An improved method and apparatus for dropping a ball, plug or dart during oil and gas well operations (e.g., cementing operations) employs a specially configured valving member with curved and flat portions that alternatively direct fluid flow through a bore or opening in the valving member via an inner channel or around the periphery of the valving member in an outer channel. In one embodiment, the ball(s), dart(s) or plug(s) are contained in a sliding sleeve that shifts position responsive to valve rotation.