Monday, 7 November 2011

A Model for 14-19 Schooling

Schools are expected to create the same outcome: young adults who are ready to contribute to society in a meaningful and fruitful way. As a benchmark for their readiness, these young people carry with them currency in the form of GCSE grades.
In industry, we are also expected to create outcomes. These are wide and varied dependent on the sector that we operate in, but in more or less all cases, there will be other organisations attempting to create the same outcomes. The models adopted for running these organisations are as wide and varied as the landscape itself.
So why is it, then, that all schools seem determined to stick to the same model?
There are some laid down constraints. Students should have access to the National Curriculum, students should have access to 190 days of schooling per year, teachers should work 1265 hours per year, universities require exam grades in order to help their selection of new cohorts.
But as far as I am concerned, everything else is up for grabs. What follows is my model for schooling.
Firstly, let's start by abandoning the notion of lessons, timetables, teachers, classes, year groups, terms, school holidays and subject areas.
Instead, simply considering the desired outcome that we create young adults ready for the world, I will build my model around the understanding that none of the above structural mechanisms are necessary.
I would like students to be able to operate in secondary schools in a fashion much more akin to the world of work and in a way that is more reflective of the lives that they will lead once they have left the education system.
In life, one never encounters a problem or situation and thinks, gee this requires me to think only in terms of mathematics or biology or geography or whatever. The mark of a learned individual is that, when faced with a situation to overcome, they are able to recognise features in the problem, connect those to knowledge and skills that they have, see how to combine these and use models or examples of similar situations to solve the problem.
So putting subject areas in to silos in secondary education and asking students to work on these subjects as though they are disjointed and disconnected is false and, in my opinion, harmful to their future success.
So no subjects.
Instead, let's think about a system that models more closely the real world. One in which problems and scenarios arise that need to be overcome or where interesting situations come to light and there is a deep desire to explore and know more.
I start my model for schooling with this premise.
At planned hook moments in the year, the school would come together – perhaps in the guise of a whole school summit or conference. At this, several interesting or relevant problems would be posed, topics discussed, debates had. These would be drawn from events that are occurring in the world. For instance, following the 9/11 attacks that would have been the summit focus, or the world banking crisis, the Olympics, climate change, the role of technology in our lives, Christmas. Students might vote on summit foci.
At the summit, each student would prepare a series of questions or points that they would like to know more about. Taking a real example, following 9/11, these questions, with my students included: Why would a human being want to kill another? Why did the aeroplane not emerge from the other side of the building? What was going through the minds of the people on the plane that had been able to call home? How many people watched the TV coverage? What is the difference between being a Muslim and Christian?
The questions and thoughts come from the students themselves, based on their own line of enquiry, linked to their own living histories. The students are all ages and their questions are equally important and valued.
Armed with the questions, reflections, interests and problems, the students are now given a period of time (perhaps a month or two) to find out the answers.
In our school, there are no teachers and no lessons and no subjects and no timetable. So how do the students find out the answers?
Well, in our school there are Experts and Knowledge Holders. It is made clear to the students from the day that they join to school community who these people are and what expertise they hold. The child wanting to know why the towers collapsed, might wish to explore the engineering issues with a mathematics, physics, engineering and design expert. With each discussion, their knowledge grows and their questions continue to evolve in to deeper thinking. They may wish to engage in independent research, using the internet or discussing with experts in the field via web-conferencing.
Each student has an assigned mentor, who is able to act as their focal point for help, but also monitors the progress and guides the learning journey via a tech solution (could be a VLE or Facebook type application).
These mentors ensure that their assigned students have the necessary access to learning. They are, returning to our industry analogy, the student's supervisor.
It may be that 60 students want to seek the input of the physics Expert. Again, tech can help here, by allowing students to register interest and pose questions. The physics Expert can then decide the best course of action – this might be to advertise an Expert Seminar from 2-5 on Wednesday afternoon. Students can then opt in to these as they feel necessary.
Knowledge Holders might be Experts too, but they can also be other students who have already studied and mastered a skill or area of knowledge. So, as well as making requests for Expert input, students can also pitch to host seminars and disseminate their own knowledge.
Can you picture the school? It is tempting to think that there might be chaos, but pause for a moment and ask yourself why you think that? It is too tempting for many teachers to underestimate students. But watch them in other walks of life, or look at a similarly sized business staffed by teenagers: people can self-program.
It is tempting to think that some students would waste time and mess about.  But what are they doing now?  And why do students waste time and mess about?  Largely because they see school as irrelevant, dull and uninspiring or because they find the work too easy or too hard.  In our school many of the drivers of poor behaviour are removed.
Of course, a large part of the role of this school is that it constantly reinforces the need and points out the means to be self-programming.
As the month (or whatever period) progresses, the problems are addressed in a deep and meaningful manner because students are given the scope and time to truly get to grips with the issues: in our example, a student's investigation might now consist of mathematics, science, engineering, theology, languages, media studies, geography, history, computer science. The problem has a defined deadline and outcome – perhaps the school will create a 1-hour TV programme to be broadcast on a set date over the internet, which could then be used by other schools.
I also said in this school model there are no terms or school holidays. Instead, at our school, students must bank 190 days of learning in each academic year (this structure only stays because of the restraints of national examinations and university entrance requirements). They can bank these days whenever they choose.
Similarly, staff (our Experts) must bank 190 days at work. They can take holiday by booking it in the way that millions of adults in industry do, day in, day out. Because the expert has no classes, there is no dent in continuity – there will be several colleagues with similar expertise that can fill the gaps. In the case where the Expert is also a Supervisor, the students are trained to understand that they won't always have access to this person, so they must take responsibility for their own learning and ensuring that they liaise with their Supervisor at appropriate times. The school operates on a full year calendar, so the learning is spread out, with students banking their 190 days when they choose. There are no points in the year when the school shuts down (well, perhaps Christmas!).
Teachers would also be required to bank at least 5 days of professional learning.
Tech would play a major role in facilitating this school model, so that access to learning in 24/7. Tech would also handle the mundane day-to-day tasks, freeing up the Experts to have rich relationships with the students.  It would also allow for Supervisors to have constant, real-time access to their students' work, thoughts, questions, suggestions and evidence.
Sounds a bit radical? Not to me.
I would love to hear your thoughts.
What would your school model be?

