What you learn in Mathematics classes...

Bryanston's Head of Mathematics, Alex Hartley, explains why Maths is more relevant outside the classroom than you might think.

As interesting and enjoyable as it is to use a pair of compasses to construct the perpendicular bisector of a straight line, I do confess that pupils have asked me when exactly they will use this skill in real life. Further, I will even concede that my usual response – that it will form part of their iGCSE examinations – is, in the language of youngsters today, a bit lame. So, in this post I will attempt to explain more generally what our pupils learn through studying Mathematics, and whether or not there is more to it than just getting to the right answer.

With a new class, my first lesson of the academic year in September might well involve what I call the Handshakes Investigation. Working in groups, we establish, by getting out of our seats and getting involved, how many handshakes might take place when, say, three, or four, or another number of people meet for the first time. Building up a table of results for various numbers of people, we might seek to explain the patterns that are evident, refining our thoughts to form an algebraic equation and using this to test and predict future results. There’s a lot in there; elements of teamwork, of identifying patterns in numbers, and predicting and testing future results. At a more advanced level, pupils are generalising a particular rule and hence using algebra to construct a simple yet elegant and powerful formula that can be used not just in the cases already discussed, but many more besides. This investigation is a journey for each pupil and there’s a lot more to it than simply getting to the right answer. It also makes for a richer experience than simply working through problems from a textbook, although there is, of course, a time and a place for that and practice does indeed make perfect. Looking towards a real-life application, it is analogous to the problem of asking how many matches take place in a league in which a certain number of teams all play each other*.

Change in the world of mathematics teaching is approaching, with both the British curriculum and the IB offering new courses within the next few years. Following the Chancellor’s encouragement in his Autumn Statement (2017), we’ve offered Core Maths as an accessible course in the sixth form. Core Maths is entirely based around the practical applications of maths – mainly statistical and financial – that our pupils are likely to need both in their personal and professional lives, regardless of the career choices they make. We’re optimistic that our first cohort of pupils, who are just completing A3 (Year 12), will earn a good set of grades which will contribute to their overall accumulation of UCAS points and may enhance their choices at university. The IB curriculum will soon change too, and mathematics will be split into two subjects; Maths Analysis (which will contain a great deal of algebra and calculus, in common with A level courses), and Maths Applications (which will focus upon the uses of maths in real-life).

What would I do differently, if it were up to me to design the curriculum? Three things. First of all, I’d make iGCSE Mathematics, and particularly the foundation tier, focus more upon the applications of mathematics to real life. More questions about, for example, personal finance and perhaps we’d cope without a pair of compasses. Secondly, I’d insist that everybody studied mathematics at some level in the sixth form (just like in the IB) and finally, I’d set more questions that drew in a range of different skills, because that would encourage pupils to better understand the rich connections between each area of mathematics that they study.

So, there’s a lot to enjoy and savour in mathematics lessons; there is of course a range of skills and techniques which do need to be explicitly taught and practised to ensure fluency. But solving problems, talking things through, and creating and testing ideas is all in there too – and this is true for all pupils, no matter what their prior attainment or ability in Mathematics.



* h = ½ x n x (n-1)  is the formula, where h is the number of handshakes, and n the number of people involved. Relating this to sports fixtures, 20 Premier League teams could play each other in ½ of 20 x 19 = 190 matches, but overall 380 matches are played each season because teams meet both home and away.

You can follow Bryanston Mathematics on Twitter here @BryanstonMaths.

Balancing act

This week Sarah Thomas reflects on the importance of balance - a topic she covered on Speech Day last weekend.

At Speech Day this year I spoke of balance and how to keep it in this turbulent and unpredictable world. I even made reference to Weebles. For those of you who were not children of the 1970s, Weebles were egg-shaped toys, weighted so that, if you pushed them over, they always bounced back upright. “Weebles wobble,” the advert ran, “but they don’t fall down.” I think Weebles could be the icon for these turbulent times. 

A year and a half ago would we have believed we would be coming out of Europe? Seeing scenes of terrorism and heroism again on the streets of Manchester and London? Enduring another inconclusive General Election? And let’s try not to mention President Trump. So how are we to deal with all this, in our own families and in school? How do we aim for our pupils to stay balanced?

