The more that 'numbers' are used in as wide a variety of ways and contexts as possible, the more confident a learner will become. How many adults still say they can't do maths?? But not many say they can't read, because text is around us all the time, and we just assimilate reading. 'Number' needs to be more consciously 'learned'.
Use Lego bricks of two colours for odds and evens, say RED odd, BLUE even, lay them out in pairs - much easier when child has something physical to see and handle.
Or Write numbers on wide lined paper; 1 3 5 7 etc on upper line, 2 4 6 8 etc on lower line, but slightly displaced so the 2 fits between and below the 1 and 3 etc.
Try and think up your own variations 'on a theme'!
Once child can do 'twos' to 20 or 30 they may realize they could go on for ever!
Then alternate the 'twos' - do one, miss one - and as if by magic you'll be counting in fours.
(late now, but I'll check tomorrow if any queries to this quick explanation.)