Thursday, 27 October 2011

Why Touch Technology is what Mathematics Education has been Waiting for

For many years, mathematics education specialists have joined forces with software and hardware developers to create new tools for learning. But still, decades on, the mathematics classroom remains one largely about teacher exposition and bookwork practice. Technology has made little impact.
Yet, technology in mathematics can help to de-abstract-ise the subject. All those apparently meaningless processes that we have all been taught at some point in our lives can suddenly be made to come to life. Just watch a Gapminder animation or use a virtual manipulative and you will see what I mean. No longer does the mathematics teacher have to explain some new concept while drawing inadequate diagrams that contradict their words. Technology can solve this. So why hasn't it?
The answer is simple: the technology, although the solution, has also been the problem. Teachers, even those most adventurous and brave, will give up when the technology is a blocker, and until now it certainly has been – whether that be the unreliability of hardware, the sheer confusion of understanding the operations of a programme or the lack of logical pathways through a piece of software.
But touch technology, in the guise of an iPad or the like, brings with it what good design always should – an intrinsic understanding of how to operate it. There are no longer blockers. Through touch, interfaces suddenly make sense. They become natural when well written apps come to life.
The trouble, at the moment, is that no-one yet has taken the step of creating a truly difference-making, meaningful, student centered, pedagogically sound app for mathematics. But they are coming.
I have talked (ranted) for years now about the need for someone to create such an app and bemoaned the deluge of opportunistic, superficial apps that have flooded the market in anticipation of securing a slice of the enormous student/teacher/parent purchasing power cake. There are many apps for mathematics, but none that bring anything new to the equation. So I have been really excited recently by a group of developers that I have met who are creating a mathematics app that will up the ante and change the face of learning apps.
Through touch-tech, there is no longer the need to prelude the learning with lengthy instruction on using the technology or learning operating systems or the idiosyncrasies of a particular piece of software. The children in our schools are already at ease with using the devices and technology is a routine part of their lives.
So we can now take the step that was always the hope for technology in the classroom – to enhance active engagement, interaction, feedback, micro-teaching, analysis and problem-solving skills, make connections across and within subjects and contextualize and internalize the learning in a way that connects to students' own realities.
The tech can at last meet the curricular objectives.
Technology, and particularly hand-held technology, can create an environment where the teacher is effectively split into 30 individual teachers. With each student having access to information, prompts, reflections, guidance, challenges and support any time they need it. Students are no longer bounded by the need for a lesson to be timed for a group of children with wildly different abilities. The technology can take them on the learning journey, while teachers guide the experience like an orchestra conductor. The teacher is in turn freed up to actually teach – not just transmit information – they can work at the individual and group level. The student remains engaged in learning for a much greater proportion of the time because they have instant access to progression.
The relationship between student and teacher can be greatly enriched when technology is integrated effectively. This takes a shift-change in pedagogy, but teachers can take on the role of advisor, knowledgeable other, and mentor.  This shift-change will require investment in terms of time and money for teacher professional development - for every penny spent, I think the breakdown should be 20% on tech, 80% on teacher professional learning.  This is not just about how to use devices, but about what the pedagogical implications are for changing from the traditional transmitter of held knowledge to one of an artist creating the right environment for children to be knowledge creators.
And in mathematics, we can finally move towards what the subject is truly about. The technology can make school mathematics less focused on calculating and more on sythesising, modeling and interpreting. Students at any age can see visualisations of the most complex mathematics and draw inferences from them – mathematics is suddenly opened up as it should be.
With the internet, students are able to access any information that they need. Information is no longer the preserve of the teacher. So students can learn from external sources, or knowledgeable others, so that they themselves can become knowledge creators.
Unlike many technological devices of the past, touch-technology becomes simpler and more intrinsic as we move forward. In many aspects of life, touch-tech is now the interface that we meet. It is epitomised by its simplicity, by its universal approach of guiding the user through the process. This removes the apprehension that many people feel about technology. And this is a key point, for it is only those of us that are adults that feel this apprehension. To children in our schools it is simply part of their life. So through touch-tech, teachers are now able to feel comfortable about creating a tech-based learning envinronment, where they do not have to understand the technology or learn how to use a keyboard or mouse.
Touch technology is what mathematics education has been waiting for. It is the conduit that will allow the generations to come together and will remove teacher bias towards their comfort zone. We're not there yet, because appropriate apps have not yet been written, but they are just around the corner. Over the coming year, I believe that a product for mathematics will enter the market that will help us all to take the last steps to integrating technology in the classroom.

Saturday, 8 October 2011

Michael Gove's speech, Conservative Party Conference 2011

Many people have asked me this week what I thought to the Secretary of State's speech at the Conservative Party Conference, and maybe at some point I will get round to writing up a response.
In the meantime, I thought that some of you might find it helpful to catch up with what was said if you were unable to attend the conference, so here is a transcript of Michael's speech.
(if there are spelling errors or such like, well tough, I was typing pretty damn fast!)
Note: Michael took to the stage immdiately following a speech by Quddus Akinwale, a pupil at Burlington Danes Academy.

