Katie,Most teaching materials present that particular teacher's approach to playing- and that's as it should be, because we should be teaching what we do best. However,
there is no one best way to play, or to hold the instrument, or strum, etc.Most people do play with the dulcimer flat on their laps, not angled up like a guitar. It's ok to do that!I believe most people also use their left thumb as well, because they feel it lengthens their useable stretch when making chords and moving about from note to note. That's ok too! lol!When i used to play chord/flatpicking style, i kept my dulcimer flat on my lap and used a strap to keep it from sliding around. I also learned that if I keep the tail end of the dulcimer firmly against my right hip and the peghead end out more sitting right on my left knee area, it enabled me to have much easier access to fretting the entire fretboard without bumping into my stomach. The angle was better for both my strumming and my fretting hands, plus the dulcimer was more stable and didn't rock or tip about. A strap enabled me to do this better.You can either have a music store or luthier add a strap button either or both ends of your instrument (cheap and easy), OR you can figure out more creative ways to attach a home made strap....see my video here:
http://mountaindulcimer.ning.com/video/noter-style-beginner-7-home I myself can't imagine trying to make chords without using my left thumb, but then some people
don't use it. Go figure. Everyone has to find their own most comfortable and practical way to play. It's YOUR style, and you get to decide what your playing style will be like. Don't be afraid to try different things, and to check out some additional teaching methods by various teachers- there are many many great teachers out there, and they all play slightly differently. That's part of the fun.Keep it happy and try lots of things- that way you will discover what's right for
you .