compelling and liberating. I came across it in my first couple of weeks of teacher training during the Teach First summer institute and I have been convinced by it ever since.

To summarise, Dweck's research sorts students into two categories: those with a fixed mindset and those with a growth mindset. Students with a fixed mindset believe that their intelligence and skills are limited by their natural ability. They aim to look smart and they fear failure because they think it will make them look dumb. They don’t want to take risks and they quickly become anxious or bored if they think that they are not naturally good at a specific subject.  On the other hand, students with a growth mindset believe that their skills and intelligence can grow and develop. They embrace challenges because they understand that challenges help them learn. They are not particularly concerned about looking smart or accomplished; they are more interested in learning and improving their skills. They react calmly to setbacks and reflect on what they can do to improve next time.

Since her initial research, Dweck has conducted multiple studies into the impact of these different mindsets and shown time and again that students with a growth mindset (and students who are specifically taught about the concept of a growth mindset), are more resilient and more likely to be successful than students with a fixed mindset.

The theory is powerful, compelling and liberating because it tells us that our intelligence and capabilities are not pre-determined. Our actions, our choices, our effort is what makes the difference to our attainment and skills. We are not stuck as either “smart” or “dumb”; we are what we make of ourselves.

At this point, some people become sceptical. This is a good thing. A healthy dose of scepticism is often very useful. Most teachers will be able to pinpoint a student who seems to have a natural aptitude for their subject and another student who faces significant struggles in even the most basic tasks. This would suggest that the fixed mindset camp have some valid points. Isn’t it the case that some people are just naturally good at things?

Well I don’t think growth mindset theorists argue that everyone is born with identical traits or that everyone can  achieve identical outcomes. The theory is more about how malleable the brain is, and about not putting ceilings on attainment.

 

I like to frame the discussion about “natural ability” by considering some people as “high starters”. They may have certain physical or mental advantages and they may make faster progress. But high starters also need a growth mindset – if they don’t practice, reflect on critical feedback, embrace challenges and take risks, they won’t continue to improve. Indeed, it is sometimes the most able students who suffer most from a fixed mindset. If they are used to finding things easy, when a challenge eventually arises, they’re not prepared to deal with it.   

And just because someone isn’t a high starter, it doesn’t mean that they won’t make accelerated progress later on in their development. After all, Einstein wasn’t able to speak until he was 4. Do we think of him as a “slow learner” and therefore someone who was “dumb”? No, his name is a byword for intrinsic genius, which is ironic considering that the man himself understood that success comes about through hard work, taking risks and making mistakes.

As an educator, I feel that Dweck’s growth mindset theories are at their most powerful when also coupled with Vygotsky’s theory of the Zone of Proximal Development. I’m not a psychologist, and I recognise that Vygotsky’s work is quite old now (1970s), but his ideas ring true with all my experiences as a practicing maths teacher and I hope that I’m not wildly outdated in setting store by his theory.

Vygotsky explained the “Zone of Proximal Development” as being  “the distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers”. In other words, students can learn new things with the help of others but they need to be related to skills and attributes that they already have.

As a maths teacher, this theory is fundamental in informing my planning. If you try to teach something that is beyond the students’ zone of proximal development, they are not able to process the new concepts and they often either panic or blindly follow a set of steps with no real understanding of what they are doing. This really hit home when I taught a relatively high ability year 11 class who were following a modular maths course. They could do complicated things like solve quadratic equations by completing the square, but they hadn’t done any shape or space work for two years. Consequently, their visualisation skills were very weak and at the start of y11 we had to go back to counting squares to find the area of a rectangle before they stood any chance of conquering more complex formulae. We had to practice estimating the size of angles for a whole lesson before we could even begin to start calculating them. (Many students couldn’t use a protractor and would measure an acute angle as being 150⁰ without any understanding that they had made a mistake). Time constraints meant we then had to rush, and a lesson on circle theorems made some of them nearly hysterical.

The modular course cemented a fixed mindset viewpoint in most of those students. I started year 11 with work that should not have been taxing for them, but because they didn’t have good visualisation skills, the work was beyond their zone of proximal development and they ended up feeling inadequate. I built a good relationship with the class and by the end of the year they achieved very good grades, but the process was exhausting. They relied heavily on me and had very little self belief. The thank you cards I received at the end of the year were very telling. “Thanks for making maths bearable! “ one of the said. “We couldn’t have done it without you!” exclaimed another.

In contrast, my exam class from this November told me how much they enjoyed the challenges of maths, how they wanted to take extra algebra courses before doing A level maths.  One girl simply wrote: “Thanks miss. You made us believe we could do anything”.

So here is the challenge of promoting growth mindset for teachers. If we tell students that hard work, effort and reflection will lead to progress, we need to make sure our curriculums are designed to support this. If we throw students in at the deep end without proper preparation, they are likely to fail and not learn much from it. Conversely, if we protect them from failure and never give them a true challenge, they cannot stretch to their full potential and they won’t know how to deal with challenges when they inevitably come along.