There are some moments in politics you never forget. And I'll never forget the first time that I heard Quddus speak. It was at a fundraising event for ARK, the fantastic charity that supports so many brilliant schools.
And when I heard his story, I was moved. As I know many of you will have been.
And I vowed then that many more people would hear his story because it is inspirational. Quddus reminds us of the real face or London's young people. Ambitious, aspirational, loving their parents, proud of their school, wanting to do well in the future. And I think if there's one image that we should carry away from this year of young London, it is Quddus and everything that he stands for.
There's another moment that stays in my mind, and that's a moment that occured when I was in China, last November on a trip with the Prime Minister. I was being shown around a school in Beijing and the headmaster handed over a book just as I crossed the threshold. I opened it and I saw lots of Chinese characters and then the odd word in English and the odd equation. "Thank you for showing me your text book," I said. He smiled pittingly at me. "It's not a textbook," he said, "this is actually a collection of all the papers in academic journals which have been published by people in this school." "That's amazing," I said, "the teachers, as well as having time to teach all the students also have time to do their own academic research. That's fantastic!" And he paused and smiled at me pittingly again and he said, "it's not the teachers who are writing the academic papers, it's the children."
Think about it. On the other side of the globe, there are15, 16 and 17 children educated so well that they can hold their own with the world's graduates and post-gradutes. If anyone asks why it is that our education system needs reform and change, remember that fact. In other countries, not just in east Asia, but in Canada, in the United States, in Australia and in New Zealand, education systems are being reformed because every single one of those nations knows that unless they are at the top of the education tree, unless they're making sure that more young people have the skills and the knowledge that they need to succeed, that their countries will fall further and further back in the global race for prosperity.
And one of the sad things about the last few years, is that under the last government we fell back in the global league tables for education.
We used to be 4th in the world for the quality of our science education and now we're 16th. We used to be 7th in the world for the quality of our children's literacy and we're now 25th. We used to be 8th in the world for the quality of their maths and now we're 28th. And it's not just our national pride that has knocked by this decline. What it means is that for millions of young people who've been through the education system under Labour they go in to a world economically more competitive than ever, where demands are more strenuous then ever, where jobs at the moment are scarcer than ever. And they are not as well equipped as children in other countries to succeed, to win those jobs, and to win those college places.
And that is why I am so angry about whay happened under the last government. Because I fear that they failed those whom they were elected to serve: the next generation.
And what makes it worse is that the big divide in education in England is not between us and other nations. The really big divide in education in England is between rich and poor. There are five schools that serve some of the richest children in England that get more children in to Oxford and Cambridge than 2000 of the schools that serve our poorest young people. No one can believe that that is either fair or just. From an economic point of view, it is an act of self harm to leave so many talented young people from poorer background in a position where they cannot use their talents. There are young men and women across this country, every bit as intelligent and bright and ambitious as Quddus, that are not getting the chance to become the engineers of the future because our education system hasn't equipped them as it should. And we are all losing out.
And that is why when people say what is this government doing for growth, I say the best long term growth strategy is a school reform strategy.
But it is not just about economics. It is also about social justice as well.
John Dunne once said that no man is an island entire unto itself. And we know what he meant. We know that I am my brother's keeper. We know that we have a responsibility to others in our society beyond simply paying our taxes and obeying the law. We know that the parable of the good Samaritan made the point that the Pharisee and the Levite, even though they obeyed the law, even though they were respectable figures, were found wanting because when someone was in need they walked by on the other side.
We're not going to walk by on the other side.
We are not going to leave those who have been languishing in poor schools and in poor schools for far too long to wait for another saviour. Children only have one childhood, it's the most precious time of anyone's life. And we want to be there to make sure that they are happy, fulfilled and that they are successful in the future.
And if we need to be reminded of the consequences of allowing children to grow up in poverty, not just material poverty but with a poverty of aspiration and a poverty of hope, then we were reminded this August of what it means to allow children to grow up without the right values.
The first and most important thing to say about the riots which scarred so many parts of urban Britain is that, when we look at them, we need to keep moral clarity. It's important to recognise that what we saw on our streets was a conflict between right and wrong. Between the police who were working so bravely to ensure that we were safe and a lawless, thuggish minority, amoral, contemptuous of the rules by which the rest of us live, intent only on the pleasure of the moment, people who had nothing to lose and were thumbing their nose at all the values that keep our society civilised.
But at the same time as we must maintain that moral clarity as our first response, we also have to recognise that a truly ordered society can't be kept peaceful by having every night thousands of uniformed officers policing our streets. Our streets will only really be safe when millions of individuals police themselves and make sure that they exercise self-restraint, self-discipline and self-respect.
And that's why it is so important that those values are instilled in the home and in school.
That's why, in the work that I do, with my colleagues in the Department for Education, I am so anxious that we should make that children have the best possible start in life. That's why we should emphasise that the most important job that any man can have is being a father. And that your responsibility to your child is life long. If you were there at your child's conception, you should be there for the rest of their life.
And schools have an important role to play as well because we all know that one of the sadnesses of our time has been that so many of those children who believed that they had nothing to lose were children who had been failed by our school system.
Let me repeat again the overwhelming majority of our young people do well at school. The overwhelming majority of our schools and teachers are doing a fantastic job. But it's still the case that far too many of our children are failed.
Sixty percent of white boys eligible for free school meals at the age of 14 are incapable of reading properly.
And there is an iron clad link between illiteracy and criminality. There are children who arrive at primary school from disorganised and dysfunctional homes, there is indiscipline in some schools, they are not taught properly to read at an early age. They arrive at secondary school incapable of following the rest of the curriculum. So they act up, they act tough, they cause disruption, they risk becoming excluded. Many of them will truant and as a result they become the recruits of the gangs of tomorrow.
Because it is so vital to break that link, it's one of my aims to do everything possible to eliminate illiteracy in England. If you can't read, then you are condemned forever to live in a prison house of ignorance. And for those children who can never read, they are all too often the recruits for our prisons of tomorrow. Because we know that more than three quarters of young men in prison are functionally illiterate. They've been failed by a system that didn't ensure that they had hope, that's the reason that so many of them went off the rails and that's why it's so important that we get reading right.
And that's why I'm so glad that my deputy Nick Gibb is a passionate crusader for better reading. He's the person who's been responsible for making sure that every school will receive additional funding so children are schooled in the best method of learning to read: systematic sythentic phonics. He's going to make sure that every child at the age of six is screened, so that any children who are falling behind, whether they are dyslexic or have been poorly taught can be identified and supported. And it's also why Nick is leading a campaign to make sure that children also learn to read for enjoyment. That the glories of English literature, the best that has been thought and written are passed on to the next generation. So that the heritage that is there for all of us, and which all of us in this hall can enjoy, becomes every child's inheritance. And for that crusading zeal, I'm so grateful to Nick.
Now, when we reflect on what happened this summer, there's one image which I know for many of us will sum up everything that went wrong. And that the image of the CarpetRight Warehouse in Tottenham, which was in flames. Torched by people who simply didn't have a respect for property, a respect for their community. And one of the many sadnesses about that image is that the person who owned that warehouse, the person who founded CarpetRight, the person who's given jobs to many young people is a great man, a great supporter of this party, Phil Harris, Lord Harris of Peckham. And the great thing about Phil is that as someone who has built his business by the sweat of his brow, he has ensured that now that he has time and a little bit of money on his hands, that time and that money is devoted to giving thousands of children a better start in life. He's set up a chain of academies across the whole of south London, taking schools out of Local Authority control when they were failing, given them great headteachers, like Greg and Sally and made sure that those schools embody what the best independent schools embody as well. So those schools have great discipline, a proper uniform, there's no bullying in the playground, and there's respect for teachers in the classroom. They teach traditional subjects in a rigorous way and they have uniformly high aspirations for all children whatever background they come from. And under Phil's leadership, those academy schools have made amazing strides forward. There's one school that he took over in Peckham, which when he took it over from the Local Authority had only five percent of children, one in twenty, getting five good GCSEs. In just a few years, thanks to his leadership and academy status, those numbers increased by ten, by a thousand percent, fifty percent of children getting five good GCSEs. And what's been achieved in the Harris Academy chains is being achieved in academies across the country. We heard a little bit about what's happening in Burlington Danes, but it's not just in London. In Leeds there is a an amazing woman called Ross McMullen, the principal of David Young Academy, who is transforming education for poor children in West Yorkshire. Just down the road, here in Manchester, in Moss Side, a school that used to be one of the worst in the country is now transformed thanks to a wonderful headteacher called Kathy August. Just a couple of weeks ago, I was in Nottingham, visiting the poorest part of that city and there's a school there, Nottingham Academy, led by another wonderful headteacher, Barry Day, which is now ensuring that every child learns a foreign language from the age of five and that every child regards themselves as university material. It's that level of aspiration and that commitment to excellence, which is the best of British education and I think that we should show that Conservatives are on the side of those hero and heroine headteachers who are fighting to give the next generation the best possible chance.
And we are on their side because those academy schools are essentially the children of the City Technology Colleges that were set up by Lord Baker, Ken Baker, one of the best education secretaries this country has ever seen, a visionary reformer who inspires us today.
So the schools are essentially a Tory invention. And it's thanks to the election of a Tory Prime Minister that we now have 1000 academies open. We inherited just 200 from Labour and we've increased the number massively and at the same time we now have 1.2 million children benefiting from academy status, academy education, real excellence in education. It's an achievement of which you should be proud.
And as we saw in the video earlier, these new schools are being joined by 24 new free schools and shortly they will be joined by new University Technical Colleges, schools which are devoted to giving children, from the age of 14, a superb training in vocational and technical education. Again, it's thanks to Lord Baker that these schools are being started, and I hope that when we announce them that we will be able to repair the historic gap in our education system that has existed since the second world war. Countries like Germany have had a superb technical education for children that want it, we haven't. For far too long the technical, the vocational, the craft skills, the apprenticeship route has been undervalued in our society. Now at last this coalition government is making sure that those who pursue a vocational or technical course can hold their head up high with the same degree of pride as anyone who pursues an academic course in life.
So new schools but also, and most important of all, a new attitude for the entire education system. This government is unambiguously on the side of teachers. And we know that there are three things that are critical if we are going to support teachers in the work that they do. The idealistic, inspiring, world changing work that they do. We need to back them on discipline, we need to give them a curriculum and set of exams which are fit for purpose, and we need to make sure that they can take pride in their profession.
So what are we doing on discipline? Well we're making sure that teachers have the powers they've been denied for too long. The powers to search children for items that might cause disruption, the power to impose detention on the same day that school rules are broken, the power to exclude disruptive children and know that that decision won't be overturned by bureaucrats outside the school, and the power to be protected from the sort of false and malicious allegations that undermine those teachers who are going the extra mile to keep order.
And on exams and the curriculum? Rigor is back. We know that people enter the classroom because they love their subject and they want other children to be inspired by it as well, so what we are doing is making sure that the dumbing down of our exam system ends. At GCSE level we're sweeping away modules, we're insisting that once again marks be given for spelling, punctuation and grammar. We're asking universities and academic experts to help us ensure that our exams are the best in the world. And we've already said that we're going to judge schools explicitly on whether or not they are teaching children more of the hard and rigorous subjects that universities and employers want and fewer of the sorts of soft subjects that were fashionable under the last government but condemned so many children to unemployment and poor prospects. And that's why, that's why, I'm so glad that in the last year as a result of those changes that we've made, we've seen the number of students studying history and geography and modern languages rise by 25 percent. And I'm so pleased, in particular, that we've seen the number of students studying physics, chemistry and biology rise by more than 80 percent.
And at the same time as making sure that we have exams and a curriculum that reward rigor and stress the importance of subject knowledge, it's also the case that we're doing everything possible to enhance the status and prestige of the teaching profession. Let me say it again, we have the best generation of young teachers entering the classroom now, we should be proud of what they're doing. But we should never stop asking ourselves what more we can do to support them. And that's why I'm so glad that teach first, a scheme that takes the best graduates from the top universities in to a classroom, is expanding under this government. It's why I'm so glad that we're moving teacher training out of the ivory towers of so many universities and back in to the classroom where practical teaching skills can be passed on from the best in their field. And it's also why I'm so glad that money has been made available so that we can give bursaries of up to £20,000 pounds to those graduates in mathematics and science who are going to give the next generation the skills that they need to succeed in the 21st century.
New schools and new attitude.
We're fortunate in this country that we have so many good schools. We're fortunate that we have so many great teachers. And we're fortunate that there are so many young people who are ambitious for the future and are doing well.
But I'm not going to rest until every school in this country is as good as the best. I'm not going to quit this job until I ensure that every new teacher is as well trained as the best. And I'm not going to leave until I make sure that every child from a poor home has the same opportunities that are currently enjoyed by the most fortunate in our society.
I'm a parent. I know that I would never accept second best for my child. I know you wouldn't either. And that's why I will never accept second best for this country
Thank you all very much. Thank you.


