This may not be the most scholarly article devoted to the subject, but it has been borne out again and again in well-developed studies: reading to your child id one of the most beneficial activities one can do with children after the obvious basics (food/shelter/love).
Above and beyond the child gaining confidence that she matters to you (because of the time spent interacting with her), reading helps
- to build a higher aptitude for learning in general
- basic speech skills
- to teach the basics of how to read a book (left to right, etc.)
- to teach better communication skills
- to teach mastery of language
- to teach more logical thinking skills
- to teach enhanced concentration and discipline
- to teach that reading and learning is fun
Please read the article for more details and tips on how and what kind of books to read. It can't be emphasized enough: one of the most important things you can do to positively influence future ability is to read, read, read to your children.
When suggesting writing letters on paper with a pen, she's initially excited but then wants me to do it, her fine motor skills are not there yet.
Exactly. Fine motor skills are too underdeveloped at that age for her to writing her letters well. Let her advance in this area at her own pace. Blend activities that teach recognition of letters (their names), the sounds they make (there are many books and articles on now to approach this), etc. If she wants to write them, think big because little is only going to frustrate her. For example, have her write letters in a sandbox (you can make one for this purpose with a shallow pan and some sand). This allows her to write using the shoulder girdle muscles, with which she is quite competent. Or a fat magic marker and a white erase board. But don't let it become work. Let her lead. Or fat chalk on the sidewalk, etc.
At some point, nature becomes vary interesting: insects and other animals, the properties of matter, etc.* Nature walks are easy and fun, and can foster a life-long love of science. Basically have fun and plenty of activities with her (even television was a group activity.)
If you want to educate her in a variety of subjects, you'll have to educate yourself. It can't be helped. But it's loads of fun, and I never felt as educated as when I was teaching my children (I took it to the extreme: we homeschooled until high school.) My life was enriched greatly, and my children did very well in school. I would have done a few things differently, but that's another story.
*I started teaching the properties of matter well before kindergarten. A solid (baking soda) and a liquid (vinegar) can produce a gas which can snuff out candles or blow up balloons! Something invisible that can do things is just like magic to young children.