No, we definitely do it forwards; fountain pens and cursive used to be a serious problem, as is having your hand over what you've just written, so I write "overhand".
(To see this, do a 45 degree '/' with your right-hand pen, then leave the tip in the middle and make your left hand into a mirror image in the plane of the '/')
My dad was left-handed. He'd use ball-point pens that didn't smear, and when he was taking notes he'd flip the notebook so that the binding was on the right.
Pens are the worst, they konk out so quickly! iPad pros are really useful here. I wish my hands were transparent, occlusion is also a real problem (it is hard to write a straight line of text if you can't see what has already been written).
(To see this, do a 45 degree '/' with your right-hand pen, then leave the tip in the middle and make your left hand into a mirror image in the plane of the '/')