Mixing or Kneading the dough
I'd be very grateful if someone could help me understand what I'm missing. I'm curious about what the difference is between just mixing and kneading. I recently took a bread class from a chef at great artisan bakery; The Essential Baking Co., Seattle, WA. There was so much to cover in the class I wasn't sure what we were doing when we actually did it! After the class I purchased the highly recommended Bread book by Hammelman and have since, been enjoying making bread. I guess I'm actually just doing what Hammelman says in the recipes without actually using a mixer. This is where my question really begins. In the class after we mixed the ingredients we had to pick up the dough and slap & fold it for like 10 minutes, but in Hammelman's book all that's done is mix the bread at a cetain spead for three minutes or so. So I've basically been just mixing in the bowl until I feel that the dough has changed perceptively; 2-4 minutes. I haven't kneaded the dough like we did in the class. So what am I doing wrong if anything? The bread I made actually turns out pretty good. (Everyone loves it).
I'm very interested in making the bread correctly though. So do I have to knead the dough? How do I apply Hammelman's recipes to making bread by hand? Is there some step that after mixing I should just assume to knead the dough for 15 minutes before starting the bulk fermentation and later steps? As you can tell, I probably "can't see the forest from the trees" now.
Thanks so much for your help!