At lunch today will an old friend and colleague, we stumbled upon the memory of a game that we used to play at the school where we were both teachers in the 90s.
Teachermon was a straight forward rip off of one aspect of the incredibly popular (at the time at least) game Pokemon – in which cards containing information about little creatures are used to play a battle. Sort of Top Trumps on speed. It exploded out of Japan in 1996 and suddenly the kids of the world went Pokemon crazy.
So when a boy in Year 10 approached me and asked if it would be ok to create a version of the cards based on the teachers at the school, I thought it simply genius.
This is how it worked:
For each member of staff, a card was created on which was a photograph (usually a very bad photograph), their name, subject and a set of scores against five powers. This was the tricky part, and the funniest part, of creating the game: what would the powers be? The lads in Year 10 wanted to score teachers against things like "interestingness" and "coolness", but we decided that this was too subjective and likely to cheese some teachers off. They ventured "bad breath", "body odour" and the like, but only jokingly and immediately knew that this was not the spirit of the game. Eventually we arrived at powers such as "Years at Our School" – this meant that long servers scored well, and on the whole we liked this idea because some of the long servers were not keen on the idea of the game.
The kids handcrafted a Teachermon logo, and got to work creating the cards.
Once printed, each teacher was given a stack of their own cards and the students started a craze of playing Teachermon at break time. This meant that they had to collect the cards. You could only collect a card if the teacher chose to give it to you. So for example, I gave each member of my tutor set my card.
The craze took off immediately and with great excitement from the students. Kids would run up to you at break time and plead with you for a copy of your card (we carried a stash around in our pockets) and you would regularly hear phrases like "swap you McCourt for Baker."
In no time at all it became obvious that what we had accidentally stumbled upon here was an amazingly effective reward system. Teachers were handing out cards like merits in lessons. Students were knuckling down to work, being helpful beyond the norm and actually doing homework for the chance of getting your card. There was one chap, who'll we will just call Mr Smith, who had worked at the school for 42 years. To be frank, he was struggling with classroom discipline. Suddenly he was a star. He got in to the spirit of the game straightaway and milked it with tongue in cheek – it was notoriously difficult to get his card. If a student managed to coax one out of him there was an immediate buzz around the school. I once heard that someone swapped 20 "normal" teachers for "a Smith". Discipline issues were completely a thing of the past for Mr Smith. He used the renewed energy that good behaviour gave him, the sense of engagement that Teachermon brought and the interactions with students beyond the lesson to rebuild his relationships with them. Even when the game died out two years later, in the year that he would retire, his connection with the students was so strong that he had automatic respect whenever he spoke.
It was great to talk about that year again with my friend this afternoon. We both scratched our heads at what the next Pokemon craze might be and how we might hook in to it. Any ideas?

