The job is daunting, however you look at it. Hull has come bottom of the GCSE league table every year since the authority was created in 1996 - a predominantly white, working-class inner city that lost its high-achieving suburbs to neighbouring East Yorkshire.
Educational aspirations are low and attendance poor. One in three children comes from a household where no one works. And inspectors have criticised squabbling councillors for holding up progress.
There was a high-profile campaign against Joan Taylor, the first director, in the local press. Interim director Simon Jenkin stayed for three months.
The last director, Peter Fletcher, won high praise from inspectors but resigned after just a year because he felt a proposed council shake-up would leave him too little contact with schools.
Mrs McMullen knows it will be tough. But this small, trim, smiling redhead has a proven record of success in every educational post she has filled.
"If I'd thought the job weren't do-able, I wouldn't be going to Hull," she says, as she sits on the sixth floor of the Department for Education and Skills, where she is until the end of today a senior education adviser in the standards and effectiveness unit.
From there, for the past three-and-a-half years, she has been advising local authorities on how to improve their schools.
She has dealt with the struggling - Swindon, Hackney, Islington, Waltham Forest - and the successful, such as Hampshire and Surrey.
"I'm not going with a ready-made solution or answers," she says. "But I have got a wide range of knowledge to draw on." That knowledge stems not only from her work at the DfES but also from her time as a classroom teacher in her native county of Cumbria, as a deputy and head in Hampshire, and as area adviser in East Sussex, senior inspector in Berkshire and deputy director in Hertfordshire.
Her priorities in Hull are to persuade parents of the importance of education and to raise attainment across the board. Last year, 28.5 per cent of 15-year-olds got five or more A-Cs at GCSE; the target for 2004 is 38 per cent.
When she starts her job on Monday, she will be one of five new corporate directors appointed in a restructuring of the authority - each sharing responsibility for the "bigger picture" as well as their own service.
But she will be in temporary lodgings, not corporate splendour, until she finds a house to share with her husband, Alistair, who is moving his packaging consultancy from their home in Surrey.