Does turning a gas stove on high move the heat to the outside of the pot? When you turn a gas stove on high, you get a big flame with a wide diameter. When you lower the heat, the diameter of the flame shrinks. (I'm not sure this description makes sense. Does it?)

Does turning the heat up all the way move the hottest part of the burner to the outside of the pot? And further, does reducing the heat just enough to shrink the diameter of the flame cause the heat to be more evenly distributed across the bottom of the pan? I've noticed that, while trying to boil water, it tends to boil first around the edges of the pot and doesn't necessarily ever get to a big rolling boil like I've seen on an electric stove.
Is your pot too small for the eye you are using? If the pot and the flame diameter are roughly the same size the effect you're describing probably happens.