Wednesday, 5 October 2011

The Ingredients of a Great Lesson?

What are the necessary ingredients of a great lesson?

This morning, a Twitter post from @tesconnect, asked "Taught a great lesson lately? Upload it to TES resources..."
The inference being that a "great" lesson is something that can be committed to paper in some way.
I think that this is not true. And furthermore, I think that the notion that it is true is contributing to a de-professionalisation of the teaching profession as well as giving a false sense of security to bad teachers.
In 2008, I inspected a lesson in Manchester. The lesson was delivered to Year 10. And it was dire. Truly dire. At one point, sat beside a boy at the back of the room, I wrote down "uncritical use of resources".
The resources that the teacher was using for the maths lesson were lifted from the National Centre of Excellence in the Teaching of Mathematics (@NCETM) website. The teacher dryly waded through the tasks as though delivering the lines in a bad TV soap opera.
At the end of the lesson, I sat with the teacher and discussed my judgment ("inadequate" in Ofsted terms). She was most perturbed by this and told me sternly that the lesson was good or even outstanding. I asked her to justify this and she told me that she had taught an NCETM lesson and therefore the lesson must have been good.

What is a lesson?

I guess if you think back to school, or watch TV, or think about stereotypes, a lesson is when 30 children sit in a room, at desks, on chairs, in a school. A teacher imparts some information, which the children take notes of, then the children undertake some task from a book, writing their responses in another book, which they carry to and from school.
But that is not a lesson.
Reducing a lesson to its most basic form, we can do away with the books and the classroom and the resources, and the pens, and the paper, the desks and the chairs. At its most basic, a lesson is when one person learns something from another person. (Of course, learning can be reduced further to remove the teacher too).
A great lesson is when a heck of a lot of learning occurs. All that this requires is the teacher to be able to impart the knowledge or skill in such a way that the student is able to systhensise, understand, interpret and embed the knowledge or skill in their own reality.
To achieve this, the teacher must have the skill (the art) to understand both the student and the knowledge or skill. They must be able to empathise with the student's point of view. The teacher then uses this knowledge to select a method of communicating the new knowledge or skill. This could be through story-telling, or modeling, through discussion and debate, through exploration of examples. It is the teacher's art to critically select the method or methods most likely to achieve learning.
The trouble with the resources debate is that, and not enough people say this, there is no such thing as a great resource. There may be resources more likely to achieve the desired effect. But in the hands of a bad teacher, a so-called great resource isn't worth the paper (or interactive whiteboard!) its written on. Conversely, with a so-called terrible resource or indeed no resource at all, the great teacher can conjure up an amazing learning experience.
Sure, having bright airy rooms, modern equipment, numerous resources and the like can all help. But only in the hands of those that know what to do with them.
When the situation exists that some teachers believe that using a resource that has worked well for someone else, without having to think about how that resource relates to their students, then there is something terribly wrong.
Would it not be more helpful then, instead of a focus on resources, for the discussion to be around how to critically review and select appropriate tools from the arsenal of resources at hand? How to develop your own personal pedagogy? How to continue to learn as a professional? How to adapt and reflect?
The TES is a fantastic website and its resource bank, grown by teachers for teachers, is a fantastic tool. But if the TES wants to take a further step in truly improving the lessons that children experience in our schools, it could, without great difficulty, add to the resources section encouragement for professional learning by asking teachers to pause for a moment and think critically about the resources that they find and debate the pedagogy around embedding them in lessons.
Oh, and the answer to the question: The necessary ingredients of a great lesson? A great teacher.

