Our little girl (she was "a big little girl" for a while, but now insists she is "a big girl") has turned three and moved up to pre-school. The room change was a bit stressful for the first week, but she seems to have settled ok now, I think largely because her best friends have all moved with her.
Her increasing independence is most visible in successful potty training: the change table and nappy bucket have gone, and while she still has occasional accidents at nursery she hasn't had one at home for months. And she eats very much like an adult, so we can take her out without carrying anything at all, though I tend to carry a water beaker and some snacks just in case. She's not so good at dressing and undressing herself, but is getting better — it doesn't help here that she has a lot of tops that are now a bit tight to get over her head, and dresses that button up at the back.
Her language skills continue to improve, and it's more the ones she lacks that are notable than the novelties. Her pronunciation is much clearer, and she can repeat back names of cheeses and dinosaurs quite accurately (though she tends to shorten them in regular use, e.g. paralophus for parasaurolophus). Her past and present tenses are mostly fine, though there are over-regularisations such as "catched" and "bringed" — one of her peers says "brang" — and obvious errors with present progressives such as "I are walking" and "do" compounds. And the remnant English case system causes problems with pronouns. Some prepositions are used, though not always accurately. There are no subordinate clauses yet, at least that I've noticed.
She has an increasing ability to tell stories, and has produced some lovely impromptu half-sung performances, where she was clearly ad-libbing off what she could see around her. And language use is connected to her social awareness. We get increasingly complex descriptions of what she did at nursery or when out for the day, sometimes unprompted. One evening when she didn't want to get out of the bath, I spent the time quizzing her about the other children at nursery and she generated two dozen names (most of the room) and divided them up into the colour groups they are divided up into for eating (these are quite an obsession, and one can almost see evidence here for some kind of drive to group distinction). Pretty much everything she reports about nursery is social. "Pinyak is a cheeky monkey, he doesn't eat his dinner all up and wants to eat pudding." "Lily May is my friend. Arthur is not my friend. He [jumped] on top of Lily May." "Aidan and Ollie hurt Navrash." "Lily May trod on my hand. Aadi kissed it better."
She can recite the sequence of numbers to 13 reliably (but then tends to jump to 16). She subitizes up to three and can count collections of up to eight or nine objects reliably. I'm trying to explain cardinal comparison by bijection, but it's hard to tell how well that's working when the numbers involved are so small.
She's fascinated by the small amount of German I've shown her. I'm not surprised about the videos appealing, since the animations etc. are designed to appeal to small children even without any language element, but she asks to be read the one little book I've got (Spielerisch Deutsch Lernen) as well.
Physically she's getting stronger and can keep going longer: she climbed the 274 steps at Cheddar gorge, then up a muddy slope to a viewpoint and back down, then up a lookout tower (all with her hand held, but walking herself), then back down almost all the steps again, only commenting afterwards "my knees hurt". We've started dance classes and for the first time she follows all the instructions and copies all the actions. This summer I think doing walks of up to four or five miles with her should be quite feasible, given a whole day, a slow pace and regular breaks.