My children didn't want to come to a museum; I didn't want to come to a museum – and yet here we are making educational Chinese face-masks at the Victoria and Albert Museum. I'm trying to be a modern, middle-class dad, enjoying quality time with his kids. Around me there are other dads sticking coloured paper to their masks. We're all attempting to have an enriching dad experience with our offspring by making traditional Chinese masks. How did we get here? What am I doing to my family? Why does my educational face-mask look like Harriet Harman?

Last month, President Obama told dads to switch off the television and pay more attention to their children. Despite his good intentions, he added to the guilty, nagging doubts that haunt a generation of fathers striving to be good in a world filled with demands, distractions, cold beer and 24-hour sports news.

Dan Miller, a father at my son's school, is often away for long periods with his work. "When I'm around there's a real pressure to have the perfect day. I plan trips and often we end up spending half the time stuck in a car. I think there are moments when they just want you to come over and play snakes and ladders, but you can't because you're too busy on the internet looking up directions to the city farm."

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Dan and I are part of a new crop of men who really want to be amazing fathers – to make up stories at bed-time, to fashion kites out of whittled sticks, to know the names of at least some trees. We really want to be outstanding, high-achieving parents but no one has ever fully explained exactly what this entails.

Martina Klett-Davies, research fellow at the Family and Parenting Institute, offers an explanation for our manic approach.

"Child-rearing has become a scientific project. Children don't grow up; we feel we have to bring them up and raise them. We are very competitive and we want to give our children the best ever. In the past, before we adopted a scientific model, parenting was about children fitting into our lives."

This is a view endorsed by my own 1970s dad who, although a notable exception, recalls a less accommodating attitude to fatherhood among his peers at the time.

"I was always entirely devoted, obviously,"(he was). "But, I think, for a lot of the dads at that time it was all about work and having enough to keep the family comfortable. They bought their kids toys but I don't know whether it would have occurred to them to play with them."

The Noughties father is already in a full Fat Controller costume before the train-set is even out of the box.

Every night I battle alongside other commuting dads to return home so I can start quality time. I'm determined, I'm focussed, but I have no idea what quality time means. All I have is a suspicion that the other dads racing by me on the platform are doing more. I burst through the front door wild-eyed, tense, shouting about museums and trees while trying to make a kite from my laptop.

I need answers; I need to know what the hell quality time really is, and I need to know exactly how much I'm supposed to deliver every week. I'm a man; I want targets, measurable targets (and ideally a league table with coloured badges).

The latest statistics quoted by the Government tell me that British dads do more than twice as much as they used to in the 1970s, but still fall short by half an hour a day.

When compared to Euro-dads we're particularly weak – research from Edinburgh University published last year shows that, in Denmark, over 30 per cent of substantial childcare time is carried out by fathers, compared with just over 20 per cent in the UK.

I set myself the task of establishing just how many hours a week I should put in to be a better dad. And I don't mean average hours; I mean really top-notch quality hours filled with educational puppetry and mask-making.

I begin by keeping a diary of my meaningful mid-week interactions with my children.

The results are shocking. Mornings are a write-off – barely a word is spoken as I prepare for work during the Disney Channel/computer-game frenzy. I kiss them tenderly as I leave – they duck away and roll their eyes because I'm blocking a Wii game blasting from the television at music-festival volume. In the evenings, I'm managing 20 minutes of reading and chat per child plus some shouty stuff before bed.

I'm reluctant to count that part as it mainly consists of me and my partner booming non-developmental things like: "Get in the bath!" and "That's my eye-socket!"

I'm looking for an equivalent to the excellent five-a-day diet initiative. I want to know when I've clocked up enough good dad time to accept an invitation to drink excessively after work.

I turn to Rich Batten, a family specialist with the Colorado Department of Human Services in the US, and ask for a definition of quality time

"We mistakenly kid ourselves that some activities count as quality time and others don't," he says. "So, typically, if we're doing something that contributes to their development or that involves an educational toy, then that feels like quality time. It isn't so much what you do – it's about how you do it. Are you tuning into your child or are you thinking about your work obligations or something else? If you give them your full attention, that's quality time."

Batten is unwilling to offer me a target number weekly hours, but his observation about distractions hits home. How many golden moments take place against a backdrop of talk-radio babble? The children I love and quietly worship are trying to tell me about their lives and I'm partially listening to a documentary about organic cheese.

Already I'm learning; already I'm a better dad.

I call Helen Bigham, who runs a Saturday dads' club in east London. The dads' club is a place where men can come and play with their children and be with other dads. Bigham talks about how men engage with their children most successfully when they are genuinely relaxed and enjoying themselves. She enforces a male-only rule at the dads' club so the men don't feel judged or threatened by the mums.

"If you're confident, then children will sense that and they will have fun. We went out and built dens in the forest one weekend – the dads had a great time and so did the children. If you choose experiences you'll actually enjoy, they will have a better time. You have to work out a way to make those things you enjoy more accessible to the children – if you love playing cards then play with your children."

This is a view reinforced by Martina Klett-Davies, who says, "If you're really enthusiastic about, say, repairing your bike, find a way to share your enthusiasm with your daughter. You'll be happy and she'll be happy. Rather than being child-centred, the child can fit in with something you really want to do."

This approach does have a certain appeal and could save me from another weekend at the Tate Britain Art Trolley overseeing miserable children working through another interactive Cubism quiz. I envisage many happy Sunday lunches in well-appointed gastropubs – my son and daughter rapt and smiling – as I explain why the films of Martin Scorsese redefined modern cinema.

But there is another school of thought, an approach less palatable to the self-centred modern father. Peter Spokes is president of the National Center for Fathering in Kansas. He talks straight and sounds a bit like John Wayne.