Friday, 30 September 2011

What State Schools Should Learn From Private Schools

Every now and then something high profile will flag up the age old debate about the relative qualities of private versus state education. So when David Cameron asked a group of headteachers from leading independent schools to attend a meeting at Downing Street, the media pricked up its ears and went in to the usual over-reactive state that is its wont.
The Prime-Minister explored with the group the idea of private schools "helping" state schools to improve. After all, these great public schools all have great GCSE and A Level results, so they must be doing something right, right?
It is entirely wrong to think that this idea has suddenly appeared. Across the country, for as long as both have existed side by side, State and Public schools have been working together. There are countless examples of partnerships and collaboration.
But now that the debate has been focused upon once more, we might at least have the discussion about what should state schools learn from private schools?
Before addressing that question it is important to establish some knowns.
The quality of teaching in State schools is diverse. There are amazing teachers, there are crap ones.
The quality of teaching in Public schools is diverse. There are amazing teachers, there are crap ones.
A little talked about known is that individual teachers are sometimes great when teaching in the State system and terrible when teaching in the Public one and this is conversely true too. It is a misconception to believe that what works well in terms of pedagogy in the Public system can simply be transferred to the State system and vice-versa. The cultures are fundamentally different. This is the exact same mistake that many large scale, international education companies make when designing programmes for other countries: you simply cannot cut and paste a system from one country to the next. You must take account of the culture within that country or community or school. As a Director at Tribal, this was one of my mantras and something that we were obsessed with trying to achieve – for example, when designing education reform programmes in the Gulf nations, we went to great lengths to ensure an understanding of the native culture, shared values and living histories, incorporating Islamic viewpoints and learning from the teachers and community that we worked in.
This is also where the current Secretary of State for Education, Michael Gove, appears to be missing a crucial importance surrounding the adoption of the Swedish Free School model. But I digress.
Of course it is possible to experiment with pedagogies in both State and Public sectors, to learn and to adopt aspects that are effective. In doing so, the teachers are acting as knowledge creators and are building their own personal pedagogy. But it is absolutely not the case that you can say as a blanket statement: Public schools do X and are successful, so State schools must also do X.
This is why many teachers find they are unable to move between working in either of the two systems.
Collaboration, when it is truly such, between State and Public schools allows for this formative knowledge creation and pays dividends to all involved.
Are Public schools better than State schools? Well, no. Some are, some aren't. Yet, misguided, many politicians want to believe that Public schools are the more effective machine. In part, of course, this is due to the fact that the majority of politicians attended Public schools and are therefore bound by their personal experience – if it worked for them, then surely it would work for all.
But surely children who attend Public schools do better than those at State schools? Well, in some cases they do. But, importantly not all. And yet in these cases where students do worse or as well as their State school counterparts, they still have more success later in life. And here we are coming to what State schools really should learn from the private sector.
My home town of Oundle nestles on the Cambridgeshire / Northamptonshire border and has for many, many years been dominated by Oundle School. It is a fine Public school, which brings prosperity to the town.
Oundle take in a wide range of students, from across the country and overseas. Many of these students, bless them, are what I can only describe as nice-but-dim types. Thoroughly decent children, maybe superb at rugger, but not a great deal going on upstairs when it comes to "academic" ability.
Let's consider a nice-but-dim Oundle boy. What will become of him? Well, he'll pick up a bunch of GCSE grades around the national average, maybe a C in mathematics and English and a handful more. He then sits his A Levels, because that is what you do, gets a couple of OK grades, maybe one fail. And off he plods to university. Let's say he signs up to a Psychology degree at a half decent uni and has three terrific years having a jolly good time and picking up a run of the mill 2:2 in a subject that was neither here nor there to him. What happens to him?
Pause for a moment and consider another lad at Bog Standard Comp in a town somewhere in England. He gets the same grades and degree. What happens to him?
Flash forward 20 years. Now if each of these scenarios were a probability distribution, it would be very likely that our Mr Nice-But-Dim is now very successful in a field that interested him (maybe the media or politics or the city). He will be earning well above the national average, his work will typically consist of leading others, he will be a homeowner, he will be happy in his work-life balance.
Our other chap? He'll be doing ok too. But probably just ok. He'll be in a stable job, and it will pay slightly above national average, he will maybe have one or two people who report to him, but probably not. He will own his own home. His work-life balance will be unfulfilling.
Why does one child find more success?
Well, this is what State schools should learn from Public schools.
Academic ability and exam results are not the most important aspects of school. They are not the fundamental purpose of a good schooling system. What the Public schools have remembered, to their credit, is that schooling is about the child as a whole. And on the whole, Public schools will work tirelessly at ensuring that the young people who leave their doors have a sense of purpose and pride instilled in them. The boys that leave Oundle are confident. The can start up discussions and hold their own in debate. They have self-belief that they can achieve in the world. The celebrate success. Crucially, they know how to network.
Recently, at a large education conference, a friend of mine asked me how I managed to be involved in so many different projects. It was lunch time, there were companies showcasing their work at stands around a large room. I asked him what he wanted to be involved with and he told me about a couple of ideas and companies that he would like to be linked to. Some of them were in the room. Go and talk to them, I told him.
In these situations, you witness where our State system has gone so wrong.
What the State school system in England has done, particularly over the last 15 years, is forgotten its purpose. Now obsessed with measuring everything, with testing, with grades, with pitching schools against each other, the system has lost sight of what education is about.
What we can learn from the Public schools of England is that by giving children the ability to adapt, to challenge, to question; by instilling in them the belief that risk taking is a good thing; by helping them to follow their dreams; by ensuring that children understand how to network they can achieve.
Education, as Einstein once said, is what remains when you have forgotten all you learned at school.
It is not about content and grades, it is not about average point scores, or giving children meaningless national curriculum levels in each and every lesson. Education is about becoming a better person. About readying yourself for the world and knowing that you count and that your opinions are as valid as everyone else.
One of the reasons that social mobility has come to a grinding halt in England is because we have removed the aspirational aspects of the education system.
There are schools that buck the trend. A friend of mine runs three academies as an Executive Headteacher. I was really interested to visit his schools and see the emphasis placed on meal times. That all the students (and these are students from the very hardest of backgrounds) would eat at the table, using cutlery correctly and engaging in quiet chatter. I asked him about why so much focus has been placed on this and he told me that one day each of those children would go to a job interview. And each and every one of them would be judged on the way they spoke, their body language, their confidence and how they behaved at lunch. How true.
By focusing so heavily on subject content knowledge and pointless measures, the State system has neglected its duty in helping childing to grow in to purposeful and proud citizens who can lead fulfilling lives.
The ability, in Academies, to re-focus your priorities comes from the autonomy that the schools are given. It is this autonomy that allows private schools across the country to recognise the stupidity of much of the initiatives that come from central government and to ignore them, instead focusing on developing the whole child. Perhaps if school leaders were freed of initiative overload, they too would be able to re-focus.