At Bryanston we offer the widest range of opportunities we can. We teach creatively and we offer the right level of encouragement and guidance, both inside and outside the classroom. We don’t expect anyone, child or adult, to be perfect. Indeed, to expect that creates a toxic effect for any child, however talented. We talk about our own wellbeing and are honest about our need for support, whether from exercise or music, or meditation, or God. Which reminds me of a Boris Johnson story I heard recently. In an interview about his Christian faith, he described it as “like tuning in to Virgin Radio

whilst driving through the Chilterns. Sometimes the signal is strong; sometimes you lose it.” A really lovely metaphor. We encourage our pupils to keep tuning in to a support system which works for them, and we let them know that’s what we, in our imperfect way, do for ourselves.

A key way we stay balanced at Bryanston is through positivity and this comes, in part, through engagement in good times. It is important to celebrate achievement and good times, as we did at Speech Day last weekend, and indeed do throughout the year. 

But finding balance isn’t easy. And it’s different for everyone. You can’t necessarily teach it in classrooms. You can’t measure it in exams. So it’s not something that many schools are prepared to shout about. Certainly not those which boast exclusively about their academic achievements. Or those which fail to recognise the connection between unreasonable academic pressure and mental health issues. Or those which shy away from the truth that so much of our educational landscape was designed to meet 20th- century challenges. In the future, our young people will need balance as

much as they will need imagination; creativity; perspective; the ability to take a step back, to take a wider view, to make links and connections; to have good ideas; to make difficult and brave decisions. Show me how each A level can test those skills. Yet a school which is not passionate about these things is not, in my view, doing its job.

As we wish our departing pupils farewell and look forward to welcoming a new intake in September, I hope that each Bryanstonian gets what they want from life and, above all, that they channel their own Weeble and find their individual balance.

You can see more photos from Speech Day here.

Turbulent times

This week we welcome our Deputy Head (Academic), Dr David James, who explains why we are hosting our inaugural Education Summit later this year.

We live in turbulent times. Every day seems to carry a strapline of ‘what fresh hell is this?’ And the politicians, who are charged by the public to provide answers, seem at best stunned into inaction by the speed of events or, worse, actively conniving to make things more chaotic. WB Yeats’s lines from The Second Coming seem especially apposite at this moment in time:

The best lack all conviction, while the worst
Are full of passionate intensity.

It is easy to see how prosaic matters, such as education, slip down the Government’s To Do list. But I have argued elsewhere that, for schools, there is only one thing worse than a busy, conviction-led Secretary of State at the Department for Education, and that is not having one. And there is no doubt that ever since Michael Gove was defenestrated by a Prime Minister who wanted to win the last election, schools occupy fewer headlines, and probably take up less discussion time in cabinet, than they used to.

This can lead to drift, and drift in turn can lead to uncertainty, which in turn can store up problems for society in the future, because the issues affecting schools (such as academic underachievement or poor behaviour) are rarely contained behind the school gate. There are worrying trends developing in the maintained sector: it is estimated that four out of ten newly qualified teachers leave the profession within their first year of teaching; at the other end of the career ladder there is a retention crisis, with record numbers of headteachers stepping down, or taking early retirement. With so much talk about the crisis in the NHS this winter it is understandable that the challenges facing schools are overlooked, but they are there, and this is something that the National Funding Formula seems to be exacerbating, with some headteachers warning of a ‘bleak’ future for schools.

You will no doubt have noticed that I have decided not to discuss new GCSEs, with their still-to-be understood new grading system, as well as the death of AS examinations and the new, more rigorous A level with high-stakes terminal examinations that nobody, including our more selective universities, has total faith in.

It would be easy to be cynical. But of course there is much good happening in schools: students continue to excel beyond their own expectations, and regardless of what happens to the courses they study, or how they are assessed, thousands of inspiring, committed teachers will continue to do their best for the young people they teach. Public trust in teachers is second only to doctors (and considerably higher than politicians and estate agents, which is reassuring). To paraphrase George Eliot, it is because of the ‘unhistoric acts’ that teachers do every day that the ‘growing good of the world’ is added to. Or I like to think so anyway.

In such a climate we felt it appropriate to run an event that addressed some of the major issues facing schools today. And so, on 7 June, Bryanston is hosting its first Education Summit, which will bring together some of the most influential and knowledgeable voices in education today. Among those speaking is Lucy Crehan, whose book, Cleverlands, has been rightly praised as providing us with a startlingly clear insight into how teachers in other national systems achieve outstanding results with their students. It has been described as ‘audacious’, but mandatory reading for all those designing future education policy. Other contributors include Professor Dylan Wiliam, a seminal figure in education, consulted by leading companies, universities, and governments. There are few who know more about teaching than Dylan. And he is joined by Professor AC Grayling, one of this country’s leading intellectuals and academics. Toby Young and Claire Fox are also going to be asking difficult questions, and no doubt provoking strong responses. Other confirmed speakers, such as Ian Fordham, Microsoft’s Director of Education, will be focusing on the role of technology in the classroom; and others will be discussing the importance of partnerships to schools, and new developments in teaching and learning.

