In American style dancing it is usual for the leader to commence with the left foot (usually forward). The basic (slow) Waltz box could be thought of as a Reverse Turn (in European or "International" style dancing) without any turn. That is, the foot positions (LF forward, etc.) are the same. (I can already hear purists disagreeing with me.) Alternatively, you could think of the American Waltz (left) box as a LF Closed Change followed by what you could think of as the leader and follower switching roles: the leader does the three steps the follower just did, and vice versa. Dancers above the absolute beginner level may rotate the box (turning left), but about 1/4 turn for each half rather than 3/8. This box does not progress down the floor. In higher (Silver and above) levels American Waltz employs continuity style, just as Foxtrot does even at the beginner level in International Style. The box is replaced by, essentially, a Quick Open Reverse with Waltz rhythm. (American Waltz and Foxtrot share a lot of figures.) But as far as I know, the "Line of Dance" is counterclockwise around the room here as well as in Europe.