"Spend the time you have with your children following their agenda. If your daughter is into dance, then take her to see a recital, watch her dance. I had a dad who came to me and said, 'I have three daughters. I get on great with two of them, but my eldest doesn't play golf at all.' Dads want to invite their children into their world, but what they need is for you to enter their child's world. It's not about finding the the intersection of your lives, it's about getting to know them."

So far none of the experts has been willing to offer me my weekly target of child hours. "How much time should I spend with my kids?" I ask the plain-speaking Spokes.

"More than you do now, I bet."

He's full of inspiring, practical tips; I have to ask him how I can create magical dad moments when my children are locked to their gaming consoles.

"You gotta spend time playing the games and be honest if you don't know how. Men hate taking advice, but we enjoy it when someone asks us for help. So ask their advice. When dad comes to them and says 'Teach me,' they love that. And they'll love to beat you."

Spokes has an unsettling test he gives dads who come to him wanting to be closer to their children. He gives them 10 general-knowledge questions. Is the stock market up or down? How much did they last pay for petrol? He then asks them 10 questions about their kids' lives – the names of their teachers, their last homework topic. The fathers invariably have only the sketchiest understanding of their children's lives.

So I'm building a better understanding of quality time, but now I need to know which method works best – should I be child-centred or middle-aged man-centred?

I decide to stage a ground-breaking social experiment – we will divide a Sunday into three parts. My son, my daughter and I will each pick an activity we truly love, and we will each attempt to share our enthusiasm. First I will try their activity, then they will try mine.

I will whole-heartedly immerse myself in whatever they choose. It is family democracy breaking out: I sense history being made. I feel slightly sorry for parents whose Sundays aren't devoted to fathering experiments.

Looking deep into my son's eyes, I tell him he can pick something to do on Sunday that he'd enjoy and that Daddy wouldn't normally want to do. My face is filled with optimism for our future and eager curiosity as to his choice.

"I could hit you in the penis with a baseball bat," he responds and falls about laughing.

Still smiling, I explain that we're looking more for an activity we can both enjoy. There's a lot of discussion about possibilities. My daughter is made to understand that flying to Italy and back on the same day is tricky but eventually we make our choices.

My son picks Pro Evolution Soccer on the PS2 – I'm not a football fan and understand nothing about this digital version. I ask him to help me. I place myself in the hands of my young teacher, reversing the father/son roles.

At first he enjoys talking me through the controls but soon it becomes clear that I'm unable to retain any information at all. He's dealing with an idiot – an idiot who's responsible for feeding and clothing him. I'm passing when I should be shooting. I have failed to master dribbling forward.

He's England and I'm Italy. Italy are playing as though they're going through a collective psychotic episode. I score two own goals – one of which I celebrate, having become totally disoriented. Being an eight-year-old boy, my son roars in my face, enjoys his victory and then does a dance at me.

It's true I've done little to build his respect, and he hasn't learnt anything about fine art, but it's tremendous fun and we manage a good 40 minutes of father and son larking. I think of asking him if he thought it was as much fun as smashing me in the genitals with a wooden stick, but don't want to spoil the atmosphere.

My daughter wants to watch an episode of Hannah Montana with me – for the innocents out there, this is a television series about a young girl who leads a double life as a famous singer and a regular American teen. I'm worried television-watching doesn't count as a joint activity but, according to Martina Klett-Davies, there are two quite different ways to watch telly en famille.

"You can use the TV as a baby-sitter and sit apart having no involvement with each other, or you can sit close to your children and actively watch with them, laughing at the jokes and making references during the day."

We cuddle up and I genuinely engage with teen America. Obviously I'm aware of the show (and on many occasions have insisted it's switched off so we can drive to a museum).

This time I ask about the characters, I sit tight, and I laugh ... loads.

It's snappy and funny in a Friends-like sort of a way. I realise that my nine-year-old's new mastery of sarcasm (surely the key life skill?) is largely thanks to Hannah's influence. My daughter talks me through each character as though she's part of the core script team and, most astonishingly, is happy to switch off once our time is up. We have had 30 minutes of Disney-driven fun and we've been sharing Hannah references ever since.

What do I choose? Well, I search inside myself for a passion that I can share, something that's personal and that will enrich their young lives and expose them to new influences – it comes to me in an instant: punk rock! I want my children to meet the pogo-ing glue sniffers who meant so much to me when I was growing up. I take them to the Proud Gallery in Camden Town, north London, to see a photographic celebration of the late Seventies. Soon I'm babbling about Stiv Bators and Debbie Harry – plus it's sort of art.

"These are the Ramones!" I say excitedly. "They're mainly dead now!"

My daughter thinks Debbie Harry had big hair; my son wants to go for lunch. They are, however, fascinated by the asking prices for framed pictures and soon I'm inventing a shaky rationale for the vast differential between the images of Keith Richards and Bruce Foxton. We easily manage 25 minutes of full-on engagement and my son hasn't made any more remarks about attacking me with sporting equipment.

The experiment is inconclusive but entirely successful. I feel I've found the secret to quality time, grown as a parent, and may well buy a picture of Bruce Foxton.

I'd still like someone in authority – the Government, the EU or Jamie Oliver – to lay down guidelines for weekly fathering hours. In the meantime, I'm just aiming for an interim target of an extra 20 minutes per day. None of this time will be spent in improving educational or art-related trips. We will instead continue to explore our enthusiasms and passions – no baseball bats or wooden implements will be permitted.

Phil Hilton is the editorial director of ShortList Media

What does 'quality time' with your kids mean to you? Tell us your stories about finding activities that you all enjoy Write to: yourstory@independent.co.uk