Why run an event like this, especially at the end of a tiring term? Because we believe that by bringing people together from across the education sector, to establish new connections, we can begin to find solutions to issues that affect everyone involved. It would be easier to not do this, to sit back and passively accept the slings and arrows hurled at us daily by opinion-formers and policy-makers, or to hunker down, and retreat into a bubble, hoping that the changes happening will sweep over us, leaving us untouched. Both approaches are unwise, especially as there are challenges and issues for all schools, including those like Bryanston. Both are also inimical to Bryanston’s ethos which actively promotes in its pupils an active engagement with the world around them. It is better to shape the debate than to be talked over and ignored.

This is not an event for teachers only: it is for everyone, including parents, who are interested in education today. Do join us, and take part in the debate.

For more information visit www.bryanston.co.uk/educationsummit.
More speakers will be confirmed nearer the time, and please do keep checking our website for further details, as well as following the summit on Twitter (@bryedusummit).

A2 Charity Weekend

This week we are delighted to welcome the Heads of School, Nancy and Sam, as guest bloggers. Alongside their team of prefects, they recently organised the annual A2 Charity Weekend, in which the entire year group worked together towards the common goal of raising funds for their chosen charity. At this year’s event pupils surpassed their fundraising target and you can read more about the weekend here. In their guest post the Heads of School explain why they chose PumpAid as their charity and what they learnt from organising the weekend.

Two weeks ago we led the A2 year group (year 13) in organising a fundraising event for a charity of our choice. This year we chose to support PumpAid, a charity based in London but which operates in Malawi. Our aim was to sponsor the building of a water pump for a village in rural Malawi.

Having done some research it really hit home how pressing the issue of access to clean water is. We had no idea the conditions that some people were living in, and indeed how far reaching the problem is. Water-borne diseases are currently the main contributor to child mortality in Malawi, so there is an obvious health impact caused by the lack of access to clean water. However, what we hadn’t appreciated was the additional social issues the problem creates. For example, the long distances that children, mostly young girls, have to walk every day to collect water is having an impact on their education, as they have less time to spend in school studying. Hopefully with the funds that we have raised we can stop this for around 240 people and provide a community with water for generations to come.

In terms of what we have learnt from the weekend itself, the experience has not only been incredibly humbling, it has also taught us a lot about organising charitable events like this. It was such a good thing to do and has really helped us to appreciate not only how lucky we are at Bryanston, but also how we can truly change other people’s lives through small events like these.

As part of the weekend a Bryanston pupil composed and performed a song especially for the event to support PumpAid. You can watch the video of it below.

The thinks you can think

“Think left and think right and think low and think high. Oh, the thinks you can think up if only you try”. 

Dr Seuss

Creativity is something you have to work at in a school because, according to a great many successfully active creative thinkers and doers, schools and the very process of growing up are pretty good at beating out the spark rather than fostering its subtle flames. Picasso famously observed that every child is an artist, the problem is staying an artist when you grow up. I think all parents would instinctively agree with what he says in terms of watching their own children’s self-confidence about expression when in primary school and how things change with the self-consciousness of adolescence.

It’s also a big ask to tell a child or adolescent “Be creative!” What does that even mean? Where do you start? I think it’s important therefore to build creative thinking and the opportunity for creative doing into all aspects of a school curriculum, wherever and whenever you can. I don’t pretend that this is always easy (being creative about the gerundive of obligation can defeat you on a damp Friday afternoon) but I do think it’s the critical aim of all teaching and learning. Open wide the windows and let in the air. To quote Vinegar Joe’s certainly very creative use of the gerundive of obligation, non illigitimis carborundum.

The advantages of retaining the childhood spark of creativity into self-conscious adolescence and then professional adulthood are, in my view, too obvious for words. I don’t see that these need rehearsing or defending (but if you do, look at anything Ken Robinson or Bill Gates say). The bit that I think matters and does need asserting loud and clear is that after a decade or more of measuring the pig (through league tables of schools, through examination and assessment change, et cetera…) we should have learned how arid and useless that activity is in terms of creating well-rounded, happy, successful, creative, contributive young men and women. And frankly I don’t think education has any other purpose than producing just that.

