Nope, big end of the rod is rotating, (along with the rod bearing and oil). The small end of the rod, piston,pins, clips, and rings, are reciprocating.
Ah, you made me look it up - I never actually knew what reciprocating meant in a mechanical sense. Although I knew the internal combustion engine converted up and down motion into rotary motion. "Reciprocating motion, also called reciprocation, is a repetitive up-and-down or back-and-forth linear motion. The two opposite motions that comprise a single reciprocation cycle are called strokes". Courtesy Wikipedia.