When Geeta Gandhi Kingdon’s parents decided to set up a school in the north Indian town of Lucknow, they had enthusiasm, qualifications and good intentions. What they did not have, however, was pupils.

Eventually, one of their neighbours took pity on them and offered to send the children from their extended family. And so, with five pupils, in a single room in a rented home, City Montessori School (CMS) was born.

Fifty-four years later, the school has expanded somewhat. At the last count, it had 45,200 pupils on its roll. No, that is not a typo. The zero key did not stick. There are 45,200 pupils at CMS. According to Guinness World Records 2013, it is the largest school in the world. For comparison, the Norfolk town of King’s Lynn has a population of about 41,200.

“It grew,” says Kingdon, in glorious understatement. “My parents’ philosophy was that you should delight the parents. They shouldn’t just be satisfied - they should be surprised by the trouble you go to to arrange a fantastic education for their children.”

Within 10 years of opening, the school was educating 2,500 pupils. In the next 10 years, this number more than trebled. By the time CMS had been running for 40 years, it had a roll of 25,000; the additional 20,000 signed up during the past decade.

“My father says, if you think you have a good idea, if you think you’re imparting good values, you shouldn’t only confine it to a few people,” Kingdon says. “As far as he’s concerned, the more the better.”

If CMS is a small town, then 50-year-old Kingdon is its mayor. Having headed CMS for half a century, her parents decided that it was time to step back and let someone else look after the day-to-day running of the school. And so they asked their daughter to take over.

It was not, however, an obvious decision for Kingdon. She had lived in Britain since she was 16, taking A levels at the independent South Hampstead High School, and then an undergraduate degree at the London School of Economics and Political Science. This was followed by a University of Oxford doctorate in development economics and a career advising developing countries on education policies.

But, apart from several years as a Sunday-school teacher at her Baha’i temple (“which I enjoyed enormously - very rewarding”), she had no classroom experience at all. And she would be leaving Britain to live in Uttar Pradesh, one of poorest states in India.

But, ultimately, she decided not to let this deter her. “It’s given me an enormous opportunity to look at the education sector in a different way. Rather than being an adviser, looking at data and informing policymakers on what might be good policy, I’m the policymaker. It’s a different kettle of fish.”

And so, in October 2010, she became head of the largest school in the world. As yet, however, this has not involved addressing assemblies of 45,000: the entire school does not ever gather together in one place. “One bus holds 50 children,” Kingdon says. “So we’d need 1,000 buses to bring them together. The whole of Lucknow would be jammed.”

Filling the state sector gap

Instead, inevitably, the school is divided into smaller campuses. There are 20 at the moment, each presided over by its own principal. The concept of “small”, however, is all relative: the largest campus educates 6,400 pupils between the ages of 3 and 18. Class sizes, however, are not to scale. Most are made up of between 25 and 50 pupils, depending on available buildings. (Interestingly, it is the purpose-built classrooms that hold the largest numbers of pupils.)

CMS’ growth may be attributable simply to demographic reality: Uttar Pradesh is a particularly populous state in a particularly populous country. Government schools are notoriously weak, sending any parent who can afford it to the private sector. CMS, which receives no government funding, charges a relatively modest 1,000 rupees (pound;12) a month in fees for younger pupils, rising to 2,500 (pound;30) a month for seniors.

Indeed there are many - including high-profile international educationalists such as Michael Barber - who believe that low-cost private sector schooling is the only way that developing countries can compensate for the failures of their state education systems.

But Indian provincial towns have schools on every corner. Something else is going on here. In part, presumably, the growth is simply the consequence of a successful school’s decision not to turn pupils away: in any other context, CMS would simply be hugely oversubscribed. But Kingdon insists that the school’s selling point has always been the service it provides for parents. “What I’ve been told is that other schools do not let parents in to see the principal,” Kingdon says. “They’re not even allowed inside the school gate. Our parents can come in any time. They have access to those figures higher up in the school.

“It’s a headache for staff, in a way, because they have to be constantly available. But it’s a very important plank of CMS. If a parent has something to say, the principal should make herself available.”