Time to stop treating children as widgets, figures, statistics. By all means ensure all children receive an equal opportunity to enrich their lives through learning. It’s about time we did. But define education as an active, creative, two-way engagement, not as some dead hand of what must be learned. Stop encouraging only a focus on core curriculum; stop telling children what they can’t do, what they are no good at.

“Think left and think right and think low and think high. Oh, the thinks you can think up if only you try”……

“Be who you are meant to be and you will set the world on fire!”

At the start of this new academic year these words of St Catherine of Siena, quoted by the Bishop of London when he married Prince William and Catherine in 2011, seem particularly apt. Like Catherine who is expecting her second child, the new school year is full of excitement and possibility, opportunity and dreams. And I have on various occasions used these words to focus our minds on what the real job of being in a school like Bryanston is all about.

Each year I speak to the new Ds (year 9) at the end of assembly on Monday of week 2 and give them some ‘top tips’ about settling in and making a success of a new school. One of the list is about being yourself. This week Peter Hardy, my irreplaceable deputy, and I spoke to the C year group (year 10) about the year ahead for them and I asked them which of those top tips had, as Ds, proved the most difficult to achieve over the course of the year. A particularly brave young man answered, “To be organised”. I was so pleased that being yourself had not proved a problem for this cohort of Bryanstonians and I hope it never will.

How do you find out who you are meant to be? How can we allow our young men and women to be themselves? It’s about offering a goodly amount of opportunity and encouraging engagement. It’s about making sure that individuals are understood and recognised and that each can contribute to the larger body of the house and then school. We want all our 682 individuals to feel that they belong: that they are recognised and valued. It’s no use, in my view, being an individual if you are also lonely. It’s about seeing where you fit in to something worthwhile. Are you going to be a supersonic runner? Or a fantastic friend? Or a genius Germanist? Thorold Coade (Headmaster from 1932 to 1959) believed that it didn’t matter what you chose, as long as you engaged with and contributed to the abundant life of the school.

I agree with him, not least because I found my niche when I discovered first Latin and then Greek, and then because I saw my own two daughters flourish at Bryanston in the hands of the Classics department and on the river as devoted rowers. Keep the curriculum wide and rich and offer an outstanding co-curriculum and we can at least get our pupils and children close to St Catherine’s rallying cry. For us as adults too it is no bad thing perhaps to remind ourselves, though long past adolescence and the school curriculum, of the imperative to be authentic and of using our full range of talents. To aim to keep on learning. To be who we are meant to be so we too can set the world on fire.

Not to do everything but to do something

‘Do all the good you can. By all the means you can. In all the ways you can. In all the places you can. At all the times you can. To all the people you can. As long as ever you can.’

John Wesley might seem an unlikely hero for a girl sent to a convent school as a small child but his famous saying is fantastically clear and keeps us straight. It would perhaps be easy otherwise to take refuge in that unpleasant First World phrase ‘charity fatigue’ as we watch the world from our comfortable armchair in Dorset. But thankfully Bryanston pupils are keen not to stand by. This term alone there has been the Nepal Fair (raising funds for Child Welfare Scheme and Right 4 Children whom we have supported for 12 years), followed by a Frugal Lunch for the children of Syria, and more recently by a day we called “Jeans for the Philippines”.

Contribution to the world we live in can be in this charitable form. And so it should be, both when there are disasters and emergencies which require all of us to respond and when we are continuing to support our long-term chosen charities. But contribution goes beyond this. Contribution is a frame of mind.

It’s about noticing others around you and looking outside your own needs and ambitions. It’s about being outward not inward looking. It’s about real life and real activity rather than a virtual version of both. Schools like Bryanston thrive on this way of living. Sport, music, drama and all social engagement are based upon this outlook on life. I strongly believe that you are not a fulfilled person without this sort of engagement and contribution to something larger than your own small orbit whether to your team or in the orchestra. I also believe this way of living can lead a child or adult to the realisation of the need for the emotional and spiritual wellbeing of others as well as themselves. Which might, for all kinds of reasons, be the most important lesson ever learned in school. All of this matters a very great deal to me.

The theme of our all being connected, even to those we might well not choose to be, by a common humanity is not a new one. John Donne was writing of this in the 1600s and before him Homer too composed epics of great scope and understanding that put victor and victim in the same humane focus. In the dark days of December, remembering what it is that really matters and looking forward to a Christmas holiday of joy and contribution can at least begin to make sense of our conflicting and complicated duties in this fast-changing world.