I was looking for some exercises , games for 2-6 month old infants that would help them exercise their motor skills and cognition. Since such infants can't even sit or rollover, what types of games, toys etc would help in their mental development?
You might have seen "play gyms" - these are mats with interesting patches. Some of the patches make noises, or have different textures, or are bright colours.
Sometimes the mats have soft frames and mobile things dangling down.
Tummy time is good because it helps with crawling and avoiding flat head. And having fun things to crawl towards helps. Having things dangling over you is interesting, and children reach their arms out to try to reach the things. But watch out! sometimes having this stuff can become gently distressing.
There's also "heuristic play" - this pretty much means that you find a bunch of everyday objects with different colours and textures and sounds, and put them near your child to play with. S/He will explore different things. Often children take things to their mouth to explore them - the lips have many sensitive nerve endings - so you want to make sure the objects are safe. You obviously need close monitoring with this, but you want to try to balance "freedom to explore" with "let's be safe".
Messy play with things like tins of baked beans or cold-cooked rice pudding (lumpy, chunky, textures) are fun because children squeeze things between fingers.
For slightly older children pens and paints introduce finger nad hand movements.