My mother and grandmother (midwesterners both) filled up the divided sink with water. Soapy water on the left, rinse water on the right.
I started out doing dishes that way, too, but then I thought, If I want to save water, lets find out how much I use. So I washed a set of dishes with the water running into an empty but plugged sink, and found that the amount I used didn't fill the sink. So, filling the sinks uses more water than letting it run from the tap over the dishes.
This validates your method, @
aster.