my boy will be 2 tomorrow. we bought him the playdough set with the letters. he can pick out about 5 or 6 of them... the first one was "m"... this is because his favourite treat is M & M's... so he sees the letter quite frequently. he's also interested in the writing on our t-shirts, so if he points to a letter, i tell him what it is... i don't push hime to learn it.
for counting, if he goes wee in the potty he gets 2 treats, if he goes poo he gets 5... so he learns to count up to five in english and cantonese. it's the same when we get into a lift, i always point out the numbers as we go up or down...he's starting to pick up on them, but often gets the english and chinese mixed up. we also count down from 10 every time we go through a tunnel. first we do it in one language as we approach the tunnel, then in the other language as we get close to the end of the tunnel.
he's now helping with our new bundle of joy and helps us get the nappies/wet wipes out. we tell him how many wet wipes, then help him count them.
when we play with puzzles, we always talk about the pictures on the pieces so that he can point out the different objects when i ask him. he's just starting to say the names himself though.
when we watch tv or movies, he names everything he sees and so do we. we were watching "lady and the tramp" last week and at the beginning lady is a puppy and is howling by the door. my son pointed to the dog, and said, " dog, no, no, yai yai, shhhh!" which i was quite impressed with.
i too agree that at this age, learning about your surroundings in a fun and natural way and being given the proper names for things rather than the "baby" names is the best way to teach your child.
i've know 6 year olds in Hk that have suffered from "burn-out"... so just relax and enjoy this time with your child.
it's not like your child is 10 years old and still unsure of his/her name (THAT would be something to be worried about!)
