rachelplotkin, I did not say "keep arms flopping around", I said "loose" . Rigidity and stiffness "solidness" through the torso and arms seems counterproductive. I am always using a certain amount of twist through the torso in turns, and my arms must be smooth and quick to check and adjust to maintain glide and balance.
I think tightness of the shoulders and arms is unhelpful. Strength through the core is good, but also the freedom to twist and rotate in turns.
Stiff nervous skaters who look petrified and paralysed are indeed obvious newbies with no flow or grace. I spend a lot of time stretching and practicing NOT to look like that. Why suggest a newbie make a point of looking that way?
Try to flow on the ice, stay soft through the knees and ankles, maintain an erect posture, use your arms to check and balance. Keep your abs pulled in and head centered on your neck.
For me it was just fooling around and playing with the edges that helped me lose some of the wobble. I began to TRUST my edges, to lean, to press, to play with shifting my weight forward and back, to learn where to position myself on two feet, on one foot, to finally manage a one foot glide on both sides, then to learn a 3 turn, then a bracket, then crossovers, then backwards glides and backwards 3 turns, then backwards crossovers, then.... The more I learned the more I see flexibility as the key to good balance and skating with flow