In truth, as with so many aspects of teaching, building a growth mindset in students is going to be a balancing act for all of us.

 

 

 

 

 

 

Suprise take-over by year 7!

This post is about how great students can be and how important it is to consider the culture you are creating with your classes, day in day out........

 

On Friday I was very busy. It had been parents evening the night before so I hadn’t had any time after school to prepare for the day ahead. We also had a very important visitor to our department – a new teacher from South Africa who will be joining us next year – and I wanted to spend as much time with her as I could. So when it came to period 3, year 7, I had a vague idea of what I was going to do, but I hadn’t put together a set of resources like I usually do.

I can’t say I was panicked – I’m sure I would have come up with something on the spot, but what happened when I arrived at my classroom really made my day.

 The students had got there before me and it was raining so I let them straight in before setting anything up. Whilst I was busy with the logistics of the beginning of a lesson: writing the title and objectives on the board, logging in to the computer, looking for the equipment I needed, getting students to hand books out, reassuring some of the anxious ones that the homework wasn’t due for today etc, etc, two of the girls in the class came up to me and said they had planned a starter for me and they asked if they could do it that lesson.

Of course I said yes and watched as they handed out bingo grids that they’d painstakingly drawn out by hand. They got the whole class to listen to them and started pulling out carefully folded pieces of paper from a tin. Each piece had a calculation on it and the answers were on the grids that had been handed out.

I stood back, finished organising myself and got the resources ready for the rest of the lesson. The class were in deep concentration as they tried to figure out the answer for each calculation before the next one came along. When eventually someone shouted “BINGO!” a small prize was handed out (I think it was a bracelet) and the two girls who had been in charge were given a round of applause.

As you can imagine, I was quite a happy teacher! Those girls had not only given me chance to get the rest of the lesson organised, they’d put together a really effective starter that went down very well with the rest of the class.

Now for the all important context :  I have been allowing year 7s to run starters since just after Christmas, so this did not come entirely out of the blue. The main difference was that on all the other occasions I helped the students to design the starter and I told them exactly when they could do it. As this is the first week back after Easter, I hadn’t got round to meeting up with any of the students to plan a starter together, but I was hugely impressed that these two girls had decided to make one themselves.

Their efforts helped me realise two things. Firstly I realised that my idea of getting y7 to run starters now has the potential to save me some time (hooray!!). (It was more time-consuming previously because I met with students outside of lesson time). Secondly, it reinforced my opinion that getting students to be outstanding learners is not about how they perform in one off lessons: it is about the culture that is created in the classroom. Do they feel that they can take the initiative? Do they think they can act in a leadership role? Do they worry about making mistakes or do they just get stuck in and have a go? Do they work individually and competitively or do they seek out opportunities to help each other and work collaboratively?

In all honesty, my year 7 class have a long way to go before they become outstanding learners. They still worry too much and they are still learning how to help themselves when they get stuck. But Friday’s lesson gave me lots of hope for the future. I wonder what they'll get up to next week!

 

You mean... you have an arts degree? *pulls horrified face*

Note: For a powerful argument about why we should stop drawing dividing lines between arts and sciences read this summary of the views of Eric Schmidt (chairman of google).  http://www.theguardian.com/technology/2011/aug/26/eric-schmidt-chairman-google-education

If you’ve had a look through this blog before, you might have read the “about me” section at the side where I explain that I did a history degree before going on to become a maths teacher. This information mildly interests some people, worries others, and sends a select bunch into a heightened state of moral outrage.

This last group – the righteously indignant - are of course the most entertaining, and I’ve learned to develop a thick skin when they air their short-sighted opinions. Upon hearing the news that I had a history degree, one man abruptly stopped the perfectly pleasant conversation we were having and started spluttering “I wouldn’t let you anywhere near children” before walking off.  Another person reacted by saying that I could never be taken seriously as a professional and surely I should be teaching primary school children.

I perfectly understand that most people are curious about the transition and they have legitimate questions about how I am able to teach secondary level maths. If the boot was on the other foot and someone told me they had a maths degree but they were going to teach history, I’d also find it strange.  I’d want to know 1) how they intended to improve their subject knowledge and 2) what their motivation was.

So I’m taking the opportunity to answer these two questions about myself. I’ve been meaning to write this post for a while not just because I want to defend my professional integrity (although clearly I do – so apologies if this post occasionally sounds defensive!) but also because I know there are other people out there who are thinking about making the jump from an arts degree to teaching maths.  I want those people to know that if they have the right attitude, they should ignore the doubters and go for it. Maths is fun!!

