My 2.5 year old (well, she will be 3 in July) started writing all her letters/numbers a few weeks back. She's been able to identify/recognize them visually for a long time and recently started putting together certain high-usage words in our house like her name, the baby's name, "mama", "dada", etc--as in, she can spell them out loud.

So at first when she started writing letters and numbers, I wasn't too surprised because it seems like a natural next step--but also, I haven't ever sat down and taught her how to write letters and numbers because of her age. But now she's really getting in to it and spent much of the last weekend writing her name, writing Dada, writing mama, etc.

But she writes her letters wrong--not in the proper stroke order, not "top to bottom", and sometimes all over the place like backwards or upside down. I just think it's cute that she's making these connections and trying, but now I'm wondering--should I be showing her how to write them properly, since she's already interested? I mean, is there a risk that she will teach herself how to do all these the wrong way and then will be in a habit of writing them all wrong later?

Also, she's a lefty and both my husband and I are righties--are their special things/ways to teach a lefty? Because often, I find when she asks ME to write a word so she can copy, she gets confused because she watches me do it right handed. So then she tries to do it right handed and can't.

Any tips? Or what should I do next? I don't want her to have an interest and not stimulate it, or let bad habits form. And early child development experts that can weigh in?