I apologize but I believe that at this age, children should learn by doing things with their hands. And by that I mean, the old fashioned way before computers. I know your question is specifically about electronic games and devices, but here are the tools that have worked for my 3 yr old dd:
Abacus-initially you are just playing with the beads, then counting, then learning place value as you start to count above single digit numbers. You can add, subtract. And a child can see touch and feel what the abstract numbers actually represent. That said I don't take out the abacus and sit her down to teach all this. But when she wondering what 2 apples plus 5 apples would be, I suggest if she could use the abacus to figure it out. So it is mostly self discovery.
Measuring cups and water buckets: good for understanding fractions without learning them
Magnets, compass, magnifying glasses
For language, we just make up silly willy songs that rhyme, read, drag the sounds of a word out so she can spell them if she wants to. I do use computer for language as she loves to type letters or make notes or grocery lists but does not want to write. We sometimes use the voice recorder function on iPad to say a word and see if the computer types it correctly or "goofs up".
I could go on and on but as I said initially at this age, IMHO, hands on play works wonders.
I would imagine the question about software and electronic toys was meant to be an idea for "enrichment" on top of the traditional hands on activities. Of course electronics should not be a substitute for the everyday child's activities. But our kids are growing up in different atmosphere than we were or than our parents were so why not allow them to enjoy it?