The question about subject knowledge is always the one that seems to cause most concern and I can understand why. Of course you need to know what you are talking about. But if I could get one point across in this whole debate I would emphasise that teachers can learn things too. We don’t pop out of university as though we are plastic dolls leaving a production line, pre-programmed with certain features, only capable of parroting what our lecturers taught us. I started my maths-teacher training with A level maths and AS level further maths and a desire to learn more about the subject than I’d ever known at school. I bought books, read articles, watched videos on you tube, and opened my eyes and ears to things I hadn’t heard of before. When I decided that I wanted to improve my subject knowledge so I could teach A level maths, I enrolled on an Open University course (M208) which was 2^nd year maths degree standard. It covered things like group theory, linear algebra and analysis, and I spent a year studying the 6 modules (which were supposed to be 600 hours worth of work). I passed with distinction.

For me, there have certainly been benefits to this approach. My lack of a maths degree means that improving my subject knowledge is a constant goal, so I’m always on the lookout to learn something new. I don’t feel like the finished article and I never will, so I’m not going to be complacent.  My AS and GCSE classes have also benefitted from the fact that I took a maths exam last summer, because I’ve been able to talk to them about my revision strategies and I’ve been able to empathise with the feeling that some things don’t “click” straight away.  I think it did me a lot of good to learn challenging things and put myself in the same position as my students, especially with the pressure of an exam. Last year, my OU exam was on the same day as the GCSE maths exam and my year 11 class told me that they really appreciated the way I had treated them during the revision period. “You get us” said one girl, “you don’t put us under too much pressure”. In that class, every student who sat their GCSE exam that summer met or exceeded their target grade. I’m biased of course, but I think that suggests that I know what I’m doing.

The second question about what motivated me to go from history to maths is, I think, a more interesting one, but I don’t get asked it as often. I’m going to give a longer (and hopefully more eloquent!) answer here than I ever manage to achieve in conversation.  Basically, I loved studying history at university because history is such as vast and varied subject and it relates to everything. Every country, every person, every academic subject, every religion has a history and (knowingly or unknowingly) we are all shaped by those histories. I also loved studying history because it’s about finding out how different people think. The Puritan idea of predestination (where they believe that some people are destined for eternal salvation, while others doomed to eternal damnation and we do not have the power to change our own path) always struck me as horrifying and I was fascinated by why so many people embraced this idea and how it affected their society. There’s a great article about it all here

http://nationalhumanitiescenter.org/tserve/eighteen/ekeyinfo/puritan.htm)

In teaching, I see similarities with the fixed vs growth mindset debate, where some people are certain that intelligence is fixed and cannot be altered (the “predestination” view) whereas others think that with effort and the right kind of feedback they can improve (the “free will” view).

How is maths similar? Well, maths is also a vast and varied subject that can be related to everything else. We can appreciate art, nature, and music, more deeply because of mathematics. We have a greater understanding of politics and economics because of mathematics. In lessons, I’m constantly looking for links between maths and other subjects and the opportunities are boundless. I love bringing context into lessons and I love the creativity and freedom that comes with it. There is simply so much choice in how you can deliver each topic – just as there was so much choice for me as an undergraduate when I realised that I could pick any time period I wanted from the Vikings onwards.

Also, every decent maths teacher knows that teaching maths is about understanding how different people think. Some students need to see the bigger picture first – they need context, they need a reason for doing things, they need to know what the end result will be. Others are happy to discover things for themselves and they enjoy the process as much as the outcome. Some are comfortable thinking in an abstract way; others need a more concrete approach. Many students impose their own rules which don’t quite work and we need to unpick what they are doing and figure out what their underlying thinking is.  I like this challenge of figuring out how people think. Studying history gave me a good grounding in understanding that not everyone sees the world in the same way.

In truth, I chose to teach maths rather than history because Teach First were recruiting maths teachers rather than history teachers. At the time I thought I’d only teach for a few years before doing something else and maths had always been my favourite subject at school, so I thought I’d give it a go. Five and a half years later, as I get ready to take on the role of Head of Department next year, I can see that the diversity and intellectual challenge I loved in my history degree has been equalled by the diversity and intellectual challenge of planning and delivering decent maths lessons for my many and varied students.

I’d like to finish by arguing that, rather than being afraid of people who cross the invisible arts/science divide, more of us should come out and celebrate it. Eric Schmidt is completely right to point out that great thinkers have often been polymaths; especially those of the Victorian era. Steve Jobs also once said: "The Macintosh turned out so well because the people working on it were musicians, artists, poets and historians – who also happened to be excellent computer scientists". I find it sad that more people don’t embrace this viewpoint. In fact, it seems to me that people within education are often the ones most desperate to sort everyone into either the luvvy-artsy box or the nerdy-sciencey box. Surely we should be the ones arguing against this unhelpful divide?

All I can say is, if anyone tries to put me in a box, I’ll soon be fighting my way out.

