Mark Francis: Arena, Abbot Hall Gallery, Kendal

To hang a body of large, contemporary, abstract paintings on the walls of a museum located in an elegant 18th-century house in the Lake District is a challenge both to the paintings and to the space itself. Can they make music together? Were they really made for each other? The space itself seems to demand intimacy and figurative content. It seems to require something tantamount to what we can see beyond the window – the serendipitous river, the fussy prettiness of a small Lakeland town, the rising hills, the soft rain that's teasing the window glass. Mark Francis gives us nothing of this. In fact, his work seems to be offering a defiant challenge to their context here.

Francis makes paintings based on grid patternings. At first glance, they look unyieldingly severe and urban. In fact, his entire practice looks and feels like a kind of analytical exercise, reports from inside the laboratory of his own mind. They put us in mind of map-making, musical notation, and of various kinds of scientific and medical practice – those stuttery, up-hill-and-down-dale readings from the heart monitor, data from molecular biology. They seem to be here to teach us lessons – not so much lessons in how to look, but in how to analyse the nature of perception itself; how to observe ourselves looking. In short, these paintings feel more than a touch impersonal, and more than a touch pedagogical. We sit at our school desk in front of them, knees knocking.

The titles of the paintings are odd and cold too, as if they are in the business of resisting our attempts to engage with them or to approach them too closely: Ecliptica, Quadric, Lenticula. These are words that we feel we almost recognise, and yet we don't quite recognise them. We recognise words that are rather like them: ellipse, eclipse...

And yet, wait a minute. Yet things are not quite what they seem. The longer we look, the longer we pace from room to room, looking first at one painting and then another, the more yielding and inviting the mark-making seems to become – and this afternoon I am locked into the gallery on my own because the hanging is still in process – and the more the paintings seem to yield up evidence of their essential humanity. Look closely at the application of the paint, or at the kinds of marks that Francis uses – much more pleasingly odd and various than they had seemed at first glance – or the often violent combinations of the colours that he uses.

Here is one little trick which he plays, repeatedly. In the upper two-thirds of many of the paintings, he establishes a certain kind of regular, rhythmical pattern-making based on a grid form, which is then overlayered in various ways. Then, not far from the bottom, he breaks that pattern by simplifying the mark-making, and changing the overall colour – a rich undersea blue breaks off all of a sudden, and yields space to a brilliant sunburst. It feels like that moment of change in a symphony, when violent agitation is transformed into something else. We are projected elsewhere.

To 3 July (01539 722 464)