I got a lot of pressure (as a stay-at-home mom) that dd1 "ought" to be in Preschool (or therefore obviously I should be doing rigid preschool at home with her but really, a preschool that was separate from me). I started to feel a little inadequate, like I was doing something wrong (even though I *knew* I wasn't) in just letting her be herself ....
Then one day she asked what 1 and 3 were (she had been recently interested in reading numbers). When I told her "thirteen," she said, "No, Mom, they make 4." And I relaxed.
What we did - lots of outside time, lots of interesting books and discussions (and some Science Channel, because dh and I both like it). dd1 is really interested in space, dinosaurs, animals - so we have sought out experiences involving those interests for her, whether it's a cool book at the library, or museum stop, or etc.
I would take a walk with her and just talk about what we were seeing. "Look, that tree doesn't have any leaves right now. That means it's a "deciduous" tree. But that tree there, is still green - it's an Evergreen, they don't lose their leaves/needles in the fall." And then we'd revisit and talk about it, or she would ask about it.
Count to twenty while washing hands; count how many cups of flour in the bread you're making (or cookies or whatever).
I started a nighttime game with dd1 where we would alternate between "I love you as BIG as a [mountain, the tree in our backyard, etc.]. I'd say one thing, she'd say the next. Or as COLD as [ice cream, icicle, etc.], or as WET as [mud puddle, the creek, the ocean]. So we were basically developing comparison skills while also having fun.
I also like Handwriting Without Tears, and they do have a preschool workbook. I didn't know about them with dd1, and taught her to write her name, and the alphabet, when she was four. We did learn the "song," and then what they looked like to identify. She also likes starfall.com, which she spent a lot of time on (and the reason that dd2, who is three, knows the alphabet and the sounds the letters make too).
Explain things - at the level you think they're at, but explain them as well as you can. When dd1 was three, I explained the tilt of the Earth as it rotates around the sun and how that creates our seasons and the amount of light in our days (answering a question about seasons). A year later she asked me again, "Why is it so cold in the winter?" When I started to explain it to her again, she said, "No, Mom, I know about our part of the earth tilting away from the sun during the winter - I want to know how to KEEP it from tilting!"
I hadn't thought she'd really absorb or remember the explanation I'd given her the year before.
Having done a child development screening when she was three, I can say that "they" expect that your child will be doing some scissor and other fine-motor-skills work by the time they're 3/4. They screened to see whether she could hop on each foot separately (something I'd not thought to teach her, my sister says that the day cares do games to teach this to kids?!). So some things like that are I suppose good to do ... although honestly, I think kids will learn those things without a lot of adult interference (the jumping etc. stuff, not the scissor stuff).
Art is often a lot of fun for kids that age - finger paints, painting with brushes, 'sculpting' with soft-dough or etc. Sidewalk chalk, coloring, drawing .... all are also going to develop color discernment, fine motor skills.
I have a friend who works as a kindergarten special ed aide, and she says she thinks that most kindergarten kiddos are actually far more interested in math than in phonics/reading -- that's been my experience with dd1, even though she LOVED stories and so on, math definitely came to her much more easily, and was the thing she was asking me questions about the most.
Honestly though I think the biggest thing to do is to make what learning happens, fun, and to have lots of free-play and outdoor play. More than anything else!!!
The only "outside" activity that dd1 was doing at 4, was swim lessons - we didn't do itty-bitty soccer or anything else (and actually still don't, we will eventually I just don't see the rush right now).
ETA: I did start reading chapter books occasionally to dd1 right after she turned four. One chapter with her other bedtime stories, usually of chapter books that were only 8-10 pages long/chapter initially. I think we started with Despereaux
, and then read a book about a dragon who didn't want to fight (with a bunny as the lead character, I don't recall the name). Then I think our next one, was Charlotte's Web
. Then Heidi