Sunday, 11 September 2011


Sam was beautiful. Her hair was a firey red and her eyes shone.
There is a collection of huge granite spires that stand thousands of feet above the Kern River at the southern edge of the Sierra Nevada in California. As eager fresh faced graduates, we took the easy drive down from Los Angeles with a trunk full of beer and the most basic of climbing essentials. The four of us had been climbing together for years, and had long since abandoned ropes in search of a purer form of excitement. When people would quiz us about the purpose of such apparent foolishness, telling us that we were risking death, our stock reply was "well that's kind of the point." It was exactly that knowledge, that gut-wrenching feeling, that your life is literally in your hands we were trying to capture. There is something about facing your own mortality nakedly that makes the pettiness of much of life disappear and allows you to taste and feel those things that truly matter.
The Needles is a tough climb. The vertical pins protruding along the top of the ridge make for difficult ascents and treacherous descents. Sam sat atop of one of the spires laughing and breathing in the success of her climb. I looked up at her – it was as though she was alight with life. She beamed down to me and yelled "I think I can jump to the next tower." It was an insane move. Any loss of grip on landing would see her plummet thousands of feet to a certain death.
I laughed it off and told her not to be silly. And then she jumped.
And that was Sam. Brave, a bit crazy, full of life and happiness, keen on squeezing every last sensation from every experience. Sam was beautiful.
She landed and gripped hard. Safe. Buzzing.
Some years later it appeared that life had tricked us into becoming grown-ups. I was a teacher, Andrew an architect, James a civil servant. Sam was a banker.
On the afternoon of September 11th 2001, I was teaching algebra to Year 11, Set 1. The air was hot and the classroom uncomfortable. Rebecca, a vibrant young girl with jet black hair, arrived late to class. Immediately she told the room, "Russia has bombed America."
The students looked at her bemused and panicked.
I am glad that the world has changed, I am glad that the students I was teaching that day had been able to grow up in a post cold war society. As soon as she said the words, with complete sincerity and a shot of distress in her eyes, my mind was thrown back to my own childhood and the world of "Protect and Survive" - those government funded public information films that would periodically appear on TV or be shown to us in school, where an animated house would be blasted and then the fallout would begin. Where quick thinking fathers would use their 4 minutes to sturdily erect a bunker inside the house by removing all of the interior doors and nailing them against a wall at 45 degrees, whilst mother painted all of the windows white.
Instantly that feeling in the pit of my stomach that used to keep me awake at night returned. When I would lie staring at the ceiling thinking about the end of the world.
All of this came in to my mind at once. My expression remained fixed. I asked Rebecca to tell me why she thought that Russia attacked the USA and she told me simply "It's on TV, Sir. Right now."
The messages that raced around the globe in those first few moments after American Airlines Flight 11 struck the North Tower were mixed and muddled. The world's media was in constant residence at the World Trade Center, so the explosion of misinformation was instant.
In the back storeroom I found an old TV. I set it on a table at the front of the classroom and tuned to BBC1. A news flash was broadcasting footage of an airliner hitting the skyscraper.
The students were shocked, but a wave of relief came over them too. This was not war. This was not an attack. A terrible, tragic accident had happened.
We all talked for a while about the tragedy. A boy towards the front of the class asked me how many people were in the building. And I knew the answer.
In August that year, Sam had transferred from her company's base in Canary Wharf to an offshoot in the World Trade Center. James, Andrew and I had spent a hurried weekend in New York helping her to get settled. In a bar on the north-east corner of Central Park, Sam had told us excitedly about her first few days in her new office. "You know there are like 50,000 people working there? The place is like a mini-city."
I talked with my class calmly about the World Trade Center for a few more moments and sensing that, although deeply saddened at the great loss of life, they were beginning to calm. We turned off the TV and tried to focus on some work, but I was happy for them to continue conversations where they needed and wanted to.
The lesson ended. I walked to the staff room. It seemed like the entire staff were huddled in to the space. At the far end of the room a large TV told the unfolding story. This was no tragic accident. A second plane had struck.
I thought of Sam and tried to call her from my mobile phone, but the line was busy. An overwhelming sense of relief struck me. She was on her phone, she was safe.
As we all watched the rolling news coverage in silence, the most horrific and unexpected thing happened. South Tower collapsed.
I thought of Sam. But I knew she was dead.
Sam had been on the phone, that much was true. Since then, every now and then, I will sit with Sam's mother and she will describe to me, with tears gently rolling down her cheeks, the 20 minutes that she spent on the phone with her daughter that day. Resigned, Sam explained calmly and with reason, that she was going to die. She told her mother that she had enjoyed her life, that she had been proud to be her daughter, that she would always be with her.
Last night, a group of us met for the first time in years. We sat in Hyde Park and watched the Last Night of the Proms together. Sam's friends and family. And we ate and drank good wine and we talked and talked and talked about the beautiful red headed girl who we all loved. We laughed a lot. And we cried a lot too.
Sam told her mother, as she waited to die, that she didn't understand why anyone would deliberately crash planes in to the World Trade Center, but that she did know that people are good and that good would prevail.
As we held each other's hands last night, singing Auld Lang Syne, I thought about the kindness, the support, the solidarity and strength of everyone that I have met. I thought about the years I have spent in the Middle East. I thought about my friends of all religions condemning the bastardization of Islam by those who don't understand its true message. I thought about the way in which Sam always looked at the world, with a positive spin on everything, seeing the best in the people that she met. I thought about her mother's words of compassion for the world's Muslims who have been wrongly associated with the acts of murderers. And I dreamed for a moment that good will prevail. If I could wish for anything to come from the horror of 9/11, I would want it to be that.

Saturday, 20 August 2011

Hidden Genius

It would appear that many mathematics teachers have forgotten (or worse still, never knew) that teaching mathematics does not have to mean transmitting lots of facts at a class full of silent children.
There has been a dumbing down in mathematics education. I see it in the UK, US, Australia, France, New Zealand, Germany and many other North-West cultures, but also in the Gulf Nations where they have fallen victim of allowing themselves to believe that companies from these North-West nations can arrive, unpack their education systems and impose them in a different society (many of the Gulf Nations have been fooled in to thinking the West knows best!)
The dumbing down is a result of a fundamental misunderstanding by policymakers of what mathematics actually is. So, more and more, mathematics is being reduced to calculations and using numbers ("numeracy" as it has been dubbed in several countries).
The main symptom of this dumbing down is that students expect to be spoon fed information and that solutions to mathematical problems should be immediate, obvious and algorithmic. But mathematics is not like that; never has been, and shouldn't be allowed to become. Mathematical problems can take a very long time to solve, or indeed remain unsolved, but along the way, through the head scratching, experimenting, errors, iterations and creative process a heck of a lot of mathematics can be learned. This learning through attempting a problem is age old in mathematics and leads to a much greater understanding of what is learned. There is no need to always tell students how to do something, instead give them a difficult problem and let them play with it.
I believe that there are many hidden geniuses out there (in fact, I believe everyone is a genius – just that we all have different fields of expertise). They are hidden because the education system that they are a part of does not provide opportunities for unlocking the genius.
Here are a few examples of moments that have warmed my heart over the years:

