Paula Polk Lillard is an “advocate” for Montessori education, “not only because of what I’ve seen with my own children but with others”. A sweet-faced, gracious woman with a regal crown of silver hair, Mrs Lillard is in town to promote her new book, Montessori Today.

In a life spent with Montessori, first in the education of her five daughters, then as a teacher and now running her own school, Paula Lillard has only got keener on the basic Montessori principles of the prepared environment, the facilitating teacher, the stages of development and on the equipment of Great Lessons, Key Lessons, timelines and charts, Pink Towers and Flat Bead Frames. As she says, Montessori methods are a way of using children’s intellectual response to their environment; the job of the Montessori teacher is to harness natural curiosity and tap it at its developmental stages.

Mrs Lillard’s own developmental stages include two previous books - Montessori: A Modern Approach (1972) and Children Learning (1982) - a stint working in deprived inner-city Cincinnati and a masters degree in Montessori primary education in 1970; a complete Montessori teacher training in 1982 and, with one of her daughters and a friend, running her own primary school since 1982.

That school, in the leafy suburb of Forest Bluff outside Chicago, began with parent-baby education and has, since 1995, expanded to offer junior high school education. Where some disciples of Maria Montessori have adapted the masterworks, Mrs Lillard has remained consistently faithful and it is those principles which her latest book expounds.

The most important underlying ideas are that children want to learn and that teachers are there to help them do so, that they need long, uninterrupted periods to concentrate, that as well as freedom they must develop their own responsibility. Thus the famous injunctions to put anything away before starting another task, to record all activity in a journal and to take time to review what has been done. From these principles spring the structures of a Montessori schooling.

Each class, for instance, includes children across a three-year age span, as Maria Montessori found this helpful to social development. The groupings, from six to nine, nine to 12 and 12 to 15 correspond to different intellectual ages, and are sub-stages of the four planes of development which result in a mature child at age 12 and a mature young adult at age 24. Montessori saw each stage as having specific sensitivities and directions, moving from the “sensitive periods” in which a young child aged three to six can suddenly master motor or cognitive skills to the “absorbent mind” which manifests in children aged six to nine, where they are seized with a desire to explore the more abstract world and develop motions of morality (“It’s not fair!” is the famous cry).

Then at age nine to 12, they focus more on working collaboratively and discovering human history and their place within it. At the end of this stage, they are “mature children”, but with the onset of adolescence they have to begin again and start to create a new identity and become independent beings in the world of work and thought. Thus the classroom for ages 12 to 15 concentrates on long projects which students research and develop themselves. Working with these vertically grouped classes of no more than 25 are one Montessori teacher and one helper.

Listening to Mrs Lillard describe her school, it is easy to feel you are hearing of Utopia. There is no homework - as she says, “we don’t tell the children what to do in the classroom, so we don’t tell them what to do outside” - there are well-maintained single sets of equipment so that children learn respect and that they have to wait to have what they need until another has finished and there are journals to develop reflective practice. And each teacher, each day, has to spend five minutes contemplating the practice in the room, the stress on “going out”, the gatherings around to hear each others’ presentations or to share Montessori’s “great lessons” (impressionistic introductions to aspects of human endeavour). It all sounds so clean and wholesome, which is lovely, except that unfortunately people’s lives are not always so clean and wholesome. Mrs Lillard staunchly refutes this, citing sweat and tears as part of her and every other teacher’s experience and decrying a general social climate which implies that education and existence can and should be without pain.

And yet, and yet. Montessori schools are mostly still private. They can cope with physical disability, but extremes of social disadvantage need, as Mrs Lillard concedes, “special help and the state system ought to pick that up”.

But she feels passionately that Montessori schools can be “harbours” for children suffering unhappiness and disorder at home, that they can expand to offer sport and music which at present are supplied by rich and stable parents, that children from Montessori schools become such rounded and capable human beings that they can transform their environment.

When I asked her how she could cope with 35 children of the same age, five of them with difficulties, in an under-resourced classroom and with no other adult helper, she was stymied. Although she rallied and suggested some sensible remedies, like enlisting local organisations to provide more adult help, scrupulously maintaining a well-prepared classroom and insisting that the teacher and students reflect on their activities, the question still remains and is even intensified by the successes of which she tells. If this works, why won’t we pay for it?