The sun sparkles through the myriad panes of the glass roof. Below, as families amble into the domed splendour of the Reading Room and tourists pause on the sunlit marble floor of the Great Court to gaze at the stone porticoes, hundreds of excited children scurry into the Ford Young Visitors Centre. Here is the revamped heart of the British Museum, and at its core lies education.

Much of the space freed by the departure of the British Library to St Pancras has been transformed: the Clore Education Centre houses a revitalised education department below the Reading Room with its landmark dome, which itself is fitted out as a public reference library. The underground Clore premises are palatial: two large auditoria, five classrooms, ICT equipment and facilities for up to 1,400 pupils a day including lockers, lunchrooms and toilets. The education programme remains innovative and exciting, but is now on a much larger scale. Two years ago the education service became a fully-fledged museum department, doubling its staff numbers.

If you want mummies, Greek vases, Roman statues, coins from all ages, Inuit carvings, Renaissance porcelain or Henry Moore drawings, the fabled collections of the British Museum have them all and much, much more. But in times gone by, school parties had to hump coats, bags and sandwiches round the gallery floors. Children, initially excited and overawed, became hot and disgruntled. Their bags and coats tripped up unwary members of the public. Teachers had to stop pupils furtively eating lunch en route, and visits to the toilets were an endless nightmare. In fact, little had changed since a Punch cartoon of the 1860s that saw the then keeper, Antonio Panizzi, who commissioned the Reading Room, admonishing urchins who crouched on the steps to eat their oranges under the blank gaze of antique statuary. The subliminal message, despite some excellent education packs and gallery teaching from the education service, seemed to be: clear off, children.

Now all is changed - the British Museum has worked towards its new school-friendly status. The lavish Clore facilities combine with the resplendent scale of the new Great Court to show children that they are special. You can see the difference in their faces: they are as excited as ever, but they stay excited longer. Richard Woff, deputy head of education, says: “They can just put down their bags and coats, take a clipboard and pencil and go off knowing they’ve got a base.” Teachers’ faces, meanwhile, no longer show the strain that betrays calculations over whether they will be able to stop pupils thinking about lunch until they are back on the bus. They know that the lunch room in the Ford Young Visitor Centre is already booked for them.

Early this month, as school parties fanned out from reception, pupils from Soho Parish school and St John the Baptist school in Bethnal Green, east London, were meeting Pythagoras (actor Andrew Ashmore) in one of the big new auditoria. Wriggling excitedly in the comfortable leather seats, they were singing four-part harmony to emulate the music of the spheres, conducted by Pythagoras’s wife, Theano (Windrose Morris). Calling out answers to such problems as why four is an important number in nature and what solid has four sides, they had no doubt that maths could be a fun part of the museum experience.

MathFest this month, along with Science Week in March, is part of an extensive programme of BM workshops for key stage 2. Others include African dance and storytelling, Mexican artefacts and excavations and Egyptian crafts. Secondary activities (for key stage 3 and GCSE) focus on native Americans and how the West was won. There are also art workshops for GCSE and A-level groups which explore Japanese printmaking techniques in the new art studio. Some of these workshops are sponsored and free; for others there is a small charge (for example, Egyptian excavation is pound;50 for a 90-minute visit for 35 pupils). All activities must be booked as demand is huge. Handling sessions, talks, education packs and trails can all be booked on a wide variety of subjects, from Islamic art to medieval ceramics. Students in special schools often gain much from handling objects, and the sessions are free.

But to get the most out of a school visit, teachers should book themselves on to special courses covering such key stage 2 subjects as history and ICT, ancient Greece, Egypt, and materials and their properties, with a wider age relevance for sessions on using sketchbooks and Japonisme (Japanese design in Western arts and crafts).

In the refurbished Reading Room (a palace to learning with its dome of cream, blue and maroon picked out in gold, and the Paul Hamlyn reference library on the collections) 50 computer terminals allow visitors to access the museum’s “Compass” system. This offers not only information on objects and departments (choose “search” or “tours”) but also a library of thumbnail images with information from which teachers can compile a folder of their own, online, to be downloaded to a school computer.

Back in the workshops, Year 4 from Coppice primary in Hainault, London borough of Redbridge, are playing a game of “give and take” with museum staff. Some are African traders, in bold prints, and some are Westerners, in topis (solar hats). They are playing with Victorian pennies from the Coins and Medals department, ordering them by date, guessing how many there are in the heap in front of them, and finding out, Billy says, “fun things - fun maths things”.

“What do you need for trading?” asks the museum education officer. Charlie knows the answer. “Goods and money.” As the pupils haggle, their teacher, Wendy Mears, says, “We really love this. The children don’t realise they’re counting, estimating, ordering. And they are so thrilled to see the huge building, quite awed. It’s a way to get them to think about their maths and to see new things.”

To book, ring 020 7323 85118854, minicom: 020 7323 8855, email: education@thebritishmuseum.ac.uk , website: www.thebritishmuseum.ac.ukeducation