As a proud parent of a toddler, I still marvel at the speed at which his young brain develops. It's already been an amazing journey from the tiny gurgling form we delicately cradled almost three years ago to the confident little chap who spent much of last weekend scooting off into the distance at our local park.

The scooter is the latest thing that my son, Krishan, has mastered. If you're a parent, then you are probably well aware of the scooter craze that has a firm grip on the nation's offspring. If you're not, then you've probably still come across the blue or pink three-wheeled micro-scooters that seem to be omnipresent on every high street. You may even have had to take evasive action as a little person weaves confidently past shoppers struggling with carrier bags.

I bought my son one for his second birthday last year. However, in hindsight, the purchase might have been a little premature. Basically he spent about six months pretending the handlebars were a microphone (actually, I was quite impressed with this) or pushing it (the wrong way round) up and down the hallway of our flat.

Then, a couple of months ago, I came home to find him tentatively perched on it, one little be-socked foot gently padding the floor. He went about a metre before abandoning it for something much more interesting in his toy box.

But the little man has persevered. Week by week, he's honed his technique, helped by his little friend from nursery.

The other month, we took him to one of the various north London parks that we tend to spend most of our weekends in these days. In the playground, an older boy of about five was adeptly sweeping arcs around the roundabout. Krishan stared at him intently for a while and then jumped on his own scooter and gave chase.

Round and round they went, skilfully steering around parents and potholes, swings and slide. It had to end in tears, of course, but is it so terrible to admit I felt even prouder when my boy carefully negotiated his way around a pile-up after the older boy mistimed a turn and clipped another toddler?

Last weekend, as summer appeared to have arrived at last, we went back to the bustling park. He couldn't wait to get back on his scooter.

I watched him zoom off along the path, carefully weaving around the dogs and cyclists, families and friends. And keep going. He sped up until I had to abandon my Sunday afternoon stroll and burst into a sprint as the little man got worryingly near the egress to the park – and a busy main road.

Krishan's new-found self-assurance and independence is also starting to filter through to the rest of his behaviour. But not always with the expected results.

Where once I could gently steer him with a pat on his back if he was in the way of "busy grown-ups", now he has started to shout, "Don't push me!" Embarrassing, I know.

Likewise, instead of demanding to be picked up and carried, now he is more intent on walking – or scooting – on his own almost everywhere. Which can create a bit of friction when faced with a main road that needs crossing or a busy supermarket car park.

He's even had the temerity to attempt to squirm out of my arms when I've tried to give him a cuddle, particularly if he's tired and grouchy.

But you can't have one without the other. My little boy is growing up fast and I suppose I will just have to accept his new-found independence. What's more to the point is that now I understand why parents of older children keep telling us to cherish the first few years. They have been unforgettable.