 
Turtle starts at ZERO (the zeroth term). The facing direction is irrelevant (can be sideways). To add the next term (it can be the first) he faces in the positive direction. To subtract the next term (take away) he faces in the negative direction. If the next term is positive Turtle walks forward. If the next term is negative Turtle walks backwards. Turtle's location gives the result, regardless of the facing direction.  
Turtle starts at the location given by the FIRST TERM with its sign. The facing is irrelevant. To add the next term Turtle faces in the positive direction. To subtract the next term (take away) he faces in the negative direction. If the next term is positive Turtle walks forward. If the next term is negative Turtle walks backwards. Turtle's location gives the result, regardless of the facing direction.  
 
 
The following Example shows the adequacy of 0th term to starting at zero:
