It is with very good reason that Mark McCourt has a stellar reputation in the world of maths education. He is respected for knowing what he’s talking about and, perhaps most importantly, for the way he talks about it.

Take, for example, his advice to a teacher whose headteacher has insisted on checking every lesson plan, even though he or she isn’t a subject specialist. “I think, by law,” tweeted McCourt, “you were allowed to tell him to fuck off and smack him on the nose with a clenched fist. I think. Er.”

McCourt doesn’t look like a fighter, but the former teacher and school inspector has the slightly Wild West walk of someone who does what they want. A maverick, then. A maverick whose life ambition is for children to enjoy maths.

“He’s very ambitious for the system,” says Alison Peacock, headteacher of the Wroxham School in Hertfordshire, England, and a fellow trustee of the Teacher Development Trust. “He’s a very clear thinker and a breath of fresh air. He can be quite provocative and there is a restlessness about him. He’s not putting up with things the way they are.”

The latest challenge McCourt has presented to the UK government, schools inspectorate Ofsted and teachers - in fact, society as a whole - is to face up to the way that maths education is failing some children. And it is very much fighting talk. “We should feel ashamed,” he writes in a blog post entitled “Every single child can pass maths”. “I am sick to the back teeth of meeting 15-year-olds who are being asked to solve algebraic equations or analyse graphs when they can’t even perform basic arithmetic or don’t know how the number system works. What the hell are we doing to these kids?”

Later, he tells TES: “As soon as I said that every child can get a grade C, I expected criticism, and I got criticism. The criticism I got was: `Well, I’ve got a kid in my Year 10 and he can’t even count to 10.’ That is completely missing the point. I’m not talking about a kid who is now 14. I’m sorry, but they’re not going to get it. But every child being born right now? They can absolutely acquire this level of competency. Grade C GCSE is laughable, frankly. There is nothing difficult about grade C.”

But last year, 38 per cent of students in England, Wales and Northern Ireland did not gain this grade by the end of Year 11 - or, as McCourt reframes it, after “1,600 hours of instruction”.

Tower of strength

“I always use the metaphor of a huge Jenga puzzle. What we do with kids who are 15 is we test them on these blocks at the top of this pile, but kids don’t fail because of these,” he says, waving his hand around the top of an imaginary Jenga tower. “They fail because of these blocks at the bottom. These things are loose.”

But he says that changing this would mean abandoning our “conveyor belt” curriculum and expecting secondary maths teachers to be able to teach primary-level lessons, where necessary. “What it requires is not giving up on children and not moving on until they have mastered basic concepts,” he says, the five basic concepts being place value, the base 10 system, proportionality, numerosity, and number operations and how they relate to one another.

He is the first to admit that none of this is rocket science, and none of it is new. Children Discover Arithmetic by Catherine Stern and Margaret B Stern was published in 1949; it’s one of McCourt’s favourite books. “All of the answers are in there - all of them. There’s nothing particularly secret about these things. We’ve known what we have to do for a long time.”

McCourt was brought up in Cambridgeshire and went to a grammar school - sometimes. He admits that he would “dip in and out of” lessons, but he was hardly a delinquent. When he skived off, it wasn’t to smoke cigarettes or hang around at bus stops; instead, he would read modern poetry or teach himself to touch-type. This project of self-improvement had been sparked by a single conversation.

“When I was 11, I had a teacher, Mr Rich, who told me about a guy called Leibniz. Gottfried Wilhelm von Leibniz,” McCourt says. “Mr Rich told me that Leibniz was the last-ever scholar to exist, the last person to know everything there was to know at the time about everything. I remember, from that point on, the important thing was to know everything about everything, and that meant to be a mathematician, but also an artist, a musician, a philosopher. That is what I tasked myself with doing as this precocious 11-year-old, and I just threw myself into that.”

So it comes as something of a surprise when he says that he didn’t learn to read “properly” until he was about 14. Not everything came easily to him, but he was determined to be word-perfect for the part of Dr Frankenstein in a school play, so he sat down and simply memorised words. He was never diagnosed as dyslexic: “My father just told me I had to work harder. I think that’s better than being labelled.”

He did work hard, gaining A levels in maths, further maths, chemistry, physics and biology, before going on to university to study maths, specialising in mathematical modelling. Then he worked as a mathematician in industry. But one day, his mission to leave education and its one-size- fits-all approach took an unexpected turn, when a friend asked him to visit his school to talk to A-level students about what mathematicians do. In McCourt’s case, it was modelling gas-compression systems.

He was “terrified” before the visit, but was converted. “When I was driving home, I thought, `I have to be a teacher’, and that was it. I signed up to teacher training.” Not that it has been smooth sailing ever since. “The education world is full of dicks”, one of his blog posts is provocatively titled. Reading on, it begins: “On 6 March 2007, I was told that I have cancer.”

At that time, McCourt was working as a director of teaching and learning at a school, but had already begun to get noticed nationally, having launched the website Emaths in 2004. Emaths was born after he had attended a conference for advanced skills teachers and had talked to other delegates about the need to work together and set up some kind of central repository of knowledge. “If you think it’s such a great idea, why don’t you do it?” he was challenged, so he did.

He doesn’t want to talk about his illness, except to say that he has the all-clear now. But in the blog post, he writes that it helped him to get his priorities in order; to see that at times he too had been a dick, lacking in empathy or too full of self-belief. That self-belief stemmed from the success he had experienced in education. He had been promoted quickly, and while this meant that his “net of influence” had widened considerably, it also meant that he had been removed from teaching.

“But what if you never step up to the mark?” he writes. “What if only those desperate to get away from the classroom take the decision to work their way up the ladder? School management teams, local authorities, government education agencies and departments need to be filled with people who are passionate about making a difference, who are steeped in what it means to be a teacher, who understand the emotions of standing in front of a classroom of children day in, day out.”

Maths minus the teacher

So McCourt took up his own challenge. He was feeling well enough later in 2007 to move to educational consultancy company Tribal, working as a director at the National Centre for Excellence in the Teaching of Mathematics. He was director of delivery by the time he left in 2011.

In recent years, he has been involved with two projects alongside his campaigning work: the Teacher Development Trust, an influential charity that aims to promote the best ways of delivering professional development in education, and, until recently, Beluga Learning. Both are about getting things done.

McCourt met the developer of Beluga Maths, Alastair Cruickshank, at a TEDx event on education in London in 2011. McCourt was interested in apps, but not what was on the market at the time, so he suggested that they work together. There are 40,000 educational apps in the iTunes Store alone, and a 2009 US study found that maths apps were the second most popular after early learning.

Could it be that the ease of digital communication will be how McCourt advances his crusade to get all children to be literate in maths?

“A lot of maths apps are just drill - really dull, horrible stuff,” McCourt says. “But instead of practising maths, what I was interested in was whether you can learn maths without an educator. There are 60 million children in the world without an educator. I was looking for a technology that could get a child to a point where they could comprehend mathematics, with technology mimicking the role of a teacher.”

McCourt the mathematician has talked for more than an hour about maths, but that is the only number he has mentioned: 60,000,000. A big number. A big ambition.