Michael Clark Company, Tate Modern, London

Perfect pros and absolute beginners

Michael Clark's dancers go stalking through the huge Turbine Hall of Tate Modern. The stage is so big that they sprint into place, stopping dead in cool, assured poses. Clark has been in residence for seven weeks, rehearsing in public on a black-and-white patterned dance space.

Besides working in public, Clark has brought the public into his dance. 78 non-dancers have taken part in workshops, learning a new dance. The first part of the residency ended with a weekend of performances. Part 2, due next summer, will be a large-scale new work.

Clark has danced in art galleries before. He has always overlapped with the art world, collaborating with artists from Leigh Bowery to Sarah Lucas. His dances often feature bold design and extravagant costuming, but this time he's stripped everything back. The dancers wear simple practice clothes – black for the non-dancers, some colour for the core company. The focus is on the movement, and on the space.

At first, it's also on how much you can see. The dance floor is at one end of the Turbine Hall. The audience is eventually allowed to watch from all sides. For the first section, danced by Clark's company, we're kept back at one end. Half an hour before the show is due to start, there's already a crush.

The crowd is 20 deep, most of us getting only glimpses of the dancers' heads and arms. People stand on benches, peering at the action through phone cameras. It's a tribute to Clark's popularity, but you can feel the nervousness: is this all we'll see?

The glimpses I got of the opening dance were elegantly precise. Clark's dancers walk slowly in, thrusting hips and rising on their toes. Two women mirror each other, standing in profile, gesturing like an Egyptian wall painting. At last we're allowed further in. The hall is suddenly full of running art patrons, all determined to get a better view.

Clark's work for the non-dancers is very strict. They're brought on in lines, moving in unison. They step neatly from one foot to another, making quarter or even eighth-turns. This is a dance full of angles, a parade ground working through gentle, tilting lines. Clark has taken a massed dance and trained it into delicacy, without losing its scale.

The big group lie down in one sequence, inching their legs to the side, until the bodies are bent into angles. Clark's own dancers join in, but they can tick their way into more extreme poses, twisting up in into shoulder balances. The same sequence is performed to different songs, Kraftwerk and David Bowie.

Building on the idea of process, Clark has his own dancers winding around a ballet barre – not using it for exercises, but leaning off it, pulling themselves into strange headstand balances. There are gorgeous skipping dances, with shoulders swaying over springy footwork.

The big group dance ends with the untrained performers lying on the ground, as one of Clark's soloists picks up her feet in quick, intricate footwork. Her solo is more complex, much more demanding – but you can see the same rigour, the same sense of shape and space, in all these dances.