Forum crashing here --
My list would be: A two year old should know:
- How to ask questions
- That splashing in a puddle is a lot of fun
- That sand is really cool to play in
- How to finger paint and make mud
- That knocking over a tower of blocks is a lot easier (and more fun?) than building it up
- How to follow an ant or a beetle as it walks somewhere
- How to blow dandelion seeds (careful, they'll inhale them first)
- Mixing up cookies/bread with mom and dad is fun (especially when you get to lick the beaters!)
- How to put toppings on a pizza
- How to make all the animal noises in the Eric Carle books (Brown Bear Brown Bear...)
- How to look for something that's hidden
- How to listen to the same story over and over again (unless of course mom and dad want to read it, then you will refuse to listen to it)
- How to catch or kick a beach ball
- How to scribble on paper
- How to make a hand print out of paint and give it to your mom/dad (and make them cry)
- How to go down a slide
- How to put things in and out of small boxes, large boxes, medium containers (dumping and filling activities are lots of fun)
- How to pretend that a really big box is a house, a cage, a tent, a crib...
- How to give a baby doll a bath
- How to drink out of a regular cup
- How to climb up on a chair/the couch
- How to sing songs with mom/dad (doesn't have to be in tune, just cheerful)
- How to scribble with sidewalk chalk
- How to blow a bubble
- How to ride a ride-on toy
- How to collect leaves, rocks, pine cones or whatever took your fancy on your walk with mom and dad
- How to dance to music
I'm sure there are lots of other things I could put If you notice, there aren't a lot of 'academic' things on my list. Two year olds need to explore their world. They need to touch, feel, examine, stomp, climb, ponder, listen, talk, sing, dance and all sorts of other things. The more they can explore their world at this age, the more the world will make sense to them. The more the world makes sense to them, the more they can learn and figure out on their own. The more they can do that, the more they will succeed in school and in life. If you're learning to count, it makes much more sense to count how many pine cones you're picking up than it does to count something on a page. You can touch and feel the pine cone. You can see that a pile of "8" is a bigger number than "2". Then when you need to know that 8 is bigger than 2, you'll have something real to connect it to.
FWIW, I didn't spend much time (any? I don't remember) teaching my toddlers much. I do remember that ds learned his colors very early because he was interested. When dd hit two, I realized that she didn't know any color words. She's 7, and she knows them all know. When ds was 2, he could barely sit still for a picture book and he never chose to draw or do fine motor work. We spent a lot of time outside. I remember hours outside splashing in puddles, floating leaves down the storm drain, climbing up the slide. Dd loved to do other things -- she loved to play pretend, she loved to 'read' books, she loved to draw and build with legos, she loved puzzles. At the end of the day, they both learned what they needed to. They can both read, write, do math, sing, and converse quite nicely.
Better yet, they're curious about their world, they know how to ask questions and they love to learn. OK, so ds is busy learning arcane facts about baseball (how many home runs does Jose Bautista have today? What was the most innings a baseball game has ever gone? Has anyone ever pitched a no hitter on opening day? In their first major league game?), he's learning. His passions have helped him learn a lot. While he's learning arcane things about baseball, he's also learning math (batting averages, ERA, how to divide by 9), rules, sportsmanship, and social skills for talking to other guys. Dd is busy learning history through books and then acting out those books.
Help your child get out in the world and explore it. Share their interests. They'll take it from there.