...moving the mat to various other places for our training sessions, to generalize the mat as a portable chill spot.
I wanted to emphasize this from my earlier post - dogs don't generalize as well as humans do, they tend to learn in more specific ways. So one thing I made a point of doing with Halo when she was young was to work on each new skill in a different place each day. So if I did our training session in the family room one day, the next day I worked on those same skills in the living room the following day. And then the bedroom, the office, the kitchen, the garage, and outside in the dog run.
You want your puppy to understand that "sit", for example, means not just to sit in front of you, toe to toe, but also at your side, or across the room from you (distance commands), when you're sitting on the floor or a chair, or laying on the couch, or are in the car, or at the vet's office or out taking a walk. I worked on training down from a sit and also from a stand, and sit from a down as well as a stand position.
To us, these things - sit and down, mean just one thing - plop your butt or your entire body on the floor/ground no matter where you are or what you're doing, but to a dog, "sit" at your side is completely different than sit facing you. Try standing on a chair, does your dog still know what the sit command means? If not, you need to work more on generalizing the command to as many different situations and places as you can.
Once Halo was old enough to go out and about, we trained at every strip mall in town, and in all the pet supply stores. We trained outside the bowling alley, in front of the supermarket with automatic doors opening and closing and people walking by with carts. We trained on busy street corners, next to gas station driveways with cars going in and out, and next to basketball courts and baseball fields while kids were practicing.