The method I use for knitting and purling has been christened "Combination Knitting" by Priscilla Gibson-Roberts, writing in the Fall 2000 Interweave Knits magazine.
As the name implies, it is a combination of the Western or German/American/English style of knitting and Eastern/Islamic knitting. I find that this method of knitting is easier and quicker, creates a nicer tension with less "rowing out" and is much easier on the hands (less wrist strain.)
If this method is different than how you've been taught, give it a try and you may discover a new love of knitting blooming! If you're a first time knitter - enjoy! You can master this right away! This method also creates an incredibly even stitch - my knitting is frequently compared to machine knitting for its regular tension and even stitching.