12 year old girl, England, 2008
I asked the child that very same question that the mathematician Guass is famed to have tackled (though whether he actually did or not is debatable to say the least!)
Add together all of the numbers from 1 to 100.
She looked at me with consternation, not best pleased about being asked to do something so apparently pointless. "I'll do 1 to 10" she told me matter-of-factly.
She wrote down the ten numbers in a column addition and then huffed and puffed as she tried to go through adding them mentally. After three attempts of losing count, she suddenly stopped and her eyes sparkled. "It's 55," she said with confidence and pride in her voice.
I beamed and asked her to tell me how she knew that.
"They're elevens, aren't they? Look."
The girl wrote down the numbers 1 to 10 again but this time in two columns:
1 10
2 9
3 8
4 7
5 6
"They always pair up to make 11. 1 and 10 is 11. 2 and 9 is 11." Her eyes were wide with delight. "And there are 5 pairs. So it's five elevens."
And this is what I mean by genius. Genius is about seeing the world differently, it is looking beyond what we have been taught, it is about breaking convention.
Adding the numbers from 1 to 10 together does not take genius. But ignoring all that you have been taught about methodology and seeing a problem in an entirely new light does.
I asked the little girl the original problem again; add together the numbers 1 to 100. She jotted down only three lines of working:
1+100= 101
"I think it's 5050," she said, a little unsure at first of her multiplication of 101 by 50. "Yep. Yep. It's 5050."
Most kids can solve this problem if given enough time and space to think. Most will need prompting to look for a different method, but occasionally you will come across a hidden genius in your class.
But to find them, you need to provide opportunities. How often do maths teachers give this space and time to just think? To create problems? Why has mathematics become so entrenched with a didactic approach? Space to see beyond the convential, to re-write a problem in a new way is incredibly important to truly learning mathematics. As Einstein said:
"The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill"

11 year old boy, England, 2007
The class teacher had posed the problem "How far can I get for £50?" The students had access to local bus timetables, maps and the infinite world of the internet.
This is an age old question in maths teaching. The kids enjoy it. The open-ended nature of the task allows them to experiment and play.
At the end of the lesson, the teacher asked for final destinations from the children. Eager hands shot up and a variety of exciting and interesting locations were happily announced.
At the back of the room, near to where I was sitting (I was observing), a small, pale, ginger haired boy sat with his faced pressed to his book still working. He had opted to work alone in the lesson (students were allowed to form teams) and had remained entirely silent throughout.
The teacher gently asked the boy to sit up and take part. "How far did you get?" he asked the shy lad. The rest of the class turned and stared. The boy gulped.
At the start of the lesson the teacher had promised a prize bounty of chocolate for the student or team that managed to get the furthest away. The routes given so far had been diverse and included bus and train fares, walking for days with the £50 used to buy food and drink, and a whole host of suggestions about hitch-hiking, which led to a great discussion about safety.
The red haired boy put down his pencil, gulped again, and then announced "Sydney. Austrailia."
The class erupted with laughter. The boy sat resolute. The teacher calmed the class and asked the boy to explain.
"I found a really nice bike in the free-ads," he started and the class burst in to laughter again. One child barked "you can't get to Australia on a bike!" Red head ignored the comment and ploughed on regardless.
"Then there was this advert in the paper," he held it up for effect, "looking for a paper boy in town. But you have to be 12. So I kept the bike until December – that's my birthday. Then I got the paper round job."
The class now were silent, the teacher grinning from ear to ear knowing what was coming.
"On the internet, Sir, you can book a flight all the way in to next year. And it's well cheap if you do. You can get an Australia flight with... er..." the boy consulted his notes, "Emirites," he said a little uncertain of the pronunciation, "and it's only £425."
The other children hung on every word.
"So. I did this paper round until June and saved up all my money. I got paid £18 per week. So I needed to work for 24 weeks and that gave me £432. I used £3.70 to get the bus to the Airport and then I even had £3.20 left to get something to eat."
The little red head won the chocolate as well as one heck of a round of applause from his fellow students.
The mathematics that the boy did was not complicated. It did not require any great mathematical skills. But I see this as a moment of genius because the boy ignored the conventional. He dared to think differently.
This is the sort of genius that we are all born with. Watch a young infant at play with some inanimate object and you will soon realise that they see more than you do. They will think of hundreds of different uses for a cardboard box, but to you it is just a cardboard box.
Somewhere along the line, this inventiveness, this genius leaves most of us. Perhaps part of the reason that we lose the ability to see a hundred possibilities, a unique approach, a different perspective in every day problems is that we all experience an education system that does not value genius. An education system that spoon feeds and gives no time to breath and create.

15 year old boy, Qatar, 2011
I sat with a boy as his class were being shown (for the nth time) how to find the area of fairly simple compound shapes, made up only of rectangles. He doodled in his book and made a show of being mindnumbingly bored by the whole experience.
"Do you have some graph paper?" I asked him, seemingly heading off on a tangent.
"Sure." He flipped open his level-arch file and unclipped a leaf of pristine paper.
"Draw a set of axes. First quadrant only." I told him with no further explanation.
He stared at the paper for a moment in thought, then produced a pencil and ruler from his case and neatly drew out the two lines required to form the x- and y-axis.
I took the paper from him and randomly drew a squiggle across the page going from left to right. He looked at me bemused.
"I want you to tell me exactly what the area under that curvey line is." I said.
Now this is a fairly standard investigation that I have done with hundreds of kids. They will start by counting the squares and realise that that is frustrating, then they will split the space in to blocks that they can calculate – imagine rectangles all over the place. Some will just estimate, some will be painstakingly accurate. Some will use square centimeters, some will invent their own units of measure.
The boy was no different. He faffed about with the problem for a while and became annoyed. "There has got to be a better way of doing this!" he laughed. After a few moments of experimenting further, he struck upon the notion of dividing the whole thing up in to vertical strips. "You can pretend each one is a trapezium," he said, justifying his approach, "and then find their areas"
He had made each vertical strip the same width. I asked him why he had chosen to do that and he explained that it was just because he was lazy, "that way they all have the same dimension, so you can do all the calculations at once."
After a few more minutes, he said to me in a conversational tone "It gets more accurate the smaller you make the strips, doesn't it?" I raised an eyebrow inquisitively. "Yes. Yes. I'm sure that's what it is. So if you could make them really small,"
"Really?" I interrupted.
"Yes. Infinitesimally?" I nodded. "Yes. If they were infinitesimally small then it would be very accurate."
"Just very?" I asked.
"No. No. It would be exact."
I have used this task countless times, and groups of children time and again will come to a similar conclusion. But it was the boy's ability to see through the structure, to imagine the abstract that makes him a genius in my eyes. Newton and Leibniz both came to the same conclusion. And this conclusion leads to the formation of The Calculus. Not bad for a 15 minute discussion on a hot May afternoon.