I have never heard of the way the teacher told you - seems more complicated than it needs to be. I always have squared up the quilt/batting/backing and then sewn the binding to the edge. I do pin it like crazy because I have run into the same problem you did - skipped places on the backing... so frustrating... pinning, pinning and more pinning has greatly reduced my frustration!! :) I pin about every inch or so - helps alot.