In addition, every CMS pupil is assigned a teacher who is responsible for his or her pastoral care. Once a year, this teacher will visit pupils’ homes, in order to understand more about their family circumstances. “It’s about bringing school and home together, to be a more sympathetic teacher,” Kingdon says.

In other schools - and here she cites the Oxford independent schools attended by her own sons - report cards are sent home with pupils at the end of term. At CMS, parents are invited into school to inspect children’s exam papers. “Of course, to be so open has led to some troubles for our teachers,” Kingdon says. “Teachers have to be scrupulous about how they mark work, because it will be scrutinised by parents. But to engender that level of accountability and access to the school - I think that’s pretty amazing.”

Strictly speaking, Kingdon is not the head of CMS: she is the president of its board. It is a title that accurately reflects the management-style hierarchy of the organisation. And it is similarly appropriate to the language that she uses to describe her role there. “Firstly, I see my job as improving the system, so that the ultimate stakeholder is the child.”

But she quickly counters this with: “I absolutely do not see it as a business. The administrative part of it should be done on business lines, so we have economic efficiency. But I do not see myself as a businesswoman at all. Parents have entrusted their most precious thing to us, so it’s my job to make sure that their child has the best possible opportunities in life.”

It is the CMS head office that determines what will be on the curriculum each year, decides how much homework will be set for each year group, and sets exams across the entire school. It also acts as an internal inspectorate. Teachers’ performance is closely monitored, with inspectors looking at how much homework is set and how well children’s work is marked.

In fact, a surprising amount of day-to-day minutiae is handled by Kingdon’s office. When a school bus failed to drop pupils home at the arranged time, it was her staff who dealt with the complaint, ensuring that the relevant campus principal followed it up. And when a 14-year-old pupil ran away from home, it was her office that arranged for counselling for the parents.

Everything on a grand scale

But much of the role is, invariably, administrative: safety, ICT, accounts, marketing. The school employs a staff of 3,800, including teachers, support staff, cleaners, rickshaw drivers, electricians, carpenters and gardeners. “Instead of getting people to come in from outside, we have our own caucus of carpenters and people like that,” Kingdon says. “It’s a whole economy, you might say.”

Occasionally, she also has to handle admissions problems. While CMS may have an onwards-and-upwards attitude to overall admissions, this is not true of individual campuses, which are limited by space and staffing.

On the whole, parents are happy to send their children to the CMS campus closest to their own homes. But where there are parents and schools there will always be competition. “Some campuses have come to acquire a reputation that these are very good schools,” Kingdon says carefully. “Some parents insist that they want their children admitted specifically to those campuses. So there’s a lot of jostling for admissions.

“We try to say: `Whatever that campus does well, the campus nearest to your home will also do well. If it was physically possible to admit your child to that campus, we would. But it’s just full.’”

Perception of “better” and “best” campuses is not limited to parents. Campus principals inevitably end up looking across at one another, and comparing pupils’ achievements. But the flip side, Kingdon insists, is that there is no teacher in the school without an immediate set of peers. “For example, all the teachers of geography for Grade 6 can discuss how they apportion the syllabus between different calendar weeks of the year,” she says. “They have people they can engage with and talk to.”

She does concede that pupils in a school of 45,200 - or even a campus of 6,500 - cannot receive the attention that they might in a school of 700. “But you also get so many opportunities to see how others are doing elsewhere in the school,” she says. “That example of others can inspire you to improve your act.”

And by the time they leave school, she adds, CMS pupils will think nothing of standing up in front of 3,000 people and delivering a speech: “Doing things on a large scale - they’re not daunted by being in a large auditorium, or in front of lots of people.” CMS alumni include Harvard University academics, leading surgeons and a senior United Nations diplomat.

At what point, then, does size actually start to matter? “If my father had his way. ” Kingdon begins. “His idea is that, as long as there’s demand, we should cater for it.” She pauses. “But there may sometimes be a trade- off between quality and quantity.

“We don’t want to become too big, too quickly. I think a gradual approach to becoming big is good, because we can take the system with us. If the system can bear it, I’d be happy to take it as big as it can get.”