(>>=) :: m a -> (a -> m b) -> m b

One interpretation of this could be as follows: 

bind takes two parameters (m a & f) and returns m b (the same type returned by f)

So extending this interpretation - can I swap the two parameters (?)

Now my new hypothetical interpretation becomes:

(>>=) :: (a -> m b) -> m a -> m b

If i further add parens:

(>>=) (a -> m b) -> (m a -> m b)

This allows me to slightly tweak my interpretation:

bind takes one param f (of type a -> m b) and returns another param f (of type m a -> m b)

This feels like a more intuitive way to think about Monads - am I on the right track?

(not that I want to switch the params permanently - just trying to get a feel for monads)