Greetings from Sacramento area CA. I have never done English Piecing but read that it is a form of paper piecing. I think it is used mostly for hexagons (Grandmother's Flower Garden) or other shapes that nest into each other. The fabric is sewn "around" the paper template and then each piece is sewn to the next. Here is a tutorial:
http://www.youtube.com/watch?v=yDrTVi0jk6w