Bringing the world of math in through play!

Children seem to have a knack of bringing the whole world around them into play!
Although I never put too much thought into this subject before I recently noticed that children seem to learn math so much easier when it starts as a playful and non-controlled activity.  Math seems very daunting and intimidating when the curriculum is forced upon students.  A perfect example would be my 2 year old daughter.  I have been trying to teach her how to count since she started saying words about 6 months ago.  Just as any child would, she refused to listen and did the opposite of what I asked her or encouraged her to do.  Just recently she started to listen to more music and pay attention to books (pursing her own interests).  Next thing I know she is counting to 10 as she is mimicking books and videos!!! I discovered that I need to let her discover her basic abilities on her own. The earliest math play commonly involves the discoveries that numbers come in a fixed sequence, that the sequence repeats itself in a regular way (base- ten) and once you understand the pattern there is no end to how high you can count.  I think I will just let her be for now and let her discover!