If only I knew then what I know now: behaviour management for friendly teachers

I’ve been musing recently on behaviour management.  After five and a half years in the classroom, I’ve gone from being a nervous and naïve 21 year old, with a very limited set of behaviour management strategies, to a much more confident practitioner who’s (usually!) able to create a sustain a positive and welcoming atmosphere in the classroom. I’m not for a minute suggesting that I always get it right or that I don’t have any issues.... the phrase “pride comes before a fall” springs to mind here... but I never get that feeling of dread that I used to have when facing “that” class or “that” student.

So I suppose this post is really addressed to my younger self. To the person who sometimes questioned whether she would ever be able to succeed in teaching. To the person who sometimes assumed that behaviour management would always be a battle because she wasn’t “scary” enough. And also to the person who disliked the idea of the “us vs. them” culture, which can build up between teachers and students. I’m not trying to tell anyone else what to do – you need to find what works for you - but if you’re new to the profession, it might help to hear what works for someone else.

Having reflected on it all this evening, I’ve decided that it boils down to three key things

1)      Lesson planning

2)      Building relationships

3)      Body language and tone of voice

I suppose I could add a fourth element: rewards and sanctions. I know rewards are important to recognise student achievement and reinforce positive attitudes and I know that sanctions are sometimes vital to help students understand that there are consequences to their actions. But neither rewards nor sanctions will act as a magic wand. They just reinforce other things you are doing. On their own, they are hollow tools. Too many rewards will make you seem like a push-over, too many sanctions will make you seem vindictive.

So back to the things that do matter. Well, it’s no accident that lesson planning is at the top of the list. Students need to be engaged by interesting work that is pitched at the right level and undertaken at the right pace. In maths, I always find that they respond best to really clear explanations and precise instructions. If they understand the topic, they’re much more likely to engage. If you confuse them, they lose trust in you and they lose faith in their own ability. Similarly, pace is vital because if you go too fast they will get lost, but if you go too slowly they’ll feel bored and patronised. It’s not easy! But if you are struggling with a class, focussing on lesson planning is often a good place to start. Can you shorten your explanations? Can you scaffold the work? Can you give them small successes so they know they are making progress? Can you make the tasks more engaging?

Second on the list is building relationships. I can’t stress enough how important this is. Above all, you need to give students the message that you are on their side and that everything you do – even giving them sanctions – is designed to help them be the best they can be. I try to make this clear as often as possible. So when setting detentions, I make it very clear that this is to help the student catch up and make progress on work they should have completed. The message doesn’t always get through, but it’s hard to argue with! Even better – try to show students that you actually like them. Catch them being good, focus on the positive things they do, and enjoy their quirks. Kids can really make you laugh if you let them. In fact, if you play to their strengths, the characters in your class can often become a real asset. 

Body language and tone of voice. This is partly about reminding yourself that you are the adult, the paid professional, and they are a child in compulsory education, where there isn’t a great deal of choice or freedom. If they are wound up, you need to make an extra effort to stay calm. If they are shouting, you need to speak either quietly or at normal volume (although be careful with speaking too quietly because this can really infuriate some students). Never mirror their negative body language or tone of voice; it will just exacerbate the situation.  The best thing you can do is calm them and reassure them so that you help them to make the right choices in their behaviour. And do bear in mind that the right choice can sometimes be time out of the lesson for stressed out students. 

When dealing with a whole class, if you want their attention, make sure that you stand still facing the group and don’t move about. I find it useful to stand at the front in the middle and look around the room saying things like “girls at the back, time to focus now” or name a specific student saying things like “Emily, thank you”. If you ask them to “put pens down and listen” whilst at the same time picking up a worksheet from your desk, or writing something on the board, you are subconsciously giving the message that it isn’t really time to stop talking – you’re still faffing about, so they can carry on too. When you are ready to start talking to the class, make sure that everyone is listening and calmly insist on silence. If anyone starts to talk I say things like “we need everyone to listen now” or “this is an explanation part of the lesson – everyone needs to be able to focus on the instructions”.

In general, if I was able to say anything to my 21 year old self, I would say that you shouldn’t expect students to get their behaviour right every time, so when they do get it wrong, you don’t need to panic, you just need to support them to help them deal with situations more positively in the future. Misbehaviour isn’t a direct challenge to your authority – it comes from a variety of different root causes. It’s sometimes to do with the nature of the work in the lesson, maybe due to lack of confidence or confusion about that particular topic; and sometimes it’s to do with personal issues that you might not be able to detect. If you have got students with personal issues, they don’t need your sympathy. Far from it. They really need you to have high expectations of them. But you also need to be willing to listen to them: to the spoken and unspoken messages they are giving. Really effective behaviour managers are teachers who can decode those unspoken messages and know how to deal with them. The best way to do it, is to make sure your students know you're on their side.

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.