Do cartoon crocodiles make your child stupid? I had the chance recently to observe two children watching a cartoon, something that was both a pleasure and a shock for me. I am without issue, as they say in the Bible. The book of child rearing by P. Byrnes is a slim volume.

The beautiful, mysterious Hannah is three, her playful brother Joshua about 18 months older. They live in another country, without broadcast TV, but they can watch DVDs. Hannah's life changed when she watched the worldwide phenomenon that is Frozen, the Disney animation that won the Oscar this year for best animated feature. Little more than a year into language, Hannah knows all the songs.

We watched cartoons so their parents could sleep in. The children chose a story about five adventurous kids who had to get to a tropical island to rescue a friend. Crossing the water, nasty cartoon crocodiles almost got into the boat. Hannah, at this point, became afraid, looking at me with pleading eyes. Joshua had to stand up, he was so excited.

Hannah could not abandon the story but she wanted to avoid the terrifying reality of unrealistic computer-generated children in danger. That surprised me: it did not matter that they were animated and stylised. The crocodiles were as real to her as I was. (Parents will be shaking their heads at my ignorance, but there it is.)

Part of me thought that was lovely. Innocence lives, and stories still have power. I could see her sense of story growing before my eyes. Then I remembered the advice of paediatricians that children under two should be discouraged from watching media of any kind. Could those crocodiles be harming little Hannah's brain, I wondered? I started looking for credible advice about when children should be allowed to watch media.

The news wasn't good: age three is OK in moderation, but under two is bad news. The consensus is that your kids could turn into obese illiterate monsters with low attention spans if you let them watch lots of media before age two. Between two and six, excessive media viewing would be less damaging, but you still risk significant negative impacts.

Digging further, though, the story became less clear: many of the studies conceded that no causal link has been found. Yes, children who watched more TV were less likely to be able to read, but those kids were more likely to come from lower socio-economic backgrounds with a parent who didn't or couldn't read to them. What came first: the illiteracy or the television?

I asked my friend Dr Michael Bowden, head of the Department of Psychological Medicine at the Children's Hospital in Westmead, Sydney. Michael is a child and adolescent psychiatrist and a very smart man. Surely he would know whether cartoon crocodiles were bad for Hannah? He looked at the most recent studies before we chatted. "What really strikes me," he says, "is that the literature is incredibly full of contradiction, and the different studies say completely opposite things. There is no actual definitive answer to it."

Aha! Just as I thought.

"But there do seem to be some issues, definitely some problems," he continued. "The size of the effect is actually quite small. And some people say yes, it might be quite small, but once you multiply it out with the size of the population and the amount of time kids are spending, then it becomes a big problem. They might be right. They can certainly demonstrate some short-term and longer-term effects, in behaviour and learning. Attention is the big thing. The longer a young child spends in front of a screen, the worse their concentration, which is a worry, because poor attention leads to problems in learning.

"But we know that when parents sit with their kids and talk about what is going on on the screen – and have that kind of relationship where they are drawing attention to the good stuff or how that character would have felt – that is good parenting and those kids do better."

Dr Bowden agrees with the recent statement by the American Academy of Paediatrics that both foreground (children actively watching) and background (the TV on, but unwatched) media have potentially negative effects and "no known positive effects for children younger than two years". The academy discourages media use for those under two, and encourages setting limits at an early age. Putting a TV in a child's bedroom is always a bad idea.

Hannah and Joshua are growing up in a different world than I did. We didn't have DVDs in cars, channels aimed at toddlers and hand-held digital devices that work like a babysitter on call, for whenever the child is unruly. That is new, and a tempting resource for a stressed parent.

"No matter what you do, parents always worry about being perfect, but they don't have to," Dr Bowden says. "They just have to be good enough. There will be times when it is perfectly proper to just put the kids in front of the TV and leave them there, because otherwise you will all be screaming."

So, it boils down to moderation, supervision and interaction. You don't have to throw the TV and iPad out the window, but you do have to turn them off, discuss the content with the child, and limit their use.

Watching Frozen isn't bad for Hannah and cartoon crocodiles won't make her stupid. It probably won't teach her anything either, but it taught me something.

Twitter: @ptbyrnes