There's not much about the every day that makes the heart leap or the pulses race.

It's too familiar to be exciting, really. So we pass it by without a second thought, let alone a glance. For something to stop us in our tracks, it has to be unusual and out of the ordinary.

Next week at the Gallery of Modern Art (GoMA) in Glasgow's city centre, that delicious notion of "expect the unexpected" takes shape in the form of a sparky new collaborative project inspired by the Every Day sculpture exhibition.

Ben Harman, curator for contemporary art at Glasgow Museums, has invited choreographer Siobhan Davies to respond to the works on show with a piece of movement. Called Manual, it aims to surprise visitors to the ground-floor exhibition hall into looking again at what they take for granted or ignore altogether. In part, that process is already implicit in the sculptures themselves. Six Glasgow-based artists – Laura Aldridge, Carla Scott Fullerton, Niall Macdonald, Scott Myles, Mick Peter and Hayley Tompkins – have, in their own quite cunning and magical ways, transformed everyday objects that tease our perceptions of what's commonplace and what is not.

Yes, those are just wooden chairs. But if (like Tompkins) you overlay one with squares of mirrored glass? Sitting on the chair isn't an option, so the function has shifted and the chair is now an object to be looked at ... a sculpture.

Harman clearly enjoys the humour and the calculated provocations of the work he selected to place in the grandiose context of GoMA's neo-classical ground floor gallery. But he hankered after something more. He'd seen the kind of choreographed interventions that the Siobhan Davies Dance company had presented in London's Whitechapel Gallery and, closer to home, at Edinburgh's Dovecot Studios, which hosted Rotor in July 2011.

"I'd been having conversations with the company for some time," says Harman. "They seemed interested, but I wasn't sure we'd be able to ask them for an entirely new piece – and in any case, I thought it would be a bit cheeky to ask them. So I was really chuffed that they came back to me saying that that was exactly what they wanted to do. It means that Every Day now has seven artists showing work, with Siobhan Davies Dance a living presence that will activate the sculpture that's already in that room."

Davies herself is boundlessly enthusiastic about the whole collaboration. In recent years, she's placed her choreography in a variety of spaces that were often dramatic in themselves, but definitely weren't conventional theatres. It was a way of making audiences aware of the movement, while at the same time the movement encouraged those audiences to look again – look differently – at the context surrounding the performance. Galleries offer a particularly intriguing environment, rich with the potential for one artform to inform an onlooker's experience of another in the kind of to-ing and fro-ing conversation that Davies declares "delicious".

At GoMA, that conversation will be about the every day, and how extraordinary it can be – if only we take time to stop, look and reflect on it.

"Dance has the potential to explore extreme physicality," says Davies. "And for a time I really enjoyed that. But then a moment came when I started wondering where is the gift to the person watching? And of course it can be a gift for an onlooker to see a dancer in full flight, doing wonderful and exceptional movement. But I felt we needed a conversation about what was common to you, as audience, and me, the performer. What expertise did we share? And how can I make you aware of how extraordinary and unusual that expertise is?"

The conduit for Davies's curiosity is a young Finnish dancer, Helka Kaski. From Tuesday until Sunday of next week Kaski will inhabit the Every Day exhibition, almost like a kinetic sculpture that visitors are invited to programme. Davies explains that Kaski will behave as if she has no movement memory. Instead, she has to ask audience members to tell her how to walk. "We're not in any kind of every day space," says Davies. "But an every-day-ness is brought in by the people who come in and walk about. That's the common point that a member of the public can share with a highly trained dancer like Helka."

Between times, if no instructions are forthcoming, Kaski holds her position and becomes a sculpture among all the other sculptures.

"We hope that our visitors have fun, enjoy engaging with Helka," says Harman. "But it's also about making people think in terms of what 'sculpture' means today. What a sculpture is, or represents, in a very traditional sense – or in a very contemporary sense as shown by these local artists who are developing international reputations for their work."

As for Davies, well she finds herself looking at the sublime complexity with the seemingly simple tasks of standing up, lying down and walking with a "real joy and amazement".

"If you look closely, there is such beauty in simple tasks. There is an art to all of us, and in our own individual ways of moving. We think it's just ordinary, but it's not."

Every Day will be performed during normal GoMA opening hours from Tuesday to Sunday.

Siobhan Davies, Helka Kaski and Ben Harman discuss the commission on Thursday, June 13 at 6pm.

Dance