Professor Areni says the security guard could not imagine a father would shop for his child's clothes; instead, he saw a pervert. ''Men in general are assumed to be depraved or likely to be foul in some way,'' the University of Sydney academic said. ''Being a good father, demonstrating the ability to love and nurture children, doesn't allow an escape from this sinister suspicion.'' Professor Areni and fellow scholar in behavioural sciences Stephen Holden are single fathers writing a book about their experiences. The Other Glass Ceiling explores gender inequalities within families, arguing that it is not only women who face discrimination. Fathers who want to be involved in child rearing are often relegated to the status of secondary parent by dominant mothers who want to make all the decisions.

Societal stereotypes assume men are likely to be incompetent parents at best and potentially dangerous at worst, the book argues. It advocates for fathers to step up and take on more of the domestic workload, and for mothers to let go of their need to be in charge at home. Professor Holden, father to 10-year-old Zachary, says research shows there are unique benefits for children who spend a lot of time with their dads, and that men have their own parenting skills. However, fathers are portrayed as ''bumbling idiots'' in popular culture, including TV shows such as The Simpsons, Two and a Half Men and House Husbands. Pressure on modern fathers is the subject of other research coming out of the University of Ballarat. The university's school of health sciences is surveying fathers with children aged under six years to determine how fatigue contributes to parenting stress.

Researcher Melissa Dunning says studies into fatigued parents have previously focused on mothers, particularly in the area of post-natal depression, with fathers largely ignored. But dads can become fatigued by a combination of interrupted sleep, long work hours and domestic responsibilities. ''Fatigue is different to tiredness because tiredness is easily relieved by sleep,'' Ms Dunning said. ''Fatigue is the feeling of persistent exhaustion … and is associated with impaired physical functioning.'' She is also researching the social support available to fathers and their attitudes about getting help, so that services can better aid their wellbeing. Stay-at-home dad Ben Hillier, of North Fitzroy, says connecting with other dads in the same situation has helped with the challenges of being the primary carer of nine-month-old son Archer. Mr Hillier attends a new parents' group of mostly mums, which is also helpful, but can feel awkward when women's issues are discussed. He recently joined a group of dads with children under five who meet once a week in their homes and parks in Melbourne's northern suburbs. A boilermaker by trade, Mr Hillier has been unable to work because of a shoulder injury. He says the older generation are sometimes surprised by the role reversal.

''When I first started pushing the pram around I would feel a bit self-conscious passing a construction site with guys looking at me, but not any more. Just to be there and see every little development … not many dads get that opportunity.'' Further information about the survey can be found at tinyurl.com/fathers-wellbeing. The Other Glass Ceiling, by Darlington Press, will be published in mid-2013.