Maggie Gyllenhaal is just gripping in this, showing us a woman moving through imperceptibly subtle stages from passionate idealism to midlife breakdown and then to something darker still: – that can only be watched through your fingers. It’s the best from Gyllenhaal since her breakthrough performance in Steven Shainberg’s 2002 cult classic Secretary.

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This high-concept psychological drama comes from writer-director Sara Colangelo, and is remade from a 2014 film of the same title by Israeli writer-director Nadav Lapid (whose latest movie, Synonyms, won the Golden Bear at this year’s Berlin film festival). It is a story of horribly intimate transgression, and also a deadpan provocation, somewhere between realism and fantasy-satire. It reminded me in some ways of Jonathan Glazer’s 2004 drama Birth, co-written by Jean-Claude Carrière, which found a similar way to test audience expectations of permissible behaviour.

Gyllenhaal plays Lisa, a hardworking and conscientious kindergarten teacher; we see her caringly taking the class through the various stages of song circle and nap time. Yet Lisa is not fulfilled personally or professionally: she feels her colleagues aren’t up to much; she’s bored by stolid husband, Grant (Michael Chernus), and dismayed and disappointed with her high-school-age children and their apparent lack of culture and facile and reactionary enthusiasms.

The key to Lisa’s restlessness is the new evening class she’s taking in poetry writing, led by the attractive Simon (Gael García Bernal). Her own attempts at imagistic, haiku-type verse are dull and derivative, and she knows it. Then one morning in school, she is electrified when a little kid called Jimmy (newcomer Parker Sevak) appears to go into a trance, composing brilliant poems that Lisa eagerly scribbles down. She becomes more and more excited by his talent, increasingly obsessed with taking personal control of his upbringing. The crisis comes when Jimmy publicly reveals his exact inspiration for a poem, and something terrible is triggered in Lisa. Gyllenhaal lets you hear the snap inside her head.

Gender plays a real part here, and the movie challenges us to consider how and why. If this was a man, the action would be dramatically red-flagged more quickly and more intensely. The innocent quasi-motherly role assigned to this kindergarten teacher camouflages what is beginning to happen, but even this diagnosis misrepresents the situation. After all, so much of what Lisa says is entirely reasonable: Jimmy’s poems are remarkable and his home background really is such that his talent is likely to wither.

Yet her behaviour is so skin-crawling. Waking him from the midday nap to receive an intense talking-to about his poetry feels like emotional vandalism, as is taking him into the bathroom ­– of all places – and asking him to cast a poet’s eye on the dullness and banality of what he sees there. Perhaps the poet in Jimmy, and indeed the sane human being, is aware that there is nothing dull or banal in the bathroom at that moment.

Great performances from Gyllenhaal and Parker Sevak, and the final line is exquisitely poignant and painful.